,transcriber's ,note3 ,punctuation has been standardised1 and possible typographical errors have been changed4 ,archaic1 variable and inconsistent spelling and hyphenation have been preserved4 ,bold text is surrounded by equal signs and italic text is surrounded by underscores4 ,footnotes appear at the end of their respective chapters4 ,,surveying ,,and ,,levelling ,,instruments ,,surveying ,,and ,,levelling ,,instruments ,theoretically and ,practically ,described4 ,,for ,,construction1 ,,qualities1 ,,selection1 ,,preservation1 ,,adjustments1 ,,and ,,uses2 ,,with ,,other ,,apparatus ,,and ,,appliances ,,used ,,by ,,civil ,,engineers ,,and ,,surveyors ,,in ,,the ,,field4 ,,by ,,william ,,ford ,,stanley ,,optician1 ,,manufacturer ,,of ,,surveying ,,and ,,drawing ,,instruments1 ,,author ,,of ,a ,,treatise ,,on ,,drawing ,,instruments1 ,,properties ,,and ,,motions ,,of ,,fluids1 ,,nebular ,,theory1 ,,etc4 ,,fourth ,,edition ,,revised ,,by ,h4 ,t4 ,,tallack4 ,,london3 ,e4 ,f4 ,n4 ,,spon1 ,,ltd41 #eg1 ,,haymarket1 ,s4,w4 ,,new ,,york3 #abc1 ,,liberty ,,street ,,and ,,of ,w4 ,f4 ,,stanley ,,co41 ,,limited #bhf1 ,,high ,,holborn1 ,,london1 ,w4,c4 #aiad ,,preface ,,to ,,first ,,edition4 ,notes were taken for many years before the production of this work of queries that came before the author for reply relative to functional parts of surveying instruments4 ,these bore most frequently reference to optical and magnetic subjects1 and to the qualities and action of spirit level tubes1 also occasionally to graduation and the qualities of clamp and tangent motions4 ,it was therefore thought that it would be useful to give notes upon these subjects in detail as far as possible in the early chapters4 ,as the work proceeded it was found that this plan saved much space in avoiding the necessity for separate descriptions when parts of complex instruments were afterwards described4 ,to show the state of the art and render the work useful1 it was necessary that the structure of surveying instruments should be given with sufficient detail to be worked out by the skilful manufacturer4 ,beyond this it was thought to be most important that the professional man1 who must have limited experience of the qualities of workmanship1 should be supplied with as many simple tests as possible for assuring the qualities of the instruments he might purchase or use1 with details also of their adjustments4 ,this matter is therefore carried into detail for one instrument at least of each class1 as very little general information is to be found on the subject in our literature4 ,in fact1 large groups of instruments in extensive use1 such as those used for mining surveying1 and subtense measuring instruments1 have remained heretofore nearly undescribed in our language4 ,the technical principles followed in working out details in these pages are given by illustrations of such parts of important instruments as present any difficulty of observation from an exterior view of the engraving of the entire instrument4 ,the plans of construction in general use are selected for illustration4 ,certain constructions that are liable to failure are pointed out4 ,many recent improvements in instruments are recognised and some are suggested1 but no attempt has been made to record the little differences of construction1 often meritorious1 which give only a certain amount of style to the work of each country and of each individual4 ,upon this point it must occur that the work done in any workshop must vary from other work according to the skill and judgment of the master4 ,it is intended1 therefore1 that distinctly typical instruments only should be described1 in a manner that details may be worked out therefrom4 ,to make this matter as clear as possible1 with few exceptions these pages were written with the instruments described upon my table1 and the illustrations1 when not taken directly from the instruments1 were taken from workshop drawings to a reduced scale4 ,in practice it is found that instruments performing similar functions may be very much varied in construction1 bearing reference frequently to the conditions under which they are to be used4 ,the same may be said of the functional parts of instruments4 ,we may also observe that ,english instruments differ in detail from foreign ones1 and upon this point there is no doubt much may be learned by comparison of some details of ,english with foreign work1 although our own is admitted to rank high4 ,comparisons are therefore freely made in the following pages1 and suggestions offered after study abroad of foreign work1 and careful inspection of nearly the whole literature upon the subject1 in which it is very observable that some modern continental books1 treating upon parts of the subject1 are much in advance of our own4 ,the surveying instruments described in these pages are nearly limited to those used in the field4 ,instruments for plan drawing and calculation of areas1 which the surveyor uses in the office1 have been described in the author's work on ,drawing ,instruments 7now in ,seventh ,edition71 to which this is intended to be the complement of the subject4 ,to render the work as complete as possible1 it was thought necessary to give briefly the manner of using many instruments in practical surveying4 ,this part of the subject1 from the author's very limited experience in the field1 is largely taken from inspection of the best works on surveying4 ,the author1 however1 is very pleased to acknowledge the kindness of many professional friends for assistance on this and many other points1 and for historical notes4 ,for the description of the #cf-;inch theodolite1 given in ,chapter ,,vii4 7now ,x471 the author is indebted to the late ,col4 ,a4 ,strange1 ,f4,r4,s41 who gave every detail of his design and discussed many points4 ,the author is also indebted to ,mr4 ,thomas ,cushing1 ,f4,r4,a4,s41 ,inspector of ,scientific ,instruments for ,india1 who has given information and his opinions upon many subjects from his large practical experience4 ,also to ,prof4 ,george ,fuller1 ,c4,e41 who has kindly read proofs1 examined formul1 and made some technical points clearer4 ,also to ,mr4 ,w4 ,n4 ,bakewell1 ,m4,inst4,c4,e42 ,major-,general ,a4 ,de ,lisle1 ,r4,e42 ,right ,hon4 ,lord ,rayleigh1 ,f4,r4,s41 for assistance on several technical points4 ,in this ,first ,edition1 entirely from manuscript1 there will no doubt be errors and omissions2 therefore the author will feel obliged by the receipt of any notes that he may make use of for future corrections1 should another ,edition be demanded4 ,w4 ,f4 ,s4 ,,great ,,turnstile1 #ahij4 ,,preface ,,to ,,third ,,edition4 ,the note at the end of the ,first ,edition of this work referred to on the preceding page has brought the author many letters from professional men1 who have kindly taken interest in the work by offering suggestions which are now incorporated as far as practical in this ,edition1 and for which thanks are tendered4 ,one important improvement of late years in the construction of surveying instruments is due to the greater perfection of modern machinery1 and the adoption of special machines to shape out many parts of the work from the solid which were formerly screwed together in many pieces1 which made the instruments heavier and also liable to become loose in parts by jars1 so as to cause the necessity of frequent readjustments4 ,another important improvement in modern surveying instruments is in their lightness1 due to the discovery of permanent aluminium alloys1 by which many parts of instruments that are shaped out in the solid may be reduced to one-third the weight of the gun-metal castings formerly used entirely for these parts4 ,in the present ,edition1 which represents forty-seven years of experience of the author's life devoted to the details of the subject1 it is hoped that some permanent improvements in surveying instruments may be shown1 and that many new designs now first described1 founded upon this experience1 may merit trial4 ,the author is pleased to acknowledge the zealous aid his working manager and at present co-director1 ,mr4 ,h4 ,t4 ,tallack1 has given in perfecting this work to bring it to its present state4 ,w4 ,f4 ,s4 ,,great ,,turnstile1 #aija4 ,,preface ,,to ,,fourth ,,edition4 ,since the publication of the ,third ,edition of this work1 the author has been taken from us1 and it has fallen to my lot to revise it and bring it up to the present time4 ,this work ,i have approached with the greatest diffidence1 having to follow one who had such profound knowledge of the subject1 and ,i have earnestly endeavoured1 as closely as possible1 to act as ,i think he would have done had he been alive1 and having enjoyed over twenty years of the happiest and closest business relations with him--actively co-operating in bringing many of the instruments to their present state1 ,i venture to hope that ,i have to some extent carried out what his wishes would have been4 ,i have carefully read over and corrected the whole work1 and the additions to it are only in the nature of bringing it up to date4 ,h4 ,t4 ,,tallack4 #bhf1 ,,high ,,holborn1 ,june1 #aiad4 ,,contents4 ,,chapter ,i4 ,,page ,,introduction3--,historical ,sketch--,classification of the ,subject-- ,purposes and ,qualities of ,instruments--,workmanship--,metals-- ,aluminium--,framing--,tools--,axes of ,instruments--,soldering-- ,finishing--,bronzing--,lacquering--,gra duating--,engraving--,style-- ,glass-,work--,woodwork--,lubrication--, preservation of ,instruments-- ,packing #a ,,chapter ,,ii4 ,,the ,,telescope ,,as ,a ,,part ,,of ,a ,,surveying ,,instrument3--,general ,description--,qualities--,optical ,principles--,refraction of ,glass--,limit of ,refraction--,reflection--,prisms--,lens es1 ,convex and ,concave--,aberration--,formation of ,images--,dispersion-- ,achromatism--,curvature of ,lenses--,telescopes--,eye-pieces--,powe rs-- ,dynameter--,construction of the ,telescope--,diaphragm--,webs--,lines-- ,points--,parallax--,examination and ,adjustment #bd ,,chapter ,,iii4 ,,the ,,magnetic ,,compass ,,as ,a ,,part ,,of ,a ,,surveying ,,instrument ,,or ,,separately3--,broad and ,edge-bar ,needles--,manufacture of the ,needle--,magnetisation--,suspension--,d ip and ,adjustment--,lifting-- ,inclination--,declination--,variation-- ,correction--,compass-,boxes-- ,description of ,compasses--,ring ,compasses--,trough ,compasses-- ,prismatic ,compasses--,stand--,surveying with ,compass--,pocket ,compasses #ei ,,chapter ,,iv4 ,,levels3--,methods of ,ascertaining--,level ,tubes--,manufacture-- ,curvature--,sensitiveness--,testing--,r eading--,circular ,levels-- ,surveyors' ,levels--,y-,levels--,parallel ,plates--,adjustments of ,y-,levels--,suggested ,improvements--,dumpy ,levels--,tripod ,stands-- ,adjustment of ,dumpy--,collimator--,improvements in ,dumpy ,levels-- ,tribrach ,head--,diaphragms--,cushing's ,levels--,cooke's ,levels--,cheap ,forms of ,level--,hand ,levels--,reflecting ,levels--,water ,levels #he ,,chapter ,v4 ,,levelling ,,staves3--,construction--,various ,readings ,discussed-- ,sopwith's--,field's--,strange's--,stanl ey's ,new ,metrical--,simple ,construction--,mining ,staff--,papering ,levelling ,staves-- ,preservation--,packing ,pads--,staff ,plate--,staff ,level--,practice of ,levelling--,index of ,bubble--,lamp--,curvature ,corrections--,station ,pegs--,refinement of ,levelling--,levelling ,books #adh ,,chapter ,,vi4 ,,division ,,of ,,the ,,circle ,,and ,,methods ,,employed ,,in ,,taking ,,angles3-- ,dividing ,engine--,surfaces for ,graduation--,vernier--,various ,sections--,reading ,microscopes--,shades--,micrometers--,cl amp and ,tangent ,motions--of ,limbs--of ,axes--,use and ,wear--,difference of ,hypotenuse and ,base #age ,,chapter ,,vii4 ,,theodolites3--,constructive ,details of #e-;inch and #f-;inch ,transits-- ,special ,additional ,parts--,old ,form with ,four ,screws--,improved ,form--,additional ,parts--,plummets--,striding ,level--,lamp-- ,adjustments over a ,point--,solar ,attachment--,photographic ,attachment #bad ,,chapter ,,viii4 ,,specialties ,,in ,,modern ,,forms ,,of ,,transit3--,theodolites for ,general ,surveying--,railway ,work--,exploring #bdf ,,chapter ,,ix4 ,,plain ,,theodolites ,,in ,,which ,,the ,,transit ,,principle ,,is ,,not ,,employed3--,the ,plain ,theodolite--,improved ,construction--,everest's ,simple--,adjustments and ,examination of ,theodolites #bfg ,,chapter ,x4 ,,large ,,theodolites ,,used ,,only ,,for ,,geodetic ,,surveys3--,stanley's #aj- and #ab-;inch--#ad-;inch ,altazimuth--,col4 ,strange's #cf-;inch ,theodolite #bic ,,chapter ,,xi4 ,,mining ,,survey ,,instruments3--,circumferentors--,plain ,miner's ,dial-- ,sights--,tripod ,stand--,adjustments--,henderson's ,dial--,lean's ,dial--,adjustments--,hedley's ,dials--,additional ,telescope--,improved ,hedley--,tribrach and ,ball ,adjustment--,reflectors--,continental ,forms--,thodolite ,souterrain--,tripod ,tables--,stanley's ,mining ,theodolite--,pastorelli's and ,hoffmann's ,adjustable ,tripod ,heads-- ,mining ,transit ,theodolites--,stanley's ,prismatic ,mining ,compass-- ,hanging ,dial--,hanging ,clinometer--,semi-circumferentor--,mini ng ,lamps #cjg ,,chapter ,,xii4 ,,instruments ,,to ,,measure ,,subtense ,,or ,,tangential ,,angles ,,to ,,ascertain ,,distances3--,historical ,notes of the ,method--,principles ,involved-- ,stadia ,measurements1 ,direct and by the ,ordinary ,telescope-- ,corrections for ,refraction of the ,object ,glass--,stanley's ,subtense ,diaphragm--,anallatic ,telescope of ,porro--,tacheometers--,stadia-- ,omnimeter--,field book--,bakewell's ,subtense ,arrangement #cee ,,chapter ,,xiii4 ,,instruments ,,constructed ,,especially ,,for ,,facility ,,of ,,taking ,,inclinations3--,inclinometer ,theodolite--,gradiometer--,clinometers3 ,abney's--,troughton's--,de ,lisle's--,stanley's--,barker's--,burnie r's-- ,watkin's--,clinometer ,sights--,rule ,clinometer--,road ,tracer #chi ,,chapter ,,xiv4 ,,instruments ,,of ,,reflection3--,octant or ,quadrant--,reflecting ,circle--,sextant--,principle--,parallax --,construction--,examination-- ,adjustment--,artificial ,horizon--,sounding ,sextant--,box-,sextant-- ,supplementary ,arc--,improvements upon this--,optical ,square--,optical ,cross--,apomecometer #dbb ,,chapter ,,xv4 ,,graphic ,,surveying ,,instruments ,,and ,,appliances ,,connected ,,therewith3--,plane ,tables--,alidades--,telescopic ,arrangements-- ,subtense ,measurements--,various ,devices for ,holding the ,paper-- ,continuous ,papers--,adjustment of ,tripod ,heads--,method of ,using--,edgeworth's ,stadiometer--,sketching ,protractor--,sketching ,case--,camera ,lucida1 etc4 #dgb ,,chapter ,,xvi4 ,,instruments ,,for ,,measuring ,,land ,,and ,,civil ,,works ,,directly3--,chains-- ,various ,tellers--,standard ,chains--,arrows--,drop ,arrows--,vice for ,adjusting ,chain--,caink's ,rule for ,inclines--,steel ,bands--,wire ,land ,measures--,linen ,tapes--,offset ,rods--,pine ,standard ,rods--,rods with ,iron ,core--,beam ,compass ,rods--,coincidence ,measurements-- ,compensated ,rods--,base ,line ,apparatus--,coast ,survey ,lines-- ,perambulator--,pedometer--,passometer-- ,sounding ,chains--,sounding ,lines--,telemeters--,hand ,rods--,rules #dij ,,chapter ,,xvii4 ,,stations ,,of ,,observation3--,pickets--,false ,picket--,permanent ,stations--,referring ,object--,heliotrope--,heliostat--,helio graph ,signalling--,morse ,alphabet--,night ,lights--,oil ,lanterns--,magnesium ,light #ecc ,,chapter ,,xviii4 ,,measurement ,,of ,,altitudes ,,by ,,differences ,,of ,,atmospheric ,,pressure3-- ,historical ,note--,mercurial ,barometer--,construction--,operation-- ,aneroid ,barometer--,construction--,various ,improvements--,hypsometer #edh ,,chapter ,,xix4 ,,miscellaneous ,,surveyors' ,,and ,,engineers' ,,instruments1 ,,appliances1 ,,and ,,accessories3--,cross ,staff--,mechanics' ,levels--,boning ,rods-- ,footner's ,railway ,gauge--,girth ,strap for ,timber ,measurement--,girth ,tapes--,timber ,marker--,slashing ,knife--,bill-,hook--,reconnoitring ,glass--,telescope--,sun ,spectacles--,whistles--,pioneer ,tools--,sketch ,block ,book--,camera--,geological ,tools--,wealemefna--,opisometer-- ,boucher's ,calculator--,slide ,rules--,fuller's ,calculator--,engineers' ,pocket-,books--,chronometer--,outfits #egc ,,index #fja ,,surveying ,,instruments4 ,,chapter ,i4 ,,historical ,,sketch--,,classification ,,of ,,the ,,subject--,,purposes ,,and ,,qualities ,,of ,,instruments--,,workmanship--,,metals-- ,,aluminium--,,framing-- ,,tools--,,axes ,,of ,,instruments--,,soldering--,,finishing- -,,bronzing-- ,,lacquering--,,graduating--,,engraving- -,,style--,,glass-,,work--,,woodwork-- ,,lubrication--,,preservation ,,of ,,instruments--,,packing4 #a4--;,historical ,sketch4--,although the aim of this work is to show the state of the art it is intended to represent at the present period1 a large amount of literature1 ancient and modern1 has been consulted for its production1 principally with the object that the authorship1 as far as possible1 should be given of the instruments described which have come into general use4 ,many of these instruments have been brought to their present state of perfection by small consecutive improvements upon older forms4 ,therefore1 it is hoped1 a brief historical sketch of the literature of the subject may be thought to form a fit introduction4 #b4--,land surveying was possibly first practised in ,egypt1 where landmarks were liable to be washed away or displaced by the overflow of the ,nile4 ,that it was also used otherwise is shown in that there is extant in ,turin a papyrus giving the plan of a gold mine of about #adjj ,b4,c4 ,the earliest surveying instrument of which we have record is the diopter of ,hero of ,alexandria1 about #acj ,b4,c4 ,this instrument appears to have been a wooden cross1 with sights to take right angles4 ,in the astrolabe of ,hipparchus1 we have a divided quadrant of a circle sighted from the centre4 ,in ,tycho ,brah's ,astronomica ,instaurata ,mechanica1 #aeih1 we have descriptions and engravings of the astrolabe of ,hipparchus1 ,ptolemy1 ,alhazen1 and of his own instruments4 ,these all embrace the principle of the quadrant1 but the sighting of the star or object with the instrument by movable parts is effected in various ways4 ,these instruments were made at first only for astronomical observations2 but they appear to have been applied1 at a very early date1 with slight modifications1 to topographical surveying4 #c4--;,in ,thomas ,digges' ,pantometrie1 #aega1 we have several instruments described for surveying purposes3--,the geometrical quadrant is an arc of #ij1 with sights to the #ij radius1 and a plummet from the radiant angle to read degrees of elevation4 ,the geometrical square1 sighted upon one edge1 with an alidade centred from the corner from which the #ij radiate to take horizontal angles4 ,in another instrument the two instruments described above are combined4 ,the theodolitus--the origin of the theodolite1 a word probably derived from theodica1 taken in the sense of perfection1 as being the most perfect instrument4 ,it consists of a complete circle divided and figured to #cfj1 mounted upon a stand1 with a sighted alidade moving upon its centre and reading across the circle into opposite divisions4 ,an artificial horizon is also described for ascertaining altitudes by reflection4 #d4--;,in #afbd1 ,edmund ,gunter1 to whom science is indebted for the invention of the slide rule1 sector1 and chain of #ajj links1 published a work giving descriptions of the cross-staff1 his improved form of quadrant1 with improvements on some other instruments4 ,in #afhf we have the first treatise on mine surveying1 the ,geometria ,subterranea of ,nicolaus ,voigtel1 published in ,leipzig1 in which we have the hanging compass1 still much in use on the ,continent1 described4 ,beyond this1 few improvements are recorded upon surveying instruments in the seventeenth century4 #e4--,near the commencement of the eighteenth century we have a somewhat important work1 published in ,paris1 written by ,nicolaus ,bion1 ,constructions des ,instruments de ,mathematique1 #agah4 ,this treatise was translated into ,english by ,edm4 ,stone1 who made many additions to it in #agbc4 ,it formed an important work in its day1 and is excellently illustrated4 ,in this we find an account of the circumferenters1 plane tables1 magnetic compasses1 and other instruments then in use4 ,the next important work treating upon the subject is ,gardiner's ,practical ,surveyor1 #agcg4 ,in this we have the theodolite much improved and brought to nearly its present form by ,jonathan ,sisson1 but it was not1 however1 perfected until the introduction of the achromatic telescope by ,john ,dollond1 about #agfj4 ,gardiner gives also a careful consideration of the best instruments employed generally in the practice of surveying4 ,nothing from this time appears except transcriptions and incidental descriptions of instruments in works on surveying1 until the publication of ,geo4 ,adams's important ,geometrical and ,graphical ,essays1 ,containing a ,description of ,mathematical ,instruments1 in #agia4 ,in this work we have an able discussion of the best surveying instruments then in use4 ,it was much extended in later editions by the descriptions of the great improvements made in the construction of instruments by ,jesse ,ramsden1 as also by the invention of the box-sextant by ,wm4 ,jones4 ,the last edition carries the subject well up to date at the beginning of the last century 7#ahjc74 #f4--;,in the last century no original work appeared on the subject till ,f4 ,w4 ,simms's treatise on ,mathematical ,instruments1 #ahcd4 ,this small work is limited to descriptions of popular instruments for land surveying and levelling4 ,it was probably called hurriedly into existence to supply a want at the commencement of the railway mania4 ,another small popular work1 by the late ,j4 ,f4 ,heather1 #ahdi1 appeared in ,weale's ,rudimentary ,series4 ,this was almost entirely compiled1 old and even then obsolete engravings being used4 ,no work in the ,english language1 from an early date in the last century1 is found to treat the subject comprehensively1 or to bring it nearly up to date with the advanced work of our best opticians of the period at which it was published4 #g4--;,in ,germany we have recent works of an altogether higher order in ,die ,instrumente und ,werkzeuge der hoheren und niederen ,messkunst1 sowie der geometrichen ,zeichnenkunst2 ihre ,theorie1 ,construction1 ,gebrauch und ,prufung1 by ,c4 ,f4 ,schneitler1 #ahdh2 and a work upon the larger instruments1 ,die geometrischen ,instrumente1 by ,dr4 ,g4 ,c4 ,hunus1 #ahfd4 ,these works are original1 and enter ably into constructive details4 ,the authors1 however1 do and mention1 and were possibly unacquainted with1 many excellent instruments in the hands of the ,british surveyor4 ,as regards reflecting instruments1 which derive their first principles from ,hadley's sextant1 there is no work in which these are treated so ably as that of the ,italian1 ,captain ,g4 ,b4 ,magnaghi1 in ,gli ,strumenti a ,reflessione per ,misurare ,angoli1 #ahge4 ,the consideration of these instruments is1 however1 in this work more in reference to astronomical and nautical observations than to surveying4 #h4--,the important class of subtense instruments1 the use of which was first proposed by our countryman1 ,james ,watt1 in #agga1 and brought out by ,wm4 ,green in #aggh1 since reinvented in ,italy by ,j4 ,porro1 #ahbc1 of which we have a description in his work1 ,la ,tachomtre1 ou l',art de lever les ,plans et de faire les ,nivellements1 #aheh1 is now in extensive use on the ,continent1 and to some extent in ,america4 ,their use is becoming more general in this country but they are not nearly so well known as they should be4 ,one of the first was ,edgecombe's little-used stadiometer1 of which we have descriptions1 without any recognition of the optical correction always required to render this instrument practical2 and some descriptions of ,eckhold's omnimeter1 given generally with an illustration of an early abandoned form of the instrument4 ,more recently we have the subject of subtense instruments ably discussed in a paper by ,b4 ,h4 ,brough1 ,c4,e41 on ,tacheometry1 as it is termed1 read before the ,inst4 ,c4,e4s1 #ahhg4 #i4--;,classification4--,the surveying instruments necessary to be employed on any particular survey will depend1 in a great measure1 upon the nature of the work to be performed4 ,thus1 if it is for a simple plan of an estate1 the surveyor requires to ascertain the positions of buildings and important objects1 the internal divisions of the land1 and the surrounding boundaries of the estate1 placing all parts in their true horizontal positions and bearings in relation to the points of the compass4 ,if it is for a topographical survey of great extent1 he requires these matters in less detail1 but1 in addition to the above1 means of finding the true latitudes and longitudes1 and the relative altitudes of the parts of his work4 ,if for a railway1 a canal1 or water-works1 he requires to ascertain1 besides the general horizontal plan1 especially the altitudes of all parts of his work very exactly4 ,if it is for coast survey1 he requires1 besides the bearings1 the exact relative trigonometrical positions of all parts of the coast-line1 as also the relative soundings on the sea front4 ,if for a mining survey1 he requires to ascertain1 besides the horizontal plan1 sections showing the position and depths of strata1 faults1 veins1 etc42 and1 as the work is principally underground1 it is necessary that he should be able to take his observations by artificial light4 ,it becomes1 therefore1 clear that special instruments can be adapted1 more or less perfectly1 to these various kinds of work without that amount of complication and of weight which would be required in any single instrument constructed to perform many of the above-named functions4 #aj4--,taking the subject in a general way1 the instrumental aid of the greatest importance in the work a surveyor has to perform is such as will provide measurements of distances and of angles by which he may be enabled to make a horizontal plan or map of the ground he surveys to a measurable scale4 ,the method employed to secure this object is by taking linear measurements in certain lines to fixed positions1 or stations1 as they are termed1 and by taking angles in relation thereto from such stations to prominent points of view1 which may be either natural or artificial objects4 ,to obtain this end1 he requires means of measuring such lines1 and some instrument that will take angles of position in the horizontal plane1 or1 as it is termed1 in azimuth4 #aa4--,the instruments used in practice for measuring the complete circle in angles of azimuth are the various kinds of theodolites1 including transits1 omnimeters1 tacheometers1 circumferenters1 also mining-dials of various kinds1 prismatic compasses1 and plane-tables4 ,instruments limited to measuring angles upon the plane1 within a segment of a circle1 are sextants1 box-sextants1 and semi-circumferenters4 ,instruments adapted to take certain fixed angles only are the optical square 7#ij71 the cross-staff 7#ij and #de71 the apomecometer 7#de only74 ,the theodolite being a universal instrument1 is used for taking angles in altitude as well as in plane4 ,the sextant is also adapted to this4 ,circumferenters and mining dials are generally constructed to measure altitudes less exactly than the theodolite4 ,in extensive surveys of countries a constant check is required by taking the latitude and longitude1 for which a good transit instrument is required to take observations of celestial bodies1 and a reliable chronometer4 #ab4--,practically for taking altitudes for railway1 canal1 road1 and drainage survey1 a telescopic level is used1 either with or without a magnetic compass4 ,for topographical work and measurements of great altitudes in extensive surveys1 the theodolite1 aneroid or mercurial barometer1 or boiling-point thermometer is used4 ,in important surveys of mountainous countries1 all of these instruments are used1 the one as a check upon the other4 ,for taking merely angles of inclination of surface1 angles of embankment or cutting1 and dip of strata1 a clinometer of some kind is used4 ,some general details of construction will be considered in this chapter before proceeding with the details of the instruments mentioned above1 and some particulars also which it would be difficult to introduce hereafter4 #ac4--,qualities of ,work4--,the qualities that instruments should possess will be separately discussed1 with the description of each special instrument4 ,it may be stated generally that much of the quality of surveying instruments depends upon the perfection of the tools used in their manufacture1 but very much also depends upon the character of the man who produces them--not only upon his intellect1 but whether his chief object is the perfection of his work1 or the amount of profit he can obtain from it4 ,it is generally known in all branches1 as a rule1 that the cheaper kinds of work1 from the less care required in details1 secure the greatest profits4 ,in the author's and some other optical works1 a completely fitted engineer's shop is employed to keep tools in perfect order1 make special tools1 and produce the heavier class of work1 for which the engineer is better adapted than the mathematical framer4 ,it is also advantageous at all times to have at least one skilled engineer1 who is styled the engineer1 in a workshop where as many as fifty men are employed4 #ad4--,metals4--,the alloys generally used in the construction of surveying instruments are brass1 gun-metal1 bell-metal1 and occasionally electrum or ,german silver1 silver1 aluminium1 gold1 and platinum4 ,these are required to possess certain qualities1 and1 where the magnetic needle is used1 to be perfectly pure or free from iron4 ,the certainty of copper alloys being quite free from iron is one of the great troubles with which the manufacturer of magnetic instruments has to contend when obtaining his castings from the ordinary commercial founder4 ,this has led the author1 and some others in his line of business1 to cast their own metals as the only means of getting them pure4 ,where the metal is had from the commercial founder1 every part of the casting should be carefully brought within the influence of a delicately-suspended magnetic needle4 ,if the slightest attraction be found in any part of the casting it should be rejected4 #ae4--;,aluminium1 from its much lower price of production than formerly1 and from its extreme lightness and freedom from tendency to oxidation1 except when exposed to sea air1 as the presence of common salt appears to completely decompose the surface1 is now recognised as a metal which may be used for the manufacture of parts of surveying instruments4 ,this metal1 in its pure state1 is too soft and malleable to be used advantageously for many parts of these instruments4 ,it1 however1 appears to alloy with many metals1 some of which increase its hardness and stiffness without making its specific weight more than one-third that of gun-metal1 and without greater liability to oxidation4 ,the following alloys are now offered in commerce3--,aluminium-nickel1 al-chromium1 al-tungsten1 al-titanium4 ,these possess many distinct qualities1 and may be found1 under judicious handling1 useful for many parts of these instruments4 ,there is1 however1 from the fineness of grain of aluminium1 even in its alloys1 a tendency to fret in surfaces exposed to friction4 ,this can be avoided in many cases by lining such parts with a suitable metal without materially changing the general lightness of the instrument4 ,the author has devoted much time to forming and testing aluminium alloys1 particularly with nickel1 but there is no doubt there is still much to be learned of the alloys of this beautiful metal1 as it is still1 comparatively1 so new to manufacturers4 ,the author has found many difficulties to be overcome in obtaining fine solid castings1 and1 as far as his experience goes1 there are only very imperfect solders offered for it in commerce4 ,it therefore remains advisable to work up all parts in the solid in this metal as far as possible1 and where there is risk of exposure to salt air to confine the aluminium alloys to such parts of the instrument as may not be seriously injured by surface oxidation4 ,on the whole this metal is only recommended where lightness is of more importance than durability4 #af4--,the general object to be obtained in the distribution of metals to the various parts of an instrument is to get good wearing surface with solidity1 and an even balance of the moving parts with moderate lightness4 ,in practice1 such parts as can be thoroughly hammered1 drawn1 or rolled in a cold state will form stiff1 elastic1 and durable parts in brass4 ,for the composition of this metal the author uses copper #fi1 zinc #cj1 tin #ja4 ,the tin is used in place of the lead of the ordinary founder1 and produces thereby a stiffer alloy4 ,for such parts as require stiffness1 where sufficient hammering is impossible1 or the metal is in considerable mass1 gun-metal should be used4 ,the author has found the best practical mixture for this--pure copper #hh1 tin #ab4 ,for centres requiring great rigidity1 as those of the theodolite1 level1 or sextant1 bell-metal is used by all the best makers4 ,this should be of such composition that it cannot be permanently bent without immediate fracture4 ,it should possess about the hardness and stiffness of untempered steel4 ,the best alloy the author has found for the bell-metal for these instruments is copper #hc1 tin #ag4 ,if very small castings are made with this alloy they are somewhat brittle1 probably from the rapid cooling of the surface in the mould1 therefore1 for small castings1 a safer alloy is copper #he1 tin #ae4 #ag4--;,in making all the above alloys1 for the best results the metals are assumed to be commercially pure4 ,the introduction of a little uncertain scrap1 which the ordinary founder is so fond of using to make his metal run down1 will often foul a pot of metal4 ,in all cases of copper alloys the copper should be entirely melted before the addition of the zinc or tin1 after which it should be thoroughly stirred with a charred stick or earthenware rod1 and then be cast in small ingots1 to be re-melted and cast a second or1 even better1 a third time before melting for the final castings4 #ah4--,workmanship4--,it would be quite impossible1 within the limits of this work1 to give such particulars of the workmanship in surveying instruments as to enable a person to manufacture them without practical knowledge of the manipulation of the various branches of the art1 but it is thought that a general sketch of the various operations entailed1 which vary somewhat in different workshops1 may be useful4 ,some of these particulars may be also useful to the surveyor1 not only as general knowledge of the instruments he uses1 but in some cases of accidents and emergencies1 and for the sake of keeping his instruments in order when he is far away from the manufacturing optician4 #ai4--;,framing ,work4--,the ordinary turning and filing of metals1 and some knowledge of the workmanship of the business1 are assumed to be understood by those who may use this book for special constructive details4 ,the tools in a mathematical or philosophical instrument-maker's workshop1 where high-class work is done1 nearly resemble in every way those of a good engineer's shop1 except that on an average the tools are much lighter1 and run at a higher speed4 ,where the works are extensive1 steam-power1 a gas engine1 or electric-motors are used4 ,in small shops the foot lathe is the only important tool4 ,there is a great advantage in using power for good work1 as the oscillation of the tool1 which is always caused by the action of the foot1 produces what is termed a chatter upon the work4 ,for turning brass and silver1 a high speed is desirable with a lathe of sufficient rigidity to give no sensible vibration4 ,a surface cut speed of about #bej feet per minute should be aimed at4 ,for turning gun-metal1 ,german silver1 and mild wrought-iron1 about #ajj feet per minute is required4 ,for turning bell-metal and cast-steel1 a very slow speed is required--about #af feet per minute4 ,the lathe should therefore possess means of ensuring these differences by back gear1 overhead motions or otherwise4 #bj4--,tools4--,the lathe of the most suitable construction for surveying instruments has the upper surfaces of the bed1 one side of section1 and the other flat--not both flat as in many engineers' lathes4 ,this ensures the certainty that rests and other tools can be firmly clamped down without possibility of lateral shake4 ,the slide-rest should have a broad base and be provided with direct perpendicular and rotatory motions1 with means of clamping the motive parts not in immediate use1 as smooth cuts can only be obtained on copper alloys by perfect rigidity of all parts of the tools4 ,the lathe should also possess a bed-screw and overhead motions suitable for applying flying cutters and milling-tools in every desired direction upon the piece of work when it is once chucked in the lathe4 ,a universal shaping machine and a milling machine generally replace the planing machine of the engineer4 ,these tools are sufficient for producing the flat surfaces for all ordinary work4 ,even when power is generally used1 small hand planing and shaping machines1 worked with a lever1 are very useful for working up single pieces and small parts4 ,a circular saw and a good grindstone are also indispensable4 ,with good rigid tools1 well applied1 very little work is left for the rough or bastard file2 on many instruments none whatever--only a little fine scraping1 superfine filing and stoning being required4 #ba4--,the greatest technical skill required in the manufacture of surveying instruments is in the principal axes of these instruments1 particularly in theodolites1 tacheometers1 sextants1 and some kinds of mining dials1 wherein a class of work is demanded which must be performed by a skilful1 experienced1 and careful workman4 ,the axis of these instruments1 as already mentioned1 should be formed of a casting of good bell-metal4 ,this axis must be turned upon its own centres1 which should be drilled up sufficiently to keep a steady bearing1 so that the truth of the work is quite independent of any fault there may be in the lathe4 ,the turning must be performed with a point-tool1 the upper angle of which should be about #fj4 ,this should be kept constantly sharp1 and be allowed to take only the finest possible cut at a slow speed4 ,the slide-rest should be set to the exact angle of the taper of the axis4 ,the socket1 if it is not very stout1 should be placed in a massive metal box and embedded in plaster of ,paris1 which must be allowed to set perfectly hard before use4 ,the socket is turned out1 if possible1 or otherwise it is roughed out with a hard steel fluted cutter1 and finally cut up by another fluted cutter which has been carefully ground to the correct cone intended for the finished axis4 ,the axis is chambered back in its central part1 so that it may fit the socket for about from half to three quarters of an inch1 only at its extreme ends4 ,after turning and boring as correctly as possible1 the axis and socket are ground together with soft oil-stone dust to true form4 ,after this1 the surface is turned1 or scraped entirely off1 with a sharp tool1 and the axis is again fitted by rubbing contact only4 ,it is most important to be sure that no grit remains embedded in the metal from the grinding1 as this will be sure to work out and abrade the axis afterwards4 #bb4--,the same care as is necessary to be bestowed upon the centres of instruments1 is required for tangent motion screws when these act directly without counter springs4 ,these should be made1 if possible1 of hard drawn wire4 ,they should be turned on their own centres1 the cut of the tool being extremely light to avoid flexure1 all screws of over #a_/h-;inch diameter should be cut direct in a light screw-cutting lathe1 although it is advantageous to run a pair of dies lightly over them afterwards to make the thread smooth1 and ensure a perfect fit in the nut4 #bc4--,soldering4--,besides the tubes of instruments1 all parts which are difficult or impossible to be formed advantageously in a single casting1 are hard soldered or brazed together where this will render the part of the instrument more rigid than by screw attachment4 ,the pins of all screws should be made of drawn metal1 to which the part to form the milled head may be a casting4 ,hard soldering in this country is now generally performed with one of ,fletcher's gas blow-pipes1 the parts of the instrument1 if large1 being embedded in a pan of charcoal4 ,the author uses a pair of gas blow-pipes1 taking the blast of a centrifugal blower driven by an electric motor4 ,these blow-pipes are placed opposite to each other1 so that the pieces being soldered together are entirely surrounded by the flames projected from both sides4 ,the flames of the gas blow-pipe may1 with this apparatus1 be reduced to mere points for small pieces4 ,the solder employed for ordinary work is fine spelter with a flux of ground borax4 ,the most convenient method of using this is to put about a quarter of a pound of spelter and an ounce of ground borax in a saucer1 and add sufficient water to cover it4 ,the borax and spelter may then be taken up together with a small spoon and placed directly upon the clean part of the metal which is to be soldered4 ,with deep or difficult joints it is well to soak the whole of the pieces an hour or so in a saturated solution of borax before commencing the soldering4 ,for soldering very small pieces1 or for soldering steel to brass1 silver solder is better than spelter2 it appears to bite the steel more firmly and it runs at a lower heat4 #bd4--,soft ,soldering1 or what is termed in the trade sweating1 should be resorted to as seldom as possible4 ,it is necessary in making attachments to drawn tubes1 as the heat of hard soldering would destroy the rigidity of the tube1 due to the drawing processes4 ,in this case1 where soft solder is employed1 the tube should be1 if possible1 surrounded by a band of solid metal1 which forms a part of the attachment1 or the attached part should be well secured with screws1 tapped dry1 before the soldering is commenced4 ,soft soldering on brass is generally very deceptive2 the solder may form a glaze round the joint with no attachment within4 ,many surveyors will recognise this who may have had one of the slop-made soldered-up levels fall to pieces in their work by a simple jar accidentally given to the instrument4 #be4--;,finishing mathematical work3 the surface as it leaves the superfine file is brought up by cutting it down to a mat with ,water of ,ayr stone1 and finally clearing with soft grey slate-stone4 #bf4--,polishing4--,where brightness is desirable1 particularly for steel work1 wash-emery and ,french polishing paper are used4 ,heads of screws and small turned parts are better finished off by a clean cut or with the burnisher on the lathe4 #bg4--,optical ,black4--,the interior parts of telescopes are painted over with a dull black paint1 the object of which is to cut off the reflection of extraneous light entering the object-glass obliquely4 ,optical black is made by finely grinding drop-black in turps or spirits upon a stone with a muller1 this is afterwards strained through fine muslin2 if it is ground in turps a little good gold-size is added2 if in spirit1 a little spirit varnish4 ,the black should be tested4 ,it should appear quite dull1 and yet be sufficiently firm to bear the finger rubbing upon it without soiling4 ,for eye-pieces1 the dull black generally employed is due to oxidation obtained by burning off an acid solution of cuprous-nitrate in a gas flame4 #bh4--;,bronzing4--,for the protection of finished metal work in surveying instruments the surface is generally bronzed1 as it is termed1 leaving bright only such parts as are required to be easily seen1 such as milled-heads1 heads of screws1 etc4 ,the dark gray of the bronze is also much more pleasant to the eye than a bright surface1 particularly when out in the sunlight1 so that bright instruments have gone nearly out of use4 ,the bronzing is effected by the application of a liquid that will corrode the metal and1 at the same time1 leave a dark pulverent deposit upon it4 ,there are a great number of bronzes to be had1 but that which the author has found to be the most permanent and safest from after corrosion is platinic-chloride1 dissolved in sufficient water4 ,this bronze is well known1 but is not used so frequently as it should be from its great expense4 ,the bronzes which are to be particularly avoided are those containing mercuric-dichloride4 ,these are very cheap1 and they give a fine dark surface2 but they are certain to rot the brass and produce a pitted or spotted appearance after the instrument has been much exposed4 ,the bronze1 whatever kind is used1 is put on with a brush upon the surface of the metal1 which must be quite clean to receive it4 ,after the colour is well brought up by passing the brush over the work several times1 the work is then thoroughly gone over with a hard brush and fine black lead until every trace of free corrosive liquid is removed1 as far as possible1 from the surface1 and the work is left quite dry in all parts4 ,some makers put a thin coat of asphaltum1 dissolved in turpentine1 over this1 which produces a light black surface4 ,some1 to save trouble and expense1 simply paint the instrument with black varnish without bronzing4 ,this looks very smart at first1 but the black is very liable to chip off in use and make the instrument unsightly4 #bi4--,lacquering4--,all parts of instruments intended to be left bright1 as well as all properly bronzed parts1 are separately covered with a thin coating of lacquer1 the application of which is technically termed varnishing4 ,the metal is raised to an equal temperature of about #bjj ,fahr41 and the varnish is applied with a fine1 flat camel-hair brush4 ,the process requires considerable skill1 so that only a few workmen do it to perfection4 ,special varnishes are made for the philosophical and mathematical instrument trades1 all of which have a base of fine shellac1 dissolved in absolute alcohol4 #cj4--;,engraving of figures1 words1 etc41 where there is much repetition1 is best done by the engraving machine--general work by the ordinary skilled engraver4 ,the method employed for the graduation of instruments will be considered further on in the discussion of instruments reading with a vernier scale4 #ca4--,style4--,this must1 of course1 depend upon the taste of the manufacturer4 ,in modern machinery1 and in scientific instruments1 there is a strong tendency to avoid all useless mouldings or ornaments1 and to finish all parts of the work uniformly with clean smooth cuts4 ,in surveying instruments which have to be handled1 it is desirable to avoid angles as much as possible1 both by form and by rounding off all corners neatly1 so as to produce a general feeling of smoothness over the whole instrument2 useless metal1 as1 for instance1 in milled heads of screws1 should be hollowed away to avoid weight1 and this object should be observed in the general distribution of metal1 never neglecting at the same time to insure the firmness of the instrument4 ,parts shaped out of the solid may be made much lighter than when screwed together in separate pieces and are of greater rigidity1 and admit of better style4 ,the leading makers all have a style of their own1 some more graceful than others2 most of the smaller makers make bad copies of these designs4 #cb4--;,glass-,work4--,the most important technical work1 except perhaps the graduation in surveying instruments1 is found in the optical parts1 of which only a brief description can be given4 ,the glass used for the lenses1 particularly for the achromatics1 is that manufactured by ,messrs4 ,chance ,bros41 of ,birmingham1 or by ,m4 ,mantois1 of ,paris1 both of which firms use the process discovered by ,guinard1 of ,solothurn1 in ,switzerland1 which was afterwards much improved by ,geo4 ,bontemps4 ,this glass is nearly white and transparent1 of uniform density1 and free from veins and stri4 ,it is also perfectly annealed1 which is important4 ,the following kinds of glass are usually employed for the object-glasses of surveying instruments3-- ---------------------------------------- ---------------- ,index of ,spectrum ,lines4 ,density4 -------------------------------- ,c ,d ,f ,g ---------------------------------------- ------------- ,hard ,crown #bdhe #aeadf #aeagb #aebcb #aebhj ,dense ,flint #cffj #afage #afbbd #afcdh #afdec ---------------------------------------- ------------- ,these particulars are given by the glass-makers who supply the glass4 ,for cheapness the optical crown-glass is often replaced by common plate-glass4 ,a specially clear and hard glass is made by ,shott1 of ,jena1 but early specimens of this glass did not appear to stand climatic influences4 ,this defect is now remedied1 and the glass is very pure in body1 but not free from air-bubbles4 #cc4--,two pairs of tools are used for glass-grinding for every curve4 ,these possess two spherical surfaces1 one of each pair resembling a shallow basin1 and the other1 of the same diameter1 fitting into this4 ,after turning the tools they are ground together1 and are afterwards kept in order by constant regrinding together4 ,these tools may be of cast-iron or brass4 ,the working surface of the tool is1 of course1 of the reverse curvature to that of the glass to be ground in it4 ,when the glass is ground by hand1 each tool possesses a screwed socket by which it can be screwed to a stump or post1 fixed in the ground1 or to a short knob-handle to be used as the upper tool by hand4 ,for working a glass1 or several glasses1 it or they are cemented upon a hand tool or holder1 which is of less curvature than the working tool4 ,the working is performed by rubbing in a straight alternately with a circular direction1 with a certain stroke difficult to describe1 at the same time walking round the post to reverse all positions4 ,the grinding is continued over the spherical tool until the surface of the glass is brought up to its curvature1 being supplied at first with coarse emery1 #fj-;hole1 which is kept in a very moist state1 and afterwards with finer emery1 #ajj-;hole1 and then by eight or ten still finer grades1 carefully washing off between the processes1 and reserving the mud most carefully for wash-emery1 which is used in completing the grinding4 ,where machinery is employed1 hand motions are imitated as nearly as possible by the motion of the tools1 particularly for the forming processes4 #cd4--,the wash-emery is formed of particles which are held suspended for a minute or so when the mud is stirred in a large vessel of water4 ,this water is drawn off for final settlement to form the wash4 ,the final grinding with the wash is continued until the emery appears jet black on the surface of the glass1 which has then a semi-polished1 almost metallic1 lustre4 #ce4--,polishing4--,this is performed in various ways1 generally moist cloth is placed over the tool4 ,the better way is to cover the polishing tool with patches of hard pitch1 which are made to take the form of the hand tool by having the fellow tool to that used in working pressed upon the surface while the pitch is still warm1 using a sheet of moist tissue-paper to prevent adhesion4 ,the polishing is effected in the same manner as the grinding1 but with peroxide of tin 7putty powder71 or rouge4 #cf4--,the great difference in the value of achromatic lenses depends upon the truth of the curvature due to the accuracy of the tools and the continuity of the grinding processes until a perfect surface is produced before polishing1 so that a given lens may have treble the labour bestowed upon it to one of inferior quality in the grinding only4 ,beyond this its ultimate perfection will depend much upon the polish4 #cg4--;,it may be well here to note how this may be observed4 ,a good test is to throw the shadow of a thin object1 as that of a piece of wire upon the surface obliquely4 ,this should show clear edges when the lens is changed to all positions for reflection4 ,the test of polish is really only the test of brightness of the surface of the glass1 which may be distinguished in many ways that will readily suggest themselves4 ,the importance of the perfect grinding is that to which attention is desired to be drawn4 #ch4--;,centring--,figuring and ,testing4--,after the above described processes1 the glass is centred by grinding off the edges until its axis is exactly central with the periphery1 so that it can be mounted in its cell4 ,it is then tested for figure4 ,the technical difficulties of figuring are too great to be discussed briefly in this treatise2 much of this work is performed by the skilled workman in the manner he works his tool and applies his grinding and polishing material1 every stroke giving a slightly different figure4 ,some method1 however1 may be given of testing1 which will be useful in estimating the quality of a lens1 irrespective of its manufacture4 ,to test the objective it may be mounted in its telescope and focussed upon a star1 or more practically in workshops1 upon the reflection of the sun as this is seen in the mercury of a small bulb of a thermometer placed conveniently on a black background at as great a distance as it is clearly visible in the telescope--a common distance is #bj feet4 ,the telescope is made to traverse the sighted object so as to cross the field of view4 ,if the focus under this test remains constant1 so that the image of the sun in the mercury bulb appears sharp and without colour1 the objective is fairly corrected4 ,further information on this subject may be gained from a very important paper read by ,sir ,howard ,grubb1 the eminent optician1 before the ,royal ,institution4#a #ci4--,the ,woodwork of the ,stands of instruments made in this country is generally of straight-grained ,honduras mahogany4 ,for occasional work the mahogany is better if seasoned for three or four years in boards which are cut to thicknesses increasing by quarter inches1 so that about the thickness of the finished work in one dimension may be used4 ,where a number of stands of constant dimensions1 as for ordinary theodolites and levels1 is required1 it is better to cut the mahogany a little over finishing size directly from the fresh log1 and then allow it to season three or four years4 ,in this manner any natural warp of the wood takes place before it is worked up1 which causes it to stand well afterwards4 #dj4--,lubrication of ,instruments4--,for the lubrication of all screws1 good watch oil should be used4 ,where this cannot be obtained1 salad oil filled up in its bottle with fresh-cut shavings of lead will produce a perfect oil free from acidity4 ,for working centres and collars1 a grease is better--that extracted from pork fat1 by leaving it in the sunshine1 answers very well1 but what the author has found best for the purpose is pure vaseline4 ,this keeps its greasiness1 and appears to be perfectly non-corrosive4 ,for the collars of tangent screws1 a mixture of tallow1 wax1 and soap is employed4 ,this mixture does not fret out to cause a bite upon the surfaces4 ,as the instrument-maker leaves the working centres of instruments they will generally perfectly maintain their lubrication for four or five years1 and it is not well to disturb them2 so that this note may be considered only for the restoration of old instruments to order1 or for cleaning them up generally1 which is nevertheless best done by skilful hands4 #da4--,preservation of ,instruments4--,instruments that have by any accident become splashed1 or dirty by exposure to rain and dust or otherwise1 may be washed with damp wash-leather4 ,if a piece of soft1 dry leather be afterwards moistened with a little linseed-oil1 and this rubbed over the instrument when it is quite dry1 it will restore the original brightness1 and tend to preserve it4 ,for wiping object-glasses some prefer a piece of clean old linen1 others an old silk handkerchief2 either will answer if kept quite clean4 ,if the glasses are only dusty1 the application of a soft camel hair brush is all that is necessary1 and this is quite safe from carrying grit4 ,if glasses are stained by slight corrosion1 this can be partially removed by clean spirit4 ,in replacing glasses1 it is important to observe that the notch marks1 if any1 on the edges of the glass agree1 and that the double-convex lens is placed outwards in the telescope4 #db4--,packing of ,instruments4--,this is really a very important matter seldom estimated at its proper value4 ,an instrument should lie or stand in its case in such a manner that its most solid parts only take the bearing surfaces1 and thus perfectly secure it4 ,when this is effected there should be no possibility of an exceptional jar on any delicate part from the jolting of the conveyance of the instrument4 ,great care should be taken to note how the parts of the instrument were originally arranged by the packer1 and this arrangement should always be followed in replacing the instrument in its case to its position1 into which it should fall with perfect ease4 ,instruments are frequently strained by being placed wrongly in their cases4 ,even with all these precautions1 the wood of the case may shrink or warp to a certain extent1 particularly in tropical climates1 so that the instrument may be exposed to external pressure from closing the case or otherwise1 so as to injure it or to spoil its adjustment4 ,in such cases it is better to examine the packing occasionally1 and1 if the case does not easily and perfectly close1 there is a risk that the instrument is being strained4 ,if this is the case1 assuming the instrument to be in its correct position1 the bearing surfaces should be lowered with the penknife or other tool1 so that it is just free1 but not to shake4 ,the author was the first to place a piece of cork under each bearing surface4 ,this gives a certain amount of elasticity1 with sufficient rigidity for support1 to preserve the instruments from injurious jar1 and it may afterwards be cut away more easily with the penknife than wood4 #dc4--,with complicated instruments there are always a number of loose pieces which are used occasionally upon or with the instrument4 ,these1 for compactness of packing1 are often placed one above the other1 and are liable to get astray4 ,it is very desirable that complete parts should be arranged1 as far as possible1 to go into their cases in any state of adjustment1--this is1 however1 not always possible4 ,as a rule1 before putting an instrument or any portions of it by1 all movable parts1 such as the telescope1 eyepieces1 etc41 should be closed in their closest form4 ,parallel plates should be left square to the instrument1 with the screws loose4 ,generally the packer leaves little liberty4 ,instruments are often packed so that they will go into their cases only just in one state of adjustment1 and in one position of the movable parts4 ,in this case1 great care must be taken at first in examining the position in which the instrument and its parts arrive from the maker4 ,the late ,m4 ,gavard1 of ,paris1 who was celebrated for his delicate pentagraphic instruments1 and to whom the writer owes many useful hints1 put initial letters on the parts of his instruments1 and placed printed labels on the parts of the cases where these should go4 ,mr4 ,hennessey1 ,first ,assistant in the great ,trigonometrical ,survey of ,india1 gives some excellent notes upon the subject of packing in his ,topographical ,instructions for the use of the ,survey ,department4 ,he recommends upon opening a case that a sketch should be made of the contents as they lie1 and all possible particulars should be recorded2 but his most useful hint is1 always to replace an instrument gently1 and in no case to use force if the instrument will not fall into its place4 ,unless the packings have been damaged in some way1 the instrument will go easily into its case1 and if it does not1 it shows that some part is not in its proper position1 and this must be carefully looked into to avoid injury4 #dd4--,leather ,over ,cases4--,for an instrument for use in the field it is better to have a solid leather case over the ordinary mahogany one4 ,this acts as a kind of buffer1 and takes off the jar of an accidental blow upon the case1 which might otherwise injure the instrument4 ,it also protects the mahogany case from the warping effect of direct sunshine and rain1 and closes the meeting-joint to keep out the dust4 ,solid leather cases are also general for all light instruments1 rendering a stiff case of wood or pasteboard unnecessary4 ,these admit most perfectly of straps being placed conveniently to adapt them to the person for carrying4 ,waterproof ,covers4--,in very rainy climates a waterproof cover for a delicate instrument is desirable4 ,this can be thrown over the instrument instantly in case of a sudden storm1 and the instrument left ready for continuing the work when it clears up4 ,,footnote3 #a ,proc4 ,royal ,institution1 vol4 xi4 p4 #dac4 ,,chapter ,,ii4 ,,the ,,telescope ,,as ,a ,,part ,,of ,a ,,surveying ,,instrument--,,general ,,description--,,qualities--,,optical ,,principles--,,refraction ,,of ,,glass--,,limit ,,of ,,refraction--,,reflection--,,prisms--,, lenses1 ,,convex ,,and ,,concave--,,aberration--,,formation ,,of ,,images--,,dispersion-- ,,achromatism--,,curvature ,,of ,,lenses--,,telescopes--,,eye-,,pieces-- ,,powers-- ,,dynameter--,,construction ,,of ,,the ,,telescope1 ,,diaphragm--,,webs--,,lines-- ,,points--,,parallax--,,examination ,,and ,,adjustment4 #de4--;,general ,description of the ,telescope4--,this instrument forms part of the theodolite1 level1 some kinds of miner's dials1 sextants1 plane tables1 and other surveying instruments4 ,for this purpose it is made of similar construction to that of the refracting telescope used for astronomical purposes4 ,the great object desirable in the telescope1 when used as a part of a surveying instrument1 is that it shall assist vision in obtaining the true direction1 or pointing to the position of an object in such a manner that it can be employed to ascertain the angular position of two or more objects in relation to the position of the centre of the instrument upon which it is fixed2 also to obtain relative altitude to this centre in relation to a distant station by the reading of a divided measure or staff placed thereon4 #df4--,the qualities desirable in a surveying telescope are1 that sufficient rays of light may be collected from the object observed for it to be clearly seen as a whole1 and in some cases that sufficient magnifying power should be available1 in order that details or divisions painted upon a staff may be sharply defined4 ,the amount of light received by the eye which is effective in producing distinct vision is in proportion to the extent of active surface of the object-glass converging the light rays4 ,the magnifying power is regulated by the sum of the convexities of the lenses of the eye-piece upon principles to be explained4 ,the surveying telescope is required to possess only a very limited field of view1 but very great focal range1 so that objects may be seen at any distance4 ,by the necessary optical arrangement of the telescope1 which will be further described1 the object observed is generally inverted4 ,this inversion of the image as it appears1 at first presents a little difficulty to the learner1 but in practice this soon becomes so familiar as not to be even recognised mentally4 #dg4--,optical ,principles involved in the ,telescope4--,to commence with the optical construction of the telescope1 that this may be thoroughly understood1 it is necessary to give brief details of some first principles upon which it is constructed1 assuming that optics have not been made a special subject of study4 #dh4--,refraction of ,glass4--,the properties of a lens depend entirely upon the fact that a ray of light passing from air obliquely into the surface of a dense transparent medium 7in this case of glass7 and equally from the glass into air is bent1 or1 as it is termed1 refracted1 to a certain angle at the surface of contact of the air and glass4 ,the ray of light entering the glass is termed the incident ray1 that proceeding from it the emergent ray4 #di4--,there is no known medium1 glass or other1 which refracts a ray of white light at one uniform angle4 ,the white ray is universally separated upon refraction1 or dispersed1 as it is termed1 into rays of all colours of the rainbow4 ,in considering refraction1 therefore1 in its simplest aspect we are compelled to take the refraction of one uniform ray which is distinguished by one colour1 that forms a part of the white ray1 as for instance the red1 yellow1 green1 or blue1 that is1 a monochromatic ray1 as it is termed1 which gives a sharp refraction of its own coloured light only in its ray4 ,incandescent soda produces monochromatic rays1 but in practice an intense flame behind a bright-coloured glass will answer the same purpose1 as the coloured glass may be arranged to absorb all1 or nearly all1 parts of the white ray1 except that of its own colour4 #ej4--;,every transparent medium has a special quality of refraction4 ,therefore1 different kinds of glass refract in different degrees within certain limited angles which will be hereafter considered4 ,the refraction is uniformly in the plane containing the incident ray1 and the perpendicular to the surface separating the two media4 ,every medium refracts monochromatic light equally according to the following law for any angle of refraction3-- ,whatever the obliquity of the incident ray may be1 when it passes from a rarer to a denser medium the ratio which the sine of the angle of incidence bears to the sine of the angle of refraction is constant for any two transparent media4 #ea4--,the natural law by which the power of refraction of any medium may be shown1 and consequently the magnifying power of a lens in the ratio of its curvative through this refraction may be exemplified1 is illustrated by the diagram on the following page 7,fig4 #a74 ,,pp1 a line perpendicular to the surface of the plane of the medium 7glass7 with air above it1 a ray of light would pass directly ,p to ,p through the glass surface ,,ss without refraction1 and so for all perpendicular incidences or emergences4 ,by this perpendicular line ,,pp1 termed the normal1 all refractions are measured4 ,the incident ray ,i to ,c is refracted to ,r4 ,then if we call the angle ,,icp ,i1 and the angle ,,rcp ,r1 it is found by experiment that the perpendicular from ,i on ,,pp 7or sin ,i7 bears a certain proportion to the perpendicular from ,r on ,,pp 7or sin ,r7 according to the density of the glass4 ,this proportion is generally expressed by the formula--sin ,i sin ,r4 ,another incident ray ,i to ,c would be refracted to ,r1 and using similar notation to the above we have sin ,i sin ,r1 and from this it follows that 7sin ,i7_/7sin ,r7 7sin ,i7_/7sin ,r7 1 which is called the index of refraction4 ,thus1 if in a certain glass the sine of ,i measure #c equal parts on any scale of length1 and the sine ,r #b parts on the same scale1 the index of refraction of this glass would be #c divided by #b or #ae4 ,illustration3 ,fig4 #a4--;,diagram of ,refraction and ,reflection4 ,if the above process be reversed1 and the ray of light ,r be refracted on passing from the glass to the air1 it will be projected to ,i in the emergent ray1 and follow the same law as that given above4 #eb4--,limit of ,refraction--,reflection4--,the sines to the angles ,,icp and ,i,,cp being constantly greater in proportion to the obliquity in the case of glass we are considering by #a_/c than the sine of the angles ,,rcp and ,r,,cp of the rays of incidence thrown upward upon the surface ,,ss1 it will be seen that at a certain angle or that in which the sine is #b_/c the radius1 namely1 #da #dh #cg1 the equation given above makes sin ,i #a its maximum value2 therefore1 at any angle of incidence greater than this1 the sine of refraction to continue in proportion would exceed the radius--an impossibility4 ,the refraction1 if possible1 would carry the ray into the substance of the glass4 ,this is therefore called the critical angle or angle of total reflection4 ,at this point we may consider what must happen4 ,by our rule1 refraction must cease at the angle refraction becomes impossible by increase of sine1 and as light cannot be extinguished in a transparent medium it must be reflected4 ,thus the ray r cannot be refracted in the proportion according to the rule given for sine ,i to sine ,r1 as this would exceed the greatest sine1 that is ,,sc the radius1 this ray will therefore be reflected at the surface from the point ,c1 and pass in the direction r4 ,this property of refraction1 continuing1 as it were1 into reflection1 is made use of in many instruments4 #ec4--;,it may be worthy of repeating1 as it is a mistake occasionally made by persons designing instruments for special purposes 7as telemeters71 that the refractions are not equal for varying angles of incidence1 but only1 as before stated1 in the ratio of the sines4 ,thus there is no refraction ,p to ,p a certain refraction ,i to ,r1 and a greater refraction ,i to ,r1 the refraction constantly increasing with the angle of incidence4 #ed4--,the ,reflection of ,light follows a very simple law1 viz43--,the angle of reflection of a ray of light from a reflecting surface is equal and opposite to the angle of incidence upon it4 ,thus1 in ,fig4 #b1 let a ray of light ,,ia fall upon the reflecting surface ,,ss at #cj of inclination to this surface1 then this ray will be reflected from ,a to ,r at the angle ,,ras1 which is also #cj4 ,if an object be at ,o1 and the eye at ,i1 then the object will appear as though it were at ,o1 as the eye only recognises the object in the direction from which it actually receives the light4 ,the apparent angle ,s,,ao is equal to ,,ias1 so that the point of a mirror from which an object reflected is received is in direct line between the eye and the apparent object4 ,this observation will be found useful in placing mirrors4 ,illustration3 ,fig4 #b4--;,diagram reflections from a plane4 ,illustration3 ,fig4 #c4--,reflection from a prism4 #ee4--,prismatic ,reflection4 ,the same law as given above applies to internal reflection from glass4 ,let ,fig4 #c represent the section of a prism ff1 two plain surfaces of glass at right angles to each other1 and the third side making an angle of #de with each of the other two4 ,the ray i will therefore pass perpendicularly through the plane f without refraction to meet the plane #de and the angle of reflection1 being equal to the angle of incidence1 will leave this plane at #de1 and reach r4 ,the angle of glass here given of #de being greater than #da #di1 its extreme angle of refraction1 the internal reflection will be therefore perfect4 #ef4--,prismatic ,reflection1 as this is termed1 is largely used in optics in preference1 where practicable1 to open reflecting surfaces1 from the certainty of keeping the reflecting surface clean2 as dirt exterior to the reflecting surface of the prism does not affect the internal reflection in any degree4 #eg4--,the reflection is shown for clearness from the plane 7,fig4 #b7 as it actually occurs1 or as it is measurable1 independent of theory4 ,in optics it is found much more convenient to take the reflection in relation to an imaginary line drawn perpendicular to the plane4 ,in ,fig4 #d ,,na is termed the normal4 ,taking the angles as before as #cj to the plane1 the optical expression of this would be #fj to the normal1 and the reflection of the incident ray ,,ia to ,r would be in the angle ,,iar #fj #fj #abj1 the amount the incident ray is deflected from its former course4 ,this principle is important to be understood in the construction of the sextant and other reflecting instruments4 ,in reflection the ray is found to follow the shortest path1--that is1 the path ,i to ,r by reflection is shorter in the lines ,,iar1 placed at equal angles to the normal1 than it would be by any other possible path4 ,as1 for instance1 it is shorter than ,ia,r1 shown by dotted lines4 ,illustration3 ,fig4 #d4--,measurement of angle of reflection in optics4 ,illustration3 ,fig4 #e4--;,diagram illustrating the principle of the lens4 #eh4--,passage of a ,ray of ,light through a ,prism or a ,lens--,convex ,refraction4 ,if we comprehend the law of refraction exemplified above1 art4 #ea1 the path of a monochromatic ray through a prism or a lens is easily determined1 taking into consideration the refraction index of the glass4 ,in ,fig4 #e let aa be the base of an equilateral prism1 which base may also represent the axis of a lens linear or parallel with the direction from the centre of the eye to ,o4 ,now1 if a ray of light pass from a small luminous object at ,o in the path a to the prism1 we may assume all other parts of the prism covered1 and the refraction of the glass be such that the ray will pass through it from this position in a horizontal direction1 or that parallel to the assumed axis aa1 then the same ray will pass through the prism to equal distance from the centre of the prism1--that is1 to the position of the eye shown by the ray continuing in the path a1 the angles to or from the prism being equal2 so that if we cover up all parts of this prism except a line parallel with its base joining the ends of the lines aa1 where it is shown passing through the prism1 any ray of light from ,o1 under the conditions given1 will appear as a spot of light on the plane parallel to the base of the prism2 or if we place our eye at the position shown1 we shall see the image of the light ,o4 ,if we take a prism of the same kind of glass1 but of less angle1 whose base is bb1 the refraction would then be less 7that is in the ratio of the sines71 that is if the ray pass through the prism at less distance from the base1 so that the ray ,ob would pass through horizontally as before1 and emerge from the prism in the path b1 also with equally less refraction1 so that the ray would reach the eye at the same point as the more refracted ray4 ,in like manner1 if the prism were of still less angle with base cc and pass through the prism at a lower position1 the refraction would be proportionally less1 and therefore reach the eye at the same point4 #ei4--;,if we take the half lens shown in section in the figure1 this may be considered to touch the surface of the prisms described tangentially in the lines aa1 bb1 and cc1 where the angles of contact of ,o1 a1 b1 or c upon the prism would be equal to those upon the lens for an infinitely small extent of surface4 ,therefore1 if we make the lens of such form that a ray of light may pass from any single point upon the line of its axis1 and be refracted by every point of the surface of the lens to a single point or focus on the opposite side of the axis1 such form would be a perfect lens4 ,for simplicity of demonstration the refractions given above are made parallel with the axis of the lens4 ,this parallelism could only occur with the object and the eye at equal distance from the centre of the lens1 and with this distance also proportional to the amount of refraction of the glass used in the construction4 ,if the rays were all parallel to each other upon incidence they would still be bent in the same ratio 7to the sines of the angles of contact and departure71 and this would bring the focus nearer to the glass2 but it is evident the same principles would hold4 #fj4--;,as regards the action of the eye in this matter1 it can only recognise the direction from which it receives the light1 and not the processes the rays may have undergone before reaching it4 ,therefore the ray proceeding from ,o in the path b1 passing through the lens or prism and emerging in the path b1 is recognised by the eye as the ray b only4 ,so that the point of light ,o appears visually as proceeding from the direction bs1 and this convergence or expansion of the point ,o1 with its coincidence from the opposite side of the lens1 produces the effect of magnification of the object represented by ,o4 #fa4--;,concave ,refraction4--,in ,fig4 #f a convex lens is shown in which the parallel rays ,l are drawn to a focus at ,f upon the principles just demonstrated4 ,if the lens were made concave1 as shown in section ,fig4 #g1 by the same principles of refraction1 it is evident that the rays would diverge1 as the refraction bends the ray uniformly towards the thickest section of the glass4 ,if two lenses are brought together1 one with convex face1 and one of the same radius of curvature1 but with concave face1 the rays in passing through would not be refracted4 ,in this case the lens would be said to be corrected4 ,a convex lens has a focus where the rays converge4 ,a concave lens is said to have a negative focus equal to the focus of the convex lens1 that will correct it1 or make it equal1 as regards refraction1 to plane parallel glass4 ,illustration3 ,fig4 #f4--;,diagram convex lens4 ,illustration3 ,fig4 #g4--;,diagram concave lens4 #fb4--,spherical ,aberration4--,if the surfaces of convex lenses are truly spherical1 it is found1 by an analysis too complex to be described in this work1 that the rays which pass through at different distances from the axis converge to slightly different points of distance4 ,this subject was at one time seriously discussed for the proper formation of objectives for telescopes2 but at present it is entirely neglected by the optician1 as it is found practically to be as difficult to make a lens truly spherical as one of the convergent or divergent form required under the special conditions present4 ,the spherical form1 as it is approximately produced from the grinding with spherical tools1 being always nearly correct1 the correct forms of object-glasses are made by figuring1 which has been already referred to1 art4 #ch4 ,in eye-pieces the spherical aberration would cause some confusion were the glasses not adjusted in such a manner as largely to prevent this4 #fc4--,the ,formation of ,images by ,refraction from a ,convex ,lens4--,if we take any double convex lens1 as that shown in section ,fig4 #f1 we find1 if it is held towards the sun at a certain distance from a solid surface1 we form a burning-glass1--that is1 we produce an image of the sun where his rays of light and heat are refracted by the whole of the surfaces of the glass4 ,the distance from the centre of the lens to the point of greatest light is called the solar focus of the lens1--that is1 the point at which it concentrates or converges parallel rays1 and forms the image of the sun4 ,with parallel rays from the sun1 the distance of focus is less than if these rays were divergent in any degree4 ,consequently the solar focus is less than that subtended by any object on the earth4 ,illustration3 ,fig4 #h4--;,diagram of the convergence of rays of light4 #fd4--;,in the diagram1 ,fig4 #h1 a candle-flame at acb forms its focus at acb1 where all rays converge to form an image in the following manner3--,every point of the candle throws its light upon every point of the surface of the lens1 and1 therefore1 throws the image of each point to its focal position behind the lens1 according to the direction of its refractions2 so that1 if we take all the separate points of light thrown from the candle1 we then have a perfect image of it formed by an infinite number of separate focal points1 and as the rays by their direction necessarily cross over the axis the image is in an inverted position4 #fe4--,the whole of these lines would form a confusion if shown in a diagram4 ,we may1 therefore1 take for illustration the exterior of a cone of rays proceeding from three points only4 ,thus the clear lines aa and aa from the point of the flame would refract to the lower part of the image a4 ,the dotted lines bb would proceed to the upper part of the image1 as shown by the continuation of the dotted lines to b1 whereas the central dash lines cc would form their images in the centre following the dash lines to c1 and thus1 from the number of luminous points1 the whole image of the candle would be produced at the foci bca in an inverted position4 #ff4--;,dispersion of ,light4--,the conditions stated above for refraction of monochromatic light would not answer for perfect vision1 which is only possible in clear white light4 ,it therefore becomes necessary in practice to correct the quality of dispersion which light suffers in refraction through any dense medium4 ,the evidence of dispersion by glass may be shown by a prism1 as in the following diagram3-- ,illustration3 ,fig4 #i4--;,diagram showing chromatism of light by the prism4 #fg4--;,in ,fig4 #i let ,p represent the section of a prism of glass1 covered except at the narrow opening a4 ,let a strong light1 as shown1 be covered1 except from a narrow slit1 then the ray from the light1 refracted from a towards a in the prism1 will be dispersed or split up at a into the colours of the rainbow1 shading from blue1 green1 and yellow1 to red1 within the prism4 ,upon emergent refraction at a this dispersion will increase so that an image of the slot near the light1 if thrown on a plane proceeding from the base of the prism to the right1 will be represented at ,,bgr by a prismatic or chromatic spectrum1 as it is termed1 shading off from blue to green1 yellow1 red4 #fh4--;,achromatism of the ,prism in the same ,quality of ,glass4--,taking the prism1 ,fig4 #aj1 ,c as before1 and applying a second exactly similar prism ,c reversed upon the face of the first--then at every part of the process of dispersion from a point of white light under diffraction into the first prism1 will by equal diffraction1 in passing through the second prism1 be brought to a point1 where it will issue a white ray at the point a1 as it entered at the point a2 or1 practically1 the emergent ray will be achromatised4 ,this principle must be followed in the manufacture of achromatic lenses1 although under various indices of refraction and dispersion from differences in qualities of glasses4 ,it is made use of in the achromatism of eye-pieces1 and in combinations1 and assures the achromatism of parallel glasses used for sextants under different angles of incidence4 ,illustration3 ,fig4 #aj4--;,diagram perfect achromatism4 #fi4--,the ,achromatic ,lens4--,the achromatism of a pair of lenses by which a large amount of refraction of pure white light is obtained1 depends upon differences in the qualities of glasses which are due to their density and chemical composition1 so that in one glass a less amount of dispersion is produced at an angle which gives an equal amount of refraction than in another4 ,the combinations of glasses in use are crown and flint1 as already described1 art4 #cb1 the crown being a light glass of soda and silica1 the flint being a heavier glass containing silica1 potash1 and lead4 ,in a certain kind of flint glass used for optical purposes1 for a prism giving only slightly greater refraction than one of crown glass1 the dispersion is about double4 ,therefore1 we may combine a pair of glasses so as to obtain a desired amount of refraction from the combination if we make the crown glass refract something over double the amount we require for the perfected lens or prism1 and diminish this quantity by the reverse refraction of the flint glass1 thereby correcting the dispersion1 as may be shown by the diagram on this page4 #gj4--;,in fig4 #aa let ,c be a prism of crown glass giving over double the amount of refraction to a prism of flint glass ,f1 but only of total dispersion equal to the thicker crown glass4 ,the compound white ray of light a will then be dispersed upon refraction at the meeting faces of the two prisms1 a certain quantity represented by the cone of rays shown1 and again converge at a1 an equal quantity on emergence from the exterior surface of the flint prism1 so as to issue again a white ray1 of which this system of prisms has refracted1 but not dispersed1 the light4 ,illustration3 ,fig4 #aa4--,showing principles of achromatism4 #ga4--,that the same principles given above for the prism will hold in the achromatic compound lens1 is already demonstrated by the comparison of lenses and prisms shown in ,fig4 #e2 but for the sake of clearness it may be again shown diagrammatically in ,fig4 #ab for an actual objective1 wherein the parallel rays ab1 proceeding from a distant object or star1 are shown refracted to ab1 and coming to a focus at ,f1 although dispersed at the meeting surfaces of the two glasses1 as shown diagrammatically1 by the internal cone of rays4 ,illustration3 ,fig4 #ab4--,showing achromatic objective4 #gb4--,practically1 the matter is not quite so simple as it would appear to be theoretically1 by the above-described conditions1 as we actually find the spectrum of a prism of flint glass of equal dispersion to one of crown glass does not give exactly similar extent of separate colours within its spectrum1 the medium ray of the spectrum in the flint glass being nearer the blue than in the crown4 ,thus1 this compound lens does not perfectly correct by inversion as it does in the perfect case discussed1 and shown in ,fig4 #aj4 ,for this reason better definition is found by slight displacement and slight difference of total extent of dispersion of one of the spectra in coincidence on the meeting planes between the lenses1 leaving in all cases a certain amount of residual colour1 blue or red1 uncorrected1 by making the glass under- or over-corrected1 as it is termed1 which does not1 however1 seriously impair distinct vision4 ,it is quite possible that1 by some future improvements in the chemical constitution of the glass1 this defect may be remedied4 ,english glass-workers prefer to over-correct1 ,german and ,french glasses are more often under-corrected4 #gc4--,the measurements of refraction and dispersion being both in one direction1 may be taken together within certain angular limits in one term in the construction of a lens as the ratio of dispersive powers1 the indices being certain dark lines which are observed uniformly in the spectrum of the sun projected from a narrow slit4 ,these lines or bands in the sun's spectrum are known to be due to metallic vapours which are present in his atmosphere1 and can therefore be reproduced by the deflagration of like metals on a small scale4 ,to certain of these lines letters of the alphabet have been applied4 ,of these letters1 a pair of lines due to sodium vapour marked ,d1 and three lines due to hydrogen1 marked ,c1 ,f and ,g1 are commonly taken for reference of dispersion4 ,achromatism is generally considered duly corrected when the lines ,c and ,g are united4 ,the middle of the spectrum between these lines is about ,e2 and chromatic dispersion of optical flint and crown may be taken to be fairly corrected if the spectra are coincident in colour at this line4 #gd4--;,curvatures in the ,achromatic ,lens4--,a large amount of mathematical power has been expended upon this matter1 but the perplexity of the subject is due to small differences of the material2 and the impossibility of working absolutely true spherical curves has rendered this work of little practical value to the optician1 who still resorts to the formul of ,dollond and ,tully4 ,those who care to follow the subject beyond the scope of this work will find numerous papers in the ,phil4 ,trans41 and in the works of ,herschel1 ,barlow1 ,coddington1 ,robinson1 and ,stokes1 wherein what is known theoretically of the subject is fully investigated and discussed4 #ge4--;,for all small achromatics1 such as are employed in surveying instruments with ,chance's hard crown and dense flint1 the following approximate formula is commonly employed1 expressed in terms of the radius of the curved surface into f1 the total focus of the finished objective1 for first working before trial3-- #ast4--,outside surface1 f_/#b convex1 crown4 #bnd4--,inside f_/#c #crd4--,outside f_/#c concave1 flint4 #dth4--,inside #d;f convex1 #gf4--;,by different makers the surfaces are changed as far as reversing the curvature of the front glass1 and indeed very good glasses are made with the #ast1 #bnd and #crd 7f_/#be74 ,in all cases true convergence of the white ray is only obtained by correction of the outer and inner surfaces1 or by figuring1 as it is technically termed1 in which the curvature is not only made greater or less1 but its character is altered generally in the direction from circular to elliptical section4 ,the qualities of the object-glass cannot be over-estimated by the practical surveyor4 ,a heavy instrument with inferior object-glass may be carried about for years1 whereas a lighter instrument with good object-glass would perform better work4 ,excellent information upon this subject was given in a lecture before the ,royal ,institution by the eminent optician1 ,sir ,howard ,grubb1 of ,dublin4 #gg4--,optical ,arrangements of the ,telescope4--,the earliest form of telescope is that of ,kepler1 ,fig4 #ac4 ,in this the rays from the object-glass cross in front of the eyeglass2 consequently1 the image is inverted4 ,this form is at present little used except in combination with a separate eye-piece4 ,illustration3 ,fig4 #ac4--,kepler's telescope4 ,illustration3 ,fig4 #ad4--;,galileo's telescope4 #gh4--;,galileo's ,telescope1 ,fig4 #ad4--;,in this the eye-piece is a concave glass4 ,this glass is placed inside the focal distance1 so that the rays from the object-glass are bent to less convergence1 that they may enter the pupil of the eye in a direction possible to reach the retina4 ,the image in this telescope is maintained erect4 ,this principle is used entirely for field and opera glasses1 also for sextants and some other instruments where it is desirable to keep the image erect1 and small power is required1 sufficient only to obtain more distinct vision4 ,the lines aa in ,figs4 #ac1 #ad are termed the axis of the telescope4 #gi4--,optical ,arrangement of the ,huygenian ,telescope4--,in surveying instruments1 where angles and directions are not taken by coincidence of direct and reflected images1 it is necessary that the direction of the axis of the telescope should be clearly indicated4 ,in this case the focus of a distant object--that is1 its exact image--is projected upon a plane termed the diaphragm1 ,fig4 #ae1 ,,ss upon which a visible object or index is placed1 the position of which is picked up by a secondary telescopic arrangement1 or eye-piece as it is technically termed4 ,illustration3 ,fig4 #ae4--;,diagram of arrangement of lenses4 #hj4--,the arrangement of lenses in a surveying telescope is shown in the illustration above1 where ,,og is the object-glass or objective1 ,e the eye-glass1 ,f the field-glass4 ,the two lenses ,e and ,f1 in their mountings1 form the eye-piece ,,ep4 ,the dotted line a is the axis of the telescope1 ,,ss is the focal plane of the object-glass1 where a metal disc is placed with an opening in its centre--this is termed the diaphragm or technically1 the index-stop4 ,across the opening in the disc1 spider's webs or other fine visible objects are placed1 to be described further on4 #ha4--;,both the object-glass and the eye-piece are fitted in sliding tubes1 which will be described presently1 in such a manner that they may be made to approach or recede from the focal plane ,,ss4 ,the nearest distance of the object-glass to this plane is the solar focus1 or the distance at which a sharp image of the sun or a star placed in the axial line would be formed4 ,the greatest distance of the object-glass from the focal-plane in most instruments is such that a clear image will be given on this plane ,,ss of an object placed at about twenty feet from it4 #hb4--,the ,ramsden ,eye-piece1 the optical arrangement of which is shown in ,fig4 #af1 is also known as a positive eye-piece4 ,it consists of two plano-convex lenses1 the convex surfaces of which are turned towards each other4 ,they are separated by a distance equal to two-thirds the focal length of either glass1 and placed so that the diaphragm is one-fourth this focal length from the field-glass4 #hc4--,this eye-piece is considered not to be quite so achromatic as another form known as the ,huygenian eye-piece1 but its spherical aberration is less than any other1 and it gives what is necessary in all measuring instruments--a flat field of view1 requiring no change of position to see the centre and border of the field with equal distinctness4 ,illustration3 ,fig4 #af4--,ramsden eye-piece4 #hd4--,the ,field of ,view should be as bright as possible4 ,to ensure this1 the field of the object-glass which is taken by the eye-piece at the position of the front of the eye should not be larger than the pupil4 ,if the whole field of light enter the eye as it should do1 the brightness will then vary directly as the square of the diameter of the object-glass1 and inversely as the square of the magnifying power4 ,the directions of the rays are shown by dotted lines as aa and aa for the ,ramsden eye-piece in ,fig4 #af4 ,this eye-piece is sometimes called an inverting eye-piece4 ,it is not really so3 the object-glass inverts its image and the eye-piece picks up the image in its inverted position4 ,two or three eye-pieces of this kind1 of different magnifying powers1 are sometimes supplied with one surveying instrument4 ,the same form of eye-piece1 being also a simple microscope1 is used to read the divisions on the divided circles of theodolites1 sextants1 and other instruments1 and for such purposes it is often desirable to ascertain its focal length4 #he4--,the ,focal ,length of the positive or ,ramsden eye-piece is found by dividing the product of the focal lengths of the two lenses by their sum1 diminished by the distance between them4 ,thus1 if the focal length of each of the lenses be #ae inches1 the distance between them #a inch3-- 7#ae #ae7_/7c - #a7 #aabe inches4 #hf4--,the ,magnifying ,power of the ,telescope4--,the focal length of the objective divided by that of the eye-piece gives the power of the telescope4 ,thus1 a #ad-;inch telescope with the above eye-piece would have a power1 #ad_/aabe #abddd1 or #ab nearly1 a very general lower power eye-piece with telescopes of this focus4 ,illustration3 ,fig4 #ag4--;,dynameter4 #hg4--;,dynameter4--,the magnifying power of a telescope may be ascertained1 without any knowledge of the focus of the glasses used in its construction1 by the use of a dynameter4 ,this instrument1 ,fig4 #ag1 consists of a compound microscope in which a finely divided transparent scale is placed in the mutual focus of its object-glass and of the eye-piece at a4 ,the divisions of the scale may be #ja1 #jb1 or #jja inches apart1 adjusted so that a disc #a inch diameter at the exterior focus of the eye-piece may read a given quantity upon the scale4 ,to use this apparatus1 the flanged face is placed in front of the eye-piece of the telescope1 previously set at solar focus4 ,the telescope throws a circular image of its object-glass through the eye-piece1 where it is picked up by the object-glass of the dynameter and brought to focus on the scale a1 where it appears as a circular disc of light4 ,if this image be measured by the scale1 and the diameter of the object-glass be divided by this measure1 the quotient will be the magnifying power of the telescope4 ,there are several other forms of dynameter4 #hh4--,the ,erecting ,eye-piece1 sometimes supplied with theodolites and occasionally with other instruments1 is the ordinary one of the common telescope1 ,fig4 #ah4 ,the glasses are so arranged that the image brought to the focus of the telescope inverted is again erected1 so that objects appear in their natural position4 ,the complete eye-piece is of the same optical arrangement as that of a compound microscope4 ,the arrangement of lenses is shown in the engraving on next page4 ,illustration3 ,fig4 #ah4--,optical arrangement of erecting eye-piece4 #hi4--;,a object lens1 ,b amplifying lens1 ,c field lens1 ,d eye lens4 ,stops are placed at d and d to cut out extreme rays4 ,the image is formed by the objective at ,o1 and the light passes in the direction shown by fine lines1 being thrown from side to side of the lenses4 ,the ray is achromatised proportionally to its dispersion by the separate lenses1 upon principles discussed art4 #fh and shown ,fig4 #aj1 as independently of the small amount of opacity of the lenses1 extreme rays are cut off1 so that central portions only are used4 ,this eye-piece suffers loss of light at each of the four lenses2 therefore1 a telescope with it1 for equally distinct vision to that obtained by using the ,ramsden eye-piece previously described1 would require a larger objective4 ,this eye-piece is rarely used now1 excepting with ,american instruments in which they are almost universal1 as the very slight advantage of seeing the image erect is far outweighed by the loss of light it entails4 ,the ,american manufacturers place them inside the telescope instead of outside1 thus the telescopes look much the same as our ordinary ones1 but the focal length of the object-glass is shortened by the length of the eye-piece1 and as this takes up from three to four inches1 a telescope which would appear to be say #aj inches solar focus is1 in reality1 only six or seven inches and consequently only about two-thirds the power4 ,illustration3 ,fig4 #ai4--;,diagonal eye-piece1 full size2 ,s ,g sun-glass4 ,it is astonishing that the ,americans1 who are usually so quick in adopting the most practical appliances1 are so slow in seeing the advantage gained by the use of the now almost universal inverting eye-piece4 #ij4--,the ,diagonal ,eye-piece1 ,fig4 #ai1 is used upon transit instruments1 theodolites1 and occasionally upon mining-dials4 ,it permits the telescope to be used by the observer looking at right angles to its axis4 ,thus1 by the natural direction of the eye1 stars or the sun may be observed to near the zenith1 or the direction of a line cut by two lights at the bottom of a shaft may be observed from above by the telescope of a theodolite having a hollow centre on its ordinary stand1 to check the magnetic bearing of the needle below ground1 if this is assumed to be subject to local disturbance4 ,the socket of this eye-piece screws upon the telescope and has a free inner tube for rotation1 so that the #ij to the axis of the telescope may be placed at any angle to the axis of its cylindrical circumference2 as1 for instance1 instead of being used vertically or for zenith stars1 it may be used horizontally1 where precipitous ground would not permit direct axial vision through the telescope4 ,the reflecting arrangement of this eye-piece may be adapted either to the ,ramsden or the erecting form4 ,in either case the reflector is placed in the central portion of the eye-piece4 ,in surveying instruments the reflector is generally a piece of polished speculum metal for portable instruments1 but a prism of glass for larger fixed instruments4 ,the general arrangement is shown in the section of a diagonal ,ramsden eye-piece on page #db1 full size4 ,a object lens1 ,d eye lens1 adjustable for distance from the reflector ,r1 ,s outer casing which permits adjustment for focusing1 ,,sg sun glass1 the diaphragm being in front of ,a4 #ia4--,when a rectangular prism is used for the reflector1 it is worked with one plane #de1 as previously discussed1 art4 #ee1 ,fig4 #c4 ,in place of one or both the #ij faces these surfaces are sometimes worked convex so as to form a magnifier1 dispensing with one of the convex lenses of the eye-piece4 ,a long diagonal eye-piece is necessary1 where stars towards the zenith are to be observed1 to prevent interference of the limb of a theodolite with the face of the observer4 #ib4--,reflecting ,eye-piece is used to observe small stars1 as for instance the circumpolar stars in the southern hemisphere1 by illuminating the front of the webs or lines4 ,a strong light thrown down the telescope from a reflector to illuminate the webs would tend to dim the effect of blackness of the sky and render these stars indistinct4 ,in the eye-piece1 ,fig4 #bj1 a piece of plain parallel glass is placed at an angle of #de to the axis4 ,this permits the webs to be clearly observed through the glass at the same time that it throws light from a lamp placed at a distance from the glazed aperture ,l by reflection of the surface of ,r sufficient for front illumination4 ,the amount of light required is regulated by the distance of the lamp from ,l4 ,this eye-piece is made to fit into the diagonal eye-piece casing1 as ,s ,fig4 #ai1 ,e ,fig4 #bj being the position of the eye1 ,f field-lens4 ,illustration3 ,fig4 #bj4--,reflector in eye-piece to illuminate the front of diaphragm4 #ic4--,sun-glass4--,sextants and theodolites are supplied with a very dark glass or a combination of dark glasses fixed in a rim to form an eye-piece front1 which screws or fits on in front of any eye-piece1 to take observations of the sun for longitude or bearing1 ,fig4 #ai1 ,,sg4 ,it needs no description1 but is necessary to be mentioned to complete the optical arrangements of a telescope1 as it is sometimes used for surveying purposes4 #id4--,the ,body of a ,telescope that forms part of a surveying instrument is constructed of a pair of triblet drawn tubes1 ,fig4 #ba1 ,,tt ,t4 ,these tubes should be truly cylindrical and straight1 so as to fit smoothly together1 the one within the other1 and slide in and out quite freely but without any play4 ,the inner tube should be as long as practicable1 so as to remain steady when racked out to the full extent required to focus near objects4 ,the object-end ,r is generally enlarged so as to take the cell in which the objective ,o is placed1 without cutting off any part of the light1 or entailing the weight of larger tubes than is necessary to make use of the full field of the objective4 ,the objective is generally held in its cell by an internally fitting screwed ring with milled edge1 so that the glasses may be taken out and separated to be cleaned1 and be easily replaced4 ,two notches or grooves are commonly made in the edges of the glasses1 each of which is deep enough to take a small brass pin which is soldered to the inside of the cell4 ,the second notch indicates relative position1 so as to secure the glasses being replaced properly4 ,in all cases the double convex crown glass is placed outwards from the telescope4 ,a glass of large size should have a loose ring within the cell to act as a spring to save distortion of the objective from expansion or contraction of the metal2 but this is not necessary in small surveying instruments4 ,in some common telescopes the object-glass is burnished into its cell1 in which case the glasses of the objective cannot be separated for cleaning4 ,illustration3 ,fig4 #ba4--;,body of surveying telescope4 ,illustration3 ,fig4 #bb4--,section ,fig4 #ba1 ,a to ,b4 #ie4--,stops4--,within the inner tube two or more thin metal rings1 termed technically stops ,,ss and ,s,s1 are placed to cut off any extraneous light that may enter the telescope obliquely1 and which1 if not stopped off1 would produce a fogginess over the whole field of view4 ,it is important that these stops should not cut out any part of the full aperture of the object-glass if it be a good one4 ,in the manufacture of the telescope this is easily seen by looking in at the eye-piece of the unglazed telescope to see if the stops clear the objective cell4 ,in the finished glazed telescope another method will be discussed further on4 #if4--,the inner or the outer tube of the body of the telescope slides towards or from the objective for focussing by means of a rack ,r and pinion ,p4 ,the rack is soldered to the inner tube1 and the pinion fitted in a cock-piece1 as shown ,fig4 #bb ,c1 on the outer tube4 ,the pinion is moved by a large milled head ,m4 ,this fitting should be made with care4 ,the pinion should be very free1 so that it does not lift the body at any tooth1 and at the same time there should be no shake on the gearing4 ,it needs considerable practice to rack a telescope properly4 #ig4--,the outward part of the object end of the telescope is generally turned to fit the interior of a separate short tube1 shown at ,r1 which is placed over it4 ,the outer end is closed by a ring to the size of the aperture of the objective4 ,this is termed a ray-shade or sometimes a dew-cap4 ,the ray-shade is extended when the telescope is directed to such an angle that the sun's rays would fall upon any part of the objective1 and thereby cause internal reflections4 ,a swivel shutter1 ,fig4 #ba1 ,r1 is placed upon the outward end of the ray-shade1 which1 when closed1 as shown in the cut1 forms a cap to the telescope4 ,the eye-piece ,,ep before described1 art4 #hb1 ,fig4 #af1 is placed in a tube constructed upon the end of the telescope1 in which it slides freely1 to focus upon the diaphragm to be presently described4 ,the telescope is mounted sometimes solidly upon a transverse axis1 or it is mounted in turned bearings1 or it has two collars placed round it which are turned quite equal and true1 and are mounted on ,y's to be hereafter described4 #ih4--,mechanical ,adjustment of the ,eye-piece4--,in some large instruments the eye-pieces are racked for adjustment in the same manner as the object-glass already described4 ,a better plan is to have an inner tube to the socket tube cut with a screw into this1 and provided with a milled edge1 so that the eye-piece may be screwed gently to focus upon the webs of the diaphragm4 ,illustration3 ,fig4 #bc4--;,elevation of diaphragm4 ,illustration3 ,fig4 #bd4--,section of diaphragm4 #ii4--,the ,diaphragm of the ,telescope is so constructed as to permit the displacement of spiders' webs or other fine objects in any direction at right angles to the axis of the telescope1 or in the vertical only in the dumpy level1 to be described1 the object in all cases being to adjust the crossing of the webs1 lines1 or points to the axis of the telescope4 ,it will be convenient here to discuss a general form of diaphragm applicable to theodolites1 mining-dials1 and plane-tables only1 which gives movement in two directions at right angles to each other4 #ajj4--,the diaphragm1 ,fig4 #bc1 is formed of a stout disc of brass having a centre hole of about #cj inch diameter4 ,upon the side which is placed next the eye-piece the hole is brought to a thin edge by an internal bevel or countersink1 which leaves the hole much larger at its off surface1 ,fig4 #bd ,p4 ,the disc is held in its place and adjusted by four capstan-headed screws1 termed collimating screws1 two of which are shown in section as ,,cc1 the screws being tapped into the rim of the diaphragm frame ,p4 ,the screws are placed through a stout collar4 ,the theodolite diaphragm has generally three spiders' webs or lines crossed in the manner shown in the centre of ,fig4 #bc4 ,the eye-piece is screwed into the thick plate1 ,fig4 #bd1 ,,tt1 and adjusts to the focus of the webs4 ,illustration3 ,fig4 #be4--,webs wound off for use4 #aja4--,webs4--,it is a somewhat delicate process to web a diaphragm1 but it is necessary that every surveyor abroad1 out of the reach of an optician1 should understand the method if his instrument were originally webbed4 ,the webs are taken from a small or young garden spider4 ,the best are taken when the spider has first commenced spinning4 ,to wind off the web a fork is bent up out of a piece of thin brass wire4 ,a long hairpin will answer for this purpose very well1 or even a fork formed of a thin branching twig of a shrub2 but if this last be used it should be thoroughly dry1 or the webs will be broken or be baggy by its warping in drying4 #ajb4--,the web in connection with the spider is first attached to one prong of the fork by looping or by any sticky matter1 if the web be not sufficiently sticky naturally4 ,the spider is then suspended from the fork and jerked down a foot or so1 and the web is wound off as shown in ,fig4 #be4 ,the last length of web being attached by gum4 ,a dozen or so of the forks may be taken from the same spider before she is exhausted4 ,the webs are then gummed or varnished to the sides of the fork1 and are ready for use at any future time4 ,they are best preserved if placed in an air-tight box1 which may have slots in an internal fitting to hold them4 ,the small amount of spring given by the fork keeps the webs always taut4 ,where a living spider cannot be found1 the open ties of an old web may be taken2 but in this case1 after the web is wound on the fork1 it should be carefully washed by immersing it in clean water1 and1 if necessary1 brushing it gently under water with a light camel-hair brush1 examining it occasionally with a magnifier to see that it is sufficiently clean and free from knots for its purpose4 #ajc4--,to ,fix the ,webs1 lines are drawn on the diaphragm1 into which the webs are to fall4 ,it is then varnished over the divided side with ,canada balsam1 laudanum1 or other quick-drying1 sticky varnish--at a pinch1 sealing-wax dissolved in strong whisky will answer4 ,the outer1 or the unused web upon the fork1 is lowered carefully over one of the most nearly vertical lines1 and lightly pressed down to assure its perfect adhesion to the varnish4 ,it is then either broken off or cut loose4 ,the second nearly vertical line is then webbed in the same manner1 and the horizontal line finally1 being sure that this last cuts the intersection of the others4 ,the diaphragm should then be put in a warm place to be allowed to thoroughly set without disturbance before it is fitted in the telescope4 #ajd4--,platinum ,wires are sometimes used in place of webs4 ,these wires are made by drawing a piece of fine platinum wire1 which has been previously soldered into a silver tube1 to the greatest fineness possible with the draw-plate1 and afterwards dissolving the silver off the platinum by nitric acid4 ,the platinum wire is thus produced of less than #jja inch diameter4 ,for a time these wires were very popular1 and it was thought that they would supersede the use of webs1 but they do not appear entirely to answer expectation4 ,the platinum drawn in this manner appears to lose some part of its elasticity4 ,it is not easily attached1 that is1 it is liable to shift from its fixing1 possibly from its contraction and expansion with change of temperature1 not being of the same metal as the diaphragm4 ,it also oxidises a little or becomes in some way corroded in use out of doors4 ,it appears to answer better for astronomical telescopes1 but the finest platinum wire obtainable is not so fine as a spider's web4 #aje4--,lines ,ruled upon ,glass4--,a glass diaphragm is frequently used in a surveying instrument to replace the webs4 ,lines are ruled upon the glass in similar positions to the webs already described4 ,they appear quite sharp in the eye-piece1 and are more permanent than webs4 ,glass is also convenient for permitting space lines to be ruled for subtense measurements1 a subject to be considered further on4 ,the objections that have been found to glass are that it obstructs a little light1 and is subject to dewing4 ,the dewing is particularly annoying when temperature is lowering quickly1 as a diaphragm may become bedewed many times in a few hours4 ,in all cases where a glass diaphragm is used it should be placed in a ground metal fitting1 so that it may be taken out in a minute to clean and be replaced with perfect certainty of its adjustment4 ,it is a very convenient practice where webs are used to have a spare glass diaphragm to replace them should they become broken4 ,this may be constructed by means of a ground metal fitting to be put in a webbed instrument in perfect adjustment in cases where it might be impossible to find a new web4 #ajf4--,points4--,the author for a large number of instruments employs very fine points in place of webs1 which he highly recommends4 ,these are fixed for support upon the margin of the diaphragm1 and projected therefrom into the field of view4 ,the points are formed of a special alloy1 #ge platinum1 #be iridium1 which has the hardness of steel1 and is perfectly non-corrosive in air or moisture4 ,they are made sufficiently stiff to be dusted with a camel-hair brush1 supplied in the instrument case1 without the slightest fear of disturbance of position in the instrument4 ,they form a perfectly permanent index of sufficient stability to last in perfect adjustment as long as the instrument lasts in wear4 ,one objection is that a point gives less field of observation for levelling than a line1 but this does not hold if there is tangent adjustment to the instrument to bring the point up to its reading position4 ,the value of the reading from these points will be discussed further on4 #ajg4--,position of the ,diaphragm in the ,telescope4--,if the objective be accurately centred1 and its mounting true1 the intersections of the webs1 lines1 or points should come exactly in the axis of the telescope2 but it would never do to accept this without critical examination4 ,therefore the webs may be placed approximately in the centre1 and adjusted true to the axis of the objective and the telescope by what is technically termed collimation4 ,the first point1 however1 to be studied in this adjustment is to get the eye-piece and the objective accurately in focus with the webs4 ,the same description of focussing which answers for collimation will answer also for ordinary use of the telescope4 #ajh4--;,adjustment of the ,eye-piece to the ,webs is effected by pushing in or drawing out the eye-piece in its tube with a slight screwing motion until the webs1 lines1 or points appear quite distinctly4 ,to prevent confusion from the sighting of objects1 it is better to take off the ray-shade1 to point the telescope to the distance in opposition to the direction of the sun1 and to keep the telescope rack fully extended1 so that it is quite out of focus4 ,when the light is not very bright a sheet of notepaper or an envelope may be placed obliquely in front of the object-glass to obtain a soft reflection from the sky4 ,this method is always employed by some observers4 #aji4--;,adjustment to ,focus of the ,objective4--,parallax4--,the eye-piece remaining in focus1 the telescope is racked out until the object desired to be brought into view1 either for the collimation or for ordinary reading1 is sighted4 ,after this the milled head is moved as slowly as possible until what is thought to be the exact focus is obtained4 ,the certainty of exact focus is not easily obtained by direct observation1 but it may be obtained by what is termed observation for parallax1 which must be taken in all cases when adjustment is required for collimation4 ,thus1 having obtained the nearest possible adjustment by sighting a small object or a division upon the staff1 bring the object to read exactly in a line above the horizontal web in the centre of the stop or the corner against a vertical web4 ,if now the eye be moved up and down as far as the range of the eye-piece will permit vision of the centre of the webs1 and the object sighted appears fixed at the same position to the webs1 the focus is perfect4 ,if1 in moving the eye1 the object sighted appears to follow its motion about the intersection of webs1 the focus of the telescope lies beyond the webs2 the objective must therefore be moved slightly nearer the webs by turning the milled head very gently4 ,if1 on the other hand1 the object sighted moves in the opposite direction to the eye about the intersection of the webs1 the focus of the telescope is towards the eye-piece1 and the telescope requires slightly racking outwards by moving the milled head in the reverse direction4 ,after a few trials the object and webs appear stationary1 however obliquely observed4 #aaj4--;,collimation is the adjustment of the crossing of the webs of the diaphragm to the axis of the telescope and its object-glass4 ,this is effected by adjustment of the opposite collimating screws1 ,fig4 #bd1 ,,cc1 in two directions at right angles to each other4 ,where the telescope is placed in ,y's or collars1 this adjustment is made by placing the webs or lines in focus of the eye-piece and the object-glass of the telescope in focus upon a small distant object4 ,then if the telescope is rotated in all directions1 and the small distant object cuts the crossing of the webs in all positions1 it is said to be truly collimated4 ,it is necessary to discuss the structure of various instruments to show the methods of collimating in special cases2 therefore this subject will be again brought forward4 #aaa4--,the ,qualities of a ,telescope of a surveying instrument are best ascertained by its performance4 ,the general method is to place a staff at the full range1 #aj to #ae chains1 and to see if the #ja foot in fine bright weather is read clearly and sharply4 ,this outdoor observation is not always possible1 particularly in large towns1 but it may very well be supplanted by reading at a short distance4 ,the author made for the late ,colonel ,strange1 ,f4,r4,s41 whose knowledge of scientific instruments was of the highest order1 a test-card for the ,lambeth ,observatory1 to be placed at #be feet from the instrument4 ,this card had on one part fine lines ruled #ja inch apart4 ,a #ad-;inch telescope was considered sufficiently good if these lines could be clearly separated at this distance by the telescope when it was in correct focus4 ,the dial of a watch1 or an ivory scale1 answers very well as a test object1 as sharpness of outline is the point to be ascertained4 #aab4--;,a more refined technical method than that described above1 which also tests the general accuracy of the optical arrangement of the telescope1 is to fix a small disc of white writing-paper1 say #a_/h inch diameter1 cut out with the point of a pair of compasses with sharp outline1 on a black surface of a board1 paper1 or cloth4 ,if this be placed as before1 #cj feet or more distant in a good light1 and be correctly focussed in the telescope1 a sharp image of it should be obtained4 ,this focal position of the telescope may be temporarily marked upon the inner tube with a fine soft black-lead pencil4 ,if now the object-glass be racked outwards or inwards from this line1 say for about a twelfth of an inch1 and the image appears to be surrounded with a uniform haze1 the objective may be considered to be correctly formed1 or to be free from spherical aberration1 as it is termed1 and the combination to be correctly centred4 ,if the haze appears more on one side than the other the centring is defective4 ,if the object remains fairly sharp when out of exact focus the curves of the lens are defective1 as the shorter the range of focus the more perfect is the correction from spherical aberration4 #aac4--;,if the curves are not sufficiently correct to bring the image from all parts of the objective to a focus1 such incorrect parts are useless1 and a good glass of smaller size would be better4 ,the fault is generally found in the marginal portion of the objective1 which requires the greatest skill of the glass-worker4 ,therefore1 a very good test to find whether the whole of the aperture of the objective is in effective use is to cut out a piece of card of the size of this aperture and to cut a second piece out of the centre of this1 of half the diameter1 so as to form a disc and a ring4 ,if the objective be now covered by the ring and accurately focussed upon a test object1 and this be then removed and replaced by the disc fixed over the centre of the objective1 and the focus remains equally sharp1 the curves may be said to be1 practically1 correctly worked4 #aad4--;,as the central part of an objective is more easily brought to correct curvature than the marginal parts it is not uncommon in inferior instruments to make the aperture of the central stop of the telescope cut off the margin of the objective4 ,this renders it only equal to a smaller glass4 #aae4--,whether the full aperture of a telescope is used may be discovered by employing a second eye-piece--outside the regular eye-piece that is placed in the telescope--to pick up the image of the object glass formed through the eye-piece which is placed against the telescope in the manner of using a dynameter1 art4 #hg4 ,with the ordinary surveyor's level1 two eye-pieces are commonly sold2 one of these may be placed in the telescope and the other used to pick up the image of the object-glass4 ,with a theodolite one eye-piece may be placed in the telescope1 and one of the readers used to magnify the divisions of the limb may be used to pick up the image4 ,the best manner of proceeding is to fix with water or thin gum two or three small pieces of paper1 say #a_/bj1 #a_/aj1 and #a_/g inch square1 close against the edge of the cell upon the face of the objective4 ,then focus the telescope on an object at some distance1 say a chain or two4 ,now use the second eye-piece in front of the one in the telescope1 and an image of the object-glass will be seen2 and if the aperture is fully open all the pieces of paper in their places will be clearly distinguishable4 ,if one or other piece is invisible1 the margin of the glass is cut off to this extent4 ,if the objects in front of the telescope tend to confuse1 a piece of white paper may be placed obliquely to reflect the light of the sky into the telescope1 which will at the same time fully illuminate the objective4 ,the discussion of the principle of the anallatic telescope1 used only with the tacheometer1 is deferred to another chapter1 wherein subtense instruments are described4 ,,chapter ,,iii4 ,,the ,,magnetic ,,compass ,,as ,a ,,part ,,of ,a ,,surveying ,,instrument ,,or ,,separately--,,broad ,,and ,,edge-,,bar ,,needles--,,manufacture ,,of ,,the ,,needle--,,magnetisation--,,suspension- -,,dip ,,and ,,adjustment-- ,,lifting--,,inclination--,,declination- -,,variation--,,correction-- ,,compass-,,boxes--,,description ,,of ,,compasses--,,ring ,,compasses--,,trough ,,compasses--,,prismatic ,,compasses--,,stand--,,surveying ,,with ,,compass--,,pocket ,,compasses4 #aaf4--,the ,magnetic ,needle1 which forms part of a great many surveying instruments1 is made of the form adapted to the special purposes of the instrument in which it is placed4 ,there are two prevailing forms commonly in use--one in which the needle is made pointed at one or both ends to read directly upon a divided circle fixed upon the instrument1 and the other form in which it is made to carry and to direct a divided circle by its magnetic force4 ,illustration3 ,fig4 #bf4--;,broad needle4 ,illustration3 ,fig4 #bg4--;,edge-bar needle4 ,the magnetism which gives directive force to the needle has been found by experiment to reside in every separate part of the magnet1 that is1 it is assumed to be a molecular force4 ,therefore1 it would not appear to be very important1 within certain limits1 of what form the magnetic needle is made1 and this is found by experiment to be to a large extent true4 ,the only important conditions appear to be that the needle shall be of such form that the inducing magnet1 to be described1 arts4 #abj-abc1 which is used for magnetising may be brought into contact upon every part of its surface1 and that the molecular continuity of the parts should mutually support the general directive influence of the magnetism longitudinally in parallel lines4 #aag4--,magnetic needles are generally made in the form of flat bars1 which are balanced upon a standing point falling into a cup which forms the centre4 ,when the greatest section of the bar is placed horizontally it is termed a broad needle1 as shown ,fig4 #bf4 ,this may be made of the lozenge form shown1 or be parallel throughout4 ,when the greatest section is placed vertically it is termed an edge-bar needle1 as shown ,fig4 #bg4 ,the north pointing end of the broad needle is commonly tempered dark blue1 or has a deep cut across it1 if the needle is left open4 ,this is not necessary if it carries a ring4 ,the edge-bar is generally used where it is required to read into a fixed circle of division1 in which case its ends are brought to fine knife-edges4 #aah4--;,from the difficulty of reading a sharp point in bright metal against the black line of a divided circle1 the author occasionally makes one point of the needle with a fine cut1 sawn vertically for a short distance from its end1 so as to form a kind of split which is afterwards closed1 so that it presents the appearance of a fine black line of the same character as the divisions into which it reads4 ,with this1 as shown ,fig4 #bh1 the reading is found to be much more easy4 ,the point is also more readily adjusted by grinding1 as the end of the needle being broad1 less care is necessary to avoid reducing it so much that it may leave the interior of the circle short where it reads into the divisions4 ,this form of needle is not adapted to mining instruments1 which have often to be read in an oblique direction4 ,illustration3 ,fig4 #bh4--;,author's plan of needle reading4 #aai4--;,in the ,manufacture of the ,needle it should be made of the finest cutler's cast steel1 or1 better still1 of steel containing #c per cent4 of tungsten4 ,if not left in a parallel strip as it is drawn or rolled1 it should be brought as nearly to its form as possible by forging at a low heat4 ,the steel should not be over-heated for hardening4 ,it should be hardened in cold water or oil1 and be tempered afterwards down to a very pale straw-colour--in fact1 the temper colour should only just appear4 ,long needles may have the temper sufficiently lowered at the centre to set them approximately straight during the tempering2 but the temper should not be lowered even in the centre below a pale blue1 spring temper4 ,after tempering1 the setting and working up to balance is best done by grinding1 and for the final adjustment1 by stoning with ,water-of-,ayr stone4 #abj4--,magnetisation of the ,needle may be performed in many ways by means of a permanent magnet or an electro-magnet1 or electrically by means of a solenoid4 ,when the magnetism is induced from another magnet it is only important that the properly hardened needle should be regularly and equally magnetised over its surface by pressure upon it of the proper poles of the inducing magnet--that is1 that the north pole of the magnet should induce magnetism in the southern half of the needle only2 and the south pole in the northern half only4 #aba4--,method of ,magnetisation by ,single-touch4--,this method is more generally applied to touching up needles than magnetising them at first4 ,the northern pole of a strong permanent magnet is stroked down the southern end of the needle from its centre to its end three times on one side of the needle4 ,the needle is then turned round1 and the northern end is stroked down in like manner with the southern pole4 ,the needle is then turned over1 and the process is repeated on the other side4 ,this may be done a second time and the edges of the needle be stroked down also4 #abb4--,method with both ,poles4--,in this process the needle is held down firmly with pegs on a board1 and a strong horse-shoe magnet with rather close poles is laid on the bare needle without its cap1 in a manner that both terminals press upon it4 ,it is then drawn backwards and forwards from end to end of the needle several times1 lifting the magnet finally from about the centre4 ,the process is then repeated on the opposite side of the needle and its edges4 ,illustration3 ,fig4 #bi4--;,divided-touch magnetisation4 #abc4--,method of ,divided-touch is a somewhat quicker process1 which does not entail removing the cap1 the general plan of which is shown in the engraving below4 ,the poles of the magnets1 or one of them1 is marked4 ,two good straight bar magnets are used4 ,the needle is fixed down on a board and the poles of the two magnets are laid upon it at an angle of about #cj1 applying one north or marked pole1 and one south or unmarked pole4 ,the magnets are then drawn apart in a horizontal direction along the needle1 with constant pressure upon it1 so as to reach the opposite ends of the needle simultaneously1 and then again pressed back to the centre4 ,after this operation is performed three or four times on one side of the needle1 it is turned over and the process is repeated on the other side1 being careful as before to use the same ends of the magnets upon the same ends of the needle4 ,the operation may be repeated several times to be sure of saturation of the needle4 ,it is better to lift the magnets off at the termination of the operation at the centre of the needle4 #abd4--;,it is found that the needle is magnetised a little more quickly if it is laid upon a strong magnetised bar during magnetising1 or upon the ends of two bars1 as shown in the engraving1 ,fig4 #bi1 or on the two ends of a wide horse-shoe magnet4 #abe4--,needles are now more generally magnetised electrically by placing them in a solenoid or coil of stout insulated copper wire through which a strong direct current is passing from a dynamo or powerful battery4 ,this method is employed in the best shops4 ,the touch system above described is convenient for the profession for remagnetising a needle when weak1 as a horse-shoe magnet at small cost may be kept for the purpose4 ,it is generally used in small shops1 as being at all times ready to hand1 less expensive1 and sufficient to ensure saturation if it is skilfully done4 #abf4--,with every care in the manufacture of the needle there remains a little difference in the qualities of needles which are apparently otherwise identical4 ,little local differences in the quality of the steel1 slight over-crystallisation from over-heating in hardening or unequal tempering1 or unequal magnetising1 are liable to form weak parts1 or even what are termed consequent points4 ,these are points in which the magnet possesses a reversal of its general longitudinal polarity4 ,this can be made quite evident by experiment1 as it is possible to make a needle not only with poles at each end1 but with intermediate poles which are easily detected by sifting iron filings over it4 ,the filings are found to adhere strongly at other local points than those near the ends1 where a good magnet is alone strongly attractive4 #abg4--,mounting of the ,needle4--,the needle for a surveying instrument has a female centre upon which it is suspended4 ,the centre1 termed technically cap1 is generally formed of a hard precious stone1 agate1 chrysolite1 ruby or sapphire1 the latter being best1 simply from the high polish it attains in grinding out with diamond dust4 ,rubies and sapphires are like minerals1 except in the colour1 which varies very much2 the off-colour stones1 which are of small value for jewellery1 are used for scientific purposes4 ,the cap is mounted in a brass or aluminium cell made as light as possible for sufficient stability4 ,the needle is supported upon a hardened steel point1 upon which it is perfectly balanced4 ,the base of the point is tempered down to a low degree in order to admit a certain amount of bending to counteract the slight warping which generally occurs in the hardening4 #abh4--;,correction of ,errors4--,the needle1 after it is mounted1 although in balance may not have the steel placed symmetrically about its axis through slight curvature1 unequal thickness about the cap1 or otherwise1 so that the magnetic direction is not perfectly linear between the points and the centre4 ,if the points and centre are not magnetically linear1 the correction for declination1 which will be presently considered1 cannot be made accurately4 ,on this account it is better for the manufacturer to mount the needle on a slate bed with two sliding heads that may be brought up to the points of the needle4 ,the heads have upon their upper surfaces lines drawn perfectly linear with the centre point of suspension of the needle1 and a few lateral divisions to these lines for determining errors4 ,on this bed the needle is placed upon the centre point to be examined how nearly its reading points are true with the axis4 ,the error being recorded1 the needle is demagnetised1 and remagnetised end for end1 and again examined4 ,corrections are then made by grinding or stoning from observations of bisections of the points cut in the separate readings1 until the needle is made symmetrical and invariable1 whichever end is magnetised for the north or south4 ,illustration3 ,fig4 #cj4--,section of mounted needle4 #abi4--,lifting the ,needle4--,the needle of a surveying instrument should never be supported upon its centre except for the time it is in use for observation1 as a fine steel point against a hard stone must1 by any jar in conveyance from place to place1 receive a certain amount of abrasion that will make it duller4 ,for this reason a lift for the needle is always provided in scientific instruments4 ,in the engraving1 ,fig4 #cj1 an edge-bar needle is shown in section with its lift4 ,the lift is made in the form of a bent lever1 whose fulcrum is upon the bottom of the box4 ,on the left-hand side of the broken line at ,b the needle is shown lifted4 ,on the right-hand side ,a the needle is shown at its position for use1 floating just slightly above the divided circle ,d4 ,the pressure of the milled-head screw ,c depresses the bent lever or lift on the bottom of the box and thereby raises the point under the centre of the needle4 ,this point has a hollow cone formed upon it which fits over the standing-point to keep the lift in position4 ,the cone fits externally into the cap to lift the needle vertically4 ,the screw ,c should always be clamped down when the needle is out of use4 ,in place of the screw a wedge shaped sliding piece is sometimes fixed inside the compass-box1 which is moved by a stud projecting through the outer case4 ,another plan of raising the lift is by a cam1 or what is technically termed a kidney-piece1 applied to the exterior part of the lift4 ,either of these plans answer1 but the screw first described1 being the gentler motion1 jars the needle least4 ,a screw is occasionally used longitudinally to the needle connected with a cam lift1 the object in all cases being to lift the cap entirely clear of the standing-point4 #acj4--,the ,inclination or ,dip of the ,needle is the position a needle balanced level upon a free centre before magnetisation takes in the vertical plane after magnetisation4 ,this inclination or dip varies in different parts of the globe1 and at different times4 ,at the present time at ,greenwich 7,jan41 #aiad7 the angle is #ff #ej from the horizontal4 ,it is uniformly nearly nil at the equator1 and increases until over one of the magnetic poles1 where it becomes vertical4 ,there are two magnetic poles in the northern hemisphere active in directing the needle1 one in ,siberia1 but the most active is about ,melville ,island2 also two in the southern hemisphere1 which are supposed to be nearly together1 but the exact positions of which are not ascertained4 ,as we require only the horizontal component in surveying and not the dip1 it is necessary to balance the needle in opposition to the direction of the dip until it keeps in a horizontal position4 ,this may be done by making the needle lighter on the dip side--that is1 the northern in this hemisphere4 ,but the plan adopted in all scientific instruments is to place a rider over the needle1 as shown ,fig4 #cj under ,b4 ,this clips the needle sufficiently to hold it firmly to its place1 and yet is loose enough to be moved by the fingers to balance4 ,the rider has to be shifted when the instrument is taken into a country where the dip is different from its position at home4 ,when a needle is taken abroad without any rider1 it may be balanced by means of a little sealing-wax placed upon its uptending end4 #aca4--,to get at the needle for suppression of dip when it is placed in the compass-box1 it is necessary to raise the spring ring1 which is placed over the glass to keep it down1 by inserting the point of a pocket-knife between the ring and the glass1 moving the knife entirely round it and using a little twist upon it if necessary until the ring is free4 ,this must be done gently or the glass will break4 ,the needle is then adjusted to read correctly to the plane of the divided circle and is replaced in its box4 ,the glass is then replaced and the spring ring is pressed down by passing the finger firmly round it until it is tight upon the glass4 ,sometimes a little extra pressure by a hard body is needed1 but this must be done with care or the glass will be broken4 #acb4--,the ,declination of the ,needle1 that is1 its variation in pointing in a true northernly and southernly direction1 is necessary to be known and considered by the surveyor where the needle is used1 both in relation to the locality and to the time1 as this declination not only varies in different countries but also from year to year4 ,for instance1 this year 7,jan41 #aiad7 it points #ae #ab ,west at ,greenwich4 ,the following chart1 ,fig4 #ca1 gives the declination variation for #aiad4 ,the whole system of declination lines is now moving westward at the rate of about seven minutes per annum1 but the rate varies slightly and from year to year4 ,the declination lines1 independently of correction1 which will be presently considered1 may not be exactly represented by the symmetrically curved lines shown in the figure4 ,there are small local deflections from the theoretical curves here given1 which are permanent and need local consideration when using the needle for obtaining very correct bearing4 ,these have been ably considered by ,professor ,rcker and ,dr4 ,thorp1 but the subject is too complicated to be entered upon here1 except for this note of observation4#b #acc4--;,for new countries1 where the needle often becomes most important from the impossibility of tying up lines by direct observation through forests and other obstructions1 reference must be had to magnetic charts which give systems of lines easily worked through by symmetry1 even for unexplored countries4 ,at present the declination is west in ,europe and in ,africa2 east in ,asia and the greater part of ,north and ,south ,america4 ,illustration3 ,fig4 #ca4--,magnetic and ,greenwich time chart for ,great ,britain1 #aiad4 #acd4--,the ,magnetic ,variation of ,declination in ,time1 becomes important in reference to old plans in which the magnetic north of the period has been plotted for the true north very much to the pecuniary advantage of the legal profession when engaged upon actions with regard to disputed boundaries4 ,the following table gives an idea of the variation in declination for ,greenwich approximately for a few dates3-- ,year #aehj1 ,dec4 #aa #cf ,e4 ,year #ahfj1 ,dec4 #bj #dj ,w4 #affc1 #j #ahgj1 #bj #ai ,w4 #agjj1 #h #bj ,w4 #ahhj1 #ah #eh ,w4 #ahah1 #be #da ,w4 #ahij1 #ag #i ,w4 #ahej1 #ai #ca ,w4 #aijj1 #af #cj ,w4 ,it will be seen by the above table that the needle pointed due north in #affc1 that it attained its greatest western declination in #ahah1 and that it is now losing its westerly declination at the rate of about #g annually4 #ace4--;,annual ,variation4--,the declination is subject also to a small annual variation which is greatest about spring time1 diminishes towards the summer solstice1 and increases again during the following nine months4 ,it varies at different periods1 and seldom exceeds #af of arc4 #acf4--;,declination ,correction to true north may be made for the compass by observation in this hemisphere of the pole star1 which is practically due north in ,january at #f p4m41 ,february at #d a4m41 ,march at #b a4m41 ,april at midnight1 ,may at #aj p4m41 ,august at #d a4m41 ,september at #b a4m41 ,october at midnight1 ,november at #aj p4m41 ,december at #h p4m4 ,most surveying instruments1 except the transit theodolite1 are not made convenient for this observation4 ,more generally observations of the position of the sun may be made where a sun-glass is provided to the telescope of the theodolite1 ,fig4 #ai1 ,,sg1 page #de1 with the aid of a chronometer or a good watch4 ,for this observation we may remember that the sun is true south at twelve o'clock on the #afth ,april1 #aeth ,june1 #ast ,september1 and #beth ,december4 ,the following table may be useful for some intermediate times to show how much the chronometer 7mean time7 is faster or slower than the sun's southing approximately at noon3-- ,jan4 #a subtract #d min4 ,july #ae subtract #f min4 #af #aj #cj #f #ca #ad ,aug4 #ad #d ,feb4 #ae #ad ,sept4 #ac add #d ,mar4 #b #ab #bh #i #ag #h ,oct4 #ac #ad ,april #a #d #bh #af ,may #a add #c ,nov4 #ab #af #af #d #bg #ab #ca #c ,dec4 #ab #f ,june #cj subtract #c #ca subtract #c #acg4--;,as variation in time of southing is from fourteen minutes fast to sixteen slow1 or a difference of thirty minutes1 correction becomes important1 as the sun passes over #g in this period4 ,in these observations the diaphragm lines1 webs1 or points must bisect the sun's disc4 ,this is done more exactly by taking the mean positions of the sun's eastern and western limbs or its semi-diameter1 which is given for every day of the year in the ,nautical ,almanac4 #ach4--,the ,compass-box4--,the needle1 as it is generally mounted for the theodolite1 mining-dial1 and many other instruments1 reads into a divided circle of #cfj4 ,the circle is raised up from the bottom of the compass-box to the height of the top of the needle1 as shown in section ,fig4 #cj1 ,d1 and is generally silver-plated4 ,the bottom of the compass-box is sometimes divided with a compass-rose giving the points ,n4 ,e4 ,s4 ,w4 ,the ,e4 and ,w4 in some cases are reversed from their natural directive positions from the centre of the box1 so as to read the letter indicating the point nearest to the division instead of that opposite to it4 ,in modern surveying instruments1 however1 no regard is paid to the points of the compass1 north being #j1 east #ij1 south #ahj1 west #bgj4 #aci4--;,in the manufacture of the compass-box very great care should be taken that the metal is quite free from iron1 and that no iron comes near it4 ,on this point the maker cannot be too guarded4 ,the author has in several instances found the compass-box of perfectly free metal2 but a single foul screw made of commercial brass wire1 being used to fix the ring or the rose plate1 has by its influence entirely destroyed the value of the compass4 #adj4--;,in the construction of the compass-box the author has found the most certain method of getting the divisions correct with the centre is to make the division directly from the standing-point of the compass1 and not to try to get this point correct to the divisions afterwards4 ,the standing-point may be fixed directly to the box by screwing1 or be attached to a brass plate before fixing4 ,it is adjusted to the compass-box by bending until the needle turns freely1 but at the same time nearly touches the circle4 ,the needle is then removed and the circle is divided with the point as its centre4 ,where the divisions read to the point of the needle1 or to a line upon it without a magnifier1 the divisions of the circle may be made directly upon the lathe by a lever to the slide-rest if the lathe has a well-divided headstock4 ,when the divisions are magnified and require great accuracy1 or where a floating ring is used upon the needle1 the circle should be divided upon the dividing engine1 which will be described further on1 the centre used being still the point or pivot on the bottom of the case1 from which the divisions are to be made radially4 #ada4--,preservation of the ,magnetism in ,needles4--,it is most important that the magnetism of the needle1 particularly in mining-dials where so much depends upon it1 should be preserved to near saturation in order to secure certain direction in opposition to the friction of the centre1 necessarily always present4 ,this is often much neglected from carelessness1 or want of knowledge of the principles of magnetic action4 ,in the first place we know that a bar of soft iron1 possessing no evident magnetism1 if it be placed in the magnetic meridian with proper dip1 will after a time manifest strong magnetic properties4 ,thus1 such a bar in ,london placed due north and south1 with a dip of #fg to the north1 becomes a weak magnet4 ,from this we may also infer1 and this experiment shows1 that a needle placed in this position will not lose its magnetism4 ,but what is most important to observe is that if the needle is placed in a contrary direction1 as1 for instance1 with its northern end towards the south1 it is in constant opposition to the influences of terrestrial magnetism1 and will certainly become weaker4 ,therefore1 although it is necessary to lift the needle when carrying the instrument1 which must necessarily place its poles in all directions1 it is not at all necessary that the needle should be lifted when the instrument is put by out of use4 ,indeed1 magnetism is materially preserved by releasing the lift to let the needle take its true bearing4 ,this does not at all injure the standing-point1 as there is no movement upon it to cause wear4 ,of course if the needle is at first magnetised beyond its permanent condition it will lose this surplus magnetism1 but the residual magnetism in this position will remain nearly constant4 #adb4--;,a valuable precaution for a needle in constant wear is occasionally1 say twice a year1 or much oftener if it is used in a dusty mine1 to take it out of its box and wipe out the cap with the point of a small sable brush4 ,the standing-point may at the same time be sharpened if necessary by gently rubbing it all round with a slip of oiled ,arkansas stone at its former pointing angle4 ,the sharpness of a needle is easily ascertained by sliding the thumb-nail over the point at an angle of about #cj to it4 ,if the point sticks and holds the nail1 it is sharp2 if it glides upon it1 it is dull4 ,the author has often had compasses of various kinds sent to him for remagnetisation whose only fault has been dulness of centre4 #adc4--,ring ,compasses4--,in modern theodolites1 levels and prismatic compasses1 the magnetic needle carries a light divided circle1 which is now generally made of aluminium on account of the extreme lightness of this metal4 ,a broad needle is used of about inch in width and #a_/ah inch in thickness4 ,there is considerable difficulty in mounting the circle to get it truly concentric and correct for bearing1 therefore ring compasses are often found to be inaccurate4 ,the author has followed two methods of construction1 either of which answers fairly well3--,the one is to leave a bar across the compass when cutting out the compass ring from a plate of aluminium4 ,in this case1 when the outer edge of the ring is chucked in the lathe to be turned1 a centre hole is also made in the cross-bar which exactly fits over the cap of the needle1 so that the adjustment for centre is practically secured1 and attention is only necessary to get the adjustment correct for bearing--that is1 the #j at true magnetic north to the axis of the needle4 ,another method1 which was suggested to the author by the late ,mr4 ,thos4 ,cushing of the ,india ,office1 answers perfectly1 and only entails a little extra trouble in setting for dividing4 ,this is to permanently mount the ring on the needle without any means of after-adjustment1 and to divide the circle from a point placed in the axis of the dividing engine1 upon which the ruby centre is placed1 being of course particular that the zero line #j cuts the magnetic axis true north in the graduation4 #add4--,mariners' ,compasses1 and an inexpensive class of prismatic compasses1 are made with a paper disc in place of the ring above described answering the same purposes4 ,the paper disc is generally made in two thicknesses with a thin sheet of talc placed between them4 ,mariners' compasses have frequently the divisions painted directly upon talc for transparency by lighting from beneath1 also for general lightness combined with stiffness4 #ade4--,the reading of mariners' compasses1 and the compasses on levels where the needle carries a divided ring1 is taken from a line drawn vertically up the inside of the box or a pointer4 ,this lead line in the mariners' compass gives the direction of the head of the vessel2 a pointer in the level compass gives a direction in line with the axis of the telescope4 ,in high-class theodolites1 a microscope is used by the author reading to a spider's web in the diaphragm4 #adf4--,trough ,compass1 sometimes termed a long compass4 ,where an instrument possesses a double vertical axis and a divided circle1 as the theodolite1 the division of the circle may take the place of the divided ring of the compass and save the repetition of the graduation1 at the same time the needle may often be made longer1 as the bulk of the compass-box is proportionately less4 ,in fact in all cases where the magnetic north only is required the trough compass is to be preferred4 ,the ordinary construction of this compass is in the form of a narrow box1 ,fig4 #cb1 ,a representing a plan1 and ,b a parallel section taken through it horizontally4 ,about #aj are graduated on each side of the meridian line1 aa being adjusting screws to bring the scale true with the needle4 ,illustration3 ,fig4 #cb4--,trough compass for attachment to an instrument4 #adg4--,magnification of ,reading4--,with the trough compass it is very common to have some form of microscope for reading the needle more exactly4 ,this may be done by a ,ramsden eye-piece being placed directly over the needle1 as is common in some ,german instruments4 ,a much more convenient plan for certain instruments is to read the needle longitudinally4 ,this is generally done by means of a transparent scale being placed across the end of the needle which is divided upon glass or horn4 ,this may read to either the near or distant point of the needle4 ,a very good form of needle reading is found in some ,french instruments4 ,this is shown ,fig4 #cc1 where the compass is shown entirely enclosed in a tube ,c which protects it from dust4 ,the needle ,n has a vertical point fixed upon its end at ,p which reads pretty closely to a scale of #aj divided upon glass at ,g by the eye-piece ,e4 ,it has a lifter ,l pressed up by a milled-head screw ,m4 ,fig4 #cd shows the graduated glass4 ,this compass is attached beneath the limb of a theodolite1 or in any other convenient position upon an instrument4 ,the author has placed a compass constructed upon this principle in a telescope1 in such a manner that the needle may be read with the eye-piece1 so as to cut a line with a distant object coincident with the line cut by the principal telescope of the instrument at #j of its graduation4 ,this plan will be more fully explained with tacheometers1 ,chapter ,,xii4 ,illustration3 ,fig4 #cc4--,needle with reader4 ,illustration3 ,fig4 #cd4--,scale at ,g4 #adh4--,the ,prismatic ,compass1 shown ,fig4 #ce1 was invented by ,charles ,august ,schmalcalder in #ahab4 ,it is the most convenient portable instrument for reading magnetic bearings4 ,angles may be taken with great rapidity within about #ae of arc by holding the instrument in the hand1 or perhaps within #e if the instrument is of #d to #f inches diameter and placed on a stand4 ,it is a most valuable instrument for filling in close details1 such as may occur among buildings1 trees1 etc41 after the principal points have been laid down from observations taken with the theodolite4 ,the principles of the reflection of a prism were discussed1 art4 #ee1 ,fig4 #c1 p4 #bi4 ,illustration3 ,fig4 #ce4--,ordinary prismatic compass4 ,illustration3 ,fig4 #cf4--,section of the same1 but with mirror4 #adi4--,prismatic ,compasses are made from #b to #f inches in diameter4 ,the compass needle is sometimes made to carry a card dial for the #b-;inch size2 for larger sizes the ring is now made uniformly of aluminium4 ,the reading of the compass ring is effected by means of a glass prism1 ,fig4 #cf1 ,p1 which is cut to #de upon one face and #ij for the two others1 one #ij face being worked convex1 so as to give magnifying power simultaneously with reflection of the ring at right angles1 so that the reading of the compass appears to stand erect before the user of the instrument1 and to be considerably magnified4 ,as the reading is made on the side of the ring nearest the observer1 the figures on the ring are engraved right to left4 ,the prism is placed in a box1 with a vertical sight slit ,,ss over it1 which cuts a line with the centre of the top of the prism4 ,the box with its prism moves upwards or downwards in a sliding fitting ,,sl by means of a thumb nail stud1 which adjusts the prism until it is in exact focus with the divisions on the ring4 ,the back of the prism-box has a hinge ,h1 so that this box may be closed down to the level of the compass-box to render it portable when out of use4 ,on the opposite side of the compass-box to that upon which the prism is placed a long vertical window ,,sv is attached1 having a central hair placed so as to cut a direct line from the slit ,,ss in the prism-box across the axis of the needle4 ,this window-piece is jointed to turn down upon the face of the compass-box and simultaneously to lift the compass needle off its centre by a part of it pressing the outer end of the lifting lever ,l4 ,to prevent too great a continuity of the oscillation of the compass needle and the ring1 through unsteadiness of the hand in holding it1 a pin is placed at ,s1 through the compass-box under the window1 which carries a light spring ,b that just touches the ring lightly when the pin is pressed in1 and thereby brings the compass ring to rest1 or fixes it for reading with some degree of certainty4 ,an open ring under the prism-box is sometimes used for placing a piece of ribbon through it1 to attach it to some part of the person to save dropping the compass accidentally when it is used in the hand4 ,when the instrument is out of use a metal cover is provided to protect the glass4 ,the instrument is uniformly carried in a leather case with strap to pass over the shoulder4 ,as these instruments are often carried by military surveyors1 they are better made of a stiff aluminium alloy1 which makes the instrument less than half its ordinary weight4 #aej4--;,additional ,parts commonly provided with the prismatic compass are a mirror and sunshades1 shown only in section ,fig4 #cf4 ,the mirror ,m is carried in a frame attached with a sliding piece to the window1 upon which it can be placed either upwards or downwards4 ,it is jointed with a hinge so as to be set at any angle4 ,by reflection from the mirror1 bearings in azimuth are taken much above or below the horizontal plane4 ,sun-glasses are also provided in front of the prism1 which are used for taking the sun's place either with or without the mirror1 a single sun-glass being also used very comfortably for working towards the sun at all times4 ,the sun-glasses1 which are simply small1 dark-coloured glass circles in frames1 are not shown in the engraving4 #aea4--,to ,prepare to take ,observations with the ,prismatic ,compass4 ,after the window and prism are opened out1 the prism is adjusted to read the divided ring sharply when the compass is about level1 by raising or lowering the prism ,p by pressure of the thumb and forefinger of the right hand upon the stud placed upon the prism slide fitting1 shown below ,,sl1 until the divisions appear clear4 #aeb4--;,in ,using the ,prismatic ,compass1 the compass-box is held with the thumb of the right hand under the prism at ,,sl and the forefinger upon the stud ,s4 ,the object which it is desired to observe is sighted through the slit ,,ss1 cutting the left-hand side of the hair in the window ,,sv1 while the division which comes opposite the reading point at its edge by the reflection from the prism is noted4 ,the ring when free oscillates for a time1 but is easily brought to rest for reading by gently pressing the pin ,s upon which the forefinger is placed4 #aec4--,where objects are observed for taking their bearings above the horizontal plane1 the length of the window will be sufficient to take in a vertical angle of #bj to #cj2 but for such altitudes it is necessary to take very great care that the compass is held level1 to get magnetic angles even approximately true4 ,below the horizon1 angles can be obtained with somewhat greater certainty by means of reflections from the mirror4 ,altogether1 except for taking nearly horizontal angles1 or for very close work in filling in after the theodolite1 it is much better to have the prismatic compass mounted upon a tripod stand4 ,with a stand1 where the angle in azimuth is much above or below the horizontal plane1 it is better to have a small glass level1 described further on1 art4 #aha1 to place across the compass when setting it up4 ,if the compass ring is very carefully balanced across #ij to #bgj two bright wire points may be placed inside the compass-box1 level with the compass ring1 which will answer for the cross levelling4 #aed4--,stands4--,the author has made a very simple and inexpensive tripod stand for the prismatic compass1 the head of which consists of a ball and socket only1 clamped by a large milled-head screw4 ,an axis through the ball permits horizontal adjustment1 shown in section1 ,fig4 #cg4 ,illustration3 ,fig4 #cg4--;,improved prismatic compass stand4 ,illustration3 ,fig4 #ch4--;,hutchinson's prismatic compass4 #aee4--;,hutchinson's ,prismatic ,compass1 ,fig4 #ch1 is now very generally used by military men4 ,in this compass the metal cover is fixed on the top of the compass-box1 and a glazed opening is placed in the cover1 occupying about one-eighth of its area1 near the prism4 ,this opening gives sufficient light to the compass card to permit it to be easily read1 and the loose cover is dispensed with2 besides which1 the cover being fixed1 this1 as well as the whole instrument1 may be made much lighter1 while retaining equal rigidity for wear4 ,this compass is not fitted with shade and mirror arrangements as before described4 ,size1 #b inches diameter1 inch in thickness2 weight1 only #h oz4 in brass2 #c oz4 in aluminium4 #aef4--;,captain ,burnier's ,military ,compass4--,this portable compass is more generally used on the ,continent than other forms4 ,it is generally combined with a clinometer1 therefore the illustration is deferred1 seq4 with clinometers4 ,the compass ring is set up vertical to the plane of the needle1 and is read by an index point by means of a cylindrical lens4 ,it has a pair of sights formed of a slit near the eye-piece1 and a hair in the window as in the prismatic4 ,when this instrument is held horizontally1 at about a foot distance from the eye1 the sight line and the index line read distinctly into the graduations of the ring4 ,a lifter is provided to raise the compass off its centre1 as with the prismatic compass1 and a spring clutch to prevent continuity of oscillation4 ,it is adapted to be set up on a plain rod stand1 the socket fitting to which is held in the hand when it is used as a hand instrument4 ,illustration3 ,fig4 #ci4--,sketching protractor for use with prismatic compass4 #aeg4--,surveying with the ,compass only4--,in modern practice very little surveying is performed with the compass1 except for sketch or exploring maps and filling in details1 wherein the prismatic compass is useful4 ,the magnetic needle was formerly much used for surface work1 and depended upon almost entirely for underground work2 but this has been found practically in many cases unsafe1 from the uncertainty of magnetic variations1 local and other1 in the district surveyed4 ,mining compasses1 or dials1 as they are termed1 are now in modern practice made with means of taking angles with the compass1 and independently of it4 ,this subject will therefore be deferred to a future chapter on mining instruments4 #aeh4--;,in ,plotting ,military ,sketch ,surveys from angles taken with the prismatic compass1 the paper employed is ruled lightly all over with parallel lines an inch or less apart4 ,the angles taken with the prismatic compass from #j to #cfj 7northern zero7 are set off with an ivory military protractor1 which has lines to correspond with latitudinal lines drawn over its face at #ij to its base1 so that the protractor may be placed transverse to any line drawn on the paper with its centre in any position4 ,particulars of this method are given in every detail in ,major ,jackson's ,course of ,military ,surveying1 and in my work on ,drawing ,instruments4 ,the military protractor is shown ,fig4 #ci4 #aei4--;,for making a sketch plan with the prismatic compass1 a very convenient way is to use the tee-square1 the upper edge of the blade of which represents magnetic east to west1 the upper end of the board magnetic north and the lower end south1 according to the reading of the compass4 ,the bearings taken from any starting-point are set off on the plot by a semicircular protractor with its base resting along the tee-square4 ,the northern angles are raised with the square at the left-hand side of the board and the southern with it at the right4 ,the distances from the station for all bearings are measured and set off by scale4 #afj4--;,it is indifferent how many stations are taken by the prismatic compass4 ,the measurements in any direction may continue all round an estate1 and will be found fairly correct if carefully made1 as the small personal errors in reading the prismatic1 which may be plus or minus1 tend to correct each other on the whole1 and to tie up the lines4 #afa4--,the rolling parallel rule may replace the tee-square1 if it is thought desirable to place the plan in a direction other than that erect to magnetic north with the paper1 or that it is inconvenient to use the tee-square4 ,in this case a few parallel lines may be at first drawn correctly across the paper1 at about equal distances1 with a sharp pencil ,e4 to ,w4 for references to reset the parallel rule at any position desired4 ,illustration3 ,figs4 #dj1 #da1 #db1 #dc4--,pocket magnetic compasses4 #afb4--,pocket ,magnetic ,compasses4--,the subject of compasses will scarcely be complete without mention of the small pocket compasses which are so useful and universal4 ,several well-known forms are shown in the next illustration4 ,the square form shown first1 ,fig4 #dj1 will be found the most useful for very rough sketching4 ,the edges may be sighted for the direction of roads1 etc41 or the box may be placed against a wall for taking the magnetic direction of a building4 ,in like manner also the compass-box may be laid on a drawing and lines drawn along by the edges of the box to the magnetic directions taken4 ,this in most cases is sufficiently accurate for architectural work1 in which the exact direction is not generally thought to be important4 ,fig4 #da is a ,french form of compass with step reading level with the upper surface of the needle4 ,fig4 #db is an old ,english form with enamelled dial1 with lifter under the bow of the handle4 ,fig4 #dc is the same make in a hunter case4 ,in this the lifter rises upon the case being closed4 ,illustration3 ,fig4 #dd4--,trough form ,egyptian compass4 #afc4--,the author has made a small pocket magnetic compass1 which is represented in the illustration above4 ,the needle is placed in a long box4 ,it reads at its point into a single line when the needle is exactly parallel with the sides of the box4 ,the lid turns up endwise4 ,the needle is lifted by closing the box4 ,illustration3 ,fig4 #de4--,the author's under slide for setting off variation4 #afd4--;,in a form of compass similar to the above1 the author has added a thin slide to the under side of the box1 by means of which the magnetic variation may be adjusted1 as shown ,fig4 #de4 ,this slide moves out just the amount of magnetic variation1 the stud ,s being made concentric for this adjustment4 ,if the slide box be made of ivory a few useful scales may be divided upon it4 ,the compass slips into a light leather case1 and is the most portable for its length of needle of any compass made4 ,the edges of the box are used as directing lines1 as above described for the square form4 ,the illustrations show a compass made for ,great ,britain1 but a similar instrument is also made universal4 ,in this case the box is a little wider1 with the centre of the slide in the middle1 so that the magnetic variation can be set off west or east4 ,a rider also on the needle enables it to be balanced in southern latitudes4 ,illustration3 ,fig4 #df4--;,barker's luminous compass4 #afe4--;,barker's ,luminous ,compass1 with floating dial of mother-of-pearl1 one-half of this being engraved with black figures and the other half painted black with the figures left white1 permits magnetic direction to be observed in the dusk and by moonlight4 ,these compasses1 ,fig4 #df1 are much used by travellers4 ,mr4 ,francis ,barker has also designed a compass in which the needle carries a bar coated with luminous paint4 ,,footnote3 #b ,see ,phil4 ,trans4 #ahif1 vol4 #ahh1 ,map4 #i4 ,,chapter ,,iv4 ,,levels--,,methods ,,of ,,ascertaining--,,level ,,tubes--,,manufacture--,,curvature-- ,,sensitiveness-,,testing--,,reading--,, circular ,,levels--,,surveyors' ,,levels-- ,y-,,level--,,parallel ,,plates--,,adjustments ,,of ,y-,,levels--,,suggested ,,improvements--,,dumpy ,,level--,,tripod ,,stands--,,adjustment ,,of ,,dumpy-- ,,collimator--,,improvements ,,in ,,dumpy ,,level--,,tribrach ,,head--,,diaphragms-- ,,cushing',s ,,level--,,cooke',s ,,level--,,cheap ,,forms ,,of ,,level--,,hand ,,levels-- ,,telescopic ,,level--,,reflecting ,,levels--,,water ,,levels4 #aff4--;,a ,level ,plane is understood technically to be a plane truly tangential to the theoretical spheroidal surface of the earth1 as represented by any spot upon the mean surface of the ocean or of still water free from local attraction4 ,the importance of having the means of constructing efficient instruments that can be conveniently employed to obtain the correct relative altitudes of points or stations upon the earth's surface1 in relation to such a plane or datum1 can scarcely be overrated4 ,such instruments are not only used for topographical surveys of countries1 but also in designing and carrying out public works adapted to the local conditions of natural inclination of the land surface1 for railways1 drainage1 irrigation1 canals1 water-works1 and other constructions4 #afg4--,the force constantly at our command to enable us to ascertain relative altitudes and to form mentally or graphically local level lines on the earth1 is that of gravity2 and it is only a question in any case how the action of this force shall be employed4 ,there are four principles which we may accept as data for employing gravity1 each depending upon a natural phenomenon3--7#a7 ,the open upper surface of a liquid unaffected by currents of air1 or the influence of solid objects in close proximity causing capillary action1 or local attraction of solid masses1 represents a level plane4 7#b7 ,the line of a plummet unaffected by currents or lateral attractions forms a vertical line to which the level plane is everywhere at right angles4 7#c7 ,the atmospheric pressure1 from the approximated equality of its density due to its weight in proportion to its height over limited areas1 gives pressure according to its gravity--therefore altitude or difference of level relatively to lesser pressure compared with a lower datum4 ,this pressure is measurable with a barometer or other form of pressure gauge4 7#d7 ,the resistance to ebullition in a liquid is inversely proportional to the weight or pressure of the arial fluid resting upon its surface4 ,this is measurable by the temperature at which liquids boil under varying atmospheric pressures4 ,various instrumental refinements have been discovered to render these natural phenomena available in practical use for ascertaining difference of height4 ,the first and most exact method employed for this purpose1 by means of the liquid plane1 will be considered in this chapter4 ,the other methods will be deferred to later pages4 #afh4--;,in taking the level of a liquid surface contained in a vessel1 we have1 as just stated1 to keep this surface free from the disturbing influence of air currents1 and to surround the surface with equal conditions of capillary attraction1 or to make these conditions equal in the direction in which we desire to ascertain our level4 ,this is found practically to be best performed by means of a sealed glass tube1 in which the liquid will by gravitation naturally occupy the lower place1 and any air or lighter fluid contained therein the space above this4 ,illustration3 ,fig4 #dg4--,level tube 7bubble74 #afi4--,level ,tubes1 or ,bubble ,tubes1 as they are technically termed1 are used as a part of nearly all important surveying instruments4 ,one of these is represented ,fig4 #dg4 ,the glass for the construction of these tubes is drawn at the glass-houses in lengths of about #f feet1 and may be ordered of any desired size and substance4 ,the tubes are drawn of as nearly straight and equal bore as possible4 ,they are1 nevertheless1 found to be1 when examined after annealing1 curved more or less in various directions at different parts of their lengths4 ,they are found also generally to be slightly tapering from end to end and of slightly unequal substance4 ,in the manufacture of level tubes parts of the tube are selected with approximately regular longitudinal curvature1 and these parts are cut off into the required lengths by a triangular file dipped in spirits of turpentine1 to be ready for the future operations of grinding1 sealing1 and dividing4 ,after the tube is cut off and carefully examined to get its most concave internal surface upwards1 this is then marked by a test mark1 with the flat of a file1 near one end for future work and reference4 ,the grinding of the inside of the glass tube to true curvature is performed by passing it over a brass mandrel or core1 which is employed to grind the glass by means of fine emery4 ,the core is turned slightly barrel-form to the longitudinal curvature intended for the upper surface of the finished tube4 ,it is made of full three-quarters the diameter of the interior of the tube1 and a little longer than the entire tube4 ,this core is attached by its ends to two stiff but flexible wires of brass1 about #h ,b4,w4,g4 for a tube of #g inch diameter1 and these wires are held firmly by their ends in two vices1 so that the core is slung1 as it were1 to permit a certain amount of flexibility under the pressure of the hand used in grinding4 ,some good makers do not use a mandrel core1 but only a strip of brass on the mandrel1 extending about #fj of the circumference4 ,in this case the strip has to be corrected for curvature during the grinding1 which plan is sometimes preferred for certainty4 ,the grinding of a tube cannot be commenced with coarse emery1 such as is used in the grinding of lenses1 as the cut of a coarse emery will quickly split the tube4 ,after the glaze is removed there is not so much risk1 so that a little time may be saved by passing a current of hydrofluoric acid gas through the tube2 but more careful testing is required afterwards1 as the cut of the grinding tool is not so evident at sight when the glazed surface is removed4 #agj4--,the operation of grinding is very much the same as that described for lenses1 p4 #ag4 ,the surface is required to be traversed in every direction longitudinally and transversely1 which is effected as far as possible by a twist of the hand alternately to the right and left4 ,the tube should also be frequently taken off and turned end for end4 ,slight variations of curvature are readily made by differences of pressure of the hand on parts of the tube2 and a little coaxing is allowed to get the centre of the tube quick where the tube is to be used for levelling only1 and not for measuring small angles1 so that in this case the finished tube is slightly parabolical4 ,the finishing touch is produced with wash-emery4 ,the inside should be left smooth but not polished1 as the slight roughness of a fine ground surface assists the capillary action by causing better adhesion of the spirit1 and gives a quicker run to the bubble4 ,where the tubes are required of a given radius they are tested frequently1 during the grinding1 upon the bubble trier1 by placing two corks in the ends of the tube1 which is nearly filled first with water for rough trial1 and then with spirit for final correction4 #aga4--,the ,bubble ,trier is a bar or bed #ab to #bj inches long1 with two extended feet ending in points at one end1 and a micrometer screw at the other1 the point of which is a resting foot1 thereby forming a tripod4 ,this stands on a cast-iron or slate surface plate4 ,the micrometer screw has a fine thread1 and a large head with divisions upon it to read seconds of arc4 ,the tube is supported on the bar by two ,y's1 which are adjustable for distance apart1 according to the length of the tubes to be tried4 #agb4--,the ,sensitiveness of a ,level ,tube1 the upper curvature and ground surface being equal1 depends very much upon the capillary action due to its internal diameter1 the larger tube1 from the freedom of restraint by capillarity1 being the more active4 ,as regards the ultimate settling to gravitation equilibrium1 perhaps there is no difference1 but small tubes are sluggish and take time to work4 ,the following are about the usual dimensions of the interior of sensitive tubes--#h inches #a inch diameter1 #g inches #i1 #f inches #h1 #e inches #g1 #d inches #f1 #c inches #e1 #b inches #de1 #b inches #d1 #a inches #ce1 #a inch #c4 ,the larger the volume the greater the expansion of liquid with heat2 the longer the tube the less torsion it is liable to suffer from sealing1 so that if possible1 as expansion is a serious defect1 it would be better to have short tubes1 if these could be sealed without disturbance of curvature4 ,much shorter tubes are used in ,america than in ,great ,britain4 #agc4--,the ,curvature of a ,level ,tube is worked to radius according to the delicacy of the work to be performed with it afterwards4 ,the radii of curvature of different level tubes used for scientific purposes vary from about #cj feet to #ajjj feet or more4 ,the radius of any curve may be conveniently measured by the relation of its versed sine to its chord of arc1 the chord being the length of the tube4 ,if this is first calculated out1 a piece of shellac may be attached by melting it down upon the centre of the edge of a parallel glass straight-edge1 to represent by its thickness the versed sine4 ,the spot of shellac may be brought to the exact height required from the straight-edge by filing and stoning1 at the same time taking its protuberance by a calliper gauge provided with vernier or micrometer to read #jja inch4 ,the versed sine of a given radius is formed for a given chord-- versed sine rad - 7rad#b - 7 cho7#b74 #agd4--,the general instruction1 however1 given to the maker is the distance of run of the bubble that is required to give seconds or minutes of arc2 and perhaps this is after all the best test for accuracy of the tube which1 like all other articles in glass submitted to the process of grinding1 is subject to a certain amount of local error4 ,by this method the local error is discovered by testing with the bubble trier4 ,when the run is given1 the radius of the curve of the tube may be found if desired by the use of a common multiplier1 as follows1 very approximately-- ,arc equal to radius expressed in minutes1 #cdcggdfgg4 seconds1 #bjfbfdhjfbe4 ,the run of a good sensitive tube is frequently made #a_/cj inch to the second1 here 7omitting decimals7-- arc sec 7#bjfbfdh7 #a_/cj inch #egc feet radius nearly4 ,for scientific purposes a millimetre run per second is commonly used1 then-- arc sec 7#bjfbfdh7 #jja metre #bjfbfd metres radius or #fhj feet nearly4 ,for an ordinary #ab-;inch dumpy level the tube is divided into minutes at about #a_/aj inch apart1 radius #bh to #cj feet2 for a sensitive #ad-;inch ,y-level of good construction the same divisions may represent five seconds1 radius of bubble tube about #agj feet4 #age4--,the ,divisions upon ,ordinary ,level ,tubes are made after the tube is finished1 but with the highly sensitive ones the divisions are made first4 ,the run is taken from ten to thirty divisions on each side of the centre of the tube1 where it is lightly marked with a marking diamond4 ,these spaces are then equally subdivided and etched in with hydrofluoric acid or marked with a hard steel edge dipped in turps4 ,if further refinement be required1 the errors of run in relation to the divisions are tabulated from the testing of the tube with the bubble trier4 ,a less careful method is employed by some makers of leaving the level tube undivided and fixing an independent metal or ivory scale over it4 #agf4--,level tubes are generally filled with pure alcohol for ordinary purposes2 for trade purposes with methylic alcohol1 which is much cheaper4 ,for very delicate tubes sulphuric ether or chloroform is used4 ,the sensitiveness of the bubble depends very greatly upon the mobility of the liquid with which it is filled1 and to the quality of adhesion of the liquid to the glass4 ,the relative mobility of the above-mentioned liquids is found by delicate tests with the bubble trier for small distances under the microscope at a temperature of #fj ,fahr4 ,taking water as #ajj3--we find commercial methylic alcohol #bb1 absolute alcohol #ac1 sulphuric ether #e1 chloroform #c1--that is1 for equal small runs taken in #ae seconds of time4 ,all bubbles appear to be more or less affected by temperature1 particularly where the spirit is not nearly absolute4 ,in the higher temperatures the bubbles are more active4 ,the objection to chloroform1 where it is likely to be subject to great changes of temperature1 and where there is no provision made for regulating the size of the bubble--the means of doing which will be presently discussed--is that its expansion from heat is so great that it is very liable to burst its tube4 ,it can therefore only be used with ordinary sealed tubes where these are small and strong4 ,sulphuric ether has the same fault1 but in a lesser degree4 #agg4--,the sealing of ground tubes requires the skill of a very experienced glass-blower1 and is a technical matter on which no written instructions would be of value under any conditions4 ,a little strain is unavoidably put upon the tube in sealing with the blow-pipe1 so that the curvature to which it is worked is more or less disturbed4 ,for this reason level tubes which are required to be of the highest degree of accuracy are sometimes left as they are ground1 and closed at the ends by small discs of glass grooved to the end surfaces4 ,these are fixed on with glue1 and when the glue is set are bound over with silk and finally varnished2 but this plan is much too delicate for instruments for use in the field4 ,illustration3 ,fig4 #dh4--;,colonel ,strange's level tube4 #agh4--;,colonel ,strange's ,level ,tube4--,these tubes1 ,fig4 #dh1 are blown with an outward bead at each end of the tube1 two outwardly screwed collars1 ,f1 being first placed over the tube before the blowing4 ,the tube is then ground to curvature4 ,a plug1 ,s1 is formed for each end of the tube from a plano-convex lens1 ground to a bevel on the plano side1 and also ground into the end of the tube as a stopper4 ,a cap1 ,c1 is screwed over the end upon the collar4 ,the springiness of the cap keeps the stopper always tight4 ,as there is no blow-pipe used after the grinding1 the tube remains constant as it is ground1 or it can be adjusted by grinding to any desired sensitiveness4 ,this cap1 for security1 is better covered with silk tied over it1 and afterwards well varnished4 ,in this class of tube there is always a little risk of evaporation4 ,the system is not adapted to instruments to be used in the open air4 #agi4--;,chambered ,level ,tubes4--,as the run of a bubble varies slightly with its size1 for exact purposes and extreme climates it is very desirable to be able to adjust the size of the bubble to the surrounding temperature1 so that it shall be kept at about equal dimensions for all measurements made with it4 ,this becomes particularly important where chloroform is used1 from the expansion being very great4 ,a general way of doing this is to have a stopper ground into one end of the tube1 which is itself a small bottle1 on the under side of which a hole is ground1 so that by turning the tube over and raising it more or less1 any amount of the highly rarefied air it contains may be taken to form the bubble that may be desired4 ,the stopper is fixed with thin glue4 ,the general construction is shown below1 ,fig4 #di4 ,of course where such a tube is used there must be means of tipping and turning the instrument in which it is fixed over1 or the bubble itself must have separate fixings4 ,the portability of a surveyor's level admits readily of the necessary tipping2 with theodolite levels at right angles to each other upon the vernier plate it would be impossible4 ,illustration3 ,fig4 #di4--;,bubble with supplemental air-chamber4 ,illustration3 ,fig4 #ej4--;,colonel ,scott's patent protected bubble4 #ahj4--;,extra ,strong ,level ,tubes4--,colonel ,scott's very ingenious device of enclosing a level tube within another tube of thoroughly annealed glass will be found valuable in all cases where the tube is much exposed1 or where it is difficult afterwards to procure a new tube in the case of accident4 ,these tubes are at present only made by the author for ,scott's telescopic gun-sights1 which are nearly like small theodolites4 ,the level tube1 ,fig4 #ej1 is made as stout as possible to be soundly sealed after filling4 ,it is then enclosed in an annealed tube1 ,,cc1 of about #jh to #ab inch in thickness1 the interspace between the two tubes being filled with ,canada balsam4 ,it is then plugged with elastic marine glue1 ,,kk and cemented over ,,pp4 ,the annealed tube is of great strength1 so that the complete naked tube thus formed will bear dropping on the ground1 and also when attached to a large gun will bear the violent vibration of firing without injury4 ,illustration3 ,fig4 #ea4--;,artificial horizon level4 #aha4--,the ,level ,tube may form a ,complete ,instrument in itself4--,in this case the lower surface is ground to a flat plane to rest on any plane surface4 ,this level is generally contained in a small pocket case1 and is most convenient for adjusting instruments to level4 ,it is commonly used with the black glass artificial horizon1 to be described4 #ahb4--,mounting ,tubes4--,level tubes when applied to instruments are generally mounted in brass covering tubes4 ,small level tubes under #b inches are conveniently mounted in such tubes with a fixing of slaked plaster of ,paris inserted at each end of the brass tube4 ,larger level tubes should be bound round with thin paper pasted round the ends1 which is allowed to get quite dry1 to be afterwards fitted to the brass tube with a file4 ,fitted in this manner the tubes admit of adjustment to the difference of expansion of the metal and glass by change of temperature without distortion4 ,there is no objection1 however1 to thoroughly fixing one end of the tube with plaster if the other be left free1 and this is perhaps advisable for portable instruments4 ,it is convenient in mounting level tubes to place white glazed paper under the bubble to reflect the light that passes through it to ensure better observation4 #ahc4--;,in ,fixing ,undivided ,level ,tubes1 or replacing them in instruments1 it is important to observe that the side with the test mark1 which is a small ground facet1 should be placed on the top4 #ahd4--;,in the ,use of ,level ,tubes generally1 it is not well to have them of greater sensitiveness than the general construction of the instrument upon which they are placed permits4 ,thus the centre of a surveyor's level that may be under constant strain from the unavoidable inequality of the pressure of parallel plate screws1 will appear never to reverse properly if it has a very sensitive bubble1 the cause of the irregularity being entirely due to the distortion from the strain on the vertical axis of the instrument4 ,the same irregularity occurs in a lesser degree with the ,y's of a theodolite1 where these and the collars become corroded by exposure4 ,the optician often gets an undue amount of credit for perfecting such instruments when he has merely replaced the sensitive bubble by a dull one--that is by doing what is really in this case the best for the instrument4 #ahe4--,when an instrument that depends entirely upon the level for its possible working is to be used abroad1 an extra tube should be taken1 as the level tube is very generally more exposed and is more delicate than any other part of the instrument4 ,the tube may not only be accidentally fractured with a slight bow1 but even the heat of the sun's rays will sometimes burst it4 #ahf4--,reading the ,bubble4--,the exact position of the capillary concave surface of the spirit in the tube is liable to deceive the observer by the difference of refraction and reflection it gives1 whether the light is towards the right or left hand4 ,to avoid this cause of error it is better1 in sunlight1 to hold a piece of white paper at a short distance over the end of the bubble during the observation taken of its terminal reading into the divided scale on the tube4 ,it is also important to note that the observer should stand at right angles to the tube to see the position exactly where the upper capillary line of the spirit cuts1 as the tube itself refracts the light unequally4 ,it is not at all difficult to read the bubble if the observer stand over it2 but generally1 as it is mounted upon an instrument1 it is at the height of the eye4 ,in this position the hollow surface round the bubble1 caused by the adhesion of the liquid to the sides of the glass tube1 reflects the light in a manner that the hollow may be taken for the end of the bubble1 and a false reading made4 ,it is better if possible to take the convenient side reading first1 and afterwards get a glance at the upper surface reading for certainty4 ,in some cases this may be much assisted by the employment of a small mirror of about the size of a spectacle eye1 which is carried open in the pocket1 or1 as the author has made it1 it may close in a horn case with a pocket lens1 as in the ,fig4 #eb shown below4 ,c sheath1 ,m mirror1 ,l lens4 ,illustration3 ,fig4 #eb4--,pocket lens and mirror4 #ahg4--;,circular ,levels have been made tentatively for a long period4 ,they consist of a worked concave lens fitted into a brass cell with indiarubber seating1 the glass being secured by burnishing over a bezel4 ,this construction answers very well when new1 but the spirit the level contains is certain to evaporate slowly under every possible care4 ,mr4 ,j4 ,j4 ,hicks has patented a hermetically sealed circular level1 in which he has succeeded in working the upper surface of the glass to curvature4 ,these levels1 of course1 are not subject to evaporation1 and are very useful and portable for approximate levelling--as for plane tables1 cameras1 etc4 ,illustration3 ,fig4 #ec4--;,hicks' patent circular level4 #ahh4--,surveyors' ,levels1 of which there are many forms1 consist essentially of a telescope with a diaphragm at the mutual foci of the objective and the eye-piece1 the axis of the telescope being placed in a direction truly parallel with the crown of a sensitive level tube4 ,the telescope with its level is mounted upon metal frame-work1 carried up from a vertical axis upon which the telescope rests4 ,the vertical axis is adjustable in relation to the axis of the telescope1 so that they may be brought perfectly perpendicular1 the one to the other4 ,the whole instrument is also adjustable to a position of verticality of its central axis1 and the horizontality of the telescope in relation to the surface of the earth in what is termed the setting-up of the instrument2 so that when it is set up in this position levels may be taken from it in any horizontal direction from one point of observation1 by rotation of the telescope about the vertical axis4 ,having these essential objects in view in the construction of the level1 the form of the instrument may be varied as to details according to the mechanical skill and taste of the maker and the special demands of the civil engineer4 #ahi4--;,in the design of a surveyor's level very important considerations are3--,that the metal should be so distributed that every part is as light as possible1 consistently with sufficient solidity to take a moderate amount of accidental rough usage1 and ensure freedom from vibration2 that the whole structure should be in equilibrium about its vertical axis when the telescope is extended at mean range1 that is1 at about the focus of three chains--this is a quality often neglected2 that there should be sufficient light in the telescope1 and that it should possess a firm and durable stand4 ,every form of level should embrace these qualities4 #aij4--,the ,oldest ,form of ,surveyor's ,level is that termed the ,y-level1 so named from the telescope being supported in ,y-formed bearings4 ,this instrument was originally invented by ,jonathan ,sisson1 a leading instrument maker of the #ahth century4 ,it was much improved and brought nearly to its present state of perfection by ,ramsden1 to whom practical opticians owe so much for many advancements of their science1 and to his liberal publication thereof4 ,this instrument is now very little used in ,great ,britain2 but it still maintains its original position1 to a certain extent1 on the ,continent and in ,america4 ,in the eyes of the optician it is still the most perfect level1 possessing all the instrumental refinements of adjustment he can desire4 ,the reasons for its partial abandonment by the profession will be discussed further on4 #aia4--,the ,y-,level in a modern form is represented in the engraving below1 ,fig4 #ed4 ,the ,y's are shown at ,,yy edgewise4 ,they are supported by standards ,,sr upon the limb ,l4 ,the telescope is surrounded by two collars which are soldered upon it at positions exactly corresponding with the ,y's4 ,the collars are turned perfectly cylindrical and parallel on the surface with the axis of the telescope1 and ground in a gauge-plate to exact size so that the telescope may be turned end for end in the ,y's without altering the linear direction of its axis in reversing it4 ,the telescope is held from shifting longitudinally in its ,y's by a pair of flanges placed on the inside of the collar pieces4 ,illustration3 ,fig4 #ed4--,surveyor's ,y-level4 #aib4--,the ,y's are erected upon the limb1 to which they are each fixed firmly by a clamping nut ,r at one end1 and a milled head clamp at ,m4 ,the telescope is held down by strap pieces1 each of which has a joint at one end and a loose pin at the other1 ,,pp4 ,the pin is secured from dropping when out of use by a piece of cord attached to a part of the instrument and to a loop through its head4 ,at the top of the inner side of the strap-piece under ,,yy a piece of cork is inserted in a cave4 ,the cork by its elasticity keeps an equal but light pressure upon the collar of the telescope4 ,it will be seen that by the above plan of holding the telescope1 it is so far free that it may be revolved on its axis1 by which perfect adjustment of the diaphragm to the axis of the instrument may be made in any direction4 ,illustration3 ,fig4 #ee4--,section of parallel plate and vertical axis--arrangement of ,y and other levels4 #aic4--,parallel ,plates as a mode of adjustment of the vertical axis will be first described1 as they present the oldest form of setting up adjustment4 ,the vertical axis of the ,y-level was formerly carried tapering downwards1 and the upper parallel plate was placed at about the centre of the socket4 ,under this construction the socket was more liable to strain from the use of the parallel plate screws4 ,it is more general now to construct the axis as represented in the illustration above1 ,fig4 #ee1 for ,y and other levels with parallel plates4 ,this construction also renders the instrument more portable1 as the parallel plates and axis may be detached and lie closer in the case2 the plan is nevertheless open to many risks1 which will be referred to in discussing a three-screw arrangement4 ,the general construction is shown in the figure1 of which the left-hand side is a half-section4 ,a is a screw by which the parallel plates are attached to the limb of the instrument2 ,m a large milled head1 by means of which the screw can be brought up firmly to its collar2 ,,ss the socket which is ground to fit the cone ,c2 ,c forms a part of the upper parallel plate ,,up2 ,b a ball pin which screws firmly into ,c2 ,,lp lower parallel plate1 part of which forms the ball socket1 so that the whole instrument rocks about the ball ,b as a centre1 by the action of the parallel plate screws ,,ps2 ,b female screw for fixing this part1 which is called altogether the parallel plates1 to the tripod head4 ,a clamping screw is sometimes placed upon the axis for slow motion4 ,the parallel plate screws are tapped1 that is1 have female threads cut into the upper plate ,,up1 and their points press the lower parallel plate ,,lp at certain points1 there being a stop-piece placed round the point of one screw to prevent rotation4 ,the pressure upon the screws can be increased as desired by means of the milled heads1 and the instrument made rigid in proportion2 but it is very undesirable that the pressure should be greater than that just necessary to support the instrument firmly1 as it is easy by the power of the screws to disturb the figure of the axis and thereby derange it4 ,the diaphragm of the telescope of the ,y-level is generally webbed with plain cross webs4 ,the diaphragm and webs were described arts4 #ii to #ajf4 #aid4--,the ,setting-up of the ,y-,level is necessary to be understood before the instrument can be adjusted4 ,the same description which answers for the setting up for adjustment will also answer for the setting-up of the instrument in the field for actual work4 ,in this description it will be convenient1 therefore1 to consider the instrument as being in this case in adjustment as it leaves the hand of the maker4 ,the after adjustments will be presently taken as from the original state of the instrument1 as the maker has to do them in the first instance4 ,practically1 the civil engineer has only to make slight differential adjustments at any time1 as an instrument1 by the solidity of its construction1 will retain the general adjustment nearly1 upon which further adjustments take more the nature of final corrections1 which become necessary only from accidental causes4 #aie4--,setting-up of the ,y or other ,level with ,parallel ,plates4--,the tripod stand is opened out so that the legs stand1 if on level ground1 inclined towards the centre of the instrument at an angle of about #gj to the horizon4 ,the toes of the legs are each separately pressed into the ground sufficiently to make the instrument stand quite firmly4 ,the instrument is then taken from its case and screwed down tightly upon the tripod head4 #aif4--,the ,eye-piece is ,adjusted1 art4 #ajh1 by sliding it gently in and out until the webs can be seen most distinctly4 ,on a bright day a white pocket-handkerchief may with advantage be thrown singly over the object-glass to prevent any confusion from objects in the field of view during the focussing of the eye-piece4 ,for the setting-up adjustment of the telescope1 it is brought in position to lie directly over one pair of parallel plate screws1 ,fig4 #ee1 ,,ps1 ,,sp4 ,illustration3 ,fig4 #ef4--;,diagram plan of parallel plate screw milled heads4 #aig4--,the milled heads only of these screws are represented in plan in the diagram ,fig4 #ef1 aa being the opposite pair over which the telescope will be assumed to be at first placed4 ,the level tube is now brought to adjustment by bringing the bubble to the centre of its run by means of the parallel plate screws aa1 by taking the milled heads of these screws1 one between the ball of the thumb and forefinger of each hand1 and rolling them simultaneously the one in one direction and the other in the reverse4 ,this action tips the axis of the telescope in one direction or the other4 ,thus by the screws being rolled inwards1 as shown by the direction of the arrows in the diagram1 the left-hand side of the instrument would be raised4 ,if turned the reverse way1 the right hand end would be raised4 ,the opposite end1 from that to which the bubble runs1 always requires to be raised4 ,where the ground is rather soft1 adjustment when nearly correct may be made partially by pressing down one or other of the legs2 in this case the telescope should be placed parallel with the toe of the leg which is pressed down and the axis of the instrument4 #aih4--,when the level tube is adjusted over the screws aa it is then placed over bb and adjusted in a similar manner1 returning again to the position aa for final adjustment4 ,when the level is in perfect adjustment the bubble should stand in the centre of its run in making a complete circuit of the horizon by rotation of the instrument upon its vertical axis4 #aii4--;,in and during the setting-up adjustment it is most important that the screws should not be made tight enough to cause1 by their pressure upon the parallel plates1 distortion of the vertical axis4 ,should this occur1 the instrument will not level in all positions by the same setting4 ,the action of the screws also1 from the great elasticity of the metal1 should distribute the pressure about equally between the opposite pairs aa and bb4 ,the difficulty of accomplishing this with certainty makes another form of adjustment1 with three screws only1 preferable for setting-up1 which will be considered further on4 ,where the instrument is set up for use1 if the adjustment of the bubble be fairly correct to the centre of its run1 the reading of the staff may be sighted and the telescope brought to true focus upon it by moving its milled head until the divisions of the staff are as sharp as possible1 and then moving the eye upwards and downwards to be sure there is no error of parallax1 art4 #aji4 ,after this the final adjusting of the bubble should be made1 noting particularly that there are the same number of divisions in its run on each side from the centre if it is a divided bubble4 #bjj4--;,adjustment of the ,axis of the ,telescope in true parallel direction with the periphery of its supporting collars in its ,y's4 ,this is performed entirely with the four capstan-headed screws which adjust the diaphragm1 one of which is shown1 ,fig4 #ed1 ,c4 ,having the adjustment of the eye-piece in focus for the webs in the manner described1 arts4 #ajh1 #aji1 the object-glass focussed upon a distant distinct small object or mark1 and without parallax1 the instrument which carries the telescope is then exactly adjusted to make the intersection of the webs cut the mark4 ,the telescope is now turned half round on its axis1 so that the lower part becomes the upper1 and observation is again made of the distant small object or mark4 ,if the same intersection of the webs falls on the same point of the object1 the collimation adjustment is perfect4 ,if it does not do so1 the upper capstan-headed screw at ,c1 or the under opposite one1 is loosened by means of the small pin provided with the instrument1 and the opposite screw tightened until the webs are brought over a point situated half-way between the points cut by the first and second observation4 ,the telescope is again directed to the point first observed1 and the adjustment checked to see if it has been done correctly1 that is1 if the level reverses1 cutting the same point1 or whether it requires further adjustment by the same process as before4 ,the other web of the diaphragm1 at right angles to the first1 is adjusted in a similar manner1 but with the other pair of capstan-headed screws4 #bja4--;,it is sometimes inconvenient to adjust out of doors3 this may be performed very well indoors4 ,by daylight a small cross may be made with ink on a sheet of white writing-paper for the sighting object1 which should be placed at as great a distance as convenient1 say #bj or #cj feet4 ,by night a pin-hole may be made through a piece of paper and a candle or a lamp be placed behind it4 #bjb4--;,adjustment of ,vertical ,axis4--,for this the eye-piece is first brought to focus on the webs4 ,the telescope is then placed directly over one pair of parallel plate screws opposite each other1 and the instrument is levelled4 ,the ,y's are then opened out2 and the telescope is directed so that the intersection of the webs cuts or covers any distinct small mark upon a distant object1 or preferably upon the centre reading of a foot line upon a levelling staff4 ,there is no objection to adjusting slightly to this by the parallel plate screws1 as this adjustment is independent of the level of the instrument4 ,the telescope is then taken out of its ,y's and is turned end for end and replaced4 ,the telescope is now turned half a revolution on its vertical axis1 and the webs are again brought to read on the staff1 if one is used4 ,if they now fall upon the same spot or foot line1 the vertical axis is perfectly perpendicular to the axis of the telescope in this direction4 ,if the webs do not fall upon the first reading or point1 the amount of difference of reading is recorded and this space is bisected2 so that now1 if the telescope be adjusted by the milled head ,m1 at its bearings upon the limb upon which it is supported1 for the webs to cut the bisection1 the axis will be perfectly perpendicular in the direction of its bearing socket4 ,the same process must now be repeated with the telescope placed at right angles to its first position1 that is by bringing it over the other pair of parallel plate screws which were not used at first4 ,there is at all times a certain amount of disturbance of the instrument due to handling it2 it is therefore necessary to repeat the whole of the above process until the instrument reverses in any direction1 but this final adjustment is better deferred until the adjustment of the level tube1 to be next described1 has been made4 #bjc4--;,adjustment of the ,level ,tube4--,the telescope is placed as before over an opposite pair of parallel plate screws1 and these are adjusted until the bubble is in the centre of its run4 ,the telescope is then turned half a revolution1 so that it is placed over the same pair of screws in the reverse direction1 and the displacement from the bubble from the centre is now noted4 ,the capstan-headed bubble screws at the end of the level ,b are then adjusted to one-fourth of the difference observed1 and the parallel plate screws are adjusted for the other fourth1 so that by these two adjustments the difference of the run in the two positions is bisected4 ,the same process is repeated over the second opposite pair of parallel plate screws4 ,if this be very carefully done with a correctly divided bubble1 the ,y's of the telescope may be opened out and the telescope be reversed end for end in its ,y's1 and the bubble remain true4 ,but it is quite as well to go over all the adjustments a second time1 as before recommended4 #bjd4--;,if the level is to be adjusted by night1 this can be done very correctly by a fine cross drawn on paper placed on a wall1 with a candle or gas burner shining brightly on it at twenty feet or so distance from the instrument4 ,for this adjustment by night the instrument must be well constructed1 as the tubes require drawing out to their full extent for focussing near objects4 ,if the tubes are not quite straight1 the object-glass suffers considerable displacement in the drawing out1 or technically droops1 which is a very common fault in badly-made instruments4 #bje4--,where webs are used for the reading1 they are liable to become baggy or dirty1 art4 #aja1 and very frequently to break2 nothing can1 therefore1 be more useful than to be able to re-web a stop in the evening1 with command of the easy and certain means of readjustment described1 when far from the optician's aid4 #bjf4--;,as the ,y-level is so perfect in its arrangement for adjustments1 and so nearly meets the optician's ideal1 it will be well to inquire what are the objections made to its use by the majority of ,british surveyors4 ,the first and most important is that it possesses so many loose parts1 to which the practical man honestly objects4 ,the author was1 many years ago1 when ,y-levels were more popular1 trying to persuade a cautious practical surveyor who appeared to be very anxious for the certainty of his work1 and who was going abroad1 to take a ,y-level instead of a dumpy one he was selecting1 when he had his arguments stopped by the following question3--,suppose you were surveying in a tropical country1 thousands of miles and an ocean voyage from civilisation1 where your native porter objected to carry much weight1 and your instrument case had to be left at a back station--when your umbrella was all the burden you felt you could support4 ,in this case1 suppose your porter1 whom you had lost sight of for a short time1 arrived with your level1 minus the telescope--lost by becoming loose1 perhaps from having been played with while he was resting--how would you praise the ,y-level8 ,this gentleman assured me that he did not1 and that this was a true account of his experience with the last ,y-level he possessed4 ,other objections1 besides loose parts1 are that ,y's and collars do not remain as perfect as when they leave the optician--that they are liable to wear by friction of constant movement in being carried about upon the points in contact between them1 and thereby form facets2 that the collars become corroded by exposure1 and that they have open spaces that collect sand from flying dust which fixes itself into the collars and ,y's1 so that this arrangement loses the perfection the optician claims for it4 ,further1 that the cross bubble1 which is uniformly placed on the dumpy level1 effects a great saving of time over swinging the telescope backwards and forwards with every movement of the adjusting screws4 ,another feature is that in the dumpy level1 to be described1 the vertical and horizontal webs of the diaphragm cannot be disturbed from their position by rotation of the telescope after the level is once set up2 and this verticality indicates conveniently at once whether the staff is held vertically1 which is otherwise a great difficulty with the ordinary form of ,y-level reading4 #bjg4--;,improved ,y-,level4--,the above-described defects the author has tried to remedy by a modification of the ,y arrangement1 by forming the ,y's with much broader bearings1 and instead of the old loose pins screw fastenings are fitted1 which firmly lock the telescope in position with the webs vertical4 ,this1 so far1 obviates the danger from loose parts1 as by this arrangement the telescope also becomes practically firmly fixed4 ,in adjustment the collars are opened out1 and in closing press a stud into the telescope by which it takes a given position4 ,this enables a cross bubble1 shown on ,fig4 #eg1 to be also placed on the telescope for approximate adjustment1 which saves the frequent disturbance of the telescope by making cross adjustments4 ,the diaphragm of this ,y-level is exactly the same as that of the dumpy1 to be described art4 #baj4 ,from the limb downwards the author uses the same construction as he now employs on his improved dumpy level4 ,this will be described with that instrument further on1 art #bca1 seq4 ,also the setting-up adjustment with it1 which is different from that already described where parallel plates are employed4 ,illustration3 ,fig4 #eg4--;,improved ,y-level4 #bjh4--,perhaps1 upon the whole1 the conditions which formerly rendered the ,y-level undoubtedly the best practical level have so much changed that the more solid construction of the dumpy may entirely supersede it1 as it seems likely to do in modern practice1 and the optician will lose his ideal4 ,some reasons for this may be stated1 but whether sufficient is a question4 ,the manufacture of object-glasses of good figure and proper centring was formerly understood by a few scientific opticians1 who were principally engaged upon astronomical telescopes1 so that1 with the exception of those made by ,troughton and ,simms1 no very good and accurately centred lenses were used in surveying instruments4 ,with bad centring alone1 in ordinary telescopes1 the webs in collimating were drifted aside1 and needed the ,y system of adjustment to make the telescope workable for levelling4 ,in the modern good object-glass1 of which there are now several makers1 the centring is so nearly perfect that the webs in adjustment fall in the centre of the diaphragm when it is placed true to the cylindrical axis of the telescope4 ,if the webs are placed as suggested without further adjustment1 no very serious interference is caused by want of collimation of the axis4 ,with this fact in view1 the instrument maker needs leave little space for adjustment of the webs for centre displacement to become a source of error to persons not used to adjustments4 #bji4--;,further1 with a well-centred object-glass1 as it leaves the hands of the scientific optician1 and a solidly constructed adjustment to collimation being provided for in the making of a level1 true working may be done even if there is a small error in the collimation4 ,the late ,william ,gravatt1 ,c4,e41 was of opinion that firm construction1 compact form1 and plenty of light in the telescope were more important than easy facilities of adjustment4 ,there is no doubt he found the less open adjustments the better in the hands of the imperfectly trained assistants who were pressed into service during the railway mania of #ahdh4 ,at any rate1 at this period we have his invention of the ,gravatt1 or1 as it was afterwards termed1 the ,dumpy level1 which has remained with us with slight modifications in its mechanical parts and with increasing popularity until the present time4 ,the late ,mr4 ,troughton1 recognising the same facts1 also made a level in which there was no adjustment to the supports of the telescope after it left the hands of the maker4 ,in his level he also left no adjustment to the bubble tube1 which no doubt would prevent tampering1 but which could scarcely be called an improvement2 as this tube is liable at all times to be broken1 therefore to need replacing with another tube1 which cannot be made quite similar1 and therefore needs easy means of adjustment for a surveyor to replace it when abroad4 ,this level has gone out of use1 but it is mentioned here1 as the old engraving of it remains in some of our modern text-books4 ,illustration3 ,fig4 #ei4--;,dumpy level4 #baj4--,the ,dumpy ,level4--,one of the most important structural improvements made by the late ,william ,gravatt in his dumpy level1 was the addition of a cross bubble1 shown end-view in ,fig4 #ei at ,,cb4 ,this improvement over the old form of ,y-level permitted the setting-up of the instrument to be completed approximately1 without turning the level a quarter revolution backwards and forwards several times during the operation1 as was necessary in the setting-up of the ,y-level4 ,the compact form1 lightness1 and large field of view in the telescope otherwise commended it to civil engineers1 when ,gravatt had pointed out the possibility of sufficient practical adjustment without resorting to the cumbrous proportions of the ,y-level as it was then made4 ,modern experience has shown that the dumpy form of telescope could very well be applied to the ,y construction1 and this has been done1 as shown in the preceding pages2 but at the time the dumpy was invented by ,gravatt1 the ,y-levels were very commonly made #bj inches or more in length of telescope1 and were altogether very flimsy affairs4 ,gravatt's #ab-;inch level was found to be quite equal in power and of less than half the bulk and weight4 ,a #ab-;inch dumpy should read the #ja foot on a ,sopwith staff1 which is described in the next chapter1 at #e chains with a webbed or glass diaphragm1 ,fig4 #fa2 with a more open reading than ,sopwith's staff a greater distance than this4 ,a #ad-;inch dumpy should read the #ja foot at #aj chains4 #baa4--,the ,dumpy ,level of modern form is represented in the engraving1 ,fig4 #ei4 ,it consists of a telescope1 fully described art4 #id1 which carries a ray shade ,,rs at the object-glass end1 to work in the field to eastward or westward facing a low sun4 ,the eye-piece ,,ep is adjustable to the webs in the telescope by pressure in or out4 ,two straps or bands are accurately fitted and soldered round the tube of the telescope2 one of these carries a hinge joint1 and the other a pair of locking nuts to support the level tube ,,gg1 and at the same time permit its adjustment4 ,the level casing tube has two three-quarter bands1 which slide upon it1 pointed at one end ,,gg3 these adjust to the length of the bubble for changes by temperature4 ,the lower part of each strap-piece is left a solid block of metal1 to give very firm support to the telescope as it rests upon the limb ,l beneath4 ,the limb may be either a casting with a socket screw only in its centre1 or a compass box may be formed in the centre and the socket screw be placed under this1 as it is shown in the figure at ,s4 ,the attachment of the telescope support to the limb is made by three screws1 two of which draw the limb down1 and one in the centre presses it upwards1 as shown in the section ,fig4 #fj--;,,cc telescope1 ,,tt drawing screws1 ,p pressing screw4 ,illustration3 ,fig4 #fj4--;,attachment of telescope block to limbs4 #bab4--;,it will be seen that by this means firm adjustment may be made either by raising or lowering one end of the telescope1 as also by a lateral rocking motion should the web or bubble not be quite to position4 ,this plan is certainly moderately solid1 and little fault can be found with it1 except that a little torsion may be put on the telescope by unequal screwing1 and that it appears slovenly in leaving an open gap between the limb and block2 therefore the author prefers in his own form of level1 which will be presently described1 that the block be solidly fitted down upon the limb1 as is shown in the section ,fig4 #fj1 and the telescope be placed permanently exactly parallel with it4 ,if the vertical axis be once fixed truly perpendicular to the axis of the telescope as solidly as possible there is very little risk of a bell-metal centre of inch or so diameter being bent2 therefore all parts may be closely fitted between the axis and the telescope4 ,some makers1 instead of screwing down at both ends of the limb1 make one end a rocking centre and adjust only by screw at the other end4 ,this plan lacks a little of the stability looked for in the dumpy system4 ,the general construction of the vertical axis is the same as that of the ,y-level already described4 ,the parallel plates1 tripod head1 and tripod are also the same1 art4 #aic1 ,fig4 #ee4 #bac4--;,as the telescope of the dumpy level does not possess any simple means of determining the accuracy of the fitting of its sliding tube1 it is a very important point in these levels that this fitting should be good1 so that the object-glass does not droop when extended4 ,for this reason the inner sliding tube of the telescope should be as long as possible1 and its adjustment by the rack sufficient to bring an object in focus at #ae to #bj feet distance4 ,this point is sometimes neglected4 ,the author was once amused by a young surveyor bringing him an invention1 which was to fix two points by the side of the telescope to enable him to read at short distances4 ,it was seen on examination of his own level that his telescope1 a badly-fitted one1 would not read at half a chain1 hence the ingenuity of his invention4 ,in some cheaply made levels the solid ring fitting to the telescope1 above described1 which connects the limb firmly with the bubble tube1 is replaced by blocks soldered on the telescope with soft solder3 the method is very unsound from risk of imperfect soldering4 ,the blocks are very liable to become loosened by a jar4 #bad4--,the diaphragm of the dumpy level is generally webbed with two vertical webs and one horizontal4 ,in use the image of the staff is brought between the vertical webs1 which indicate whether it is held upright4 ,the upper margin of the portion of the horizontal web between the two vertical ones is the index of level to which all readings are made1 either for adjustment or for reading the levelling staff in the field4 ,the somewhat loose and slovenly four-screw adjustment for a level diaphragm used in rough work with capstan-head screws1 shown ,fig4 #bc1 p4 #ej1 which is necessary for the adjustment of the telescope in ,y's1 has been abandoned for many years in the better-constructed dumpy levels by all good makers1 and the more solid construction1 shown below1 ,fig4 #fa1 used in the place thereof4 ,in this plan there is no lateral adjustment3 the diaphragm is carried as a frame in a dovetail slide1 and is adjustable by vertical screws only4 ,the figure shows the face of diaphragm3--,,bb slide pieces1 ,a slide moved by capstan-head screws4 ,illustration3 ,fig4 #fa4--;,diaphragm of dumpy level with webbed stop4 ,illustration3 ,fig4 #fb4--,same1 with stadia webs4 #bae4--,subtense or ,stadia ,webs4--,it is very advisable in all levels to have two extra webs1 or lines cut on glass1 placed one on each side of the central horizontal web or line1 fixed at such a distance apart that the image of #aj feet of the staff when placed at #aj chains distance may exactly cut the inner space between the lines4 ,these webs or lines may be used as a means of measuring distances often more exactly than can be performed with the chain if the surface of the land is irregular2 or1 in any case1 they form a good check upon chain measurement4 ,if the webs or lines are separated so as to subtend an arc whose chord is #aj feet at #aj chains1 it is easily seen that #a foot of the staff will represent this chord at #a chain1 and that each #ja of the foot on the staff will represent #a link in distance4 ,a diaphragm webbed or lined in the manner described is shown in ,fig4 #fb4 ,there is some difficulty in placing webs in exact position1 and allowance should be made for the optical conditions by the addition of a plus factor4 ,this important subject will be fully discussed hereafter in ,chapter ,,xii4 ,illustration3 ,fig4 #fc4--,tripod4 ,illustration3 ,fig4 #fd4--,section of one turn-up leg of the same4 ,illustration3 ,fig4 #fe4--,section of tripod4 #baf4--,tripods1 or ,stands4--,this matter was deferred when describing the ,y-level4 ,the same form of tripod is used for both ,y-level and dumpy4 ,in this country the tripod is generally made of straight-grained1 well-seasoned ,honduras mahogany1 which stands better than any other wood4 ,when the tripod is folded up for carrying or for putting by it forms a cylindrical pole which is bellied out at about one-third its length from the top1 and diminishes downwards and upwards from this point4 ,for a #ad-;inch ,y-level or dumpy the dimensions of the tripod are about #c inches at its greatest diameter when closed1 tapering off to #b inches at both the top and the bottom ends4 ,for a #ab-;inch level the section is somewhat less4 ,each leg of the tripod takes an equal section of the cylinder1 the inner angle meeting in the axis being at an angle of #abj1 as shown in section ,fig4 #fe4 ,shovel-pieces are shown in ,fig4 #ei ,,aa 7p4 #aaj71 attached to the top of each leg by four screws passing from the brass to the wood4 ,there should be also two screws from a brass plate inside the leg to the shovel-piece1 making connection brass to brass3 this is important1 as fixings from the brass to the wood only become loose and shaky by shrinkage4 ,the shovel-piece is formed into a strong tenon at its upper end1 through which a bolt passes connecting the book-pieces together4 ,the book-pieces are plates cut to an angle of #abj1 so as to fall true on the tenons of the shovel-pieces4 ,where hand-work is used for making the tripod head1 the book-pieces are attached by three screws2 where machinery is used1 the head is made in the shaping machine out of a solid casting1 which is much better4 ,the tripod head carries a screw about #a inches diameter with coarse thread1 which fits into a socket on the lower parallel plate of the level1 whether ,y or dumpy4 ,there should always be a plain piece1 technically a lead1 above the screw4 ,this holds the instrument steady before it is screwed down1 and also leads the screw directly to its corresponding thread1 thus saving risk of crossing the thread4 ,a common defect in tripod heads is the thinness of the tenon1 so that the leg1 if twisted1 is felt to be rickety4 ,this tenon is better made wide1 as shown in the staff head in ,fig4 #gj;,a1 seq4 #bag4--,there is a little difference of opinion as to the form of the woodwork of the tripod for #ad-;inch levels1 some preferring an open framed stand in place of the solid form shown in section ,fig4 #fe4 ,these open framed stands are not so compact to carry1 and1 as the author thinks1 unnecessary for levels of #ab inches and under where the tripod head is solidly made4 ,they are well adapted for larger levels and for theodolites1 therefore the description of a framed tripod will be deferred to the discussion of these instruments further on4 ,a few engineers prefer yellow pine for the tripods instead of mahogany3 this is much lighter for its relative stiffness1 but it is rather soft for the fixing to the shovel-pieces1 and therefore scarcely so reliable as mahogany for durability4 ,where lightness is important the author employs cedar1 which is as light as pine but harder4 #bah4--,the lower points of the legs1 technically toes1 are pointed to an angle of about #fj1 and are shod on the insides with steel plates to bite the surface upon which the tripod stands when the legs are extended for use4 ,two brass rings slip over and bind the legs together when the tripod is out of use4 #bai4--,many years ago the author introduced the plan of having one of the legs to turn up at about #a foot distance from the toe4 ,this is shown ,fig4 #fc at ,a1 and in detail section ,fig4 #fd4 ,the joint is made perfectly firm by a winged screw at ,s1 which screws from a boss cast on the hinge ,j to a solid metal shoe ,p4 ,when the leg is turned up1 the screw fixes it in the female screw ,s4 ,this plan is very convenient for use in mountainous districts1 as it enables the level to be set up fairly well without an uncomfortable angle to any of the legs1 or risk of the instrument toppling over4 ,this plan is now nearly superseded by a ball joint as a part of the setting-up adjustment4 ,the tripod head shown under the level of ,fig4 #ei is by no means the best1 but it is the easiest made therefore1 it is the general trade form in use1 both for the level and theodolite4 ,some very superior forms will be discussed further on in description of the instruments to which they are attached4 #bbj4--,the adjustments of the ,dumpy ,level4--,as this instrument does not possess the means of revolving the telescope upon its axis as with the ,y-level1 the adjustments are somewhat more complicated1 and are performed in an entirely different manner when they are to be made by the civil engineer4 ,the differences are not so great in the hands of the optician1 as he generally possesses a movable pair of ,y's upon which he can adjust the telescope conveniently for collimation within his own works1 by supporting the telescope tube in ,y's at a position exterior to the bands which surround it4 ,the tools for this adjustment the author has occasionally supplied upon demand with the dumpy level4 ,but what is necessary here will be to give the mode of adjustment which the civil engineer can accomplish at any time without supplementary apparatus4 ,the bubble is handier to work with when adjusted to reverse in the centre of its run1 but it does not really matter1 as equally accurate work can be done with it in any other position4 ,should the bubble not reverse in the centre of its run1 adjust the instrument by the levelling screws until it reverses in some position4 ,say you start with bubble in the centre1 and on reversing1 it runs towards the eye end of the telescope six divisions1 then alter the levelling screws until it is only half this1 or three divisions towards the eye end1 then1 if properly levelled1 the telescope will make an entire revolution with the bubble in that position1 which will prove that the axis is vertical4 ,the bubble can now be adjusted by the opposing nuts at the one end by means of the tommy pin 7provided in the case7 until it is in the centre of its run1 and it will then reverse in that position instead of three divisions towards the eye end4 #bba4--;,adjustment to ,collimation4--,upon a fairly level piece of ground the staff plate1 fully described further on1 is trodden well down on the ground1 and the level is set up at say #c chains from this1 in which position the staff is read as a back sight4 ,now in the opposite direction in the same line1 at #c chains distance from the level1 a second staff plate1 or in defect of this if the surface be not firm1 a stake or a boulder1 is driven firmly down in the earth1 and the staff is placed upon this erect and face to the instrument as a foresight4 ,the instrument is turned half round and the second station is read4 ,these readings of the staves taken will be truly level with each other1 if the axis of the instrument has been set up quite vertically1 so that the bubble has kept its centre in all positions4 ,this is true although the axis may have been out of collimation4 ,this arrangement is shown in ,fig4 #ff1 ,l the first position of the level taking sights at equal distance from ,s and ,s4 ,let the level be now removed to ,l3 if correct it should cut the staves ,,ss at equal distances above or below the first readings at aa1 which are at equal distances from bb readings from ,l1 therefore level and parallel with the first reading4 ,illustration3 ,fig4 #ff4--;,adjustment of dumpy level4 #bbb4--;,in the dumpy level1 as it leaves the hands of any respectable maker1 the subsequent adjustments required can never be great1 unless the level has suffered a serious fall so as to bend the limb4 ,the rewebbing the stop1 if carefully done1 would require only a slight readjustment2 but it may be convenient to give an exact method for extreme cases1 which may be given in detail for clearness1 and at the same time we may also consider the influence of the curvature of the earth4 #bbc4--,original ,adjustment of the ,dumpy ,level to ,collimation with consideration of the ,curvature of the ,earth4--,suppose the readings of the two levelling staves at #aj chains apart1 taken with the level placed at intermediate distance as before1 read #gej and #dej1 and that we now place the level linearly at #a chain outside the first reading and it reads the near staff #fej and the distant staff #eej1 by the inclination of the ground1 this would be a and a - reading2 but we require both readings of one sign1 and as the distant staff reading is much too high1 it is clear we require - readings for correction4 ,the correction will be of the difference of reading in proportion to the distances1 calling the lower reading minus-- #gej - #fej -#a1 #dej #eej #a1 difference #b4 ,that is -#b1 as our readings are - and as the -#b is in #aj chains1 at #a chain the distance of - the near staff -#b1 and #aa chains the distant staff -#bb4 ,the correction will therefore be for the near staff #a chain distant #fej - #b #fcj1 and for the distant staff at #aa chains #eej - #bb #ccj -#ab below each of the first readings4 ,if the telescope be now collimated to the near staff reading #fcj1 by adjusting the screws immediately under it for distance between the limb and the telescope1 and the bubble be readjusted to the telescope without moving the instrument or touching the parallel plate screws1 the adjustment will be perfect1 less the small error due to the earth's curvature in #a chain4 ,if the telescope be adjusted to the distant staff #ccj1 curvature of the earth will be corrected by the level for #aa chains1 which is #jjajf foot or #ja nearly1 the smallest reading we have on the staff4 #bbd4--;,it was claimed by the late ,william ,gravatt for his method of adjustment1#c which was equivalent to that given above1 but more complicated and with three staves1 that the fixed correction for curvature at #aj chains would be uniform in the working of the level pro rat for all distances4 ,there is some difference of opinion on this subject3 at any rate1 a #aj chain correction would only be applicable to very approximately level ground where average #aj-;chain stations could be taken4 #bbe4--,where space is not at command and curvature correction is not desired1 adjustments of the level may be made with care at #a chain distance on each side of the setting-up of the level with one staff only1 which can be moved from one stake to the other1 and with the final setting-up of the instrument at #a chain distance from these stakes as before1 art4 #bba4 ,for this the staff only requires moving twice1 if the collimation adjustment is to the last reading only calculated out as above4 ,this close system has a certain amount of merit1 that by reading from one staff only for both stations it is more accurate1 as any inequality between the divisions of two separate staves is avoided4 ,illustration3 ,fig4 #fg4--;,collimator for adjustments to horizontality of the telescope4 #bbf4--;,collimator4--,optical manufacturers in populous districts1 and some observatories1 as that of the ,india ,store ,department at ,lambeth1 adjust by means of the collimator by the exact method due to the late eminent ,german mathematician1 ,carl ,f4 ,gauss1 which is hence termed the method of ,gauss4 ,the collimator consists of any good telescope permanently adjusted to solar focus1 with a webbed diaphragm placed in the focus1 where it may be illuminated by a lamp or by the reflection of daylight1 and provided with means of bringing the telescope to a level position4 ,as the collimator is generally constructed1 it consists of an #ah-;inch telescope1 ,fig4 #fg1 of the same description as that used for a ,y-level1 described art4 #id1 in which the telescope is surrounded by accurately turned collars formed to rest in ,y's4 ,the ,y's are supported upon a heavy cast-iron stand1 of somewhat triangular form1 of nearly the length of the telescope1 about #f inches wide at one end and #b inches at the other4 ,the stand has two feet extended to the full width at the wider end1 and one foot at the narrower end under the telescope4 ,each foot has an adjusting screw4 ,the complete collimator is supported1 at about the height of the telescope of the level on its stand1 on a very solid pier of stone or brickwork in cement capped with a stout slate slab4 ,the telescope is brought to perfect collimation as with the ,y-level1 already described art4 #bjj1 and the level is fixed true with the axis of the telescope1 when the collimation is perfect4 #bbg4--;,a lamp or gas flame is placed at a short distance from the eye-piece end of the telescope1 so as to illuminate the webs that they may be distinctly seen when looking into the objective end of the telescope4 ,in bright daylight1 if there is a skylight over1 a reflector will answer the same purpose4 ,at the ,lambeth ,observatory a fine needle-point hole is used instead of webs4 #bbh4--,the instrument to be adjusted may be placed at any convenient distance from the collimator4 ,for adjustment of a level1 where the collimator is already in adjustment1 the level is raised upon its stand until the axis of the telescope sensibly coincides with the axis of the collimator2 then if the telescope of the level to be adjusted be focussed into the objective end of the collimator1 the illuminated webs will be clearly seen2 and if these webs be brought by adjustment of the level exactly to coincide with its own webs1 the collimation lines of the two instruments are exactly parallel4 ,in this adjustment it is only necessary to be sure that the vertical axis of the level is truly vertical1 so that the bubble reverses without displacement1 in which case the whole instrument must then be in perfect adjustment4 #bbi4--;,it would be very difficult to use this method of adjustment if it were necessary that the axes of the level and collimator should exactly coincide4 ,it is only necessary that they should nearly coincide1 on account of the imperfection of object-glasses1 which rarely work so well near the edge as towards the centre2 otherwise any directly parallel position in front of the object-glass would answer1 as the next diagram will show4 ,let ,o1 ,fig4 #fh be the object-glass of the collimator1 whose solar focus is at ,f4 ,then the rays ,,pp1 and all other parallel rays falling on the object-glass1 will be brought to a focus at ,f2 and reciprocally all rays departing from ,f in passing through this object-glass will leave in parallel lines ,,pp4 ,let ,o be the object-glass of a telescope to be collimated1 ,f its solar focus4 ,then all rays from ,p to ,p departing from ,f that fall within the parallel space ,p,p will be brought to focus at ,f4 ,when the image at ,f is illuminated by a lamp ,l1 the webs or other index will be clearly seen by the eye-piece at ,f when the two telescopes are exactly parallel with each other4 ,in this position the webs of the level are adjusted to make this coincidence4 ,it is easily seen that by this method we eliminate all errors of atmospheric refraction1 and are quite independent of the state of the atmosphere for obtaining distinct vision for adjustment4 ,illustration3 ,fig4 #fh4--;,diagram of collimation by two telescopes4 #bcj4--,when two levels are at command1 one a ,y-level1 or even a dumpy in perfect adjustment1 the one may be used as a collimator to the other by setting them up at a distance within their focal range on a firm basement floor4 ,a candle or a lamp will give sufficient light to illuminate the webs of the instrument1 which is used as a collimator1 being certain1 of course1 that this instrument is first placed in level adjustment and set at solar focus1 and that the instrument used as a collimator has a good object-glass4 ,illustration3 ,fig4 #fi4 ,illustration3 ,fig4 #gj4--,stanley's model #ad-;inch dumpy level4 ,illustration3 ,fig4 #gj;,a4--,tripod4 #bca4--;,improved ,dumpy ,level4--,the writer has made some improvements in the dumpy level1 which have so far met with very general approbation from the profession1 ,fig4 #gj4 ,these improvements are directed to ensure much greater sensitiveness in the longer bubble1 therefore greater accuracy in the work performed by it2 more solidity of construction without increase of weight2 and permanence of reading index1 with some additional matters4 ,in these improvements the mounting of the longer level tube1 instead of being placed in a stiff joint at one end1 or between rigid clamping nuts at both ends1 has a barrel-fitting at one end which is ground into a parallel hole4 ,this plan admits of circular self-adjustment to the bubble tube1 which the clamping of the nuts can never twist or strain during vertical displacement2 and the joint can be made perfectly sound with certainty1 which saves the risk of accident to the bubble from expansion by heat and some other conditions4 ,a more recent form of cross level1 ,fig4 #fi1 shown in perspective near the ray-shade in the engraving ,fig4 #gj has been designed by the author1 in which the level casing is bored entirely out of the solid4 ,it is supported upon the side of one telescope strap by three stout pins1 the centre one fitting its hole1 and the two outer ones are loosely held by cross screws to permit a small amount of adjustment1 which is all that is necessary4 ,by this construction the level fixings are made in five pieces only1 including screws1 instead of thirteen as usual1 at the same time making the level more portable and solid for hard wear4 ,the telescope straps are fitted at their stumps solidly down upon the limb1 as shown ,fig4 #fj1 p4 #aab4 ,adjusting screws are placed under this as in the dumpy level described1 but the pressure screw is not employed except in case of accident far away from an optician1 when it is found to be there ready for use4 ,the limb is framed out into two edge bars3 this gives greater vertical sectional strength and resistance to torsion without increase of weight in the instrument4 ,where a compass is used1 this is included in the frame of the limb1 as shown in the engraving4 ,the compass is read with a prism1 this being much more convenient and exact than looking down upon the divided circle1 the instrument being necessarily placed for use at nearly the height of the eye4 ,the compass ring is made of aluminium4 #bcb4--,the further improvement1 which the author considers of the greatest moment1 is that the vertical axis is fixed directly and firmly upon the limb1 and not through a loose screw fitting for separation at this point as in the ordinary dumpy4 ,this is shown to be important in that1 with the dumpy1 where a loose screw is employed1 any little difference of screwing down upon the axis when the instrument is set up causes so much derangement of a sensitive bubble in relation to the vertical axis1 that the optician is bound to use a rather dull bubble with the ordinary dumpy4 ,further1 a particle of grit or the slightest bruise on the collar in replacing the instrument in its case throws it out of adjustment at this important point4 ,the objection to the author's plan is that it makes the case for the instrument somewhat larger2 but the advantage of certainty of permanent adjustment appears to him very far to counterbalance this objection where accuracy is aimed at4 #bcc4--,tribrach4--,the setting-up adjustment of the instrument is upon tribrach limbs with three screws only4 ,these screws can never strain the vertical axis1 which in this instrument is somewhat deeper and more firmly made than that of the dumpy4 ,in the old form of tribrach the points of the screws were held down by a spring plate placed above them4 ,this plate1 in carrying the instrument upon its stand over the shoulder1 which is the most comfortable way if the stations are not far apart1 was very liable to strain sufficiently for the screws to get loose4 ,the author patented a much more solid method1 by which the old spring plate is entirely dispensed with4 ,in this plan each screw has a ball at the lower end1 which is inserted in a tubular fitting formed in a solid tribrach1 made of exact dimensions to take it4 ,the tube is open on the upper side1 as shown in longitudinal section ,h1 ,fig4 #ga4 ,many years' experience and the fact that numbers of makers have copied this form since the expiration of the patent1 shows this plan to be perfectly successful4 ,the general construction of the lower part of this level may be seen from inspection3 ,l limb1 fitted with compass2 ,c axis1 in one casting with the limb2 ,s sprang1 carrying the socket and supporting the instrument4 ,,ph shows the ball head arrangements to the screws4 ,a central screw in this part detaches the tripod4 ,one point is shown at ,p1 of which there are three1 to support the level upon a wall or rock in cases where the tripod cannot be used--a most important advantage in town levelling4 ,the tripod head is made much more firmly than that of the ordinary construction1 by extending two wing fittings from the top of the shovel-plates as wide apart as possible1 instead of the narrow tenon fitting before described4 ,the shovel-plates are screwed to the staff by means of a stout nut-plate inside the tripod ,f4 ,those who have experienced how much defective levelling is due to a shaky tripod head will appreciate this precaution4 ,the general arrangement is also shown in ,fig4 #gj;,a4 ,illustration3 ,fig4 #ga4--;,details of ,stanley's dumpy level3 half elevation to left1 half section to right4 #bcd4--;,as the tribrach system of adjustment is of somewhat recent adoption to ordinary surveying instruments in this country1 it strikes the stranger to it as being more difficult in use4 ,it is really the most simple and expeditious system as is clearly explained by the foregoing diagrams1 ,figs4 #gb1 #gc of the plan of a level1 omitting its lower parts4 ,illustration3 ,figs4 #gb and #gc4--,tribrach adjustment4 #bce4--,the bubble of the level is placed parallel with two of the screws of the tribrach1 that is as ,b and ,c1 ,fig4 #gb1 and is adjusted to the centre of its run4 ,it is then placed at right angles to the first position1 so that the screw ,a comes directly under the bubble1 to be adjusted by this screw only until it again comes in the centre of its run4 ,fig4 #gc shows this second position with the screw ,a underneath4 ,the level should after this read all round true1 but it is well to try it round parallel with the different pairs of screws in all positions to give small adjustment if required4 ,where there is a cross bubble the level may remain for adjustment in its first position1 but it is well to try it all round1 as the long bubble is made uniformly the more sensitive4 ,illustration3 ,fig4 #gd4--,ray shade4 #bcf4--,the ,ray ,shade to the telescope used in the above-described level has two narrow slits opposite each other at #ahj4 ,a zero line is carried from one slit to a line on the ray shade fitting when the slits are quite horizontal4 ,sights through the slits at zero enable an approximate cross-level to be taken4 ,the edge of the tube of the ray shade is divided #cj on each side of the zero line to #b1 so as to take approximate lateral inclines of the surface of the land in levelling4 ,this useful plan of cross-sighting was originally proposed by ,gravatt4 ,illustration3 ,fig4 #ge4--,stanley's platino-iridium point level stop4 #bcg4--,the most important variation from the telescope of the dumpy level described is in the diaphragm1 where webs or lines of any kind are entirely done away with1 and are replaced by a special form of index4 ,this is represented in ,fig4 #ge4 ,the movable part carrying the opening of the diaphragm is placed in a sliding fitting1 as previously described1 art4 #bad1 for the dumpy level4 ,the index which replaces the web is a finely-pointed needle formed of platino-iridium 7platinum #ge1 iridium #be74 ,this alloy has about the hardness of spring-tempered steel1 and is1 as far as known1 perfectly non-corrosive in air or moisture4 ,a pair of vertical points indicate the position for holding the staff4 ,it will be found by experiment that the point reading is much more exact than with the web1 as irradiation due to edge reading of the web is entirely avoided1 and also the covering of the object as it would be intersected by the web due to the angle its thickness subtends upon the staff1 which is very palpable at #aj chains distance4 ,the iridium point is sufficiently strong to be kept perfectly clean by touching it occasionally with the point of a camel-hair brush if it appear dusty4 ,with care this point will last in adjustment for as long a period as the level itself remains in use4 ,upon first impression the point may not appear so fine as a web1 but practically it is more exact1 as the previous exaggerated images will show--,fig4 #gf is the image of a division of the staff partially covered by a web ,,ww2 ,fig4 #gg that of a magnified image of the point ,p brought towards a division for reading4 ,it will be readily observed that the fractional part of the #a_/ajj foot block1 which the point ,p cuts1 is much more easily estimated than that in which the web ,,ww covers a part of a similar block4 ,illustration3 ,fig4 #gf4 ,fig4 #gg4 ,difference of reading with a web and a point1 shown much magnified4 #bch4--;,in early levels of improved construction1 as shown ,fig4 #gj1 a difficulty was experienced in practice in bringing the index point exactly up to the edge of the line as it is shown in ,fig4 #gg at ,p4 ,this difficulty has been obviated in recent highest class instruments by making a tangent screw adjustment to the axis as shown under the level in ,fig4 #gh4 ,there was a great objection to the old form of tangent adjustment by clamping on the axis1 as this was found to disturb the centre4 ,in the plan shown in the illustration the clamp is left free by jointing to the axis until it grips one of the arms of the tribrach upon a vertical surface2 in this way it cannot disturb the axis4 ,the level1 ,fig4 #gh1 is shown mounted on a framed stand1 which is preferred by the ,indian ,government1 and is generally necessary for rigidity for large instruments of over fourteen inches4 ,this will be described further on with theodolites1 art4 #ddg1 on framed stands4 ,illustration3 ,fig4 #gh4--,stanley's improved dumpy4 #bci4--,stadia ,points4--,the author commonly makes the points1 ,fig4 #ge1 ,,vv stadia points1 by making the distance of the extreme ends of these subtend an angle1 equal to #aj feet of the levelling staff at ten chains distance1 or #a foot of the levelling staff at #ajj feet distance 7 a constant to be discussed ,chapter ,,xii471 by which measurements of the distance of the staff can by taken or checked by observation through the telescope only4 ,illustration3 ,fig4 #gi4--,stanley's quick setting-up level4 #bdj4--,quick setting-up ,tribrach4--,one objection has to be made to the tribrach over the four-screw system of adjustment1 that the four-screw admits of greater inclination to the tripod1 which is important in hilly countries4 ,to remedy this defect the author designed a ball arrangement to the axis1 which permits the level to be set #ae to the inclination of the tripod independently of the screw adjustment1 so that the level1 when the tripod is set at its best angle1 may be brought immediately to nearly its final position4 ,the arrangement is shown in the engraving ,fig4 #gi4 ,the axis carries a cup formed in the metal casting1 which can be clamped down upon a ball-shaped recess formed upon the tribrach by means of a winged nut placed under it1 the wings of which project between the tribrach screws4 ,a very slight pressure is sufficient to firmly clamp the ball4 ,this form of level is now very popular with civil engineers4 ,with a point diaphragm and a tangent screw to the axis1 not shown in the engraving1 it is1 in the author's opinion1 the best practical level he has been able to design4 ,illustration3 ,fig4 #hj4--,stanley's ,engineer's level4 ,since the last edition was written the reviser of this work introduced1 in conjunction with ,mr4 ,stanley1 his new solid bodied engineer's level1 which has practically revolutionized the form of dumpy level and has proved such a success that more of this form are now made than all other forms put together4 ,in this level1 ,fig4 #hj1 the centre1 body of telescope1 object end and bubble fitting are all combined in one piece of gun-metal1 so that although of vastly greater strength and rigidity it does not weigh as much as the old form of tubular body with its collar and stage4 ,this does away with many separate pieces which are usually soldered and screwed together4 ,it thus forms the strongest and most compact level yet made1 and with ordinary care it will last in perfect adjustment a lifetime4 ,the pinion for focussing is fitted to the side of the cast body1 instead of to a tube1 thus greatly increasing its firmness4 ,its form is equally adapted to the four-screw levelling if desired1 as shown on next page1 ,fig4 #ha1 in which it will be seen the four-screw levelling is of much improved form1 giving greater strength and far more wearing and bearing surface to the levelling screws4 ,illustration3 ,fig4 #ha4--,stanley's ,engineer's level4 ,the reviser has also patented a new form of spherical joint1 which has met with equal favour4 ,this improvement consists of a section of a ball 7screwed to fit the stand head7 fitted within the lower plate and a simple means of clamping it in any position1 which1 when released allows of sufficient rocking movement in any direction to compensate for any uneven setting up of the stand4 ,it does not add to the height of the instrument1 may be instantly set nearly level1 and less than half a turn of the levelling screws will bring the instrument into true position4 ,it is shown fitted to the new engineer's level at ,fig4 #hb below1 but is equally applicable to any other form of instrument4 ,illustration3 ,fig4 #hb4--,stanley's ,engineer's level fitted with quick setting spherical lower plate4 ,as ninety per cent4 of the orders now for levels are for the form shown at ,fig4 #hb1 the reviser ventures to think that this must be favoured by the profession as the best practical instrument yet made4 ,a further improvement has been made by making the diaphragms interchangeable1 so that any form of diaphragm that is preferred may be instantly fitted without disturbing the adjustment1 and when lines on glass are used it may be removed for cleaning1 and replaced without interfering with the adjustment4 ,the diaphragms illustrated below1 ,fig4 #hc1 are usual forms1 and it is recommended that when webs are preferred a glass one should be carried as a spare in case of accidents4 ,illustration3 ,fig4 #hc4 ,e ,stadia points for clamp and tangent levels4 ,f ,stadia points for ordinary levels4 ,g ,stadia glass diaphragm4 ,h ,webs4 ,j ,stadia webs4 #bda4--,the further discussion of the subject of high-class levels becomes somewhat difficult4 ,leaving out of consideration the levels sold by the trading optician1 who deals in the commercial article but sometimes superadds a little fad1 every genuine manufacturer has his pet plans of carrying out details1 some of which may be very meritorious1 but which could scarcely be described without a fuller discussion than our space permits4 ,there is also1 no doubt1 a great number of mistakes that have been made in the construction of surveyor's levels4 ,the direction in which the scientific optician generally fixes his attention is to give the advantages of the ,y-level in the dumpy form1 assuming the civil engineer holds a certain amount of prejudice against the use of the ,y1 for which1 in its old form at least1 the writer must admit that he was fully justified4 ,whether the professional man1 nevertheless1 will ever depart from the solid construction of the dumpy remains an open question4 ,illustration3 ,fig4 #hd4--;,cushing's #ab-;inch improved level4 #bdb4--;,cushing's ,level4--,the level illustrated above1 ,fig4 #hd1 by the late ,mr4 ,thos4 ,cushing1 ,f4,r4,a4,s41 ,inspector of ,scientific ,instruments for ,india1 would under any circumstances claim attention1 from this gentleman's well-known high technical scientific attainments4 ,it has also the merit of being in practical use in ,india at the present time4#d ,the principal improvement in this instrument over the dumpy form1 which it otherwise represents1 is in the construction of the telescope1 which is said to possess all the necessary adjustments of the ,y-level4 ,the telescope is firmly fixed in collars soldered to the tube1 as in the dumpy4 ,the tube at each end is formed into a stout socket collar4 ,these socket collars are exactly alike1 and are ground to fit either the objective or the eye-piece end of the telescope1 so that these parts may be reversed1 the one for the other4 ,this reversing is nearly equivalent to turning the telescope end for end in the ,y-level4 ,the end also rotates in its fitting1 which is nearly equivalent to rotating the telescope half a revolution in the ,y-level4 ,the reversible ends of the telescope are held in their ground fittings by studs and slides 7bayonet notches74 ,it is easily seen that by this plan adjustments may be made of collimation and of fixing the line of collimation perpendicular to the vertical axis1 as with the ,y-level1 if the object-glass be originally correctly centred4 ,the stop is of the slide form described for the dumpy1 ,fig4 #fa1 and a glass diaphragm is used4 ,one important arrangement is also made in this part of the instrument--which is necessary1 as glasses become frequently bedewed in the telescope--viz41 that the eye-piece end may be removed from its ground fitting and the glass cleaned and replaced without disturbing the adjustment in any injurious degree4 ,the general construction of the instrument can be seen from the illustration4 ,the supports of the telescope have a rocking axis at one end1 and are adjusted by capstan-headed nuts at the other4 ,the adjustable support for setting up the instrument is upon ,everest's tribrach system for theodolites1 to be described further on1 in ,chapter ,,ix4 ,the tripod head has also wider bearing than is general1 which is attained by extending the book-plates into the form of a socket fitting4 ,the illustration given is of a #ab-;inch level2 in the #ad-;inch an open framed stand is used in place of the solid tripod1 as in ,fig4 #gh1 which will be described further on1 for theodolites4 ,the level is a decidedly good one2 but the author has experienced with it some slight defects when compared with his own ,y form4 ,the ground collars are a little inclined to bite1 particularly if the instrument has been laid by for some time1 so that in reversing for adjustment there is great risk of disturbing the instrument4 ,the glass index1 although permanent1 has the same defect as the web--of covering the image of the staff reading4 ,it also obstructs a little light1 and is subject to dew1 which the point system avoids4 ,the weight of the instrument is increased by the collar fittings4 #bdc4--;,cooke's ,level4--,an instrument somewhat equivalent to the above has been patented by ,messrs4 ,t4 ,cooke ,sons4 ,in this1 instead of the objective and eye-piece ends of the telescope only being reversible in the collar fittings1 as in ,mr4 ,cushing's level1 the entire telescope reverses end for end in an extra outer tube1 which is fitted between the collars4 ,this tube also permits the rotation of the whole optical parts about the axis of the telescope for adjustment for collimation1 although in a manner more frictional1 and therefore more likely to disturb the instrument than in the simple ,y adjustment4 ,in this instrument1 again1 it is easily seen that it is the perfection of the ,y-level1 without its outward appearance1 that is aimed at1 and to gain this the weight is increased by extra fittings and double tubes1 which are liable to become fixed by a slight dent upon the outer tube4 ,taken altogether it is not quite so convenient or so simple as the best constructed ,y-level2 but if it gives the adjustments the optician holds to be most important1 in a disguised form it may be acceptable to the civil engineer4 ,we may in this manner1 perhaps1 from the optician's point of view1 count it a certain gain in the same direction as ,mr4 ,cushing's level just described2 but if we may accept the late ,mr4 ,wm4 ,gravatt's ideas1 already mentioned1 the complication is unnecessary4 #bdd4--;,a few other structural variations of details may be mentioned1 as these are constantly cropping up as new inventions4 ,the bubble tube is sometimes placed upon the stage instead of being upon the telescope4 ,this is thought to protect it4 ,it is not1 however1 so easy to read it in this position4 ,the compass is sometimes made a loose part--when it is not required on the work its weight is saved4 ,various forms of locking screws are made to the supports of the telescope2 these are only necessary to correct imperfect work4 ,the axis collar is sometimes extended to a limb bearing4 ,this is common in ,french instruments2 it makes the movement stiffer1 and is quite unnecessary unless the axis is made too short4 ,a well-known ,german firm recently brought out a level with internal focussing1 by means of an auxiliary lens mounted in a tube inside the telescope1 moved by a rack and pinion1 but any internal lens is a source of trouble1 as it cannot be got at to be cleaned1 and in hot1 damp climates it becomes bedewed4 ,the device is very old1 having been patented in ,america many years ago and discarded4 #bde4--,supplementary ,parts to ,levels4--,as a rule1 supplementary parts fixed to the instrument1 beyond the magnetic compass sometimes required1 are very objectionable if the object of the level is to be levelling1 as these additional parts inevitably increase the weight which has constantly to be borne in carrying the instrument4 ,supplementary parts have been carried1 in various schemes1 to the extent of combining the entire level with the theodolite1 at the same time nearly combining the united weights of the two instruments4 ,as a rule1 professional men rarely care for complex combinations2 and even after a limited popularity is granted to extra parts not absolutely required1 these are generally finally abandoned4 ,mention of two such parts1 therefore1 only will be made1 as these owe their introduction to the late ,william ,gravatt1 and are found applied to many levels in use1 or at least contained in the case with the instrument4 #bdf4--;,bubble ,reflector4--,this was formerly placed upon all dumpy levels4 ,it consists of a small mirror about #b inches by #e_/h inch fixed in a frame that is jointed at its lower end to a short piece of tube partly cut away so as to form only a little over a semi-cylinder4 ,this tubular part just clips firmly upon the brass casing tube of the spirit level4 ,the reflector1 when placed vertically on the level tube1 can be adjusted by its joint1 so that the run of the bubble may be observed by reflection in looking above the eye-piece to see that it is in adjustment at the time of taking an observation4 ,its use was thought to be a precaution in levelling1 particularly on marshy ground4 ,the observation of the bubble is less exact than by a side reading1 and cannot be relied on4 ,illustration3 ,fig4 #he4--;,compact cheap form of dumpy level4 #bdg4--,sight ,vanes4--,two sight vanes are placed above the telescope1 either as loose fittings or to hinge down upon the level tube4 ,one vane has a vertical narrow slit and cross hair2 the other has a window with a vertical horse-hair placed in its centre4 ,this arrangement gives sight of distant landmarks in line with the direction of the telescope1 upwards or downwards1 beyond its field of view4 ,a slider1 fixed upon the window sight1 reads at its upper edge into divisions cut on the vane1 by means of which an approximate rate of forward inclination of the land may be taken4 ,this sighting arrangement adds about half a pound weight to the instrument4 ,it was useful with object-glasses of small field of view1 but is useless with good modern glasses of wide angle4 #bdh4--,lower-class ,levels4--,a level is often required by an architect or a contractor for works of limited area1 where it is quite unnecessary to go to the expense of a civil engineer's level of refined manufacture4 ,in such cases the level may only be used occasionally and under favourable circumstances1 so that extreme solidity is not demanded1 neither is distant view in the telescope required4 ,the level generally made for such work is a simple dumpy1 without cross bubble1 compass1 or any extra fittings1 and with one eye-piece only4 #bdi4--,the instrument ,fig4 #he illustrates the author's newest design for a simple level4 ,it has a light form of tripod4 ,the legs clamp directly between angle plates--these are not quite so portable or so neat as cylindrical legs1 but they are easily made1 very firm1 and will bear considerable wear and keep in order4 ,a still cheaper form is made with smaller telescope and turned legs for the tripod4 ,illustration3 ,fig4 #hf4--;,contractor's or builder's level4 #bej4--,the illustration ,fig4 #hf represents the cheapest form of level with a tripod stand that has been constructed1 which contains the important factor of a telescope4 ,the telescope has a sliding fitting1 which is moved by a knob outside1 this being made more quickly than a rack and pinion fitting4 ,the level tube is solidly supported in collars4 ,the adjustment is in one direction only1 so that the bubble must be set and examined at the time of reading the staff4 ,the instrument is supported on a sprang1 jointed at one end and held by a milled-headed screw at the other4 ,any shakiness of the thread of screw there may be is taken up by a stiff ,german silver spring between the sprang and the limb4 ,it is sometimes made with a ball and socket joint for first adjustment1 but this renders it nearly as costly as a superior level4 ,the tripod head is of simple construction4 ,the legs are oak or ash1 and are clamped on the head by bolts4 ,this simple tripod is fairly firm in use4 ,the level is good enough for ordinary building works1 laying short drains1 etc41 within limited areas4 ,it is much more accurate than any form of open sighted level without telescope4 ,sir ,george ,leach has recently made a modification of this old form of level by placing a pendulum to rock the axis to cross level position1 which is a refinement1 although rather a costly one4 ,illustration3 ,fig4 #hg4--,sighted reflecting pocket level4 #bea4--,sighted ,pocket ,level4--,this consists of a tube1 which is generally drawn of square section4 ,a pin-hole sight is made in the closed end of the tube1 ,fig4 #hg1 at ,e4 ,the field end of the tube is left open4 ,the sight is taken by looking through the centre of the pin-hole across the edge of the reflector ,r4 ,a level with a small bubble is placed or inserted in the top of the tube at ,b4 ,the metal casing of this is cut away on the upper and under sides to render the bubble visible from the interior of the tube by means of the reflector ,r1 which occupies one half vertical section of the interior of the tube4 ,this is placed at #de to the axis4 ,the reflector is fixed upon an inner tube so that it may be withdrawn to be cleaned4 ,when the level is set horizontally1 a distant object in the direct sight line is seen through half the tube1 and simultaneously the reflection of the bubble in the other half appears4 ,a line engraved upon ,r indicates when the bubble is central1 and when these coincide the distant object and the eye are level4 ,the instrument is about #d inches long1 and weighs about #h oz4 in its case4 ,illustration3 ,fig4 #hh4--,pocket telescopic level4 #beb4--,pocket ,telescopic ,level4--,in the above-described pocket level1 where it is made short1 the average middle-aged man will not have sufficient accommodation of vision to be able to see the bubble and the screen sharply defined simultaneously with the distant object to which the level is to be taken4 ,in ,captain ,barrie's#e level these objections are avoided by making the reflector and bubble form part of a telescope1 ,fig4 #hh4 ,an achromatic glass of short focus is used1 and the eye-piece is of long focus so as to bring the bubble to focus in the centre of the mirror1 which is made of curved form to decrease the apparent size of the bubble4 ,the image of the bubble does not give by bisection a very definite index4 ,the author has found that this level may be much improved by placing a point in the telescope at the mutual foci of the object-glass1 eye-piece and the bubble4 ,the appearance of the mirror and point is shown at ,b4 ,the point is shown by a dot at ,p4 ,the curved mirror ,r4 ,the dotted line shows the path of reflection from the bubble4 ,this level will work with very fair accuracy as a hand instrument4 ,size1 about #d inches by inch4 ,weight in case1 about #h oz4 ,illustration3 ,fig4 #hi4--,reflecting level4 ,illustration3 ,fig4 #ij4--,the same construction in protecting case4 #bec4--,reflecting ,level4--,this simple level1 ,fig4 #hi1 the invention of ,colonel ,burel1 is one of the most portable4 ,when it is used with a fair amount of care it will give good approximate results4 ,it consists of a piece of parallel glass1 which has half the surface silvered to form a reflector4 ,it is suspended in such a manner that the glass hangs vertically by gravitation4 ,the position of the mirror to the plain glass may be that shown in the engraving1 or horizontally if preferred4 ,the mirror1 ,fig4 #hi1 is inserted in a solid metal frame suspended from a gimbal1 which permits it to hang perfectly free to the action of gravitation4 ,the centres of suspension are made with slightly-rounded knife-edges4 ,a ring at the upper part of the instrument is placed over the thumb or finger to support the instrument when in use4 ,a stout pin passes through a prolongation of the lower part of the frame1 screwed or otherwise1 which permits adjustment by filing to bring the mirror when it is suspended exactly into a vertical plane4 ,the instrument1 fitted into a neat case1 weighs from #e oz4 to #i oz4 #bed4--;,in using the ,reflecting ,level1 it is held upon the thumb at about arm's length1 and adjusted by raising or lowering the arm until the reflection of the pupil of the eye seen in the mirror is exactly bisected by the line cut by the mirror against the clear glass4 ,the distant object seen in front1 that cuts this sight line and the image of the pupil of the eye1 will then be in true level position with the eye of the observer1 provided the air is still1 so that the mirror is not deflected from verticality4 ,from the natural unsteadiness of the hand there is some little difficulty of getting this level quite free from oscillation4 ,this may be obviated1 or nearly so1 by clutching a picket or staff with the hand and suspending the level from the thumb projected out for the purpose1 or by resting the hand against a tree or other firm support4 ,capt4 ,a4 ,h4 ,east1 ,r4,a41 has suggested to the author a very capital device which he employs for hand instruments4 ,this is to place the handle of a stick 7or umbrella7 in the waistcoat pocket1 to clutch the body of the stick with the hand which holds the instrument1 and to steady it with the other hand4 ,in this manner the two arms and the stick form a tripod of surprising steadiness4 #bee4--,reflecting ,level in ,case4--,in windy weather much greater exactness may be secured by placing the pendulous level1 just described1 in a tubular case1 ,fig4 #ij4 ,the case is made of double tubes1 so that the aperture cut on one side may by a half turn of the outer tube close and protect the instrument when out of use4 ,the transparent side of the inner case is sometimes closed by thin glass tube of its own internal diameter4 ,it is much better if made with two vertical sides glazed with parallel glass4 ,when this form of instrument is used1 it may be1 if required1 made to fit on the top of a light staff4 ,the eye is then brought with much greater certainty to the point of bisection on the edge of the mirror1 and much greater accuracy is thus attained in levelling with it4 #bef4--,water ,levels4--,the antique form of level1 composed of two vials fixed on the ends of a tube and partly filled with water1 by which a level is sighted in looking over the surface of the water1 is still used to a limited extent in rural districts on the ,continent2 but the spirit level in some simple form is fast superseding it4 ,the same principle of level1 but with long tube1 has been found convenient for the surveyor in measuring through close buildings1 ,fig4 #ia4 ,illustration3 ,fig4 #ia4--,tubular water level with open vials4 ,illustration3 ,fig4 #ib4--;,browne's standard water level4 #beg4--;,browne's ,water ,level#f is found to be a convenient instrument for levelling in close towns4 ,it consists of a pair of glass tubes of about #b feet in length1 placed in a casing tube for protection4 ,the casing tube is divided into inches and parts1 or the scale is a detached piece of painted wood1 or any rod or rule4 ,a cock at the bottom admits the water to flow to level in the pair of tubes1 one of which is shown1 ,fig4 #ib4 ,there is a handle at the top which unscrews to fill the level1 and a small air cock4 ,it is easily seen that the water finds its level1 and the difference of reading of the two standards is the difference of level of the surfaces upon which they are placed4 ,by closing the cocks the level is made portable4 ,in this position it does not matter how high the centre of the pipe is placed--for instance1 in crossing over a wall--as the water will still find its level when the cocks are released by syphoning the water from the one side or the other4 ,it is a very convenient and exact level for laying drain pipes in open weather1 and for making foundations for heavy machinery1 etc41 but of course it will not stand frost4 ,platelayers' levels and mechanics' levels generally are deferred to consider with useful hand tools and apparatus employed by surveyors in the final chapter4 ,,footnotes3 #c ,see ,simms' ,mathematical ,instruments1 p4 #c4 #d ,see pamphlet on ,a ,new ,form of ,levelling ,instrument1 by ,thos4 ,cushing1 ,f4,r4,a4,s41 #ahgi4 #e ,patent ,no4 #fi1 ,wm4 ,barrie1 #ahef4 #f ,patent ,no4 #fgdb1 ,john ,browne1 ,june1 #ahcd4 ,,chapter ,v4 ,,levelling ,,staves--,,construction--,,various ,,readings ,,discussed-- ,,sopwith',s--,,field',s--,,strange',s-- ,,stanley',s ,,new--,,metrical--,,simple ,,construction ,,mining ,,staff--,,papered ,,levelling ,,staff-- ,,preservation--,,packing ,,pads--,,staff ,,plate--,,staff ,,level--,,practice ,,of ,,levelling--,,index ,,of ,,bubble--,,lamp--,,curvature ,,corrections--,,station ,,pegs--,,refinement ,,of ,,levelling--,,levelling ,,books--,,ink ,,bottle1 ,,etc4 #beh4--,levelling ,staves4--,since great improvements have been made in the telescopes used as part of all modern surveyors' levels1 particularly by increasing their light-receiving capacity1 all systems of vanes which were formerly made to be seen distinctly at a distance have disappeared from use by ,british surveyors2 it is now found that the plain reading of a divided staff can be taken by means of the telescope at a sufficient distance from the observer for all practical purposes4 ,in this country one construction of staff is now generally adopted2 and the only variations that are made in this are found occasionally in the readings4 ,the construction of the level staff in common use is that invented by the late ,thomas ,sopwith1#g called the telescopic staff1 the face view of which is shown ,fig4 #if4 ,for ordinary open field work this is made #ad1 #af1 or #ah feet in its extended length2 but generally1 except for levelling on mountainous land1 the #ad feet is used4 ,this staff when closed is about the same length as the tripod1 #e feet #d inches1 and may be conveniently stowed away under the seat of a railway carriage4 ,sopwith's staff1 as it was formerly made1 consisted of two square parallel tubes and one inner solid parallel slide4 ,made in this manner it was liable to be rather shaky when extended1 besides which it frequently got jammed in the telescopic boxes if put away damp from rain3 this tended at first to limit its use4 ,it is now usual to make the boxes slightly conical1 that is1 diminished towards the upper part1 so that they are rigid when opened out but are very free when closed1 which quite remedies the defects just mentioned4 ,illustration3 ,figs4 #ic1 #id4--,section of ,sopwith's staff4 #bei4--,the ordinary construction of ,sopwith's staff and the best mode of manufacture is shown1 with the joints grooved together1 in section ,fig4 #ic4 ,the outer tube or case ,a1 which in the #ad-;feet staff is #e feet in length1 is made of mahogany #e_/af inch thick1 the front being inch4 ,the outer dimensions of the section are #c-a_/h inches by #b inches4 ,the second tube ,b is #e feet #a inch long1 of outer dimensions #b-c_/h inches by #a inches4 ,the inner slide ,c is solid1 #e feet #b inches long1 #a inches by inch4 ,all the slides are sunk on the face about #a_/af inch to prevent the divisions being rubbed by exposure in sliding together4 ,the slides have each a brass shoe and cap4 ,they are held when extended by a spring catch1 the detail of which is shown in ,fig4 #id1 section y to z of ,fig4 #ic--,s spring of ,t form screwed firmly to the edges of the box4 ,the catch is made at ,a over the edge of the brass cap ,a4 ,the spring should be of very hard rolled brass4 ,it is well to have one or two brass bands round the body of the outer casing to secure this as far as possible from being split by accident4 #bfj4--,the most important consideration in the manufacture is that the telescopic work should fit well1 and that the boxes should be glued up quite square and out of winding4 ,the boxes should1 after the glue is quite set1 be screwed with brass screws at distances of about #f inches apart1 to secure the joints which may afterwards in use be exposed to long-continued rain4 ,the fittings should be carefully made1 so that when the staff is extended there should be no shakiness sufficient to cause serious vibration when it is used in windy weather4 ,the interior of the slides when finished should be thoroughly oiled with raw linseed oil1 and the outer surfaces be well soaked in shellac dissolved in spirit1 and then ,french polished over this4 ,the brass work should be well lacquered4 ,illustration3 ,fig4 #ie4--,section of semi-cylindrical staff4 #bfa4--,semi-circular ,staff4--,this is another kind of telescopic staff1 with ,sopwith sliding arrangement1 which possesses a certain merit1 but is more expensive to make4 ,it is semi-cylindrical1 the cylindrical part being made without any joint4 ,this is shown in the section ,fig4 #ie4 ,the general dimensions of the face of the staff are the same as those given for the ,sopwith staff4 ,this staff is a little stiffer1 but there is more risk of its not standing true4 ,as in the union of four pieces of wood in the square form1 previously described1 the tendency of one piece to warp in a certain direction is resisted by the other pieces2 but in this cylindrical form there is no such resistance1 so that it is found that these staves when exposed to wet are much more liable to become warped and fixed in their slides4 ,there is also more difficulty in getting the conical form fairly accurate in the working4 ,one particular merit1 when a pair of staves of this kind is used1 is that the two go together and form a cylinder1 which is a very compact form1 but perhaps a little more difficult to carry1 owing to the tendency of a cylinder to roll off the shoulder4 ,illustration3 ,fig4 #if4--,sopwith pattern staff4 ,illustration3 ,fig4 #ig4--;,field's pattern4 ,illustration3 ,fig4 #ih4--,stanley's old pattern4 #bfb4--,what was originally considered as the defect of the ,sopwith staff1 besides its shakiness1 as it was first made1 was the diminished width of reading of the upper length1 this being only #a inches wide4 ,this caused for a long period other forms of staves1 which maintained the same width of reading surface quite to the top1 to be preferred by many4 ,this fault has been partly remedied by the author in making the feet readings of the upper staff by dots1 instead of the narrow figures1 which were very difficult to read4 ,in other respects the light and portable form of the ,sopwith staff has ensured its general use4 ,illustration3 ,fig4 #ii4--,sopwith's staff4 ,illustration3 ,fig4 #ajj4--,rogers ,field's staff4 ,illustration3 ,fig4 #aja4--;,col4 ,strange's staff4 #bfc4--,the original form of reading designed by ,sopwith is still much more in use than any other4 ,it is similar in pattern to ,fig4 #if1 shown in detail for #a foot ,fig4 #ii4 ,the dots at the end of the lines shown in the figure were introduced by the author to render this staff more distinct than when lines only are used1 as in the ordinary pattern4 #bfd4--,sopwith's pattern is sometimes printed on paper for pasting on the staff1 and in this manner the staff comes out much cheaper than by drawing the readings in solid paint4 ,paint1 however1 is strongly recommended1 not only because it wears much better and keeps cleaner1 but that the painting and varnishing add very much to the durability of the staff1 exposed as it must necessarily be to rainy weather2 further1 the paper1 however well it is fixed at first1 is liable to creep away from the edges of the staff1 and leave a space into which rain enters very freely by capillary attraction2 but it does not again freely evaporate1 so that it rots the staff and makes the paper reading after a time mouldy4 ,it is1 nevertheless1 convenient to take a set of first length papers if a surveyor is going abroad1 as from accidents--grazing by carrying the staff with the tripod of the level1 etc4--the first length of surface is very liable to become too much injured and effaced for fair reading4 ,a description of fixing the paper will be given further on4 #bfe4--;,for ,reading the ,sopwith ,staff1 the foot readings are taken from the tops of the red figures4 ,the #a foot figures are in black1 and are all odd numbers1 #a1 #c1 #e1 #g1 #i4 ,these read also from the top4 ,the height of the figure is exactly #a foot1 so that the bottom of each figure reads the lower even number--thus the bottom of #c reads #b1 of #e reads #d1 of #g reads #f1 and of #i reads #h4 ,the #f and #i foot figures if made alike1 from effect of telescopic inversion1 may cause error4 ,the author has for many years made the head of the #i a solid black block to avoid this4 #bff4--,various ,readings4--,a very large number of surveyors design their own staff readings4 ,this was formerly very much the fashion1 consequently a great number of patterns come before the manufacturer4 ,the author for about twelve years kept a copy of what he considered the most meritorious of these patterns1 both for future reference and to judge of their comparative merits4 ,this was discontinued1 as it was found that the number of designs became a little perplexing1 and they were rather dangerous to show to a customer1 who often selected from its appearance a pattern which proved afterwards unsatisfactory in use4 #bfg4--,rogers ,field's and ,colonel ,strange's ,readings4--,the author made some experiments to obtain a clear staff1 readable beyond the ordinary range of staves with a #ad-;inch level2 but much more complete experiments were made with the author's set of patterns by ,mr4 ,rogers ,field1 ,c4,e41 whose ingenuity is well known4 ,this gentleman finally designed a staff which in the author's opinion is still one of the best1 but it has not generally pleased the profession3 this is illustrated1 ,figs4 #ig1 #ajj4 ,the author has tried it at all distances3 at #bj chains he has found a reading of #ja foot could be taken approximately with a good #ad-;inch level with his point index-stop level1 ,fig4 #ge4 ,the late ,colonel ,strange made a series of experiments with the author's patterns placed at #aj and #bj chains distance4 ,he also had for these experiments one of ,mr4 ,rogers ,field's staves4 ,he arrived at the conclusion1 for distant reading particularly1 that the black markings on all the twenty staff patterns he had were excessively heavy1 so that the lightest and most open readings were the clearest4 ,this led him to design a staff1 a part of which is shown in ,fig4 #aja1 which has been since generally used on the great ,india survey4 ,this staff somewhat resembles the ,english ordnance pattern4 ,the fault found with these patterns is that they do not read the #ja foot1 which is necessary for close reading in hilly districts1 otherwise they may be read very clearly at a distance of #bj chains1 where the ,sopwith becomes a blur4 ,we may take it that the surveyor1 if he be a fairly good draughtsman1 would subdivide the #je block to the #ja foot2 but it is argued that his assistant1 who might be a fair leveller1 might not4 ,another objection is that the reading is on one side and is not cut through by the horizontal web1 so that a white margin can be seen in the telescope on both sides of the vertical webs1 between which it is most pleasant and exact that the reading should be taken4 ,this objection does not1 however1 hold for the point reading1 ,fig4 #ge4 ,colonel ,strange's pattern has not been very generally accepted by civil engineers4 ,the author tried to meet the matter by making the block #je foot1 but so subdivided as to indicate #ja foot4 ,this has frequently been preferred to his dotted ,sopwith4 ,illustration3 ,fig4 #ajb4--;,details of ,stanley staff2 ,a bottom length1 ,b middle1 ,c top with dot figures4 #bfh4--,the author designed another staff especially for his point index4 ,this is shown above1 ,fig4 #ajb4 ,it has had a very fair popularity1 being good both for distant and near sighting4 ,in this staff for the close figures #aa1 #ab1 #ac1 on a #ad-;feet staff1 which are with great difficulty distinguishable at a distance1 the author employs dots only as before mentioned--one dot for the #aa1 two for the #ab1 and three for the #ac1 as shown ,c for the #ab and #ac in the right-hand figure4 ,it must be remembered that a good clear staff is a great desideratum1 as it means less size1 weight1 and cost in the level necessary to be used with it for equal exactness4 ,a clear staff with a #ad-;inch level is quite equal to a complex misty one with a #af-;inch level1 with the advantage of saving expense in the purchase1 and about #b lbs4 in the weight of the level to be carried in work4 #bfi4--,our space will not permit the discussion of the various staff readings that have been designed1 many of which are1 in the author's opinion1 superior to the ,sopwith2 but some variations are necessary occasionally for personal reasons4 ,some surveyors1 from imperfect colour vision perhaps1 strongly object to the red foot figure as being indistinct at a distance1 hence in many patterns a clear black figure is employed4 ,some get confused with the number of equal lines of #ja foot in the ,sopwith1 what is sometimes termed ,sopwith's ladder4 ,in this case these lines may be made unequal in different ways3 several patterns have this peculiarity4 ,some persons cannot get over the inverted figure as seen in the telescope4 ,in this case it would be much better1 perhaps1 to read with an erecting eye-piece to the level2 but practically the manufacturer has to invert the figures4 ,other less important variations are common4 #bgj4--,metrical ,staves4--,these are in this country generally made #ad feet1 to keep the length the same as the tripod4 ,the most approved patterns are shown ,figs4 #ajc and #ajc;,a4 ,in using the metre pattern at short distances often a complete metre cannot be taken in the field of view1 so that there is a little difficulty in being certain to what metre interspace the subdivisions belong4 ,to avoid this the author places a dot or dots after the decimetre figures that follow the metre--one dot for #a metre1 two dots for #b metres1 three dots for #c metres4 ,thus #ad metre reads #d2 #bd metre reads 3#d4 ,the dots need only be very small1 as they are not required except for very close readings1 that is1 within about #cj metres3 at #dj metres distance one complete metre comes into the ordinary telescopic field4 ,illustration3 ,fig4 #ajc4--,metres and ,half ,centimetres4 ,fig4 #ajc;,a4--,centimetres4 ,stanley's metre levelling staves4 #bga4--;,feet and ,inches ,staff4--,for building works1 drainage1 and some other cases1 the staff is divided into feet and inches1 and subdivided again into eighths or tenths of inches4 ,this is most convenient when the work has to be carried out with #e or #aj feet rods and the #b-;feet rule4 ,the intermediate inches between the feet are better marked #c1 #f1 #i only than fully figured4 ,for rough usage the author has made a solid #aj-;feet pine staff1 well painted4 ,this has a strong hinge in the centre1 and is kept stiff when open by a strong open hook4 ,it closes face to face in two parts1 which keeps the face clean4 ,this is important for dock and drainage works1 where the staff holder's hands in many cases necessarily get dirty by climbing2 otherwise it bears much more rough usage than the telescopic staff1 and is much cheaper to make4 ,fig4 #ajd4 ,illustration3 ,fig4 #ajd4--,stanley's rough levelling staff4 #bgb4--,mining ,staves4--,for levelling in mines1 large sewers1 and other cases were there is no height for the ordinary staff1 the ,sopwith staff is made in its closed form commonly #b feet #c inches and #c feet #c inches only in length1 to open out respectively #e feet and #h feet1 or in some few instances even shorter than these dimensions4 ,the mine staff is in every way1 except its length1 similar to the ordinary ,sopwith1 art4 #bei4 ,illustration3 ,fig4 #aje4--,stanley's patented mine staff4 #bgc4--,stanley's ,portable ,staff4--,the writer has made a portable staff in lengths of #ah inches1 somewhat like a ,french folding rule4 ,it may be formed of three1 four1 five1 or six lengths1 opening out respectively #d feet #f inches1 #f feet1 #g feet #f inches1 and #i feet4 ,the separate pieces are flat boards1 slightly sunk on the face to prevent the divisions being scratched in opening and closing1 but left solid at the joint ends4 ,the boards are attached together with a kind of rivet at each joint4 ,a strong spring at the end of each piece with a catch and notch keeps the length opened or closed with sufficient rigidity4#h ,the entire length of the staff when closed in #bj inches4 ,the same kind of staff forms a very useful builder's or drainage staff1 divided in this case in feet and inches2 and it is conveniently portable for carrying abroad4 ,fig4 #aje--;,e shows back view1 ,f front view1 ,g cross section1 ,a longitudinal section4 ,the holding springs are shown at ,,bb,b4 #bgd4--;,a portable mine staff designed by ,mr4 ,g4 ,j4 ,jee1#i is said to be a useful staff for colliery work4 ,it is constructed in three lengths1 sliding one into the other4 ,the bottom length of three feet is graduated in the ordinary way4 ,the top of this length has a band attached to it1 painted to continue the lower division of the staff upwards4 ,the other end of the band passes over a roller attached to the top division of the staff4 ,the roller contains a spring which keeps a constant tension on the band4 ,by extending the lengths of the staff and clamping them1 the staff may be lengthened out any distance to #i feet4 ,the weight of the staff is #e lbs4 #bge--,papering or ,repapering a ,sopwith ,staff4--,the staff1 if new1 is painted with three coats of rather flat1 thin white-lead paint on the face1 and left to season till the paint is quite hard4 ,it is then washed thoroughly with a sponge dipped in stout1 until this adheres without beading1 and is again left to dry4 ,for repapering an old staff1 this is soaked with hot water in which there is some washing soda1 and rubbed until the old paper is brought off4 ,after the staff is in either of the states described above1 it has to be made warm and coated with one or two coats of size4 ,the size may be made of a piece of glue left in water for a night1 and then melted in a jam-pot placed in a saucepan of water over a slow fire4 ,when the staff is sized and dry1 if ordinary papers be used1 it has to be divided carefully into foot lengths1 which are marked with a set square in pencil across the face of the staff4 ,the foot lengths may be set off accurately from an engine-divided chain scale1 or by beam compasses4 ,the papers1 which are printed short1 are then pasted over1 preferably with paste made of starch with boiling water1 but not afterwards boiled4 ,as the lengths of paper are pasted they are laid aside1 pasted side upon pasted side1 to thoroughly absorb the paste for a few minutes1 the time varying according to the increased length required above that of the original printed paper4 ,while still wet1 the upper paper of the two is lifted up and cut with scissors1 at the same time fitting to the boundary lines4 ,this wet cutting ensures the paste being equally distributed quite up to the edges4 ,the foot length of pasted paper is then laid by setting the upper edge exact to the upper foot line1 and gradually bringing the paper down from this by dabbing with a clean cloth or straight hat-brush4 ,if the paper does not reach the foot mark when laid1 it is again lifted1 and a little more pressure used in laying it the second time1 which will lengthen it out as required4 ,other lengths are laid in the same manner4 ,the skilled workman requires no lap to the joins of the papers1 but brings them up edge to edge2 with the amateur a lap of #a_/h inch is advisable4 ,to avoid the trouble of marking off and stretching each foot1 the author has introduced jointless levelling staff papers1 so that the entire length of each section may be put on in one piece4 ,these are of special paper1 and it is only necessary to paste the face of the staff well and smoothly1 and lay the paper unpasted down in position upon it4 ,after the papers are thoroughly dry they require two coats of thin isinglass size1 and then a coat or two of varnish4 ,paper varnish can be bought2 but in defect a varnish may be made of ,canada balsam dissolved in oil of turpentine4 ,this should be laid on with a flat bristle brush 7varnish brush71 and set in a warm room to dry for a day or two4 #bgf4--,preservation of the ,levelling ,staff in ,use4--,where two staves are used they may be placed face to face for carrying1 and be strapped together1 and will take little harm with moderate care4 ,where one only is used it is generally strapped to the tripod4 ,a strip of wood is sometimes used to protect the face of the staff4 ,illustration3 ,fig4 #ajf4--,pad for holding a staff and tripod4 #bgg4--;,for carrying the staff with the tripod1 a convenient plan is to have two pads formed of stout ox-hide butt1 each pierced with two slots near their ends at the exact distance apart of the width of the staff1 ,fig4 #ajf4 ,the strap of calf leather is passed from one slot round the staff into the other slot1 and then passed round the tripod and pulled up tightly and buckled4 ,the pad of course protects the front of the staff from grazing by the friction of the tripod against it4 ,there is a certain amount of risk1 under any circumstances1 of the cylindrical tripod pressing against the front of the staff and splitting it4 ,to avoid this the author has lately made the pads with a mahogany bridge piece1 so that the pressure is distributed1 coming upon the edges of the front where the staff is strongest to resist it4 ,this is shown1 ,fig4 #ajg4 #bgh4--;,for the entire protection of the staff a leather-bound sailcloth case is very generally used4 ,this may be divided into two compartments for the staff and the tripod1 with pads between4 ,the whole case has a neat appearance1 and forms a protection from slight bruises and dirt1 either in travelling or when set up in an office corner for future use4 ,illustration3 ,fig4 #ajg4--;,improved pad for staff and tripod4 #bgi--,repairing ,figures and ,divisions4--,surveyors going abroad will find it very convenient to have a few tubes of artist's oil colours--white1 black1 and vermilion1 with one or two sable brushes to touch up any divisions or figures upon the staves that have become accidentally injured or worn off by friction4 ,a tube of medium is also useful1 which will cause the colour to dry quickly and leave it bright4 ,the tubes of colour will keep any number of years if the caps are carefully replaced4 ,the brushes after use should be well washed with soap and hot water1 rubbing the soap in quite thickly till they are quite clean1 and then well rinsed before putting them by4 ,illustration3 ,fig4 #ajh4--;,iron triangle to support a staff4 #bhj4--;,iron ,triangle4--,for use of the staff in the field1 particularly in open grass or moist lands1 a triangular plate of iron1 as represented ,fig4 #ajh1 is very useful4 ,this is trodden down firmly by the staff holder before he places the staff upon it4 ,in use it gives a certain base to turn the staff upon from fore to back sight4 ,it is very inexpensive4 #bha4--,staff ,level4--,this is a small circular level1 shown at ,fig4 #aji1 the upper surface of which is formed of a glass worked slightly concave and fixed into a short cylindrical box4 ,the glass is hermetically sealed after being nearly filled with spirit4 ,the circular level is mounted on a plate with a dovetail fitting which fits in a slot in the holding plate attached to the back of the staff4 ,in use the staff holder has to observe when the bubble under the concave glass is in its centre4 ,a very little practice is required to hold the staff vertically by means of this little contrivance1 which only weighs1 about #b oz4 ,illustration3 ,fig4 #aji4--,staff level1 scale4 ,illustration3 ,fig4 #aaj4--,staff-holder1 #a_/aj scale4 #bhb4--,staff-holder4--,this implement1 shown ,fig4 #aaj1 striding a staff1 is very generally used in ,germany and other parts of the ,continent4 ,the staff is sunk into one side of a hardwood block4 ,the block is turned at one end to form a handle4 ,a second similar handle is cut with a strong screw and screwed into the end of the block4 ,this screw handle by turning brings up a following piece1 shown inside next the staff1 which is covered with leather4 ,when it is screwed up1 the staff may be held firmly by the handles only1 without the risk of the fingers coming in front4 ,with this accessory it is also held more easily and truly vertical4 ,it is a comfort in use in cold weather4 #bhc4--,practice of ,levelling with the ,staff4--,this subject can be followed here only so far as to exemplify the uses of the instruments and of accessories connected with such instruments4 ,for practical levelling we have the standard original works of ,simms1 ,ainsley1 and others1 with many modern works4#aj #bhd4--;,for ,holding the ,staff1 ,mr4 ,holloway1 in the work referred to in the last note1 gives instructions in such concise form that they may be quoted with advantage4 ,he says3--,i generally enter into confidential chat with my staff holder1 in which ,i explain to him the vast importance of his duties1 i4e41 ,i endeavour to make him a man of importance in his way1 and ,i never fail to get those duties properly performed4 ,my instructions to him are seven in number3-- #a4 ,draw out the slides of the staff1 and be sure the joints are properly locked4 ,draw out one length only unless signalled to do otherwise4 #b4 ,when the staff is once on a point never move it unless signalled to do so4 #c4 ,examine the staff regularly before setting it down to see that no dirt is sticking to the bottom of it4 #d4 ,always stand erect behind the staff1 so that the figures face the level4 #e4 ,do not let any part of the hand come before the face of the staff4 #f4 ,in no case put a downward pressure on the staff4 #g4 ,if the grass be long1 mossy1 or spongy1 tread it down1 so that the staff shall have a firm footing--select a firm spot if the selection is left to yourself4#aa #bhe4--,the manner of setting up a level has been already described in the previous chapter4 ,the leveller generally follows a definite track which he has previously arranged and marked out on a map4 ,the distances apart for placing the staves or staff are measured by the chain1 or by the subtense system to be fully described hereafter4 ,where the levelling is very important1 as for canal work1 topographical survey1 etc41 wooden pegs are driven down at the measured stations where the staff is to be placed from which the levels are to be taken4 ,a general rule followed1 as far as practicable1 for starting is to select an easily recognised1 permanent1 solid station for first placing of the staff--a mile-stone1 large boulder1 or other solid object answers3 a datum line is generally assumed to be at a certain depth below this1 to which all levels are referred4 ,from this station1 if the ground be fairly level1 #e chains is the ordinary advanced position where the level is set up and the first staff reading taken4 ,the level is set up at the measured distance from the staff1 which is indicated by a mark left by the chainman4 ,illustration3 ,fig4 #aaa4--,level height tape4 #bhf4--,occasionally in town surveys the height of the level has to be taken4 ,for this a small steel spring pocket tape is used to take the height of the axis of the telescope1 ,fig4 #aaa4 ,the tape may be adjusted by taking a piece off the first end1 and allowing for the width of the tape case1 so that by placing the ring of the tape upon the hook under the instrument and bringing the case just to the ground1 the height of the axis of the telescope above the ground may be read off at the point where the tape leaves its case4 #bhg4--,the ,reading of the ,staff4--,the first position1 which is afterwards termed the back reading1 is taken at a distance behind the first forward position of the level4 ,this is recorded exactly as it appears in the telescope1 the height of the telescope being also noted in the levelling book1 to be described4 ,thus in ,fig4 #aab1 ,s the first staff2 ,l the first station for taking levels4 ,the fore reading ,l to ,s reads to a higher part of the staff ,s2 ,l next level station back sight4 ,l,s reads high on the staff ,s2 fore sight ,l,s reads low2 back sight ,l,s again low1 following the contour2 fore sight ,l,s low2 thus giving data in the levelling book from which the contour can be plotted from the datum line1 which is taken low to make all readings plus4 ,illustration3 ,fig4 #aab4--,practice of levelling4 #bhh4--,the staff reading1 as already described1 is divided into feet1 with two places of decimals4 ,the safest method of taking this reading is to take the second decimal place first and then record it1 then the first decimal1 and finally the foot4 ,in this manner no effort of memory is required1 and the staff being sighted three times assures the certainty of the reading4 ,the telescope should not be touched during the operation1 so that the reading in this manner is only a cautious transfer4 #bhi4--;,if two staves are used on fairly level ground1 the second staff is now advanced #e chains from the level to a measured station1 the staff holder here sighting the line through the level to the back staff1 and firmly treading down the staff plate if the land is soft or grass1 or otherwise requires it1 or an iron triangle is used4 ,when time is given to hold the staff vertically by means of the staff level1 the reading is taken in this position by the leveller as before1 and this is recorded in the levelling book4 ,the level is now moved forward #aj chains1 that is1 #e chains ahead of the forward staff4 ,the staff is carefully turned half round without pressure upon its standing place or plate to face the level as now placed1 in which position it is then read off by the level as the back sight1 the back staff now being moved #e chains forward of the level1 and so on alternately staff and level until the distance required to be levelled is completed1 if there is no obstruction which causes another method of procedure to be adopted4 ,a similar plan is pursued with a single staff2 but care has to be taken in securing the right line of march1 which will be by placing the staff in a sight line through the level with a fixed landmark instead of the back staff mentioned4 #bij4--,the equal back and fore sights as far as practicable are insisted upon by all levellers1 as by this means any inaccuracy in the level1 if the run of the bubble is kept constantly true1 is thereby compensated2 but it is not always convenient1 and when it is not the accuracy of the work must depend largely upon the qualities of the level4 ,it is not necessary or convenient at all times to take the back and fore sight in a line--obstructions of woods1 rivers1 etc41 may occur4 ,in these cases very often what is quite equivalent may be done by taking equal angular back and fore sights from the apex of an equilateral triangle thus3--,say an obstruction occurs for the chain by a pond or wood1 but that both points to which the levels are to be taken are visible at some lateral position4 ,levels may be taken from this place1 and if the intermediate point of distance is equal from both stations there will be no instrumental error4 ,thus1 suppose the direct level line east 7#ij71 and that the two stations can be seen and the staves read at #aej and #baj2 here1 evidently1 this is equivalent to a direct back and fore sight1 the right angle to the level course being #ahj--the one station is #aej #ahj - #cj1 and the other #baj #ahj #cj4 ,if these equal angles can be even approximated with a fairly good level the error will be small4 ,in this manner intermediate and extended points may often be conveniently taken by previous arrangement with a good staff holder4 ,it is in this angular levelling that the greatest use of the compass is found to give the angles1 to make entries of the work in the levelling book4 #bia4--;,in levelling hilly ground great loss of time would sometimes be incurred from taking equal back and fore sights2 the best plan in this case is to make as much use as possible of the length of the staff in use4 ,it is in hilly districts only that a staff longer than #ad feet is advantageous4 ,with any staff in descending a hill only #e feet of the staff can be used for the back sight1 that is1 a part of it equal to the height of the level1 and sometimes #d feet or less if there is grass1 brambles1 or other obstruction4 ,whereas for the foresight all the staff upwards of the height of the level1 that is1 about #i feet in a #ad-;feet staff1 can be used with certainty4 ,the distance of setting up of the levels and staves must in this case entirely depend upon the length of the staff and other conditions present4 #bib4--;,for near reading of the staff on sharp inclines1 reading to two places of decimals is not near enough1 as errors may accumulate rapidly4 ,it is in such cases that a fully divided staff is best4 ,the divisions upon a near staff appear in the telescope much magnified2 and three places of decimals may easily be taken by anyone used to reading a chain scale1 particularly if a point diaphragm be used4 ,through valleys the level may be often checked at some point from hill to hill by a back sight3 the contour must nevertheless be followed for the section4 ,it is in these shorter unequal ranges and in distant sights that accuracy in the level is demanded2 and it becomes interesting to know how nearly this may be depended upon for such readings4 #bic4--;,as already mentioned1 a sensitive #ad-;inch level of ,y construction1 or a dumpy in perfect adjustment supported on the tribrach system1 will work with a level tube divided to read #e seconds in divisions #a_/bj inch apart4 ,there will be a little personal error in reading the bubble from difference of reflection1 according to the direction of the light from the two ends of the bubble1 as before discussed2 but the bubble may be assumed to be read within less than half a division1 that is1 within #b seconds--say #b seconds4 ,a distinct staff may be read with a good glass within #a foot at one mile4 ,a second of arc subtends #jbeeih of a foot approximately #c inch at a mile distance4 ,therefore a back reading at this distance can be taken within an inch or so of allowance for instrumental errors4 ,a reading taken in this way at a mile distance would require a plus allowance for curvature of the earth of #h inches1 minus say #a inch for refraction #g inches4 ,from these data we can get a fair check level for hilly ground1 possibly more accurate than by contour levelling for a distant station1 even if we allow double the probable error1 say #a foot for error of reading the staff at a mile distance4 ,illustration3 ,fig4 #aac4--;,calder stove used as a lamp4 #bid4--,lamp4--,at heights between hills in wide valleys check levels may be taken from five to ten miles very well with a good #ad-;inch level in still clear weather in dark nights by the use of an oil lamp4 ,coincident points above datum being selected1 the lamp is set upon the ground1 or at a measured height at a calculated point1 or raised or lowered to lantern signals1 allowance being made for curvature and refraction4 ,the wide band of light is read very easily by shifting the observer's position and raising or lowering his tripod4 ,the ,calder lamp stove answers very well as a lamp4 ,it has a wick about #c inches wide1 and by means of a masked chimney may be made to present a clear white line of light of #a inch in depth1 ,fig4 #aac4 ,the heliostat is sometimes used for check levelling in sunlight4 ,this will be described further on with the theodolite4 #bie4--;,curvature ,corrections of the earth and of ,refraction to be made use of occasionally for check levelling4 ,the rule for finding curvature is ,that the difference between true and apparent level is equal to the square of the distance between two places or stations in miles--divided by the earth's mean diameter1 #giaf miles2 consequently1 by this rule the correction is always proportional to the squares of the distances4 ,by proportioning the excesses of height to the squares of the distances1 we may obtain a curvature table for corrections4 ,this is1 however1 always in excess of the true curvature by the refraction caused by the increase of density of the air towards the earth's surface1 which bends the visual ray4 ,the curvature of the earth may be corrected for refraction one-fifth to one-sixth1#ab which varies according to the atmospheric pressure4 #bif4--,the following table1 which takes curvature minus refraction1 will be found useful to have at hand3 it may be written out and pasted inside the lid of the level case3-- ,table of ,differences of ,apparent and ,true ,level for ,distances in ,chains4 ,distances in ,curvature minus ,distances in ,curvature minus ,chains4 ,refraction in ,chains4 ,refraction in ,dec4 ,ft4 ,dec4 ,ft4 #a #jjjjhi #ad #jage #b #jjjceh #ag #jbeh #c #jjjhjd #bj #jceg #d #jjadce #bb #je #e #jjbbcc #bd #jf #f #jjcbaf #bf #jg #g #jjdcg #bh #jh #h #jjeg #cj #ji #i #jjgb #dj #ad #aj #jhi #fj #ca #aa #jaa #hj #ef ,where great precision in levelling is required1 as for important trigonometrical surveys1 many precautions are required to be taken which would be quite superfluous1 for instance1 in railway work4 ,thus much greater exactness and freedom from personal error is secured by having two levellers to go over the same ground simultaneously4 ,errors by two persons in the same part of the track are very unlikely to occur1 and by comparing books every part may be checked4 #big4--,pegs4--,where the work is to be entirely pegged for chain measurements1 the pegs may be made of natural sticks sawn off and pointed up with a bill hook4 ,if they are sawn from timber they are generally made about #i inches long and sawn to a point1 the head being full #b inches by #b inches4 ,where great precision is required a cast-brass or iron nail is driven into the head after the peg itself is driven down4 ,this is used to turn the staff upon1 ,fig4 #aad4 ,a the peg shown with a nail in its head1 #a_/h size4 ,b nail about full size4 ,illustration3 ,fig4 #aad4--;,a1 staff pegs of sawn timber1 #a_/h scale2 ,b1 nail1 full size4 #bih4--;,it is considered a precaution with an ordinary level to mark one leg of the tripod and always place this in the same position to the staff4 ,thus1 if the marked leg is placed to the forward staff at first1 it is put at the next station backward to the back staff4 ,this corrects any general error from defective work in the instrument and want of adjustment2 and if the staves are placed at equal stations any instrumental defect whatever1 to act cumulatively upon a distant station1 is then prevented1 as this principle produces an alternate plus and minus error4 #bii4--;,differences of true level have been found between working southward towards the sun from working northward from it1 which are caused by the expansion of the instrument and bubble tube upon the side heated by his rays4 ,these matters of higher refinement may be followed in some of our best works on levelling4 ,most excellent instructions in this matter will be found in the appendix of ,a ,manual of ,surveying for ,india1#ac in a paper by ,colonel ,j4 ,t4 ,walker1 ,r4,e41 ,f4,r4,s41 etc41 of the great ,trigonometrical ,survey of ,india1 wherein levels have been carried across from ocean to ocean for over #aejj miles of land surface4 #cjj4--,levelling ,books which record the levels as they are taken are considerably varied in form1 much influenced1 no doubt1 by the method pursued by the civil engineer for the execution of his work4 ,the illustration1 ,fig4 #aae1 shows the most general forms1 but there are many others4 #cja4--;,entries are very generally made in levelling books in black lead4 ,faber's artists' pencils1 which require no cutting1 are very generally used1 ,no4 #b being black and moderately hard4 ,it is very convenient to carry a small file for sharpening the lead frequently4 ,in the author's surveyor's knife1 described further on1 a file forms one of the blades4 #cjb4--,where it is desirable to make the original levelling book readings permanent for reference or otherwise1 they are very commonly written in ink1 ,morrell's registration ink being very generally used1 or the author's drawing ink answers2 this being permanent is not liable to corrode the pen1 nor permit the writing to be effaced in any degree by moisture4 ,illustration3 ,fig4 #aae4--,specimens of levelling books1 #a_/c scale4 ,ordinary ,level ,book with columns for ,no41 ,back ,sight1 ,intermediate1 ,rise1 ,fall1 ,reduced ,level1 ,distance1 ,remarks4 ,collimation ,level ,book1 with columns for ,back ,sight1 ,intermediate1 ,fore ,sight1 ,height of ,collimation1 ,reduced ,level1 ,distance1 ,remarks4 ,railway ,engineers' ,level ,book1 ruled for ,back1 ,intermediate1 ,fore ,sight1 ,rise1 ,fall1 ,distance1 ,reduced ,level1 ,formation ,levels1 ,cutting1 ,embankment1 ,remarks4 ,tacheometer ,survey ,book1 ruled as above illustration4 ,traverse ,survey ,book1 ruled as above illustration4 #cjc4--,the ,ink ,bottle mostly used is that known as the excise bottle4 ,this is of a smooth1 oval form1 covered with black leather1 with a tab and buttonhole to hang upon a button of the coat1 ,fig4 #aaf4 ,one of the numerous fountain pens is now generally used instead of the bottle described4 ,illustration3 ,fig4 #aaf4--;,excise ink bottle4 ,,footnotes3 #g ,brit4 ,assoc4 ,report1 #ahch1 p4 #aed4 #h ,patent ,no4 #abeij1 #ahhi4 #i ,colliery ,guardian1 vol4 xxxviii4 p4 #egf1 #ahgi4 #aj ,a ,treatise of the ,principles and ,practice of ,levelling1 by ,f4 ,w4 ,simms1 #ahdb2 ,a ,treatise on ,land ,surveying1 by ,john ,ainsley1 revised by ,william ,galbraith1 #ahdi4 ,quite modern works--,aid to ,survey ,practice1 ,l4 ,d',a4 ,jackson1 ,crosby ,lockwood1 #aiaj2 ,on ,levelling and its ,general ,application1 by ,thomas ,holloway1 ,spon1 #ahhg2 revised #aiad4 #aa ,levelling1 p4 #di4 #ab ,deschanel's ,natural ,philosophy1 by ,prof4 ,everett1 p4 #ajah1 #ahgf4 #ac ,a ,manual of ,surveying for ,india1 by ,colonel ,h4 ,l4 ,thuillier1 ,c4,s4,i41 ,f4,r4,s41 etc41 and ,lieutenant-,colonel ,r4 ,smith4 ,thacker1 ,calcutta1 #ahge4 7,now out of print74 ,,chapter ,,vi4 ,,division ,,of ,,the ,,circle ,,and ,,methods ,,employed ,,in ,,taking ,,angles--,,dividing ,,engine--,,surfaces ,,for ,,graduation--,,vernier--,,various ,,sections--,,reading ,,microscopes--,,shades--,,micrometers-- ,,clamp ,,and ,,tangent ,,motions--,,of ,,limbs--,,of ,,axes--,,use ,,and ,,wear--,,difference ,,of ,,hypotenuse ,,and ,,base4 #cjd4--;,division of the ,circle4--,sexagesimal ,division4--,all true surveying instruments depend1 as their special function1 upon taking the direction1 or angular position1 of surrounding objects or definite parts of the surface of the earth from positions which are at first accurately measured or ascertained4 ,the instruments required for such work must possess an accurately divided circle or arc1 with means of subdividing the visible divisions of this to greater closeness than any possible method of drawing lines simply would permit4 ,the lines upon the circle in general practice in ,great ,britain are divided into degrees1 which are subdivided to #cj1 #bj1 #aj1 or #e minutes1 according to the size of the instrument1 and arranged for further subdivisions by means of a vernier into minutes or #cj1 #bj1 or #aj seconds of arc4 ,upon large circles1 say of #aj and #ab inches diameter1 and with modern #e1 #f1 and #h inch diameters1 angular displacements in the direction of the telescope are ultimately read off with a microscope by means of a screw with divided head1 termed a micrometer1 placed tangentially to the divided circle2 or by a series of lines placed at equal distances apart in front of an eye-piece or within a microscope2 but in the ordinary portable instruments1 or those that a surveyor can personally carry about the country1 the ultimate subdivisions of the circle are still generally made by a vernier scale only1 which will presently be described1 although the smaller modern micrometer reading instruments are slowly but surely coming into favour for all high class work4 #cje4--;,centesimal ,division4--,ten to fifteen years ago on the ,continent generally1 and in ,america occasionally1 the division of the circle into #djj-;grades and -grades1 and the subdivision of these decimally to centigrades1 appeared to be coming more and more into use1 particularly with the more extended use of the tacheometer4 ,under this system it will be seen that the right angle subtends #ajj grades4 ,this division1 with its centesimal parts1 was found to blend conveniently with logarithmetical calculation and to permit the free use of the slide rule with great saving of time over ordinary calculation1 but it is now very little used4 ,the decimal division of the ordinary degree of #ij to the quadrant greatly facilitates the calculation compared with what is necessary with the sexagesimal division into minutes and seconds1 and the reading of the verniers is much simpler and less liable to errors2 moreover1 the mental conversion of the sexagesimal division into decimals of the same degrees is much simpler than the conversion into the centesimal degrees of #ajj to the quadrant4 #cjf4--;,dividing ,engine4--,this important tool is used for cutting the graduations on all surveying instruments4 ,if possible a position should be secured for it on a ground floor at a mile or more distance from any railway1 and at a good distance from roads upon which there is heavy traffic1 as small vibrations are sufficient to cause unpleasant working and some error in the division of large instruments4 ,for very accurate work some makers divide at night for the sake of stillness4 ,the principles of construction of this machine1 as at present in general use1 were invented by ,jesse ,ramsden1 of which an account was printed by the ,board of ,longitude in #aggg4 ,refinements of detail have been added to the invention1 and the steady action of steam or electric power has been applied in place of the foot1 but otherwise the machine remains practically the same4 ,therefore a brief description of this machine as originally invented will be sufficient for the purposes of this work1 which is not intended to fully describe the tools used in the manufacture of instruments4 #cjg4--,ramsden's ,engine consists of a circular brass surface plate1 made generally of #cf inches diameter4 ,this plate is supported from below upon a hollow vertical axis1 which moves in an adjustable collar placed at its upper end and in a conical point or pivot at its base4 ,the pivot rests in a cup of oil and supports the weight of the plate and axis1 so that this part rotates with little friction4 ,the outer edge of the surface plate is cut with #bafj teeth or threads1 into which an endless or tangent screw works1 so that the plate can be revolved any desired quantity by means of the screw4 ,six turns of the tangent screw moves the plate #a4 ,the head of the tangent screw is divided as a micrometer into #fj parts2 therefore the movement of one of the divisions of this head revolves the plate #aj of an arc4 ,a ratchet wheel of #fj teeth is attached to the tangent screw1 and so arranged that by reciprocating motion applied to a rack which works into it the circle can be advanced any multiple of #aj4 ,motion is given to the tangent screw by a catgut over a pulley worked by the foot4 ,the work is centred and clamped down upon the surface plate4 ,while the divisions are being cut this surface plate remains for the time quite stationary4 #cjh4--,the dividing knife is attached to a swinging frame having a reciprocating motion4 ,the forward extent of its swing is regulated by a detent wheel with teeth of varied heights1 which1 as they are brought by the mechanism consecutively forward1 stop the knife at a definite position2 so that the cuts upon the circle--technically the limb--are regulated for lengths to represent #aj degrees1 #e degrees1 degrees and parts4 ,in the use of this dividing machine the divider who worked it had alternately to press his foot upon a treadle and then pull a cord attached to the dividing knife frame4 ,these motions are now performed by self-acting mechanism4 ,for full particulars and details of the dividing engine see ,troughton's ,memoir1 ,phil4 ,trans41 #ahji3 ,memoirs of the ,royal ,astronomical ,soc41 vol4 v4 p4 #cbe2 vol4 viii4 p4 #ada2 vol4 ix4 pp4 #ag and #ce4 ,for various plans that have been tried see ,holtzapffel's ,turning and ,mechanical ,manipulation1 pp4 #fea-iee4 #cji4--,the ,material upon which the limb or circle of an instrument is divided is almost uniformly of silver1 except for mining survey instruments1 which need a very strong cut4 ,silver being dense and of extremely fine crystallisation1 or grain1 as it is technically termed1 bears a uniform smooth cut with sharp outline4 ,occasionally circles or arcs are divided on platinum1 certainly the best metal1 as it keeps constantly clean2 but it is expensive4 ,the verniers are then made either of this metal or of gold4 ,the silver of the circle1 when this metal is employed1 is rolled down from a surfaced cast plate of about #be inch in thickness to about #jde inch1 by means of which it becomes uniformly dense and fine grained4 ,in all cases possible1 that is1 upon all flat internal surfaces1 the silver is placed in an undercut groove and planished down to fill the groove without any other fixing being necessary4 ,this plan of insertion is employed for all vertical circles--the horizontal circle of ,everest's theodolite1 limbs of sextants1 box sextants1 etc4 ,in ,fig4 #aag the silver is shown at ,a1 in the section to which it is drawn by a plate after it is cut in slips4 ,it is shown placed in its groove ,b ready for planishing down4 ,by this method certainty of dense surface is obtained for the future division4 #caj4--,upon bevelled edges and outer surfaces the rolled silver is planished to form1 and then soldered to the metal of the part of the instrument to be divided4 ,the surface1 after being made as dense as possible by planishing or otherwise is turned to form and stoned to surface ready for the dividing knife4 ,illustration3 ,fig4 #aag4--;,insertion of silver in circle4 #caa4--;,graduating4--,the object aimed at by the skilful divider is to obtain as deep a sharp-edged cut as possible1 which shall be at the same time as fine as it can be read clearly by the microscope with which it is to be used4 ,this matter is most important to the possessor of the instrument afterwards for use1 as in the atmosphere the silver soon forms an oxide and a sulphuret upon its surface which has to be cleaned off2 and at every cleaning a portion of the silver is necessarily removed1 so that in old or badly divided instruments the divisions become dull or lost from this reason4 ,illustration3 ,fig4 #aah4--,piece of charcoal4 #cab4--;,after the instrument is divided it is engraved with figures and stoned off with fine blue-stone1 and finally finished with willow or pearwood charcoal1 which has just sufficient cut in it to leave a hard edge to the division lines4 #cac4--;,it may be useful to the surveyor1 far from aid of the optician1 to know that divisions on silver which are much oxidised may be brought up to sharp lines by the use of a piece of fine-grained charcoal1 sharpened by a clean file to a chisel point4 ,this should be frequently dipped in water1 and rubbed lightly with the flat of its end surface1 ,fig4 #aah1 keeping the motion of the hand in the direction of the circumference of the circle4 ,the piece of charcoal before being used should be first tried upon a piece of plain1 smooth metal--an old coin which is worn smooth will do--to see that it is not scratchy4 ,no kind of polishing powder should in any case be used for cleaning limbs or verniers1 as this is sure to rub down the edges of the cuts and thereby ruin the divisions of the instrument4 #cad4--;,it must be understood that the above directions are not intended for the ordinary cleaning of the circle for an instrument in general use1 as such would be injurious to it4 ,in the ordinary daily use of the circle1 if it is not in any case touched by the hand1 and is kept carefully brushed with a large1 soft camel-hair brush when taken from the case1 and the same when returned to it1 it will keep a long time in an excellent state4 ,if the circle is slightly tarnished1 this tarnish may be removed by a piece of quite clean wash leather2 but the brush is always the safest if sufficient4 ,if the vernier gets grubby against the circle1 a piece of clean thin writing-paper may be passed between these parts1 which will clear out any dirt or grit there may be between sufficiently4 #cae4--,the ,vernier ,reading ,index4--,this is one of the most important inventions ever applied to instruments of precision for measuring upon the circumference of the circle4 ,it was invented or brought into practical use by ,pierre ,vernier1 a native of ,ornans1 near ,besanon1 in ,burgundy4 ,the first publication of the invention appears in a pamphlet published in ,brussels in #afca1 ,construction1 ,usage1 et ,proprietes du ,quadrant ,nouveau de ,mathematique4 ,this invention was possibly foreshadowed1 as it is mentioned by ,cristopher ,clavius in his ,opera ,mathematica1 #afab1 vol4 ii4 p4 #e1 and vol4 iii4 p4 #aj2 but he did not propose to attach it permanently to read into an arc1 that is1 to place it in its practical form4 #caf4--,the value of the vernier as a means of reading small quantities depends upon the fact that the eye cannot separate lines1 drawn at equal distance apart1 of above a certain degree of closeness1 there being a point for all vision where such lines appear to mix with the ground upon which they are drawn and form a tint2 therefore1 an index reading into such close lines would be1 unless under extreme magnification1 most indefinite2 whereas the eye can see a single separate line clearly and detect any break in it4 ,the vernier for reading subdivisions depends upon the functions of the eye having power to detect any break in an otherwise straight line1 so that a line that appears without a break may be taken as the index of reading from among others that appear broken or separated4 ,it is found in practice that a line as fine as it can be clearly seen will appear broken in its continuity with another equally fine line1 if at the meeting the rectilinear displacement is as much as #be to #b part of the width of the line4 ,it therefore follows that we may read closer by displacement of parts of a single line than by any possible series of lines that can be drawn in spaces apart upon a surface2 so that if we can arrange lines in such a manner that they open out or separate into distinct lines to admit of this principle1 we obtain the full value of the unbroken single line reading1 and this is the principal aim of the vernier4 #cag4--,on the same principle that we can find the straight or most direct line of a series of lines to take as our index1 we can also estimate the amount of the displacement of our selected line1 if this does not read perfectly straight from the vernier division to the circle division4 ,this small difference is detected in practice by many experienced surveyors1 so that a vernier reading nominally to minutes only is recorded n #ae1 #cj or #de1 that is to #ae4 ,there is no doubt that this will be approximate1 but it may be much nearer than the even minutes1 say to the #cj on a #e-;inch1 or the #ae on a #f-;inch sharply divided circle4 ,illustration3 ,fig4 #aai4--,origin of vernier scale4 #cah4--,the ,vernier ,scale1 as employed by ,vernier1 was divided to read minutes upon a circle or limb divided to half degrees1 by taking thirty-one divisions of the scale and dividing these in thirty equal parts for a separate scale to read against it4 ,this plan is now termed an inverse reading1 the reading being the reverse to the direction of that of the arc4 ,in modern practice the vernier to read minutes is divided to the length of #bi half degrees1 and this length is subdivided into thirty equal parts3 consequently1 where the vernier and scale are placed edge to edge or reading to reading1 every division of the vernier advances consecutively on the scale one-thirtieth of the half degree1 that is #a of arc on the scale divided to half degrees4 ,in the above diagram1 ,fig4 #aai represents the scale and vernier at the position from which the description is taken1 wherein the vernier is shown to cover #bi half degrees or #ad #cj1 and this length is divided into thirty parts4 ,the consecutive advance of the vernier on the scale is shown #a for each half degree4 ,in this position of the vernier1 or at a similar position in relation to any other half degree of the circle the arrow placed at the zero of the vernier reads direct into the degree or half degree1 so that this reading must be n or n #cj at any equivalent position in relation to any line on the limb4 ,illustration3 ,fig4 #abj4--,vernier scale1 reading #bc #ab4 #cai4--;,in ,fig4 #abj the arrow upon the vernier scale is shown reading at a position beyond #bc1 which we then know must be #bc n4 ,now1 if we look along the vernier1 the lines of this and the scale appear coincident at the twelfth division of the vernier2 consequently1 the n is #ab1 and the reading is altogether #bc #ab4 #cbj4--,learning the reading of the vernier is very similar to that of the clock1 wherein a child at first gets confused by the difference of value of the minute hand and the hour hand4 ,in the case of the vernier we have only to get clearly in our minds that the degree reading and the vernier reading are quite distinct processes1 in which the vernier reads minutes only1 and this by coincidence of lines only1 and that it has nothing to do with degrees1 which are indicated by the arrow only4 ,the arrow may be assumed to be placed on the vernier scale to save an unnecessary line of division2 but this practically might just as well be placed quite outside of it1 as it has nothing whatever to do with the vernier reading4 ,illustration3 ,fig4 #aba4--,vernier scale1 reading1 #bc #dg4 #cba4--;,it is important to make this matter of reading the vernier clear2 therefore in ,fig4 #aba the index arrow and vernier are shown reading past a half degree4 ,at this position the arrow reads #bccj on the limb the vernier1 or #bc #cj n of the vernier reading4 ,we find the coincident line of the vernier with the limb is at #ag1 therefore the reading is #bc #cj #ag or #bc #dg4 #cbb4--,the principle of the vernier1 upon which it takes its reading from the coincidence of lines1 as just stated1 points out that the figuring of values of points of coincidence may be varied at discretion1 and the zero index may be in any convenient position4 ,the above described is the common reading to the theodolite and many other instruments4 ,in mining dials and some other instruments the zero is placed in the centre4 ,we may1 for example1 take a central reading with a vernier reading to #c1 wherein the circle being divided into degrees2 the vernier is then1 necessarily1 in the direct method1 divided into twenty divisions 7#bj #c #fj7 which correspond with nineteen degree marks of the circle4 ,with a central reading the vernier in this case is figured #cj1 #de1 #j1 #ae1 #cj4 ,this is rather a simple reading1 as the zero to which an arrow is attached gives the true bearing1 and it is readily seen to which degree it refers4 ,illustration3 ,fig4 #abb4--,vernier reading centrally to #c4 ,illustration3 ,fig4 #abc4 ,in ,fig4 #abb the #de of the vernier is coincident with a line of the limb1 this must1 therefore be #de2 and as the index arrow is past #dd1 it is #dd #de4 ,if the vernier had read the division next past the #de1 the division being to #c1 this reading would have been #dd #de #c #dd #dh4 ,the same principles may be applied to any subdivision4 ,circles are commonly divided by the vernier in various ways to give readings from #e to #e4 ,theodolites reading to #cj seconds are usually divided degrees and thirds of degrees on the circle and minutes and halves on the vernier1 as illustrated 7,fig4 #abc71 the reading in this case being #aec degrees #dj minutes on the circle and #h minutes #cj seconds on the vernier1 giving a total reading of #aec #dh #cj4 ,a #bj second reading usually has divisions of #bj minutes on the circles and these are subdivided into minutes and thirds by means of the vernier4 ,illustration3 ,fig4 #abd4 ,fig4 #abd is an illustration of this1 showing a reading of #bh degrees #dj minutes on the circle and #ab minutes #bj seconds on the vernier1 giving a total of #bh #eb #bj4 ,a #aj second reading is designed in the same manner as the above1 but each division of the circle is #aj minutes instead of #bj minutes1 with minutes and sixths on the vernier4 ,fig4 #abe is an illustration of this1 showing a reading of #g #af #cj4 ,illustration3 ,fig4 #abe4 #cbc4--;,for ,centesimal ,division the vernier to read minutes is generally divided #ej into #di for the half grades1 for small circles #d inches to #e inches4 ,for larger circles1 #f inches to #h inches1 verniers are cut #be to #bd4 ,the circle is then divided to #be4 ,where there is space for five divisions to the grade1 #bj1 the third decimal place1 may be estimated or read exactly to #jje by a vernier #dj to #ci1 or more closely if desired by a micrometer1 to be described presently4 ,illustration3 ,figs4 #abf1 #abg4--,sections of scales and vernier for circular readings4 ,illustration3 ,figs4 #abh1 #abi4--,sections of scales and vernier for circular readings4 #cbd4--,surfaces of ,limb and ,vernier4--,to get a perfect reading of a vernier the scale and vernier should be brought into contact upon a plane4 ,this1 for many reasons1 is impossible in a great number of cases upon an instrument1 from the conditions of its construction1 convenience of vision1 and in some cases for want of means of ensuring durability of the edges which work together4 ,therefore verniers and scales are more commonly constructed upon the methods shown in section ,figs4 #abf1 #abg1 where ,,vv are verniers1 ,,ll limbs4 ,the plan shown in section ,fig4 #abh gives a nice reading on a new instrument2 but the part of the edge not covered by the vernier is open to accident1 or if nearly covered by a part of the instrument1 open to the introduction of gritty dust1 which wears the meeting line open1 and thereby causes loss of edge to edge reading4 ,fig4 #abi shows a section we find on some ,french instruments4 ,this plan was introduced by the late ,colonel ,a4 ,strange for the section of the limb reading of theodolites for ,india1 but it was found in practice awkward to use upon this instrument1 as it required unpleasant stooping to read it4 ,it is1 nevertheless1 one of the best permanent vernier readings1 as the division remains constant under the amount of wear occasioned by the sliding of the vernier upon its circle4 #cbe4--,with the reading planes shown in section ,fig4 #abf we require great care to bring the eye1 whether open or through the microscope1 directly radial with the centre of the circle at the line into which the vernier cuts4 ,if we read the line in the slightest degree one-sided it is quite possible to make a difference of a minute on a #e-;inch or #f-;inch circle4 ,this is the section of the general reading plane of theodolites1 where1 from the necessary height of the telescope1 the limb has to be placed much lower than the eye4 ,with this section the circle comes fairly square to a comfortable position for reading4 ,it will be noticed that there is a slight lap shown to the vernier over the limb at a1 ,fig4 #abf1 which is always found in new instruments of this section4 ,it gives an allowance for wear between the vernier and the limb caused by the fretting of the metals together1 as also by the intrusion of grit1 which is always present in instruments used in the open air4 ,the lap should not be great1 and it should be nearly equal along the edge of the vernier1 although it is a difficult matter for the maker to get it perfectly so4 ,fig4 #abg is a section of the reading planes common to sextants and parts of many instruments4 ,this plan requires the same care to obtain a truly perpendicular reading to the division as that described above for ,fig4 #abf4 #cbf4--;,in the very best of work there is at all times a certain amount of error1 both between the divisions themselves1 and in the place of the axis in relation to the centre of the divided circle1 and of the position of the vernier in relation to both these4 ,it therefore becomes necessary1 where exactness is required1 to place at least two verniers to read opposite sides of the circle4 ,these bisect every reading through the axis of the instrument1 and detect very small errors in the work1 as well as personal errors of the observer1 of which the mean reading of the minutes or seconds only may be taken and used for correction to mean position4 ,where very great precision is aimed at1 three or even five verniers are sometimes placed round the circle1 and the mean reading is taken of the small differences in minutes or seconds1 after calculation for correction1 to find the direct position of the axis of the telescope required for the record of the observation4 #cbg4--,reading ,microscope4--,the microscope usual for reading the vernier is either a simple plano-convex lens of short focus or a ,ramsden eye-piece of the kind described for observing lines on the diaphragm of a telescope1 art4 #hb4 ,frequently the microscope1 technically called the reader1 is made of a compound form1 sometimes with a diagonal prism or mirror4 ,it is uniformly mounted in such a manner that it may move concentrically to the divided circle into which it reads4 ,in ,english instruments it is placed normal to the surface of the vernier1 so that following its curvature it may read opposite any line upon it4 ,in ,french instruments the reader is frequently placed obliquely1 so as to look along the line of the limb into that of the vernier1 which is said to be advantageous in certain lights4 #cbh4--;,in theodolites for reading the horizontal circle1 the reader is sometimes mounted to slide in an undercut groove near the circumference of the limb to follow its curvature4 ,this motion is not pleasant2 it is better in this and all cases of vernier reading1 if possible1 to mount the reader on frame-work proceeding directly from and moving upon the axis4 ,where it is practicable1 it is much better to have two readers where there are two verniers1 and in all cases to have one to each vernier1 than to shift one reader about after the instrument is placed in position1 which is liable to disturb it4 ,with opposite readers mounted on a pair of arms formed of one piece of metal1 where these bisect the circle working through its axis1 by the setting of one reader truly normal to the coincident division of the vernier the opposite reader will be set also2 so that this does not only save time1 but the instrument need not be touched for reading the second vernier4 ,the same principle should be applied to any greater number than two verniers as nearly as it may be practical4 #cbi4--;,instruments that have to be packed in cases for conveyance should always have readers removable from the instrument1 with proper fittings in the case provided for them1 or they should be hinged to turn up to a secure position1 the latter being a more expensive but a much better way4 ,it is better also1 if possible1 to remove the light frame with the reader if this does not turn up1 so that it cannot be injured in replacing the instrument in its case4 ,illustration3 ,fig4 #acj4--,reader fixed normal to surface4 ,illustration3 ,fig4 #aca4--;,jointed reader to set to any angle4 #ccj4--;,fig4 #acj shows a good rigid form of reader for an oblique plane of division3--,v vernier1 ,l limb4 ,this reader is placed on an arm radial from the centre of the instrument1 more generally in pair with an opposite reader4 ,the connection with the arm is commonly made for portability with a dovetail slide fitting to the reader1 sprung by a saw-cut down it to ensure constant contact after wear1 as shown in section ,fig4 #acb2 ,n arm of reader1 ,o fitting to arm4 ,the better form is shown in ,fig4 #aca4 ,in this the arm is jointed1 so that the reader out of use is turned up into the central part of the instrument4 ,this plan admits of adjustment of the reader for reflection of light from the division1 or for reading down the lines if preferred4 ,the magnifying power of either of these microscopes is generally two to three diameters4 ,the adjustment of the glasses should be such as will produce a flat field 7,ramsden's principle1 p4 #da71 so that several divisions of the vernier and limb may be read sharply when it is in focus1 although the central division only is taken for the reading4 ,illustration3 ,fig4 #acb4--,section of movable arm fitting to reader4 #cca4--,surface ,reflection to ,reader4--,in reading with the microscope the silver surface1 from its brightness in certain lights1 gives unpleasant reflections which render the reading difficult4 ,in practice the hand or a piece of white paper is used to shade the open vernier in such cases4 ,in large instruments a piece of ground glass is fixed in a frame over the vernier1 which throws a soft light1 producing the effect of a dead surface upon the silver1 or the light is reflected from a cardboard or ivory surface4 ,fig4 #acc shows a common form of microscope for reading a vertical circle1 by which the light is reflected from a white surface surrounding the field-glass end of the reader4 ,illustration3 ,fig4 #acc4--,reflecting surface reader4 #ccb4--,shades for ,vernier4--,it is very general on the ,continent to place the divided reading of the circle and its vernier on a plane perpendicular to the axis1 ,fig4 #abh1 and to place the reader at a fixed angle for down-the-line reading1 the object-glass of the reader being constructed to focus parallel rays4 ,in this way the division of the circle is followed into its vernier or vice versa4 ,in this case the silver may be shaded by ground glass1 which gives a soft1 pleasant reading in most lights4 ,the general arrangement is shown1 ,fig4 #acd2 ,l limb1 ,v vernier1 ,s shade of ground glass1 ,m reader4 ,objection is made to glass shades by civil engineers as being too delicate and liable to fracture1 with risk of the particles of glass getting into the working parts of the instrument4 ,to obviate this the author has made the shade of a piece of thin horn or transparent ivory1 which appears to answer very well and to save this risk4 ,illustration3 ,fig4 #acd4--,oblique reading microscope with shade1 ,french plan4 #ccc4--;,for ordinary instruments with no provision for shading1 a piece of transparent horn about #b inches by #a inches may be carried in the waistcoat pocket1 and will be found a great comfort if held over the vernier when the lines appear glary1 or the horn may be placed in a pocket frame with the case containing reflector for bubble reading1 ,fig4 #eb4 ,in large theodolites1 used for geodetic surveys1 the object-glass of the micrometer microscope is sometimes surrounded by a thin belt of turned ivory4 ,this throws a very soft light upon the divisions4 #ccd4--,micrometer ,microscope1 for ,reading ,subdivisions4--,where more exact reading is required than is possible with the vernier1 as in the case of the reading of circles #aj inches or more to seconds1 a micrometrical microscope is employed1 which gives means of measuring the distance from line to line of the division upon the limb by the displacement of a web1 point1 or line moved by a fine screw with a divided head4 ,the great demand of late years for reducing the size and increasing the accuracy of theodolites has induced the highest class makers to introduce micrometer reading instruments of six1 five1 and even four-inch circles1 and their accuracy is far greater than is possible with any instrument of the same size that reads by verniers4 ,of course the workmanship in these instruments has to be of a higher order1 and the reviser estimates the accuracy of the micrometer through magnification and the necessary refined workmanship to be at least four times as great as the vernier reading1 with the advantage that the micrometer is much more certain and easier to read4 #cce4--,the construction of the reading micrometer as originally designed by ,troughton has not been materially modified in those in general use4 ,certain refinements have been introduced for astronomical work3 these are sometimes expensive and often cumbersome1 so that they need not be considered in relation to surveying instruments4 #ccf4--;,in all cases where micrometers are used1 the structure of the framework of the instrument which carries them should be made extremely rigid1 as very minute deflections or vibrations render the reading to seconds of arc impossible4 ,the number of micrometers applied to a circle is generally #b1 #c1 or #e4 #ccg4--;,if a circle is to be read by micrometers1 the vernier is generally dispensed with4 ,the circle is usually divided to read in #e4 ,the first approximate reading used to be taken by a single index line with the aid of the ordinary reader1 ,fig4 #acj4 ,from the index line the degrees or minutes were taken to the last #e line indicated4 ,since the introduction of high-class engraving machinery the figuring is made at each degree and is clearly read in the microscope1 so that the index reader is unnecessary4 ,this engraving is quite a nice piece of work1 as to figure from #j to #cfj means nearly a thousand figures1 and on a #e-;inch circle these have to be less than #a_/ajjth of an inch high4 ,only the highest class makers are able to do this work4 ,when a microscope is adjusted to one line it should be observed that all the other microscopes upon the same circle should also read exactly to a line that should be true from microscope to microscope to the arc they subtend between each other4 ,illustration3 ,fig4 #ace4--,side elevation of ,troughton's micrometer4 ,illustration3 ,fig4 #acf4--,section of micrometer4 ,illustration3 ,fig4 #acg4--,micrometer slide4 #cch4--,the ,micrometer1 as it is now technically termed to include the whole piece of apparatus1 is a compound microscope consisting of three lenses1 with measuring apparatus at the mutual foci of the field-glass and of the two lenses which form the eye-piece4 ,the field-glass1 which is placed nearest the divided arc1 is generally an achromatic microscopic lens of an inch or more in focus4 ,the eye-piece is of the ,ramsden form1 ,fig4 #af4 ,by the construction of the compound microscopic arrangement the eye of the observer may be placed at any convenient distance from the limb1 and any desired magnification may be obtained to assure micrometric nicety of measurement4 ,the engravings represent the micrometer1 ,fig4 #ace in side elevation1 ,fig4 #acf longitudinal section1 and ,fig4 #acg the micrometrical slide1 which is shown partly in section for demonstration in all the figures2 a the micrometer1 q microscope body tube4 ,this has a male screw outside at b1 upon which there are two collars dd with capstan heads4 ,these collars hold the microscope upon the reading frame b at any required distance from the limb to secure proper focal adjustment4 g objective tube4 ,this screws into the body tube and permits adjustment of the objective to the division of the limb and the micrometer index web by the milled head s4 ,this tube has a locking nut i to secure it from after movement when it is once properly adjusted4 h an achromatic object glass of half an inch or over in focus4 e the casing that receives the eye-piece which screws into the outer plate of the micrometer4 f the eye-piece1 generally made about one inch long4 ,this slides by friction in its cell to produce distinct vision of the spider lines in the micrometer4 #cci4--,the micrometer frame1 ,fig4 #acg1 a has a fixed scale or comb1 with five or more points or teeth formed upon it1 and a movable sliding frame1 upon which a spider web or webs are inserted and cemented in finely engraved lines to form an index1 brought as nearly as possible to the mutual focal plane of the object-glass and the eye-piece4 ,the index web frame has a fine screw of about a hundred threads to the inch tapped into it4 ,the micrometer screw1 divided drum1 and milled head are now generally constructed as shown in ,fig4 #acg4 ,two springs press upon the index frame and the outer frame1 and thus keep the drum up to its collar4 ,the drum r is divided upon its edge into sixty equal parts1 to read seconds of arc generally to a single line index4 ,the screw is moved by the milled head beyond the drum1 so that the divided surface of the drum need not be touched4 #cdj4--,the portion of the arc measured being generally #e1 the distance of it1 as it appears at the magnified image of the arc at the position of the index of the micrometer1 is made to correspond with five turns of the micrometer screw1 the head of which divides each turn into #fj4 ,by this means the #e is divided into #cjj1 that is1 to single seconds1 and by approximation of the interspaces on the micrometer head1 as far as the reading is concerned1 to fractions of a second4 ,the fixed scale1 or comb1 as it is termed1 is commonly placed in the focus of the eye-piece with five webs upon it1 fixed to agree with five turns of the screw or a rack with points at the bottom4 ,these webs or rack divide the #e of arc in minutes1 and indicate the number of revolutions of the screw1 as shown by the displacement of its index line4 ,a pair of lines or webs are commonly placed in modern instruments at #a part1 to ensure certainty of reading by the mean of two observations4 #cda4--,the magnitude of #e of arc depends necessarily upon the radius of the divided circle2 therefore the microscope of the micrometer has to be made to suit the division it is required to subdivide--that is1 using the same micrometer1 the smaller the circle the higher the magnifying power is required to be to take register by the same screw4 ,within a wide range the micrometer is perfectly adjustable1 to ensure exactness upon this point1 by varying the distance of the object-glass from the limb1 for which purpose the microscope is made adjustable by the pair of screws dd which clamp it to its standard as already mentioned4 ,the principle of this adjustment is easily seen1 for if we place the object lens at a distance equal to its solar focus from the limb1 the image will emerge in parallel lines2 but as we cause it to recede from the limb1 the image may be brought to any position within the tube greater than the solar focus of the objective of the microscope4 ,the image is therefore brought to a position where it may be picked up conveniently by the eye-piece4 ,in this manner we have only to make the adjustment of the object-glass from the limb such as the space of any pair of divisions of the limb may be magnified up equal to the displacement of five turns of the screw for seconds measurement4 #cdb4--,the two points where the divisions and their images are situated are termed the conjugate foci of the lens1 and the magnifying power is proportional to these distances2 thus1 if we call the distance of the object1 that is the limb1 from the object lens f1 and the distance of the focal plane of its image within the tube ,f1 the image will exceed that of the object in the ratio of ,ff1 or ,f_/f will represent the magnified image4 ,by this method it will be seen that the expression ,f_/f will have an increased value1 if we either increase ,f or diminish f1 which we have to consider in the construction of the microscope to bring it to the conditions under which it will adjust to bring the micrometer screw exactly to its required reading4 ,illustration3 ,fig4 #ach4--;,grubb's plan of securing micrometer screw4 #cdc4--;,it is very general in instruments at the present time to tap the micrometer screw directly into the micrometer frame1 and to make the drum and milled head a part of the screw4 ,in this case a very soft motion may be given to the screw by dividing its nut longitudinally and bringing the parts together with a certain amount of spring4 ,sir ,howard ,grubb1 of ,dublin1 has placed a spring ball fitting1 as shown ,fig4 #ach at ,,ee1 over the screw upon his astronomical instruments1 which gives a very soft motion to the screw4 ,these refinements are very important1 as it is not desirable that any undue pressure should be put upon a delicate instrument which under all conditions must be made rigid enough to resist it1 and the greater the pressure required to bring the instrument to bearing the stronger it must be made4 ,illustration3 ,fig4 #aci4--,stanley's micrometer slide4 #cdd4--,stanley's ,micrometer4--,the author has made an arrangement in which the screw has a long1 double tubular sliding stem1 ,fig4 #aci4 ,the inner stem which carries the milled head has a groove cut down it1 into which a stud from the inside of its covering tube slides4 ,this arrangement permits the milled head to be pressed inwards or outwards in turning it without any pressure coming upon the micrometer greater than the friction upon the sliding tube1 and that of a weak spring which keeps the stem nearly extended in its tube4 ,a simple ,hook's joint ,h is formed at the head of the screw1 so that no part of the weight of the hand comes upon the screw4 ,a tubular guard-piece ,t prevents the milled head hanging down too far when out of use4 ,when the screw is used it is lifted to about the centre of the guard tube4 ,with this arrangement1 as no practical weight or pressure comes upon the micrometer from handling it1 the supporting frame-work may be made much lighter than is necessary with any other form of micrometer4 #cde4--,the author prefers to form the micrometer scale and the index of fine lines engraved upon parallel worked glass for surveying instruments4 ,this avoids the risk of breaking webs1 and1 what is much more important1 he finds that with engraved lines on glass he is able to bring the scale and index exactly and permanently into the plane of mutual foci of the object-glass and eye-piece by placing the lines upon the same faces of glass1 thus avoiding the great difficulty of focussing to guess-work of an intermediate position between two sets of webs at different distances4 ,the strip of glass ,a is fixed by a clamp and two screws to the side of the micrometer box4 ,the slip ,b is ground and polished to fit ,a4 ,b is carried by the micrometer frame ,f1 which holds it in a clamp by two screws4 ,a spring1 not shown1 presses ,b against ,a1 so that any displacement of the micrometer lines may be made by the milled head4 ,the lines upon ,a are adjusted to the position of the circle they are intended to read at exactly #e or other quantity4 ,for the smaller instruments which will be much more frequently used by the surveyor a simpler form of reading is used1 and as the reviser is convinced that in future this form of reading will gradually replace the vernier for all high-class work1 a full description of this very simple reading is here given4 ,the reviser is confident1 after many years of practice for the most accurate form of index1 that a point certainly stands first1 a pair of webs or lines on glass1 between which the division is seen1 second2 and a single web or line on glass placed over the division1 third4 ,the comb mentioned in art4 #cci is done away with1 and one revolution of the micrometer screw made to carry the index over one division of the limb4 ,for clearness the engravings show only a #aj reading2 for a #e reading the divisions on the limb are to #e instead of #aj1 and the micrometer head is divided and figured accordingly4 ,illustration3 ,fig4 #adj4--,stanley's micrometer reading4 ,fig4 #adj shows at ,c a portion of the theodolite circle as seen through the micrometer microscope4 ,p is the movable pointer1 ,m the micrometer head1 and ,i the index or reading line4 ,to use the micrometer the first steps are to carefully focus the pointer ,p by means of the eye-piece until it appears clear and perfectly sharp1 and set the reflector at the bottom of the microscope so that it reflects sufficient light to illuminate the divisions on the circle4 ,then1 by turning the micrometer head ,m1 set the pointer ,p to the centre of its travel1 so that it covers the ,v cut in the bottom of the slide1 and leave the #j of the micrometer head exactly opposite the index line ,i4 ,now proceed in the same manner with the other microscope4 ,after setting the microscopes as described above1 lightly clamp the lower clamp screw of the instrument and release the upper one4 ,now revolve the upper part of the theodolite until #cfj degrees on the circle appears exactly under the pointer of one of the microscopes4 ,the other will then be pointing to #ahj degrees1 and the instrument is set ready for measuring the first angle4 ,illustration3 ,fig4 #ada4 ,we will presume now that a bearing has been taken by the telescope and it is required to read the angle1 and that on inspection of the micrometer it is seen to be in the position illustrated at ,fig4 #ada1 viz41 between #bbg and #bbh degrees4 ,now as the degree is subdivided into #f parts1 each of these subdivisions must represent #aj minutes of arc1 therefore the pointer is situate between #bbg #cj and #bbg #dj4 ,it is now necessary to measure exactly the distance of the pointer from the division #bbg #cj1 which is done in the following manner1 by means of the micrometer head ,m4 ,illustration3 ,fig4 #adb4 ,this micrometer head is so constructed that one complete revolution of it causes the pointer to exactly travel over the space of one division on the circle4 ,the head itself is divided into #aj primary parts1 which indicate single minutes1 and these are subdivided into #f parts of #aj seconds each1 therefore in order to measure the exact position of the pointer in ,fig4 #ada it is only necessary to turn the head ,m until the pointer is exactly over the previous division of the circle 7as shown in ,fig4 #adb7 and read the distance on the micrometer head ,m4 ,in this case the head has been turned through six main divisions of #a minute #f minutes and two subdivisions of #aj seconds #bj seconds1 giving a total reading of #f #bj1 this1 added to the circle reading of #bbg #cj1 gives #bbg #cf #bj1 which is the correct reading of the angle4 ,it will be seen that this method is very much simpler and a great deal more accurate than any form of vernier reading1 and also that its greater accuracy permits the use of smaller instruments4 ,thus a #e-;inch micrometer reading theodolite is more accurate than a #f-;inch one with verniers4 ,six-inch micrometer theodolites are usually divided to read to #e seconds of arc4 ,the method of reading is the same as described above1 but in this case the circle is divided to spaces of #e minutes each and the micrometer head to #e main divisions of #a minute1 each of these having #ab subdivisions of #e seconds1 which it is possible to again subdivide by estimation and so measure angles to #b seconds4 ,another feature in favour of micrometer reading instruments is the ease with which they can be adjusted4 ,with verniers1 should they get out of adjustment through damage1 the instrument must be returned to a maker2 with micrometers1 if through rough usage or accident1 it is found that after bringing the pointers to the centre of their ,v's and setting the micrometer heads to #j they are not exactly opposite one another 7#ahj degrees apart71 then their setting has become disturbed and must be readjusted in the following manner3--,first bring the ,v of one micrometer to the #cfj on the circle1 then see if the ,v of the opposite micrometer is exactly at #ahj1 if not this can be easily set to it by means of the small adjusting screw which will be found at the left end of the micrometer box1 that is1 the opposite end to the divided head4 ,having examined the ,v's and adjusted them if necessary1 the next step is to set the pointers ,p exactly to #cfj and #ahj respectively1 in which position the divided heads should both read #j2 if they do not do so reset them as follows3 ,take a screw-driver and slacken the small screw which is in the centre of the divided head2 this will free the divided rim so that it can be turned without shifting the position of the pointer4 ,turn the divided rims until they read exactly #j at the index line and retighten the screws4 ,this completes the adjustment4 ,illustration3 ,fig4 #adc1 #add4--,sections of clamp and tangent in two directions4 #cdf4--;,clamp and ,tangent ,adjustment4--,the vernier reading to the circle1 when this was adjusted by the hand1 was scarcely practicable at nearly its full value until the discovery of the clamp and tangent screw motion was made4 ,this useful invention is due to ,helvetius1 the celebrated astronomer of ,danzig 7about #afej74 ,by this mechanical arrangement the circle or arc is left quite free to move about its axis until the clamp is screwed down1 which then fixes it firmly4 ,the fixing arrangement of the clamp is attached to a solid part of the instrument1 but is so constructed that when it is clamped it may yet be moved without unclamping1 in relation to the fixed part of the instrument1 by the tangent screw which1 as its name indicates1 is placed in a direction tangential to the circle or arc4 ,this arrangement may take many forms in detail1 two of which1 the most general and especially adapted to surveying instruments1 will be described4 ,illustration3 ,fig4 #ade4--;,elevation and part section of clamp and tangent4 #cdg4--,the above illustrations1 ,figs4 #adc1 #add1 represent a clamp and tangent motion in two sections at right angles to each other4 ,this form is common to vertical circles and arcs generally1 of a theodolite1 arc of sextant1 circles upon some mining-dials1 protractors1 and many other instruments4 ,fig4 #ade is partly a front elevation of the same1 but with part of the clamp screw ,a cut off4 ,the stem of the tangent screw is shown in section at ,e4 ,in all the figures ,l is the limb of the circle or arc4 ,this has a groove at its under side at ,g1 into which a fillet of the clamping piece ,c is inserted to make the clamp slide freely about the periphery of the circle when the clamping screw ,a is loose4 ,a spring is sometimes inserted to open the clamp between the sliding piece ,k and the clamp ,c4 ,,ff1 ,figs4 #adc1 #add is the tangent nut to ,e4 ,this nut is sawn down and has a cross screw to keep sufficient tightness to prevent loss of time1 and yet to allow the tangent screw to work pleasantly at the same time that it holds the circle and vernier quite dead to the position to which it is adjusted by the screw4 ,the tangent nut ,f has to move to the direction horizontal to the plane of the tangent screw2 therefore it has an axis vertical to the plane of the clamp4 ,this is shown at ,k4 ,the axis is held down firmly by a nut and a washer fitted with a square hole1 to prevent the nut unscrewing4 ,the tangent screw has a collar fitting or shank at the tangent boss ,b1 which is turned down from the full-sized metal of the screw4 ,the fellow collar on the outer side of the boss is formed by the shank of the milled head of the tangent screw ,d4 ,the hole through the milled head is made square1 so that it can be adjusted up to the boss without risk of after unscrewing by friction by the screw ,e4 ,this is tightened up by means of a screw-driver applied at ,e4 ,the boss ,b has a vertical axis ,n1 similar to the tangent nut1 and is attached to a solid part of the instrument by the washer and nut shown at #j4 #cdh4--,the above construction is solid and good1 and will bear considerable wear2 but there is a little delicacy of touch required to adjust the collars to the boss and to give pleasant tightness to the screw2 a better plan is to dispense with the split in the tangent nut and the inner collar turned on the tangent screw1 and place a spiral spring over the tangent screw which follows the adjustment1 or in some cases a long bow spring may be conveniently used in place of the spiral4 ,these plans answer very well3 one of them will be presently described for axis clamping4 ,in place of the groove at ,g the clamp is sometimes constructed to move on an arm direct from the axis of the circle4 ,this is on the average a pleasanter motion1 but in complex instruments it would often interfere with the motion of other necessary parts4 #cdi4--;,axis ,clamp and ,tangent4--,this is generally used to bring the horizontal axis of an instrument to bearing1 and is made independent of the circle and vernier4 ,the ordinary form1 which is very effective when properly constructed1 is shown ,fig4 #adf4 ,this form is used for clamping the vertical axis of a theodolite1 mining-dial1 ,y-level1 and some other instruments4 ,the clamp ,c surrounds the axis as a collar1 from which two lugs in the same casting are projected at a4 ,these are brought tight upon the outer axis socket ,b by means of the screw ,w1 which has a wing-nut head to give good purchase4 ,in the construction of this form of clamp the collar should be fitted and ground to its bearings with the lug in the solid1 and the cut at a be sawn through afterwards4 ,illustration3 ,fig4 #adf4--;,clamp and tangent to a vertical axis4 #cej4--,the tangent screw adjustment is shown at ,t1 moved by the milled head ,m1 the boss ,e being fixed to the instrument4 ,this part of the arrangement is just the same as that described above for a vernier tangent4 ,objection has sometimes been made to this form of clamp1 that it tends to become weak after a time from the constant clamping and releasing1 which causes loss of elasticity in the metal4 ,when this occurs it is no doubt due to the metal of the clamp not being good gun-metal2 or1 if brass1 not thoroughly pressed or hammered before the piece is made up4 ,a plan1 in not uncommon use in ,germany1 of avoiding this supposed source of weakness is to bring up a tumbling piece direct on the axis by a screw4 ,this is shown in ,fig #adg1 screw ,w2 tumbling piece ,a4 ,this produces a direct clamp upon the axis socket ,b4 ,the clamp ring ,,cc is made loose on its socket4 #cea4--;,in practice it is found impossible to clamp the axis of a theodolite without disturbing the centre more or less4 ,in some experiments the author made he found the direct or tumbling piece clamp ,fig4 #adg1 although it holds firmly1 disturbs the centre much more than the clasping clamp ,fig4 #adf4 ,therefore when the former is used the clamp should be upon a strong flange4 ,this increases weight1 and it can scarcely be so well for a portable instrument4 ,in all cases1 in the construction of the instrument1 clamps should be fitted and screwed down before the centre is ground and finished4 ,this ensures the centre being made correct in its clamped position1 in which it will afterwards be used4 ,illustration3 ,fig4 #adg4--;,clamp and tangent to vertical axis1 ,german plan--,hunus4 ,the arrangement ,fig4 #adg shows also a spring ,s falling upon a stud at ,e1 fixed upon a part of the instrument upon which it acts as a fulcrum4 ,the spring should be of hard rolled ,german silver4 ,in this case the tangent screw needs no split or other adjustment to make it tight1 as all loss of time is taken up by the spring4#ad ,the plan is found practically to answer fairly2 but unless this is very carefully made there is a want of solidity in the movement which a well-fitted1 direct-acting tangent screw possesses4 #ceb4--,the ,french generally in all their superior instruments clamp upon a flange carried out from the lower rim of the socket1 with the screw placed longitudinally to the axis4 ,when this plan is very carefully carried out1 so that the clamping has neither tendency to raise or lower the socket-piece1 it is no doubt very good4 ,in large instruments1 where weight is no object and the flange may be made large1 it is certainly the best plan4 ,in such cases the clamp may be released as a free fitting to prevent the possibility of strain4 ,fig4 #adh shows the ,french plan attached to a tribrach3 ,s socket1 ,f flange1 ,c clamping screw1 ,t tangent screw4 ,the tangent in this arrangement acts against a spiral spring contained in a tube ,a1 which gives a very steady motion to the instrument4 ,illustration3 ,fig4 #adh4--;,french axis clamp and tangent4 #cec4--,some particulars of the care required in the manufacture of the tangent screw were given1 art4 #bb4 ,the test for the equality of this screw1 which is important when it moves a vernier1 is to loosen its clamp and to see whether it works equally1 firmly1 and smoothly at all parts when it is turned down from end to end4 ,the test for its straightness is to screw down the clamp1 then to notice any little mark on the milled head of the tangent screw1 or make a slight mark upon it1 and to place this mark uppermost1 and then to take a reading with the vernier1 then to turn the milled head a quarter turn and take another reading1 and again another quarter1 and so on consecutively4 ,by comparing the rates of reading of the vernier at the quarter turns1 if we find these equal the screw is straight4 ,a little allowance is necessary for imperfect work4 ,if the work is very bad at some quarter turns there will be an advance at the opposite quarter of nearly double the proper mean quantity4 #ced4--;,for ,testing and ,adjusting the ,fitting of the ,tangent ,screw4--,the clamp should be tightened down and the ball ,b1 ,fig4 #add1 held tightly between the thumb and forefinger2 then1 by using a gentle reciprocating motion in the direction of the tangent just sufficient to move the circle1 if there is any looseness in the screw or the ball fitting ,b it will be felt as a jar1 or technically1 a slight loss of time4 ,if this be in the ball ,b it can be taken up by the screw ,e at its end4 ,if it be in the screw it can be taken up by the cross clamp screw4 ,if it be in neither of these1 it may be in one or both of the axes ,n and ,k4 ,in this last case it will need refitting4 ,it appears a somewhat simpler test with a theodolite to lightly press the telescope on one side of the eye-piece and take a reading of the vernier1 and then to press the other side and again take a reading4 ,this1 possibly1 indicates loss of time in the clamp and tangent if there is found any difference in these readings2 but this would not be with any certainty1 as the fault might be in some other part of the instrument4 ,it1 nevertheless1 is a simple plan to test the whole instrument1 including the clamp and tangent1 although this does not localise any defect there may be in any special part of it4 #cee4--,use and ,wear of the ,clamp4--,the common fault of a novice when he commences to use an instrument is that he applies too much violence to all clamping parts4 ,thus we find the lower parallel plate of an instrument soon becomes deeply indented1 and the clamp of the tangent screw often strained1 or its screw worn loose by extreme clamping4 ,the best rule to avoid this with a clamp is to make a personal test of how little force is required to produce sufficient hold for the action of the tangent screw1 and when this is found out to try to clamp only slightly in excess of this4 ,a novice scarcely recognises the power of a screw4 ,it is1 perhaps1 a fault of some makers of giving much too large heads to clamp screws which to a certain extent permits this overstraining from clamping4 ,in discussing this matter with a scientific civil engineer upon an instrument which had been very much strained1 to which small clamping screw heads were suggested1 this gentleman replied that he looked to the optician to supply instruments1 not brains1 and made the user responsible2 but1 really1 a young surveyor is generally so intent on the object of his work that he cannot consider the mechanical details of his instrument1 to which his attention possibly has never been properly directed2 so that there is a policy in cutting off possibility of injury to the instrument where this can be conveniently done4 #cef4--,use and ,wear of the ,tangent ,screw4--,seeing that the axis of an instrument is quite free to the extent of the loss of time on the tangent screw which holds it1 and that this freedom1 by any slight touch of the telescope1 may cause a difference of reading--in some cases of several minutes of arc--it becomes important to observe that the tangent screw is in good order4 ,this matter considered at its full value1 we may wonder1 perhaps1 what kind of work may have been done with the tangent screw loose and worn down in its central part1 as we find it in many old instruments sent for repair4 ,a great amount of the common defects we find in worn tangent screws might have been prevented by using certain precautions2 and even the much-worn tangent screws would sometimes go on fairly by a different method of use from that to which they have evidently been submitted4 ,the wear of a tangent screw is due principally to the fact that this screw is necessarily oiled to make it work freely1 and that the oiled part being exposed to dust1 this dust attaches itself and works into the thread with the oil so as to cut both the screw and the nut4 ,precaution is necessary that this should be obviated as far as possible4 ,one precaution may be taken1 that when the screw is oiled1 say once in three months1 the parts outside the nut should be cleaned off quite dry with a few strands of thread4 ,the oil left in the nut1 if the screw has been turned through it1 will be quite sufficient to lubricate the screw4 ,another better precaution is to use only one part of the screw for a period1 say one month4 ,the screw may be divided mentally into three parts--near part1 middle part1 and end part4 ,if one part only be used for a period1 and the vernier be set in using the instrument so that not more than about #a of motion is required of the screw1 no grit can be carried far into the centre of the nut2 and if the precaution of cleaning the screw with thread be taken every time the instrument is returned to its case after a day's work1 the screw being left at about the same place on the screw and nut1 it will keep true with little wear4 ,when another part of the screw is taken into use1 this part should be first cleaned with thread and then oiled with watch oil1 after which the former position of the nut should be cleaned quite dry with thread4 ,treated in this manner a tangent screw will last1 in constant wear1 for ten years or so1 keeping in fairly good order4 ,where a spring is used to take up loss of time there is less risk1 and the only precaution necessary is to be sure the spring continues to act properly4 ,there is generally1 however1 a little more wear with a spring than with a free thread4 #ceg4--;,if the instrument be not touched after the tangent is set1 and there is no wind to cause vibration1 the instrument will read correctly although the tangent may be out of order4 ,but after the adjustment by the tangent screw1 which may cause a disturbance1 it is always necessary to set the microscope to the vernier4 ,this is one important reason why the microscope should move as softly as possible1 and that it is advisable to centre it upon the axis4 ,where any doubt of the quality of the tangent exists1 the telescope should be reobserved for verification of its position after reading1 which is also undoubtedly the safest in all cases4 #ceh4--,some contrivances have been applied to tangent screws to prevent wear from dust1 and also to take up the nut after wear4 ,a very good plan1 common in ,american instruments1 is to insert the end part of the screw beyond the nut in a closed tube4 ,this entirely prevents dust from resting on this part2 and if the precaution be taken to clean the exposed part of the screw after use it is very effective for preservation4 ,this plan the author has combined with a spring arrangement1 which appears to render it very safe from loss of time and much wear4 ,this arrangement is1 however1 a little expensive to make1 therefore can only be applied to high-class instruments4 ,fig4 #adi1 ,c nut1 through which tangent screw passes2 ,b tangent boss1 ,a milled-head1 ,h covering tube to the point of the screw1 ,,gg ,,ee pair of telescopic tubes which cover the screw4 ,a ,german silver or platinum spring works inside these tubes1 keeping a constant separating pressure between ,c and ,b to take up any loss of time in the screw4 ,illustration3 ,fig4 #adi4--,protected tangent screw with helical spring4 #cei--;,free ,tangent ,screw4--,there is always a risk of a tangent screw of any fixed kind producing a certain amount of strain upon the instrument1 therefore1 where practicable1 it should be made free4 ,the illustration1 ,fig4 #aej1 shows the form of free tangent the author now applies to many instruments4 ,the centre stud is clamped to the lower part of the instrument by the screw shown in dotted lines4 ,to the left hand a piston containing a spiral spring carries a pressing-rod against which the screw to the right hand works4 ,illustration3 ,fig4 #aej4--;,free tangent adjustment4 #cfj4--,loss of ,time by ,wear of the nut is variously taken up when no spring is used4 ,one plan was shown of splitting it up4 ,a plan common in ,germany is to make the nut in two pieces1 which are brought up by two screws4 ,this is a very effective plan4 ,the author has found a tumbling piece arrangement also effective4 ,fig4 #aea1 ,s section of tangent screw1 ,t tumbling piece moved by the adjusting screw1 shown above1 for wear of the tangent screw4 ,this adjusting screw ,a should be tapped tight without oil1 and put together dry to prevent its receding by pressure4 ,illustration3 ,fig4 #aea4--,tumbling piece adjustment for wear of tangent screw4 #cfa4--;,hypotenuse and ,base4--,other trigonometrical values besides the division of the circle into equal parts are occasionally placed on instruments for special purposes4 ,the most common of these is the scale of difference of hypotenuse and base1 which is generally placed upon the back of the vertical arc of a theodolite and upon some dials and clinometers4 ,the division for this purpose is generally done by hand4 ,the scale gives a percentage difference for certain angles4 ,thus when used with chain measurement1 it gives the number of links of the chain to be deducted per chain of #ajj links for the inclination of land that the theodolite or other instrument indicates in following the surface contour4 #cfb4--;,a ,horizontal ,scale of ,tangents was placed upon the surveying theodolites by ,ramsden4 ,this was divided upon a scale carried by the vernier plate1 which read to the zero line 7#j7 of the limb4 ,it is found in practice more accurate to take the tangent to any curve from a scale of tangents1 as1 for instance1 that in ,molesworth's pocket-book1 and set this off upon the limb by means of the vernier4 #cfc4--;,gradient ,scale4--,civil engineers engaged on railway work occasionally have a scale of gradients upon the back of the vertical arc #a to #ajj1 #aej1 #bjj1 etc4 ,these are better read from the circle with vernier from a table of gradient arcs4 ,,footnotes3 #ad ,the illustration is taken from ,die geometrischen ,instrumente1 ,dr4 ,g4 ,chr4 ,k4 ,hunus4 ,hanover1 #ahfd4 ,,chapter ,,vii4 ,,theodolites--,,constructive ,,details ,,of #e-;,,inch ,,and #f-;,,inch ,,transits-- ,,special ,,additional ,,parts--,,plummets ,,with ,,screw ,,adjustments ,,of ,,improved ,,form--,,striding ,,level--,,lamp--,,adjustment ,,of ,,axis ,,over ,a ,,point--,,solar ,,attachment--,,photographic ,,attachment4 #cfd4--,the ,theodolite is the most perfect instrument for measuring both horizontal and vertical angles by the aid of a telescope and graduated circles4 ,for the purpose of surveying1 the theodolite is mostly employed to take a system of triangles upon the horizontal plane of the surface of the land1 and of objects at any position in which they may be placed4 ,when altitude angles are taken separately these are generally applied to give corrections to chain or other actual measurements upon the surface by calculation of the difference of hypotenuse and base4 #cfe4--,the theodolite in all its essential features1 as differentiated from sighted compasses for taking angles1 mentioned by ,digges1#ae was the invention of ,jonathan ,sisson1 a celebrated mathematical instrument maker of the beginning of the #ahth century4#af ,great improvements were afterwards made in this instrument by ,ramsden1 who brought it up nearly to its modern efficiency by the introduction of the transit principle4#ag ,later improvements in portable instruments consist in the application of the transit principle to the telescope1 which was formerly applied to astronomical and the larger geodetic instruments only4 ,other improvements have been made more recently in constructive details4 #cff4--,theodolites were commonly made of two distinct types1 which were originally distinguished as plain theodolites and transit theodolites4 ,in the plain theodolite the telescope moves through an arc of about #de upwards or downwards from the horizontal plane1 but very few of these are now made compared with the number of transit theodolites in which the telescope may take a complete revolution upon its horizontal axis1 so that a back and fore sight may be taken by a half revolution4 ,this difference of construction entails a difference in the manner of mounting the telescope to correct its adjustments4 ,in the transit the accuracy of centring and reading is easily discovered by taking a back and fore sight at a distance as equivalent to an arc of #ahj1 which may be read on any part of the limb by transitting the telescope1 wherein the correspondence of this arc to the reading of the limb to right and left hands will detect error4 ,with the plain theodolite the equivalent method of examination is effected by placing the telescope in ,y's1 as previously discussed for the ,y-level1 and turning it end for end on its bearings1 a process liable to disturb the direction of the telescope unless special care be taken4 ,in the following description of the details of construction of a theodolite it will be convenient to take the transit form of instrument1 as this is more comprehensive1 the original pattern being selected1 as this may be constructed with the limited amount of tools generally found in a surveying instrument workshop4 ,illustration3 ,fig4 #aeb4--e-;inch transit theodolite 7old form74 #cfg4--,the size of a theodolite is fixed technically by the diameter of the line of division upon the horizontal circle4 ,a #e-;inch or #f-;inch theodolite is the largest size that may be carried comfortably in a single case2 and no great advantage is gained by having an instrument beyond this size if the work is that of the ordinary surveyor on town and county surveys4 ,the verniers of #d- and #e-;inch instruments read sharply to single minutes of arc1 which is as nearly as can be plotted with any degree of certainty with an ordinary protractor reading by vernier also to minutes only2 #f-;inch instruments read to #cj but generally to #bj seconds4 ,occasionally #d-;inch theodolites are selected for lightness at a sacrifice of capability and of distinct and exact reading4 ,the following table gives the average weight of the transit theodolite illustrated on the last page3-- ,instrument4 ,case4 ,overcase4 ,tripod4 #d-;inch ,transit4 #aa lbs4 #h lbs4 #d lbs4 #h lbs4 #e-;inch #ac #i #e #i #f-;inch #ai #aj #f #aa #h-;inch #cf #bj #aj #ah ,if with lamp extra about lb4 ,if with striding level extra about lb4 ,it will be seen that the #e-;inch instrument of this class with cases and tripod1 say altogether #cf lbs41 is really of quite as much weight as a fairly strong man can carry through a hard day's work4 ,the #e-;inch instrument is therefore becoming more and more popular with practical civil engineers1 and its performance1 if of good modern work1 is quite equal to the #f-;inch of less than half a century ago4 #cfh4--;,by giving a description in detail of a transit theodolite1 the general principles of a great number of other instruments1 particularly those of larger dimensions1 will be included1 except for certain details that the specialities of the particular instruments demand4 ,the most convenient plan to follow in this description will be to take the structure of a #f-;inch transit theodolite of common construction1 as it is built up from its base1 piece by piece1 according to the rule of ordinary structure2 where more modern theodolites vary mostly from this is in having many parts shaped out of the solid1 which are screwed together in the form illustrated4 #cfi4--,the ,tripod ,stand of a theodolite of #f inches and under is generally made identical with that of a level1 a common form being that described for a dumpy1 art4 #baf4 ,the arrangement of one turn-up leg1 as shown ,fig4 #fc1 is very advantageous for the theodolite if it is to be used on mountainous or even very hilly ground4 ,for instruments exceeding #f inches a framed stand1 which will be described further on1 is better4 ,some makers use a framed stand for a #f-;inch instrument4 ,the rigidity of the stand ought to be quite equal to that of the work in the theodolite1 or a little in excess1 and when this is attained it is sufficient4 ,where the stands of theodolites so often fail is from the defective construction of the tripod head1 not at all from deficiency of timber in the tripod itself2 and overloading this1 in adding weight without attention to scientific construction1 is worse than useless4 #cgj4--;,in the following description of the transit theodolite the parallel plate setting-up arrangement is taken1 as this is at the present time 7#aiad7 still in use in this country and in ,america4 ,there is nevertheless great probability that it will not long continue to be so1 as year by year the tribrach system1 described art4 #bcc1 for levels is coming more forward1 both for levels and theodolites4 ,this tribrach system the author holds to be much more scientific1 and when thoroughly understood1 more simple and expeditious to work with4 ,it is also to be recommended1 as there is no possible risk of strain upon the general work of the instrument1 nor risk of error from distortion of the vertical axis from strain in setting it up to adjustment4 ,a constructive drawing of a common transit theodolite with parallel plates is shown ,fig4 #aec1 of which the following is a detailed description4 ,illustration3 ,fig4 #aec4--f-;inch transit theodolite--back view1 with sections4 #cga4--,the ,lower ,parallel ,plate ,n4--,this has a large boss-piece taken up from its central part1 which forms a dome of a hollow globular section1 technically termed the socket1 shown at ,x4 ,in the interior of the lower part ,n a coarse female screw is cut1 of about fourteen threads to the inch1 which is used to attach the instrument to its tripod4 #cgb4--,the ,upper ,parallel ,plate is constructed as a flange from a solid boss ,l4 ,this piece is generally made in gun-metal of a form as solid as possible1 to resist the straining action of the parallel plate screws4 ,the boss is prolonged downwards by a stem-piece1 upon the lowest part of which a ball collar of globular section is firmly screwed4 ,the screw is turned by means of two opposite holes1 into which a powerful forked screw-driver is inserted1 until it is jambed up too tightly against its shoulder to ever become loose by the ordinary use of the instrument4 ,the ball collar fits into the socket carried up from the lower parallel plate4 ,the whole of this globular arrangement is termed the ball and socket4 ,the boss ,l of the upper parallel plate1 with its stem1 has a hollow conical hole through its axis1 into which the body-piece1 to be described1 fits accurately4 ,upon its outer upper part an inset collar is formed which acts as a guide to the clamp ,k4 ,at the outer edge of the parallel plate ,m four vertical1 conical holes are made1 which take socket-pieces1 which are tapped as nuts to the parallel plate screws ,m4 ,these socket-pieces are jambed into their holes tight home to their shoulders4 ,the socket-pieces are made separate1 both to give a greater length of female screws than the thickness of the plates1 and that they may be easily restored at any time if worn loose in the threads by the action of the plate screws4 #cgc4--,the ,parallel ,plate ,screws4--,one in elevation is shown at ,m1 with its point dotted1 and one in section at ,m4 ,the four parallel plate screws are in opposite pairs1 placed exactly at right angles to each other in a line passing through the vertical axis of the instrument4 ,these are made of gun-metal about #c_/h inch in diameter1 with a deep thread of about thirty-two to the inch4 ,they require cutting on a nice steady screw-cutting lathe4 ,the lower points of the screws are slightly domed1 sufficiently only for the amount of rocking they have to take1 so as to impress the lower parallel plate as little as possible4 ,the milled heads ,m are placed between the parallel plates1 not above1 as previously described for levels4 ,there being a constant strain upon these screws in use and by intrusion of grit from flying dust they soon become worn4 ,after wear the threads may be recut deeper1 and new socket-pieces fitted to the upper parallel plate4 ,to prevent wear the upper parts of these screws are sometimes encased in tubes--a plan very generally adopted in ,america4 ,at the foot of one of the parallel plate screws a stay-piece is fixed to the lower parallel plate1 which forms a kind of ring round the screw4 ,this prevents the parallel plates from shifting upon the axis at the ball and socket4 ,the parallel plate screws should be without any shake or what is technically termed loss of time4 ,they should move firmly but softly4 ,they should support the instrument against the ball and socket upon which the whole rocks to position by their aid1 but not be screwed down too tightly1 as this has a tendency to disturb the axis of the instrument however solidly it may be made4 ,makers often have instruments in their hands for repairs in which the parallel plate screws have been deeply indented into the lower parallel plate1 with the centre of the instrument permanently strained more or less4 #cgd4--,the ,body-piece4--,the only outward part seen in elevation of this is shown at ,t3 it is shown in section ,t4 ,this piece carries the limb of the instrument ,,ss by a centred collar to which it is attached by screws4 ,about the centre of the body-piece an inset collar is formed to take the clamp ,,kk which bites upon it4 ,the lower outer part of the body-piece forms a conical fitting in the boss of the upper parallel plate ,l4 ,the interior is a hollow conical axis4 ,the body-piece is generally made of hard gun-metal4 ,the greatest possible care is required in its manufacture1 art4 #ba4 ,the interior and exterior should be perfectly concentric at every part4 ,much of the value of the instrument depends upon the perfection of the work in this piece4 #cge4--;,axis ,collar ,clamp ,k has been already described1 art4 #cdi1 and is illustrated in ,fig4 #adf1 which is taken from a theodolite1 so that only specialities in relation to the instrument ,fig4 #aec need be noted4 ,this clamp surrounds the body-piece and clamps it by means of the screw ,k shown on the left hand4 ,the clamp is connected with the upper parallel plate through the tangent screw1 the head of which is shown at ,p1 so that when the screw ,k is tightened the parts ,l and ,t are fixed together1 except that a slow motion can be given to these parts by the tangent screw ,p4 ,by this clamp and tangent arrangement the whole of the upper part of the instrument is rendered free to revolve1 to bring the instrument to bearing when the clamp is loosened1 the final adjustment being secured after clamping by the tangent screw4 ,it is this part of the instrument which is used after setting it up to bring the magnetic needle true to magnetic north1 or otherwise to direct the telescope to any established distant mark1 object1 or star that may be fixed for the zero or other index point of the horizontal circle1 to which all readings from its position are referred4 #cgf4--,the ,central ,vertical ,axis is shown only in half section at ,z4 ,this is made uniformly of bell-metal1 in the form of a truncated cone1 extending from the horizontal circle plate ,s to the interior of the socket ,n4 ,its fitting surfaces are at the two ends of the cone1 extending about half an inch1 the central part being chambered back4 ,at the upper part a pin-piece centres the vernier plate1 to which it is attached by a wide collar with three or four screws4 ,a square shoulder rests with weight only just sufficient to support the instrument upon the body-piece4 ,this part has to be so adjusted that the axis perfectly fits and yet moves freely4 ,a square-hole collar and screw are fixed on the lower end of the axis1 just to touch the socket of the body-piece1 so as to secure the axis in its position when the instrument is lifted4 ,an eye or a hook is fixed into the screw at the lower end to take the cord of the plummet used for fixing the instrument over a definite point on the ground4 ,this is not shown in the engraving4 #cgg4--,the axis of an ordinary theodolite is made the weakest part4 ,it is generally considered in the trade right for it to be so1 as in case of accident no other part of the vertical axis system is likely to be deranged2 and this is the easiest part to replace1 being1 as it were1 independent of other fittings4 ,whether this should be taken cum grano salis is a question2 at any rate with the axis weak it is not policy to load the upper part of the instrument with metal--which in places at least1 is generally made ten times as strong as the axis--when the instrument has to be carried about by a person over his shoulder4 ,some suggestions will be made on this point hereafter4 #cgh4--,the ,horizontal or ,lower ,plate or ,limb4--,sometimes the whole of the piece ,,ss is termed the limb1 but more generally this word is applied to the divided part only4 ,this plate is of brass1 and is attached to the body-piece by screws4 ,the outer rim1 which is somewhat triangular section1 is undercut upon the inner side of its lower surface to support the clamp-piece1 the outer edge being turned to a fillet to take the clamp which is rebated to fit it4 ,the upper surface of the rim1 or the limb proper1 is turned to the frustum of a cone of about #de4 ,this part is covered with silver1 which is beaten out to the conical form and soldered down upon it1 and afterwards turned to true form4 ,the dividing has been discussed in the last chapter4 ,the #f-;inch instrument is generally divided to #bj1 but sometimes to #cj1 and the vernier reads to #bj or #cj4 ,the figuring is from #j to #cfj1 right to left1 taken facing the instrument4 #cgi4--,the ,vernier ,plate is shown in section under ,p4 ,the vernier from which it is named is shown at ,,vv1 ,fig4 #aee4 ,the vernier plate is carried from the central axis and forms the foundation for all the superstructure4 ,the upper and lower plates are left very free where they are brought together1 the verniers being generally sprung down just to gently touch the limb4 ,the vernier surface is let down some distance into its plate for protection4 ,the reading of the vernier has been discussed in the last chapter4 #chj4--;,it may be particularly noted1 as already stated1 that the central axis and the body-piece are attached to the vernier and horizontal plates by screws4 ,this plan might strike one as being unsound3 it is not really so1 the reason for this construction being that these axes are1 or should be1 of bell-metal1 and that this metal being very hard and brittle it would not be so easily worked1 or so serviceable as brass for the limb and vernier plate1 neither would there be means of correcting errors which generally occur both in the workmanship and in the dividing of this delicate part4 ,the adjustment for fixing the limb and vernier plate1 technically called centring1 in particular requires considerable technical skill4 ,it is generally performed by the divider1 who is a specially intelligent artisan4 ,in the author's improved theodolite1 to be described further on1 the axis is in one casting with the standard2 but in this case the construction is different1 the axis being made larger and the whole body being in a special gun-metal which approaches bell-metal in hardness4 #cha4--,the vernier plate carries the ball nut of the tangent screw1 shown at ,fig4 #aec;,j4 ,the general arrangement may be seen by the section1 but is more fully described art4 #cdg4 ,one thing is important in this screw1 viz41 that it should range without strain quite parallel with the plates1 so as not to give the slightest tendency to elevate or depress the edge upon which it is placed during motion in any part of its thread4 ,the clamp is sometimes placed between the plates4 #chb4--,the ,compass-box4--,the general construction of this is shown1 ,fig4 #aee1 ,w4 ,in the transit theodolite it is fixed firmly by screws to the vernier plate and is made to form a steadying piece to the ,a-frames ,c ,c which support the upper part of the instrument4 ,for this purpose the compass-box is made as a solid casting in brass1 which is much stiffened by the raised step which forms the divided circle4 ,four solid lugs in the same casting project from the rim of the compass1 and form stiffening pieces between the lower parts of the ,a-frames2 these are secured to the lugs by four screws1 one of which is shown1 ,fig4 #aec1 at a4 ,the lug screws hold the whole superstructure together quite independently of the vernier plate1 to which it is afterwards firmly fixed4 ,the compass needle is lifted by means of a milled head1 just inside one of the standards1 not shown4 ,for a general description of the compass-box see art4 #ach4 ,the vernier plate carries two or more verniers4 ,the verniers are read by a pair of microscopes1 ,fig4 #aee ,,mm placed one on each end of a radial arm ,n having its axis of motion upon a large collar of the vertical axis4 ,by this plan1 when one microscope is set to read by the coincidence of lines upon one of the verniers1 the other microscope on the other arm or arms will be set also in like position over the other vernier or verniers4 ,illustration3 ,fig4 #aed4--,vertical circle with clipping arm of transit theodolite4 ,the verniers are adjusted ready for reading when the telescope is accurately directed upon any object of which it is desired to ascertain the angular position in relation to magnetic north1 or a definite object4 ,the vernier plate also carries a spirit level at ,o1 ,fig4 #aec1 which is adjustable by a pair of capstan-headed screws4 ,illustration3 ,fig4 #aee4--;,cross section of the upper part of a transit theodolite4 #chc4--,the ,standards or ,a-,frames1 shown ,c ,c ,fig4 #aee1 are solid castings in brass of about #g inches in height4 ,they are set up upon the vernier plate1 to which they are attached by four stout screws1 as also by cross screws to the compass as stated4 ,this renders the superstructure of the transit as firm as may be in a built-up construction4 ,upon the front of one of the standards a spirit level1 ,figs4 #aec1 #aee1 ,i1 is placed adjustable by two capstan screws4 ,this level1 and one shown ,fig4 #aec at #j on the vernier plate are used entirely in setting up the instrument2 and being placed at right angles to each other1 are a means of making the vernier plate quite level4 ,upon the inside of each of the standards1 at about #b inches from the vernier plate1 a clip-piece1 ,figs4 #aed1 #aee1 ,p is secured by two screws4 ,this takes the clipping screws1 ,fig4 #aed ,,hh to be described4 ,at the top of the standards two ,v's are formed1 upon which the transit axis rests4 ,one of these is cut out of the solid casting4 ,the other as shown in half section ,fig4 #aee c is formed as a parallel sliding piece with the ,v at the top placed in a vertical slot formed in the standard4 ,this sliding piece has a screwed stem continued from its lower surface that passes through a vertical hole at the top of the ,a-frame1 which is formed here as a cross-piece4 ,upon the screw two capstan nuts are placed1 one on each side of the cross-piece1 ,fig4 #aee xx2 these permit the adjustment of this in height so as to get the transit axis perfectly horizontal when the vertical axis is perfectly perpendicular to the horizon4 ,the sliding piece is covered by plates back and front to render it firm in its position4 ,the transit axis in practice is adjusted with a striding level which will be described presently4 ,with the author's theodolites from #f inches downwards the old-fashioned adjustment to one upright for levelling the horizontal axis has been dispensed with for many years1 and is only fitted if specially ordered1 as it has been found to be a frequent source of error4 ,long experience has proved beyond doubt that the fewer adjustments there are1 and the more parts that can be fashioned from the solid metal correctly1 the longer will the instrument keep in adjustment4 ,should there ever be any wear on either of the ,v's a few strokes with a piece of very fine emery paper upon the opposite one will put it right in half the time that it could be corrected with the old-fashioned adjustable ,v1 and no amount of vibration can alter it as with the adjusting screws4 ,an axis cover cap bb is placed on the top of each standard4 ,the cap is screwed down at one end with a cut screw and collar4 ,the screw is used for adjustment to gentle pressure on the axis4 ,the second screw is a milled head ,,ee4 ,under this screw the cap is slotted out to one side1 and turns on the cut screw as an axis to open the cap without removing its milled-head screw1 so that the telescope can be lifted out to turn its face to the opposite side of the instrument4 ,in the under side of the centre of the cap a cell is bored out1 into which a small cork is fitted1 which produces1 when the cap is clamped down1 a soft elastic pressure on the axis4 #chd4--,the ,transit ,axis which supports the telescope rests at its ends upon two trunnions1 ,figs4 #aed1 #aee ,,aa1 technically called pivots1 in the ,v's of the standards already described4 ,the pivots are turned as true as possible1 and afterwards ground to exactly equal size in a collar1 so that they may be reversed end for end in their bearings without changing the linear direction of the transit axis1 except by the little difference of pressure that one end of the axis imposes by the weight of the vertical circle and its attachments being eccentric4 ,in larger instruments this difference of weight is counterbalanced1 as shown in dotted lines at p1 ,fig4 #aee4 ,the centre of the transit axis is formed into a collar e of about #a inches in width1 which exactly fits the outer tube of the telescope1 and to which it is fixed with soft solder4 ,the collar is directly connected with and supports a flange f4 ,upon this flange the vertical circle ,,ff is fixed by three or four screws4 #che4--;,in front of the vertical circle a flanged collar-piece carries the vertical vernier frame ,,vv1 ,fig4 #aed1 centred upon it4 ,the vernier frame is attached by three screws to the clipping arm to be described1 and in front of this the vertical microscope arms are centred4 ,these carry two readers ,u1 ,fig4 #aee1 exactly similar to those which read upon the horizontal circle1 and they are similarly centred1 so that by setting one1 the other is set at exactly #ahj from it4 ,in front of the centre of the microscope arms on the transit axis1 an axis collar-piece j is attached by three screws cut directly into the axis4 ,this collar and one at the other end of the axis ,a1 turned out of the solid1 are nicely fitted to the opening between the standards to prevent lateral displacement of the axis4 #chf4--,the ,clips4--,the clipping arm1 which is centred on the transit axis and attached to the verniers1 is shown ,fig4 #aed ,,bb,b4 ,it is fitted to move freely on its axis at ,a1 so as to permit unrestrained motion of the telescope4 ,a milled-head clamping screw with clamp1 ,fig4 #aee1 ,k1 and the same partly cut away to show the slot in which it works1 are shown at ,k ,fig4 #aed4 ,this is used to fix the verniers stationary on the circle1 except for the adjustment by the tangent screw ,g1 which has its collar attached to the clipping arm1 and its ball nut attached to the clamp at ,d when using the telescope for levelling4 ,this clamp and tangent sets the vernier to zero on the circle4 ,it is also used in setting the telescope before angles of altitude or depression can be measured4 ,the clipping screws ,,hh are used to bring the principal bubble ,b1 ,fig4 #aec1 on the top of the telescope to the centre of its run after the verniers have been brought to zero by means of the clamp and tangent screws4 ,the clipping screws hold the clips1 ,fig4 #aee1 ,p or ,p to the one standard or the other4 ,the whole of the vertical adjustment is exactly equivalent to that already described for the horizontal motion1 except that it is placed in the vertical plane4 #chg4--,the ,vertical ,circle1 ,figs4 #aed1 #aee1 ,f is carried by four arms from a central boss attached firmly by screws to the transit axis4 ,it is grooved at the edge to take the clamp-piece4 ,the silver is inlaid in this circle in the manner shown ,fig4 #aag4 ,the vernier is read upon the circle on the plan shown ,fig4 #abg4 ,the circle is divided generally to half degrees or #bj1 and is figured #j to the horizontal with #ij upwards and downwards4 ,the zero lines are made directly coincident with the optical axis of the telescope when it is level4 ,the vernier reads to half minutes or #bj1 in either direction1 the rising arc above the level datum being considered as plus1 the falling arc as minus4 #chh4--,on the outer edge of the circle or at the back a scale of difference of hypotenuse and base reads to a line on a fiducial edge upon a part of the clip ,,bb1 ,fig4 #aed1 at ,n4 ,this scale is calculated for decimal quantities1 and gives the percentage number of links1 feet1 or metres to be deducted from the chain measurements upon the ground line to give the horizontal distance corresponding to the angle of inclination at which the telescope is set for observation4 #chi4--,the ,telescope1 ,fig4 #aec1 ,,dd has been described art4 #id4 ,its general construction is also shown in partial sections in the figure4 ,its body tube passes through the transit axis in which it is soldered4 #cij4--,the ,principal ,level ,tube is generally mounted on the telescope upon two stiff screws which rise from plates attached to the telescope body by pairs of screws4 ,each level screw has a pair of capstan nuts4 ,the level is mounted in a brass tube with stop-pieces at the ends1 each of which carries a tenon with a hole in its centre through which the level screw passes to be clamped top and bottom by the capstan nuts4 ,these nuts give adjustment to the level1 so that the centre of its inner upper surface may be placed parallel with the optical axis of the telescope4 ,illustration3 ,fig4 #aef4--,stanley's new model of #d-screw transit theodolite4 #cia4--,until #ahih the author was unwilling to attempt to remodel the old form of transit theodolite1 believing the #d-screw adjustment would soon become a method of the past1 but as a small demand continued from the ,colonies and ,united ,states for this form of instrument he felt bound to make it of more solid construction to bring it somewhat up to date4 ,the illustration shown1 ,fig4 #aef1 is of an instrument1 following in construction the transit theodolite already described in many details1 the marked exception being that the standards are in one casting with the compass-box and axis1 these being entirely shaped out in the solid metal4 ,the upper parallel plate is of special design1 being far stronger1 yet lighter1 and gives a much longer bearing to the levelling screws4 ,the lower parallel plate is also shaped with three feet so that the instrument may be set up without its stand when required4 ,it has also modern spring tangent adjustments with covered screws4 ,the limb is covered1 and the readers are jointed across the axis to turn up without separation4 ,it has a floating aluminium compass read by a microscope1 so that the instrument1 except in the four-screw arrangement for setting up1 embraces many modern improvements formerly applied only to special high-class theodolites4 ,the improved construction permits greater rigidity with fifteen per cent4 less weight4 ,illustration3 ,fig4 #aeg4--,the plummet4 ,illustration3 ,fig4 #aeh4--;,gurley's plummet4 ,illustration3 ,fig4 #aei4--,loop4 ,illustration3 ,fig4 #afj4--,ring plummet1 ,shortt's ,patent4 ,of later years1 however1 the demand for four-screw levelling instruments has been maintained1 especially from ,canada1 owing to the influence of the ,american school of teaching1 and in consequence all the author's improved theodolites are fitted with either three- or four-screw levelling1 whichever is desired4 ,it is a strange fact1 however1 that with all the ,american makers1 although they list all their ordinary instruments with four-screw levelling1 their refined ones1 which they term precision instruments1 will be found with three-screw levelling4 #cib4--;,detached parts of a ,theodolite4--,the ,plummet supplied with the theodolite is made to hang from a hook under the centre of the axis of the instrument1 the cord1 which is of soft silk1 being looped or knotted to hold in the hook4 ,the lower end of the plummet is brought to a point which1 when in use1 falls directly under the vertical centre of the instrument upon the surface of the ground4 ,in ,fig4 #aeg the screw and plummet are shown detached4 ,the cord ,c is attached to the plummet by passing it through a hole in the milled-head screw ,s at the top of the plummet1 and by making a knot ,k in the cord4 ,fig4 #afj shows an ingenious ring plummet recently invented and patented by ,mr4 ,w4 ,h4 ,shortt1 ,a4,m4 ,i4,c4,e4 ,the chief object was the production of a plumb bob whose plumbing point should be situated at1 or very close to1 the centre of oscillation in order that the position of the point might be unaffected by oscillation of the bob itself1 apart from any swing which it might have about the point of suspension of the string4 ,a further object was to shape the bob so that a person holding the string1 or standing close to it when attached to an instrument and looking down at the bob1 should be able to see readily the exact position of the plumbing point4 ,these objects have been attained by making the bob in the form of a ring1 so that the centre of oscillation which lies in the centre of the ring can itself be used as the plumbing point1 since it can be readily seen and indicated by the extremities of pointers projecting towards the centre from the inside of the ring4 ,a great advantage of this bob is that when plumbing on to a flat surface it does not fall over when lowered1 but may be allowed to actually lie on the surface while the position of the point is being marked4 ,also it can best be steadied by lowering into contact with the ground and raising again4 ,the plumbing pointers are largely protected from injury when the bob is in use1 and when not in use the suspension string can be wound diametrically across the bob1 in recesses provided for the purpose1 thus completely protecting the points4 #cic4--,the ,loop4--,it is somewhat difficult in the ordinary way to adjust the plummet to the station mark on the ground or on a peg4 ,the cord is sometimes placed in an ivory runner fixed to the top of the cord1 ,fig4 #aei4 ,this gives friction on the cord and permits extension and contraction of the loop for adjustment4 ,where the plummet has to be suspended from the instrument as well as from a hook inside the stand1 which is sometimes convenient1 it is better to have the runner cut out on one side4 ,this permits easy change and it is just as firm4 #cid4--,messrs4 ,gurley ,bros4 of ,troy1 ,n4,y41 have a good plan for shortening the plummet line4 ,this is effected by making a reel in the plummet1 which is wound by a milled head at the top of it1 ,fig4 #aeh4 #cie4--,screw-drivers1 ,tommy ,pins1 etc4--,a screw-driver and a tommy pin1 the last to turn the capstan heads1 are placed in the case with the theodolite4 ,two screw-drivers with proper handles are better1 as there are small and large screws4 ,a camel-hair brush to dust the instrument1 a piece of wash-leather1 a little vaseline1 and a small bottle of good watch oil are also very useful4 ,these little refinements are generally kept out to keep down the price of the instrument4 #cif4--;,additional ,parts1 and ,variations in ,theodolites4--,illuminated ,axis4--#d1 #e and #f-;inch transits sometimes1 and larger instruments always1 have the transit axis bored on one side through to the interior of the telescope1 as shown on ,fig4 #aee4 ,through the hole a small pencil of light is sent by a lamp l with a plano-convex lens front1 to a lens placed in the end of the axis4 ,this1 by a slight adjustment of the lamp on its stand1 focusses the light upon a small mirror placed within the telescope1 which reflects its rays to the diaphragm4 ,the lamp gives a faint light only sufficient to distinguish the webs for night and underground observations4 ,the mirror is about #a_/aj inch in diameter1 and is generally mounted upon a milled head screw tapped into the trunnion band of the telescope m4 ,the point of the screw is extended as a thin stem into the axis of the telescope1 where the mirror is held by it4 ,this arrangement permits the mirror1 which is generally made of silver1 but is much better of platino-iridium1 to be removed for cleaning4 ,the lamp is mounted upon a wooden stand w carried upon a slide n or upon two brass pins direct to the ,a-frame4 ,the wood is employed in this case to cut off conduction of heat to the near standard from the lamp as much as possible to prevent disturbance of the axis from expansion by heating4 ,the stand may be removed when the lamp is not required and placed in the case4 ,in large theodolites a pair of lamps are used1 that the transverse axis may not be heated more on one side than on the other4 #cig4--,the ,lamp1 which is found so convenient for bringing a star or distant light to read with the webs1 becomes difficult to use when the object is very faint1 as the light thrown into the telescope by the lamp takes off the effect of blackness of the night sky or that of total darkness4 ,this becomes important in taking observations of small stars1 as for instance1 the circumpolar stars of the southern hemisphere4 ,in some theodolites1 made first for the ,sydney ,government1 the author placed a very small lamp to throw light upon the face of the webs only1 making these appear as light lines on a black ground4 ,the reflecting eye-piece1 ,fig4 #bj1 will be found to answer very well1 and this is a simple1 inexpensive contrivance4 ,any amount of illumination desired may be thrown on the front of the diaphragm1 according to the distance at which the light is held from the eye-piece3 generally a very faint light only is required4 #cih4--,the author has illuminated the webs front and back by means of a very small 7one-quarter candle power7 incandescent lamp1 which is charged by a portable battery1 or a secondary battery where a dynamo is at hand for charging it1 and for countries where these cannot be renewed or where the extremes of temperature are too great for their use1 he has devised a small hand dynamo for generating the current and a rheostat for controlling the power of the lamp1 so that resistance may be employed to reduce the light to the faintest possible glimmer4 ,the electric lamp is far superior to the old oil lamp and safe to use in gaseous mines2 it is far cleaner1 does not give out a tithe of the heat1 and may be removed from its socket and used in the hand for reading the verniers in a bad light4 ,all the author's modern instruments that are required with illuminated axis are now fitted with electric lamps4 ,illustration3 ,fig4 #afa4--,trough needle for transit theodolite4 #cii4--;,a ,trough or ,long ,compass1 used in place of ,circular ,compass4--,a long compass1 ,fig4 #cb1 p4 #gd1 is often applied to a theodolite1 either upon the top of the telescope1 or more generally and conveniently for reading under the limb4 ,in this last case the trough needle is a separate piece1 which is only attached to the limb of the theodolite by means of loop slides or bayonet fittings under the limb1 when required to take a bearing4 ,the engraving ,fig4 #afa shows the long compass with bayonet fittings4 ,there are four slots1 two of which are shown ,,ss1 which fit in under the heads of round-headed1 shouldered screws4 ,the author has somewhat modified this pattern recently by making it slide into grooves4 ,the trough needle is generally made #e or #f inches long1 and reads into a short scale of about #aj at each end4 ,the divisions are best placed upon sliding fittings1 so that they may be adjusted by four screws from the outside of the box--screws shown ,,aa4 ,this enables the needle to be adjusted to its own axis1 and also to the #j reading of the horizontal limb of the theodolite4 ,a slide lift to the needle is shown at ,l4 ,when the same form of compass is used upon large instruments a reader is placed at each end of the needle4 ,illustration3 ,figs4 #afb1 #afc1 #afd4--,striding level4 #djj4--,striding ,level4--,for the adjustment of the transverse axis of a theodolite a very sensitive spirit level is used4 ,this is mounted upon a bed1 which may be formed of brass tubing1 from the two ends of which adjustable legs descend1 the ends of which are forked1 the hollows of the forks forming ,v bearing surfaces4 ,the ,v's rest upon the pivot of the axis4 ,by reversing the striding level on the pivots the transverse axis of the telescope1 or transit axis1 can be readily adjusted truly perpendicular to the vertical axis4 ,in the construction of the striding level1 shown in detail in ,fig4 #afb1 the two striding standards ,,ss are carried down from the ends of the casing tube ,b of the spirit level4 ,these are adjustable3 one1 ,fig4 #afd1 by raising or lowering the end of the level tube by the capstan screws ,,cc1 and the other1 ,fig4 #afc1 by a lateral adjustment of the capstan screws ,,pp that act upon the stud ,s1 which is fixed upon an arm centred upon the axis of the tube4 ,this connection is shown by dotted lines4 ,by these two motions the standards are brought to perfect parallelism with each other for their bearing surfaces and adjustment of the crown of the bubble tube4 ,illustration3 ,fig4 #afe4--,wallis' shifting centre for theodolites4 #dja4--;,adjustment of the ,axis for ,setting it up over a ,point4--,every surveyor experiences an amount of difficulty in getting the plummet to fall from the axis of the instrument exactly over a point upon the ground1 or a mark upon a rock1 or still more so upon a point in street paving in a town1 which is necessary for exact work4 ,it is easily set near the point1 that is1 within half an inch or so1 by pressing or shifting the legs2 but the difficulty increases as the exact point is approached1 so that the setting has generally to be left at a certain state of approximation4 ,there are a great number of schemes in use for moving the axis by adjustment of the instrument the small quantity required1 without disturbing the legs of the tripod when they are firmly set down nearly correct to position4 ,one of these would no doubt be generally applied to the theodolite1 except for the reason that every means yet devised adds to its weight1 and also to the expense of the instrument4 ,a moderately simple plan1 which is especially adapted to the parallel plate adjustment1 is to make the lower flange of the theodolite1 upon which it stands when set down off its tripod1 somewhat larger and thinner4 ,this flange1 instead of being screwed directly down upon the tripod head1 is placed between two ring plates1 which are clamped together when the theodolite is set in position4 ,the large hole in the centre of the ring permits movement of the lower plate of about #a inch4 ,fig4 #afe is an arrangement of this kind by ,mr4 ,j4 ,wallis4 ,this is made entirely independent of the theodolite1 and may be used or not as required4 ,i is a screw that corresponds with the head of the tripod which takes the theodolite2 ,t similar female screw to take the tripod head when the shifting centre is used2 ,,cc a box formed by screwing two tray-pieces firmly together2 ,s clamping flange2 ,,hh clamp screwed into the top of box ,c4 ,this has two handles by which the screw is moved to clamp when the instrument is in position4 ,the weight of this additional part is about #c lbs4 ,the arrangement is particularly adapted to parallel plate adjustments4 #djb4--;,in an ,american plan of a transit by ,messrs4 ,heller ,brightly1 the flange is lifted by the parallel plate screws1 which tighten it at the same time4#ah ,messrs4 ,troughton ,simms have a plan of shifting the axis by means of a pair of eccentric plates1 which carry the instrument in two directions nearly at right angles to each other4 ,by this arrangement an amount of leverage is secured which produces an easier motion than that of shifting the weight of the instrument on the plans mentioned above4 ,the author's schemes will be described as a part of his new theodolites a few pages on4 #djc4--,stadia ,webs or ,lines used for taking subtense angles by the telescope for measuring distances1 which are frequently applied to theodolites1 will be fully described1 ,chapter ,,xii41 in treating of subtense instruments generally4 #djd4--,solar ,attachment to a ,theodolite4--,this appliance is an adaptation to the theodolite of the solar compass of ,w4 ,a4 ,burt1 of ,michigan1 which was made to replace the magnetic compass in determining a true meridian1 or north and south line1 by observation of the sun only4 ,it was brought into general use in the surveys of the ,united ,states public lands4 ,the solar compass consists mainly of three arcs of circles by which the latitude of a place1 the declination of the sun1 and the hour of the day can be set off4 ,in the solar attachment to the theodolite the latitude arc is found unnecessary1 as this is formed by the vertical arc of the theodolite2 therefore the hour and declination arcs need only be described4 ,illustration3 ,fig4 #aff4--;,burt's solar attachment to a theodolite4 #dje4--,the ,hour ,circle1 ,fig4 #aff1 ,h is fixed upon the centre of the telescope upon a socket axis ,s1 which is placed perpendicularly to the optical axis and to the transverse axes or pivots of the theodolite4 ,this circle is divided to read five minutes of time1 and is figured ,i to ,,xii twice1 or ,i to ,,xxiv1 the index being a fine line carried down on a plate from the lower arm of the declination arc1 which is fixed to the socket ,s4 ,the hour circle1 when set to any reading1 may be clamped to this position by means of the milled head placed over the socket ,m4 #djf4--,the ,declination ,arc is of #e inches radius1 divided to read on the same plane with a vernier ,v to single minutes of arc4 ,the vernier arm is fixed by a clamp at ,c1 which carries tangent adjustment ,t4 ,at the back of the vernier arm two spur-pieces are carried out directly from it1 ,l and ,i4 ,these are blocks of metal about #a by #a by inches1 which carry each a lens of a focus ,l to ,i1 and a silver plate to be presently described1 upon which the sun's image is received in one direction or the other4 ,illustration3 ,fig4 #afg4--;,image plate of solar attachment4 #djg4--,the ,image ,plate1 ,fig4 #afg1 is marked with two sets of lines intersecting each other at right angles4 ,the lines bb are termed hour lines1 the lines cc equatorial lines2 these lines having reference respectively to the hour of the day and the position of the sun in relation to the equator4 ,the intervals between the lines bb and cc are just sufficient to include the circular image of the sun formed by the solar lens on the opposite end of the vernier arm4 ,the axes of the solar lenses and corresponding image plates are placed parallel with each other1 and with the direction of the vernier arm4 ,below the lower line c three other lines are cut at #e minutes apart4 ,these are useful for making allowance for refraction4 ,the following description for the use of the instrument is partly extracted from ,messrs4 ,gurley's manual4 #djh4--,when the instrument is made perfectly horizontal1 the equatorial lines and the opposite lenses being accurately adjusted to each other by a previous operation1 the sun's position in the heavens with reference to the horizon will be defined with precision4 ,suppose the observation to be made at the time of one of the equinoxes2 the arm ,r set at zero on the declination arc ,v2 and the polar axis is placed exactly parallel to the axis of the earth4 ,then the motion of the arm ,r1 if revolved on the polar axis around the hour circle ,h1 will exactly correspond with the motion of the sun in the heavens on the given day and at the place of observation2 so that if the sun's image be brought between the lines cc on the image plate in the morning it will continue in the same position1 passing neither above nor below the lines as the arm is made to revolve in following the motion of the sun about the earth4 #dji4--;,in the morning as the sun rises from the horizon1 the arm ,r will be in a position nearly at right angles to that shown in the illustration1 the lens being turned towards the sun and the silver plate1 on which his image is thrown1 directly opposite4 ,as the sun ascends1 the arm must be moved around1 until when he has reached the meridian1 the graduated side of the declination arc will indicate ,,xii on the hour circle2 and the arm ,r1 the declination arc ,v1 and the latitude arc1 that is the vertical arc of the theodolite1 will be in the same plane4 ,as the sun declines from the meridian the arm ,r must be moved in the same direction1 until at sunset its position will be the exact reverse of that it occupied in the morning4 #daj4--;,allowance for ,declination4--,let us now suppose the observation made when the sun has passed the equinoctial point1 and when his position is affected by declination4 ,then1 by referring to the ,nautical ,almanac and setting off on the arc his declination for the given day and hour1 we are still able to determine his position with the same certainty as if he remained on the equator4 ,when the sun's declination is south1 that is1 from the #bbnd of ,september to the #bjth of ,march in each year1 the arc ,r is turned towards the plates of the instrument in the opposite position to that shown in the engraving1 using the solar lens at ,i1 with the silver plate opposite at ,l4 ,the remainder of the year the arc is turned from the plates1 and the lens at ,l and plates at ,i are employed in the position shown in the figure4 #daa4--,when the solar compass is accurately adjusted and its plates made perfectly horizontal1 the latitudes of the place and the declination of the sun for the given day and hour being also set off on their respective arcs1 the image of the sun cannot be brought between the equatorial lines until the polar axis is placed in the plane of the meridian of the place1 or in a position parallel to the axis of the earth4 ,the slightest deviation from this position will cause the image to pass above or below the lines and thus discover the error4 #dab4--,we thus1 from the position of the sun in the solar system1 obtain a certain direction absolutely unchangeable from which to run our lines and measure the horizontal angles required4 ,the transit theodolite will1 without the solar compass1 perform the same functions2 but by means of this instrument the calculation for position is much more simple4 #dac4--,photographic ,apparatus in ,connection with the ,theodolite4--,the application of photographic apparatus as an accessory to surveying instruments has been tried tentatively for many years4 ,a practical introduction to the subject was first given by ,m4 ,laussedat in a paper published in the ,comptes ,rendus de l',academie des ,sciences1 #ahei4 ,the subject has since been well studied by many writers1 and is written up extensively by ,dr4 ,e4 ,deville1 ,,ll4,d41 ,surveyor-,general of ,canada1 in a work entitled ,photographic ,surveying1 published in ,ottawa1 to which we must refer the reader for full discussion of the subject4 ,in ,england1 ,mr4 ,j4 ,bridges ,lee has invented a very suitable camera in which a negative glass photograph of #d #c inches is taken1 with an axis line from the shadow of a hair permanently photographed coincident with the axis to the telescope as it appears to view4 ,at the same time degrees and subdivisions are taken on the photograph to right and left of the axial line4 ,the edge of the magnetic circle is also photographed upon the plate1 indicating clearly the bearing of the station taken by the axis line4 ,the whole of these operations are performed at once in a perfect manner4 #dad4--,mr4 ,j4 ,bridges ,lee's photo-theodolite was made in excellent workmanship by ,messrs4 ,troughton ,simms4 ,the inventor has published a paper on the subject1 to be had of the ,society of ,engineers1 ,westminster4 ,illustration3 ,fig4 #afh4--,light camera upon the telescope of a theodolite4 ,at the present time a camera is very commonly taken by a civil engineer for prospecting in new countries1--a convenient form of this will be discussed at nearly the end of this work--but it is not generally held that photography will ever offer a means of expeditious surveying1 except possibly in very mountainous countries where the necessary stations for observation become difficult of approach and of clear definition4 ,the objections to the more general adoption of photography are1 otherwise1 that the processes are in degree tedious1 and require special skill in manipulation1 and that the apparatus is heavy and expensive with sensitive glass plates for use with it4 #dae4--,there are many cases1 no doubt1 where a photograph would be valuable for the exact definition of a station4 ,to meet this case the author has made a small light camera1 shown ,fig4 #afh1 giving photographs #b #b inches only1 with axis line from shadow of a point4 ,the camera to be placed when required upon the telescope of a theodolite for special cases4 ,he has lately used his patent slide for this camera that carries films which will be further described at the end of this work4 ,the films are unbreakable1 and remain sensitive many years if kept dry4 ,the weight of this camera with its double slides and #ajj films is about #a lb4 ,there is ample room for it in the ordinary theodolite case4 ,,footnotes3 #ae ,digges's ,pantometria1 see p4 #b4 #af ,gardiner's ,practical ,surveying1 p4 #ei1 #agcg4 #ag ,adam's ,geometrical ,essays1 pp4 #bag-bbi1 #ahjc4 #ah ,civil ,engineers' ,pocket-,book1 by ,j4 ,c4 ,trautwine1 ,c4,e4 ,,chapter ,,viii4 ,,specialities ,,in ,,modern ,,and ,,improved ,,forms ,,of ,,transit ,,theodolites ,,for ,,surveying--,,railway ,,work--,,exploring4 #daf4--,the description given in the last chapter of a #f-;inch transit theodolite gives all particulars of the original ,old ,english form1 which in a general way comprises the constructive principles of all others4 ,when we consider modern instruments the details are found to vary greatly1 but most particularly in the direction of uniting in solid castings many parts that may be shaped out by machinery in a manner impossible by hand-work1 which avoids the instability of the work being screwed together in many pieces1 and makes it at the same time lighter1 more rigid1 and less liable to jar out of adjustment4 ,this direction of construction is also followed in the best modern work on the ,continent and in ,america4 ,it would extend this work beyond convenient limits to offer details of the wide variations employed in practice1 but as the author has made this subject a life study1 and has embraced1 modified1 and endeavoured to improve this class of work in all its details1 freely adopting any improvement he has observed1 his own instruments will represent largely his present ideas of the best forms1 with the economy of having engravings for illustration to hand4 ,transit theodolites of portable form will be considered here1 leaving larger stationary instruments to another chapter4 ,illustration3 ,fig4 #afi4--,stanley's patent new model theodolite4 #dag4--,new ,model ,transit ,theodolite4--,in this instrument the principles of construction are the same as in the ordinary transit theodolite fully described in the last chapter1 but the distribution of materials and details are very different4 ,the general arrangement of a #e-;inch instrument is shown in ,fig4 #afi4 ,one important difference1 as before mentioned1 is that the work is not built up so much in separate castings and pieces as is usual1 but every possible casting is shaped out of the solid to the finished form4 ,the vertical axis is of nearly the same construction as the ordinary transit1 except that the central axis is about double as strong1 being of once and a half the ordinary diameter4 ,it is made in one casting with the upper framework4 ,the vernier plate is formed of thin hard hammered gun-metal1 which is screwed upon the axis4 ,this plate has not in this construction to support the superstructure as in an ordinary theodolite1 but has only to hold the two axis bubbles1 which are thereby brought distinctly in view1 and the clamp and tangent motion1 which is also placed conveniently for use upon this upper plate1 in a position where there is less risk of accident than when it is placed upon the outer edge of the limb4 #dah4--,the ,readers to the horizontal limb are jointed to turn up against the standards and adjust for reflection1 as shown ,fig4 #aca4 ,in this manner the readers do not need detachment to place the instrument in its case4 ,illustration3 ,fig4 #agj4--,section of standards of new model theodolite4 #dai4--,the ,central ,axis and the standards are made in one casting in hard gun-metal4 ,the standards are of light cylindrical and ribbed section4 ,this construction1 although of only about one-half the weight of the ,a-frame arrangement with its attachments1 described in the last chapter1 was found upon testing to have more than double the rigidity in resisting deflection1 with perfect certainty of avoiding the accidental occurrence of imperfect fitting of parts1 or of screws jarring loose1 ,fig4 #agj4 ,the making of the vertical axis and the standards in one piece was in a certain sense an experiment4 ,it has been found in practice of many years now to give much greater resistance to all ordinary strains and jars1 and ensure the instrument keeping in order and adjustment when jolted by carrying over the shoulder1 just as the same principle acts in the dumpy level2 but at the same time1 in cases of violent accident1 such as the fall of the instrument from a height1 it renders repairs somewhat more expensive1 as this entire part might have to be reinstated instead of the axis only1 the axis of the theodolite being generally made very weak that it may go first1 often indeed with a slight jar4 ,many details are the same as the transit theodolite before described1 adopting what is thought to be the soundest principle in all cases4 #dbj4--,the ,compass-box in this instrument is attached under the limb4 ,it is of the trough form shown ,fig4 #cb1 page #gd4 ,the magnetic north is set to zero4 ,the tribrach is of the form described for levels1 illustrated ,figs4 #gb and #gc1 p4 #abh4 #dba4--,the weights of transit theodolites of this construction are about #f-;inch in gun metal #ad lbs41 aluminium1 #h lbs4 #e-;inch #aa #f #d-;inch #g #d ,this pattern embodies all the essential features of a thoroughly reliable and convenient instrument for all-round general surveying4 ,it has no unnecessary elaborations and is a strong1 light and compact instrument suitable for continuous hard wear4 ,it has fewer pieces than any other design and is packed in its case complete in one piece ready to screw upon its stand upon being taken out of its case4 ,illustration3 ,fig4 #aga4--,stanley's simple sliding stage for tribrach theodolite4 #dbb4--,the author has devised a special arrangement for displacement of axis for this theodolite1 which does not interfere with its valuable quality of standing the tribrach on a wall or flat surface1 ,fig4 #aga4 ,in this scheme the arms of the tribrach are slightly elevated by the foot screws4 ,a flange is formed on the top of the head with a leading tube through it to the upper surface of the lower tribrach plate2 upon this tube an upper flange is screwed1 so that the plate comes between the two flanges1 where it may be fixed by means of rotation of the flange by a thumb-piece4 ,the engraving shows the arrangement with the axis displaced to its extreme point1 about of an inch from the centre4 ,illustration3 ,fig4 #agb4--,stanley's #d-screw sliding stage4 ,illustration3 ,fig4 #agc4--,stanley's solid round form tripod with sliding head4 ,illustration3 ,fig4 #agd4--,stanley's telescopic tripod with sliding head4 ,a somewhat similar arrangement is made for four-screw levelling instruments shown on page #bej at ,fig4 #agb1 but in this the sliding motion is fixed to position by the action of the levelling screws4 ,it is sometimes preferred to have the sliding adjustment upon the tripod head instead of upon the instrument1 and in some cases for getting a greater range of movement1 on both1 and for this purpose the reviser has designed the two tripods shown at ,figs4 #agc and #agd1 the former being of the round solid pattern1 and the latter having adjustable sliding legs4 ,a somewhat similar arrangement is made for a sliding head to a framed tripod as shown below1 ,fig4 #age4 ,illustration3 ,fig4 #age4--,stanley's framed stand with sliding head4 #dbc4--;,improved ,transit with ,adjustable ,axis4--,this instrument1 ,fig4 #agf1 in general1 resembles that last described1 except that it has a larger telescope and it is mounted on a sliding stage with screw adjustments1 which is particularly described below4 ,it is frequently provided with a tacheometrical eye-piece for giving horizontal distances by subtense taken on the incline1 which will be described in ,chapter ,,xii4 ,illustration3 ,fig4 #agf4--,stanley's patent new model theodolite1 with mechanical stage4 #dbd4--,the ,mechanical ,tribrach ,stage4--,this important addition to the theodolite above described permits exact adjustment over a station4 ,the upper plate of the tribrach with the movable stage is shown in ,fig4 #agg4 ,a dovetail slide is fitted upon the base of the stage adjustable for wear by a slip-piece with two screws at the narrow part4 ,the slide is adjusted to position in the direction of its dovetail fitting by a large milled screw so as to move the whole instrument above it for centring in this direction4 ,an upper slide acting in the same manner1 with dovetail fitting pieces at sides moves for an equal distance for centring transverse to the lower slide by a milled head4 ,this gives the same kind of motion of displacement that we have in the slide rest of a lathe or the mechanical stage of a microscope1 except that in this case we have a kind of three-point bearing surface4 ,the motion given to the screws permits the perfect adjustment of the theodolite over a point on the ground corresponding with the suspended plummet1 after the instrument is set up to nearly its true position by movement of the tripod legs4 ,the range of motion is from to #a inch1 a quantity quite sufficient for final adjustment1 but which does not materially affect the equilibrium of the instrument upon its rigid tripod1 as it has in this case a broad solid base even in the extreme positions of the slide4 ,illustration3 ,fig4 #agg4--,stanley's patent tribrach mechanical stage4 ,this movement being above the levelling screws1 the adjustment of the instrument for level is not affected by its use1 as in the case of all sliding arrangements below the levelling screws4 ,suitable means are provided for taking up any wear that might occur in the slides4 #dbe4--,the above stage is supported upon three foot screws1 the female fittings being specially long to give plenty of bearing surface to prevent wear2 they are sawn down on one side so that they spring lightly upon the screws1 and are provided with cross capstan screws for tightening up when necessary4 ,this plan gives the screw about inch of thread1 and permits adjustment for comfortable movement and for wear without any risk of shakiness4 ,the screw in larger instruments of this class has a cap to exclude dust4 ,the foot of the screw has a ball which rests in a slotted tube before described1 ,fig4 #ga1 p4 #abg4 #dbf4--,this theodolite with mechanical stage is generally fitted with illuminated axis for tunnel work1 art4 #chc4 ,the lamp is not shown in the illustration4 ,the weights of this make of theodolite are about #f-;inch in gun-metal #ah lbs41 aluminium #aj lbs4 #e-;inch #ac #g #d-;inch #i #d #dbg4--h-;inch ,transit ,theodolite4--,for ordinary surveying the smaller instruments are sufficient4 ,for opening a survey in new countries the #h-;inch instrument1 ,fig4 #agh1 or a larger one1 is generally used for the superior triangulation1 particularly for observations at night of distant lights when greater light-grasping power is demanded of the telescope4 ,the larger circle gives a more exact reading of the limb1 which is generally divided to read clearly to ten seconds of arc1 and by estimation sufficiently near to obtain five seconds reading very approximately with the verniers4 ,when instruments exceed #h-;inches1 the reading is by means of microscopes1 the application of which will be described further on4 ,illustration3 ,fig4 #agh4--h-;inch transit theodolite4 #dbh4--,the #h-;inch transit illustrated is of the author's model4 ,it is in general structure similar to the #f-;inch just described1 except in certain specialities4 ,the instrument does not clamp upon the vertical circle1 but a similar circle is provided upon the opposite side of the axis4 ,this answers two purposes1 it balances the pressure upon the pivots and obviates disturbance of the division by the clamp4 ,the principal bubble is supported upon the vernier frame1 as special exactness is not required for the instrument to be used as a level4 ,the base support is upon the ,everest tribrach system1 which will be described in the next chapter4 ,a long compass is shown1 but a telescopic compass is sometimes used4 ,the instrument is shown with an axis-lamp and diagonal eye-piece for star observation4 ,illustration3 ,fig4 #agi4--,stanley's quick-setting transit theodolite4 #dbi4--,the vertical axis of this instrument is sometimes pierced for a look-down telescope to sight its vertical position on the ground to the centre of a peg4 ,this will be described with geodetic instruments in the next chapter4 ,it is an expensive refinement1 seldom necessary1 as the axis with plummet may easily be brought within the tenth of an inch4 ,theodolites of eight inches and over are uniformly packed in two cases4 ,the lower part is packed in a case by itself1 the upper parts connected with the vertical circle and all the accessories1 eye-piece1 plummet1 etc41 forming the contents of another case1 each part being sufficient for one man to carry without the tripod4 ,the weight of the entire instrument is #bi lbs4 #dcj--,quick-setting ,theodolites4--,the demand for instruments with quick-setting arrangements has greatly increased of late years4 ,they save a great deal of time in setting up1 and also save wear of the levelling screws1 as the instrument may be instantly set nearly level by its means1 so that less than half a turn of the levelling screws will bring it to true level4 ,an ordinary transit is shown ,fig4 #agi1 fitted with a similar arrangement to that described art4 #bdj1 p4 #acb4 ,illustration3 ,fig4 #ahj4--,railway theodolite4 #dca4--,railway ,theodolite4--,there are objections made to the transit theodolite by some civil engineers that it is a large and heavy instrument1 only to be accepted for its perfect convenience over lighter forms4 ,to meet this objection the author has made a special transit theodolite1 ,fig4 #ahj1 which is sufficient for railway work and general surveying upon moderately level country4 ,the transit principle is conserved by balancing the telescope on its axis to permit it to transit over the eye-end only4 ,the vertical arc is omitted as being unnecessary for railway work4 ,the instrument is constructed especially low and of great rigidity and solidity1 with light weight4 ,the compass is of the trough kind4 ,the limb is covered for protection4 ,it is extremely portable4 ,weight of #d-;inch1 #g lbs42 #e-;inch1 #i lbs42 #f-;inch1 #ab lbs4 ,being constructed for rough1 hard wear and local use it is not made in aluminium4 #dcb4--;,for tunnelling underground railways the mining theodolite described further on will be found the most valuable for railway engineers4 #dcc4--,mountain ,transit ,theodolite4--,this instrument1 ,fig4 #aha1 is designed for geographical exploration1 and making sketch surveys4 ,it embraces the transit principle for the convenience of taking zenith stars4 ,it is made in #c-;inch and #d-;inch sizes4 ,it has two verniers to the horizontal limb reading to minutes1 and a single vernier to the vertical circle4 ,it has been made by the author in aluminium alloy only1 the total weight being #b lbs4 for the #c-;inch and #c lbs4 for the #d-;inch4 ,the eye-piece reads direct or diagonally4 ,it has clamp and tangent adjustment to both circles1 and a trough compass4 ,the tripod slides up to half length1 each leg being adjustable to fix to any length within the range of the slide to accommodate it to the surface of inclined rocks4 #dcd4--;,a ,mountain ,theodolite is a term applied to any very small or light theodolite4 ,these are generally made to order1 very frequently to a reduced model of a larger theodolite1 #c inches being a common size4 ,the telescope is occasionally placed upon the side of the horizontal axis to transit4 ,theodolites of this class generally weigh much more than the above-described instrument1 a common weight being #e to #g lbs4 ,illustration3 ,fig4 #aha4--,stanley's mountain transit theodolite4 #dce4--;,improved ,solar ,attachment4--,the reviser's improved solar attachment admits of a full vertical circle being employed2 it also has a clamp and tangent to the hour circle and declination arc and quick acting clamp and fine adjustment to the solar arm4 ,an instrument so fitted is shown on p4 #bfj1 ,fig4 #ahb4 ,illustration3 ,fig4 #ahb4--,stanley's solar attachment4 #dcf4--,micrometer ,reading ,theodolites4--,the favor with which the smaller micrometer reading theodolites have been received and the ever increasing demand for them owing to their much greater accuracy has induced the reviser to introduce a whole range of these instruments4 ,in many cases where greater accuracy is required for horizontal than for vertical angles1 the micrometers are only fitted to the horizontal circle and the vertical circle has verniers as usual4 ,a useful instrument for general surveying without any unnecessary elaboration is shown below at ,fig4 #ahc4 ,illustration3 ,fig4 #ahc4--,stanley's micrometer transit theodolite4 ,the #f-;inch instrument reads to #e seconds of arc on the horizontal and to #aj seconds of arc on the vertical circle1 and the #e-;inch instrument to #aj seconds of arc on the horizontal and to #bj seconds of arc on the vertical circle4 ,a full micrometer reading instrument is shown at ,fig4 #ahd1 the #f-;inch reading to #e seconds of arc on both circles and the #e-;inch reading to #aj seconds of arc on both circles4 ,illustration3 ,fig4 #ahd4--,stanley's full micrometer transit theodolite4 ,a specially light form of micrometer reading transit 7,fig4 #ahe7 has recently been designed by the reviser which has met with much favour4 ,it has a #d-;inch horizontal circle reading by micrometers to #bj seconds of arc which may be approximately read by mental subdivision to #e seconds1 and a #d-;inch vertical circle reading by verniers to single minutes4 ,it is also made micrometer reading to #bj seconds of arc to both circles4 ,the compass is of circular form reading by microscope to -degrees1 which may easily be estimated to a third of this4 ,illustration3 ,fig4 #ahe4--,stanley's light micrometer transit4 ,an example of a more refined micrometer transit is shown at ,fig4 #ahf4 ,this instrument was designed by ,dr4 ,e4 ,deville1 ,,ll4,d41 ,surveyor-,general of ,canada1 and is arranged for latitude determination by ,talcott's ,system1 and general geodetic work4 ,illustration3 ,fig4 #ahf4--;,dr4 ,deville's transit4 ,it has a #f-;inch horizontal circle reading by micrometers to #e seconds of arc1 and a #d-;inch vertical circle reading by vernier to #a minute1 with zenith spirit level graduated to #b seconds of arc1 detachable and interchangeable with a small level for ordinary use4 ,the telescope is #ad inches solar focus with large object glass so that observations may be taken of stars up to the sixth magnitude2 it has a revolving micrometer diaphragm and electric illumination to micrometers1 to diaphragm both front and back1 and to zenith spirit level1 it has also a rheostat for regulating the amount of light1 and a dynamo generator for supplying the current4 ,illustration3 ,fig4 #ahg4--,stanley's patent universal transit theodolite4 ,the universal transit designed by the reviser is shown at ,fig4 #ahg4 ,this is an #h-;inch instrument1 reading by micrometers on both circles to #b seconds of arc1 and is fitted with all the necessary arrangements for universal work4 ,a description of the larger geodetic instruments is given in a subsequent chapter4 ,,chapter ,,ix4 ,,plain ,,theodolites ,,in ,,which ,,the ,,transit ,,principle ,,is ,,not ,,employed--,,the ,,plain ,,theodolite--,,improved ,,construction--,,everest',s-- ,,simple--,,adjustments ,,and ,,examination ,,of ,,theodolites4 #dcg4--,the plain theodolite is of nearly its original form as invented by ,sisson4 ,it still retains a limited popularity1 which is principally due to its portability1 being of less bulk and weight than the transit of equal diameter of circle4 ,if we consider the railway theodolite described in the last chapter as a simple form of transit1 this must be considered as an exception with regard to the bulk and weight1 not being greater than that of the plain theodolite4 #dch4--,the ,plain ,theodolite4--,for the general description we may follow that given in ,chapter ,,vii4 for the #f-;inch transit for all parts of the instrument below the vernier plate1 and for the compass-box above this plate4 ,the construction of the instrument varies from the transit in having a half vertical circle only1 with a single vernier1 and in the differences in the arrangement of the fittings connected with the telescope4 ,a single microscope is generally used on the horizontal circle1 and this passes in a groove from one vernier to another1 instead of having two microscopes on arms jointed upon the vertical axis1 as in the better construction of transits before described4 ,the standards or ,a-frames in the ordinary plain theodolite are attached to the vernier plate1 but not generally to the compass-box4 ,the pivots of the transverse axis1 which are made exactly equal in size1 rest on coupled bearings on the tops of the standards1 which are in construction made together1 and therefore exactly alike4 ,the transverse axis is not adjustable1 as in the transit theodolite previously described2 the standards have therefore to be adjusted to height in the manufacture by filing1 with the application of a special striding level1 until the transverse axis is brought permanently perpendicular to the vertical axis4 ,illustration3 ,fig4 #ahh4--e-;inch plain theodolite4 #dci4--,the vertical arc is fitted over the transverse axis2 that is constructed with a turned flange to which the arc is firmly screwed4 ,the arc is divided to #cj and reads with a vernier to minutes4 ,the vernier is fixed directly to the vernier plate1 and reads generally with a microscope jointed on the transverse axis1 but sometimes with a loose magnifier for economy4 ,divisions for difference of hypotenuse and base are occasionally divided on the back of the arc4 ,the vertical arc has a clamp and tangent placed at the back1 therefore this cannot be shown in the engraving4 ,along the bar above the vertical arc a stout plate is attached by screws4 ,from this a pair of ,y's with clips and eye-pins1 as described for the ,y-level1 art4 #aib1 supports the telescope4 ,the telescope is of the same construction as that described for ,y-levels1 with turned collars4 ,the diaphragm is cross-webbed4 ,for economy a simple cap is generally put to the telescope instead of the better plan of a ray shade4 ,the principal level is fixed to collars fitted round the telescope1 to which are attached one slot-piece for lateral adjustment of the level1 and one screw-piece for linear adjustment by means of two capstan nuts4 ,the level is placed under the telescope for compactness4 #ddj4--,the parts of the plain theodolite below the standards are the same as those already described for the transit theodolite1 except that the vernier plate carries one level only at right angles to that of the telescope4 ,the telescope is therefore set to zero by the vertical arc1 and the two levels are then used as the pair upon the vernier plate of the transit4 ,the means provided for the adjustment are the same as those of the ,y-level1 but the ,y's are adjusted firmly by the maker by fitting them down upon the ,y-plate in the manufacture4 #dda4--,the plain theodolite1 except where price is the first consideration1 appears to be going gradually out of use1 being superseded by the transit4 ,it has had a long day since its first conception by ,sisson about #agcj4 ,for #d-;inch and #e-;inch instruments the makers still find a small demand4 ,the #f-;inch is rarely enquired for4 ,the plain theodolite cannot compete with the transit for perfect utility1 but it holds the merit of less weight and of greater portability4 ,the weights of the three sizes in general use are as follows3-- ,weights of ,plain ,theodolites4 ,instrument4 ,case4 ,outer ,case4 ,tripod4 #d-;inch #g lbs4 #g lbs4 #c lbs4 #h lbs4 #e-;inch #aa #h #d #i #f-;inch #ag #aj #e #aa ,very light #c-;inch and #d-;inch plain theodolites of from #e lbs4 to #g lbs4 complete are made occasionally for travellers4 ,illustration3 ,fig4 #ahi4--,stanley's new model plain theodolite4 #ddb4--,the author has recently modified the plain theodolite1 ,fig4 #ahi1 for which there still remains a small demand in the ,colonies1 by making the construction much more solid by shaping the work out of single castings in gun-metal for parts formerly screwed together in many pieces1 which formerly was necessarily arranged to permit facility of construction by hand-work4 ,there are also in the new instrument some improvements made in detail4 ,the limb dividing is covered for protection4 ,the readers are joined through the vertical axis and are hinged to turn up4 ,the compass has an aluminium ring with a microscope which permits it to be read at a convenient height and much more accurately4 ,the tangent screws are covered to exclude dust1 and some other improved details4 ,illustration3 ,fig4 #aij4--;,everest's theodolite4 #ddc4--;,everest's ,theodolite1 ,fig4 #aij1 designed by the late ,sir ,george ,everest1 and used for details of the great trigonometrical survey of ,india1 is built up very much upon a well-known common ,french model4 ,in service in ,india it has proved an excellent instrument4 ,the horizontal circle or limb of this instrument consists of a single plate1 upon which the silver is inlaid flat upon the surface1 upon the plan shown1 ,fig4 #abh4 ,in place of the ordinary vernier plate three arms are extended from the central axis1 which carry each a vernier at its end1 reading to a fiducial edge1 ,fig4 #abg1 p4 #ahf4 ,the verniers trisect the circle1 and are marked ,a1 ,b1 and ,c4 ,a fourth arm1 proceeding from the same relative position of the centre as the arms of the vernier1 carries a clamp and tangent which is similarly constructed to that of the ordinary theodolite described4 ,the instrument has also an under clamp and tangent for setting the telescope to bearing1 or for repeating1 as in the ordinary theodolite4 #ddd4--,the horizontal axis carries the telescope in a cylindrical fitting as in the transit theodolite1 terminating in two pivots which are set to permanent position as in the plain theodolite4 ,the pivots rest in bearings upon short standards carried out from the centre upon a flat horizontal bar to which a spirit level is attached for adjustment of the pivots to horizontality4 ,vertical angles are read off upon two arcs which have a horizontal axis as their centre attached to the telescope1 so as to move with it in the vertical plane1 with clamp and tangent adjustment4 ,an index1 upon the same centre carries two verniers and has a spirit level attached to it4 ,the verniers are read by a pair of microscopes4 ,upon the upper side of the telescope a trough needle is placed4 #dde4--,this instrument has been used in military surveys by the ,royal ,engineers4 ,the objections that civil engineers have made to ,everest's theodolite are that the working parts are made very open1 so that the wet and dust intrude2 further it lacks the general convenience of the transit principle1 which is necessary for astronomical observations4 ,the tripod is sometimes made of the ordinary solid section1 art4 #baf2 but for ,india1 where carrying labour is cheap1 a heavy framed stand is used1 which is special1 as follows3-- ,illustration3 ,fig4 #aia4--;,everest's locking plate tribrach4 #ddf4--;,everest's ,tribrach4--,the upper part of the engraving1 ,fig4 #aia1 shows this tribrach that supports the upper part of the instrument directly upon its vertical axis4 ,the three arms of the tribrach carry each a milled-headed adjusting screw1 the nut of which is formed in the arm4 ,the arm is sawn up to admit of adjustment1 that the milled head may turn softly but without any shake4 ,the lower points of the milled-headed screws1 technically feet1 fall into ,v-grooves in the head of the tripod4 ,the ,v's are not shown in the engraving4 ,above the upper surface of the tripod head1 a thin1 three-armed plate of metal1 termed the locking plate1 is centred upon the hollow axis of the head1 so that it will move laterally4 ,the locking plate has a hole and slot at the end of each of its arms1 the holes of which admit the toes of the feet of the tribrach into the ,v-grooves formed in the head of the tripod4 ,the locking plate when moved laterally locks all the toes in at once1 so that the instrument is secured by this means to a certain degree from accident4 ,this locking plate has commonly a milled-headed screw clamp which fixes it in its locked position4 ,the head of this screw is under the tripod head1 and consequently cannot be shown in the engraving4 ,it is a defect of this locking plate that the screws1 unless they fall perfectly in the ,v-grooves have a tendency to ride4 ,to avoid this the author has for many years made the ball feet fall upon a plain surface1 being at the same time held in their places by a slotted plate which fits over the neck of the balls4 ,this plan1 which is not shown in the engraving1 is now adopted by other makers4 ,the author uses also his patent tribrach sometimes on this instrument4 ,illustration3 ,fig4 #aib4--,stanley's ,everest theodolite4 #ddg4--,the ,framed ,tripod of ,sir ,geo4 ,everest's design is made of straight-grained mahogany1 each leg being formed of two side-pieces1 with one or two cross-pieces4 ,the engraving1 ,fig4 #aia1 shows the head of a tripod of this construction4 ,the side-pieces are spliced together at the lower ends1 where they form a rather obtuse point1 which is shod with a gun-metal shoe4 ,the upper ends of the side-pieces carry strap plates that receive a bolt which holds them firmly by means of winged nuts to the tripod head4 ,the legs can be detached after use and the tripod head be placed in the case with the instrument in a packing provided for it4 ,some modification of this form of tripod is generally used for all large field instruments4 ,the author's improved ,everest theodolite is shown at ,fig4 #aib4 ,illustration3 ,fig4 #aic4--,simple theodolite4 #ddh4--,simple ,theodolite4--,the plain theodolite being of the cheapest construction may be stripped of its superior functions1 which are used for testing its adjustments1 and be made into a simple angle measurer for laying out or plotting small parcels of ground1 small estates in building ground1 local sewage1 gas and water works1 and many other cases of small surveys1 for which purpose it will be found sufficient1 with a saving of about half the cost of a perfect theodolite4 ,the instrument shown above1 ,fig4 #aic1 was designed by the author to meet the above cases4 ,in this instrument there is no vertical arc4 ,the telescope has a socket axis carried upon a single standard4 ,the axis cannot be seen in the figure from interference of the telescope placed in front of it4 ,the telescope is arranged to be fixed in a level position by means of the loose pin being pressed in a pair of holes4 ,it may then be used as a level by means of the spirit level shown on the vernier plate4 ,the horizontal circle is divided to read with a single vernier to #c of arc by means of a hand magnifier which is placed in the case with the instrument4 ,there are internal and external axes1 each provided with clamp and tangent motions to the horizontal circle1 as with the plain theodolite4 ,it is supported on a tribrach1 the legs of which are upon the plan1 art4 #bdi4 ,if it be made with two verniers and divided upon silver it becomes a useful light instrument for filling in details of superior triangulation4 ,weight1 about #d lbs4 #ddi4--;,examination and ,adjustment of the ,theodolite4--,the description given of a transit theodolite1 arts4 #cfi to #chi1 will show that this instrument is provided with means of adjustment in every requisite direction4 ,larger transit instruments possess the same means of adjustment1 but in some parts these have greater refinement4 ,plain theodolites have the like methods1 except in the case of the transverse axis1 which is adjusted once for all by the maker4 ,it will be necessary1 therefore1 to limit our space to a discussion of the examination and adjustments of the transit theodolite only1 of which we have given a full description1 arts4 #cfi to #chi1 noting only where variations occur from partial differences between this and others4 #dej4--;,a theodolite as it comes from a respectable maker is usually carefully adjusted in all its parts4 ,if it has travelled a long journey it is1 however1 well for an experienced surveyor to put it through its various adjustments4 ,the corrections1 if any are required1 will be generally very small1 and these in all probability will be of the same kind as will occur in the use of the instrument and in the accidental conditions to which it may be subjected during conveyance from place to place upon a survey2 therefore it is well to be familiar with them4 ,when a new instrument is received from the maker1 it is necessary to observe attentively the manner of its packing as it lies in its case4 ,it is well at first to lift the parts a few times gently out of the case and replace them1 so that this may be done at any future time with certainty and without any risk of strain upon the instrument1 remembering always that an instrument in conveyance is much more liable to be thrown out of adjustment by carelessly replacing it in its case than from its ordinary use1 art4 #db4 #dea4--;,for examination or adjustment of the theodolite the tripod stand should be at first firmly fixed with legs extended to an angle of about #gj to the ground1 which should be solid and hard4 ,as the telescope has to be brought to the height of the observer's eye1 it is well to mention his stature in ordering an instrument4 ,the tripods that are made for tall men are often awkward and unsteady if the legs are extended to bring the telescope down to the height of a short person4 ,they may always be cut down and refinished by the maker4 ,when the tripod is set up the toes should be each separately pressed down1 so that future slips are impossible4 ,this being done the instrument is taken from its case and grasped firmly by the body part under the horizontal circle1 and placed on the tripod at once1 then screwed firmly but not too tightly down upon its bearing surface4 ,with a #f-;inch transit theodolite the upper part is sometimes detached and packed separately in its case4 ,where this is so1 after the body part is fixed on the tripod1 the cleats on the top of the standards must be opened out1 and the upper part of the instrument1 lifted by its telescope1 be slowly lowered into its bearings1 being particular at the same time that the clips under the telescope embrace their stay-piece on the standard4 ,the cleats must then be closed over the pivots4 ,the instrument being set up to position1 all levels may be adjusted to the centres of their runs1 and every part clamped sufficiently to make the instrument firm1 but in no case using violence to produce a strain in any part4 ,the clamps or other fittings are afterwards separately released as they are required for examination or adjustment of the parts to which they relate4 #deb4--;,examination for ,coincidence of ,exterior and ,interior ,vertical ,axes4--,the theodolite being set up solidly1 and all clamps fixed as above described1 unclamp the lower or exterior axis clamp and set the vernier plate levels parallel with opposite pairs of parallel plate screws if the instrument adjusts on the parallel plate system1 art4 #aic1 or one level parallel with one pair of foot screws if it is made on the tribrach system1 art4 #bcd4 ,now adjust both levels4 ,turn the instrument half round 7#ahj7 and observe if the levels keep the centres of their runs4 ,if they do so they are in adjustment to the exterior axis4 ,if found imperfect1 the adjustment by the capstan heads of the levels is set1 by means of the tommy or pin which is provided in the instrument case1 for half the error as it appears by the bubble1 the other half being given by readjustment of the parallel plate or tribrach screws4 ,in these adjustments it is necessary to be particular always to observe the bubbles after the hands have left the instrument1 not during the adjustment1 which produces strain upon the instrument4 ,now clamp the lower clamp and note if this clamping has disturbed the levels4 ,if the levels are very sensitive it will do so in a slight degree1 but the disturbance should be very small if the clamp is perfect4 ,now unclamp the vernier plate and note again if this clamp disturbs the levels3 this should also affect them very little4 ,now observe the levels if they stand exactly as they did when the exterior axis was unclamped at their present position1 and also at right angles to this4 ,if they remain as before the axes are truly concentric4 ,if they do not1 there is no remedy except at the hands of the maker4 ,the vertical axis to which the above examination applies is considered the most important part of the instrument1 and the work should be thoroughly well done2 nevertheless1 if the levels are very sensitive1 which they seldom are1 such minute faults may be detected1 that a small allowance may be made for imperfection of work1 and the instrument still be considered a sound one4 ,in the use of the instrument it is always well1 after the circle is set either by the magnetic compass or by sighting a distant point for direction1 to clamp the lower clamp and readjust the levels to the vernier plate4 ,in this way the axis that will afterwards be used for triangulation will be vertical1 and small errors due to want of coincidence of axes be eliminated4 #dec4--;,examination of the ,azimuthal ,level4--,this level1 which is placed over the telescope1 being made of superior sensitiveness to the vernier plate levels1 is much more accurate for adjusting the vertical axis1 but much slower in operation for testing4 ,the verniers of the vertical circle should be accurately set to zero1 in which position the run of the bubble should exactly agree with those on the vernier plate when placed parallel with them in any direction1 but this level may also be considered by itself4 ,assuming the circle and verniers correct1 or otherwise1 it may be reversed over the axis by half turns in all positions over the parallel plate or tribrach screws1 and adjusted by the capstan heads half the error1 as before described1 for the vernier plate levels4 #ded4--;,examination of the ,divisions and ,centring4--,the vernier plate being unclamped1 the verniers1 if two1 should be brought approximately to #j 7#cfj7 and #ahj1 and then the plate be lightly clamped4 ,the microscopes or readers are then to be set truly radial with the zero reading of the verniers1 and the tangent screw adjusted to make one of the readings1 say the #cfj1 exact4 ,the opposite reading1 #ahj1 is then carefully examined1 and the error discovered1 if any1 is due to the imperfection of centring1 assuming the dividing perfect4 ,at this point it is well to record the amount of difference4 ,the same examination is then repeated with the #ij and #bgj4 ,in a properly centred and accurately divided #e-;inch or #f-;inch theodolite this difference will not amount to more than #a error1 in larger instruments proportionately less4 ,owing to the difficulties at all times of reading the circle correctly from difference of direction of light1 and what is termed personal error1 it is well to entirely repeat this examination1 turning the instrument half round4 ,it is also well to repeat the examination at what are termed the half points1 #de1 #bce1 and #ace1 #cae4 ,this will sometimes detect the error of centring1 if there be any1 in its true direction4 ,the purpose of the two verniers is to discover this error4 ,in practice the two readings are always taken1 and the mean is considered as the true reading4 ,where there are a greater number of verniers exactly the same principle is followed1 but the mean of three or more readings is taken1 which of course assures great accuracy4 ,examination of the telescope has been discussed arts4 #ajg to #aae4 #dee4--,testing an ,instrument for its ,stability4--,the stability of an instrument will depend principally upon the quality of the workmanship2 but the same test will also indicate1 at any time1 whether the instrument has been submitted to sufficient wear to need the repair of the optician4 ,for this examination the eye-piece of the telescope requires to be focussed against a piece of white paper held obliquely in front of the object-glass so as to throw a soft white light into the telescope4 ,after the eye-piece is focussed1 any distant point may be taken for a sighting object upon which to direct the telescope4 ,this point should be focussed by the telescope so that its image falls centrally upon the intersection of the webs4 ,the eye should then be shifted up and down or sideways within the range of clear vision of the webs in the eye-piece to ascertain that there is no parallax1 that is1 that the adjustments of the eye-piece and the telescope are in true focus upon the webs4 ,this preliminary arrangement being made1 which will serve in future examination for other adjustments1 all parts of the instrument should be examined to see that the clamps are firmly clamped4 ,the object to be used as an index or sighting point should be brought by the clamp and tangent motions exactly upon the intersection of the webs as they appear in the telescope1 when the following examinations are to be made4 #def4--,tripod ,head ,examination4--,the telescope being sighted upon an index point1 and all clamps screwed down and the tripod firmly fixed on the ground1 take the tripod head of the theodolite in both hands and give it a twist of about a pound pull in one direction2 then examine the telescope to see if the index point is displaced in the telescope4 ,if it still stands correct give a like twist in the opposite direction and again examine the telescope4 ,if it stands these opposite firm twists retaining its position the stand is good and in good order4 ,if it does not1 assuming good construction of stand1 the remedy may be found in tightening up all its screws2 but if its construction is bad it will not1 even after this tightening1 keep in order4 ,there is no doubt that more inaccurate triangulation is caused by defective tripods than from any other cause whatever4 ,a perfect instrument is useless on a bad tripod4 #deg4--;,general ,examination of ,fixed ,parts4--,the stand being found good by the above process1 the general fittings of the instrument may be examined1 after clamping all parts and directing the telescope to a distant point1 by taking a quill pen by its root or pipe and pressing its feathered end upon one side of the eye-piece of the telescope sufficiently to bend the quill1 and afterwards examining the telescope to see that the webs are not displaced from the index point4 ,this may be done first to the right hand and then to the left4 ,if the webs still cut the same object it is clear that the whole of the centres1 fittings1 clamps1 and tangent screws of the horizontal circle are correct4 ,if any displacement be discovered1 the amount of difference between the right and left handed twists will be the total error due to imperfection of work or wear as the case may be4 ,in exactly the same manner1 but by pressing the eye-piece upwards and downwards1 the transit axis and its fittings may be examined4 ,if the instrument be not generally sound enough to bear the above tests1 other critical adjustments become necessary4 ,for the correction of faults that may be included in the above operations1 the parts of the instrument must be separately examined4 #deh4--;,examination of the ,transit ,axis4--,the best means of adjusting this axis in a theodolite is by a striding level1 art4 #djj4 ,when this is not provided with the instrument1 and it is often omitted for economy1 the axis is generally better to be left as it is adjusted in this particular1 by the maker4 ,to adjust the transit axis the vernier plate bubbles are set exactly true by reversing angles of observation4 ,the cleats are opened and the striding level is mounted above the instrument resting upon the pivots4 ,the telescope is placed exactly over an opposite pair of parallel plate screws1 or parallel with two screws if the base adjustment be on the tribrach principle4 ,the striding level is then carefully observed and reversed on the pivots4 ,if there be any difference in the run of the level bubble the transit axis is adjusted by raising or lowering the movable ,v on which one pivot rests by turning the capstan nuts until it is quite correct1 if the instrument has this old-fashioned arrangement1 or if not1 by a few strokes of fine emery paper upon the ,v which is higher4 ,this adjustment is almost superfluous1 as the axis is generally set right at first1 and is not subject to change1 especially if solid without an adjustable ,v4 #dei4--;,for larger theodolites of #ab inches and over1 the transit axis is much better adjusted by means of an artificial horizon1 which will be described further on4 ,by the use of this instrument in the northern hemisphere the pole star is first observed directly by the telescope1 and then by its reflection from the horizontal surface of clean mercury placed on the ground at #ab feet or so from the instrument4 ,if the star and its reflection cut the webs equally in directing the telescope by movement of its transit axis only from the one to the other1 this axis must be truly horizontal4 ,if the vernier plate be then turned a quarter of a revolution and the exterior axis a quarter of a revolution1 the telescope transitted and observation be repeated1 the verticality of the principal axis may be adjusted with perfect certainty4 ,the principal axis should be moved one-eighth of a revolution all round and the bubble examined at every position to assure perfect adjustment4 ,with the plain theodolite1 ,everest's and some others1 the transverse axis is fixed to position by the maker1 therefore cannot be adjusted4 #dfj4--;,examination and ,adjustment of ,webs1 ,lines on ,glass1 or ,points4--,the ordinary manner of webbing the diaphragm of a theodolite was shown ,fig4 #bc4 ,horizontal angles are taken by the upper intersection of the diagonal webs or lines4 ,a single web is placed horizontally for taking vertical angles3 it is necessary that this should be nearly true4 ,when the theodolite has its axis vertical1 as shown by the vernier plate bubbles being in the centre of their runs1 if one end of the horizontal web or line be set to cut a small distant object by sight in the telescope1 the same object should keep on the web while the tangent screw of horizontal circle is moved a distance sufficient to traverse it1 the hand being always taken from the screw while the observation is made4 ,if it does not do so1 the collimating screws should be lightly tapped with the back of a penknife in the direction to set it right4 ,these screws have a slot in the body of the telescope1 under the loose covering plate1 sufficient to permit of this small adjustment4 #dfa4--;,adjustment of the ,telescope to ,vertical ,collimation4--,the eye-piece is first focussed as before against a piece of white paper held obliquely in front of the object-glass until the webs are sharply seen4 ,the axis of the telescope is then examined for vertical collimation error4 ,the method of doing this has been already described for a telescope placed in ,y's1 as it is in the ,y-level1 and the plain theodolite1 art4 #bjj4 ,the only difference with the transit theodolite is that instead of turning the instrument in its ,y's1 the telescope is transitted1 as it is termed1 over on the transverse axis exactly half a revolution1 or #ahj as seen by the vernier reading2 and the horizontal circle is moved also half a revolution1 so that the telescope points again on the same distant point which is used for an object4 ,if the webs or lines still cut the same point or small object1 they are in vertical collimation1 or truly in the optical axis of the telescope1 as regards the vertical direction which this adjustment is intended to secure1 presuming the circle has been correctly divided and centred and the verniers accurately set4 ,if the webs or lines do not cut the same point1 half the error is corrected by the top and bottom collimating screws near the eye-piece4 ,this process is repeated until it is exact1 being particular to observe1 as before mentioned1 that there is no parallax4 ,this adjustment cannot be made with the plain theodolite2 but the zero of altitude may be examined on both sides of the arc4 ,for the transit theodolite1 adjustment by means of a collimator1 art4 #bbi1 is much more convenient and exact1 as lateral and vertical errors in the position of the webs can be detected in one operation4 ,when a ,y-level is at hand1 this may be used as a collimator if it is first set to solar focus4 #dfb4--;,examination for ,perpendicularity of ,transit ,axis and ,telescope4--,the whole of the lower part of the instrument retaining its position with all clamps firm1 open the cleats upon the top of the standards so as to release the transit axis4 ,now release one of the clip screws and gently lift the upper part of the instrument out of its bearings4 ,turn the telescope the reverse way upwards1 which will be in this case bubble downwards4 ,release the clamp and turn the clips to the reverse position of the telescope1 and reverse the position of the pivots in their bearings4 ,if the telescope be now directed to the same point as before1 and the webs still fall upon it1 the telescope adjustment is at right angles to the transit axis4 #dfc4--;,examination of the ,magnetic ,needle4--,if the needle be placed in a circular box1 as shown in the engraving1 ,fig4 #cj1 it admits of no adjustment4 ,if it is placed in a trough1 ,fig4 #afa1 it admits of adjustment generally by lateral screws to a portion of its division4 ,if the needle is used for a survey1 it is set to the zero of the horizontal circle by clamping the vernier plate and bringing the northern vernier to zero1 then releasing the exterior axis and bringing the needle by the motion of the lower tangent screw to the zero of its circle4 ,the corrections of the needle for giving true north have been discussed1 art4 #acb4 ,it is difficult to read an ordinary edge-bar needle correctly1 it is also difficult to mount it perfectly true4 ,it may be read at both ends1 and if the #j and #ahj points cut the line fairly it is considered correct2 if not1 the mean of the difference may be taken4 ,in some instruments a microscope is mounted over the needle point that the needle may be adjusted to a web2 but ,british surveyors seldom feel confident of surveys by the magnet1 and for triangulation generally prefer to employ a certain number of distant fixed points1 the bearings of which are at first as accurately ascertained as possible1 for referring objects1 rather than to refer frequently to the magnet4 ,when the needle is out of use it should always remain lifted off its centre4 ,when the instrument is put by for a long period it is better to place it in a vertical position and free the needle1 so that it rests in the magnetic meridian1 in order to preserve its magnetism as much as possible4 #dfd--,use of the ,theodolite4--,in setting up a theodolite1 place the tripod nearly over the position in which it is to be used4 ,this is frequently the socket hole formed in the earth by the removal of a ranging pole or picket1 to be described ,chapter ,,xvii4 ,then1 after it is set up1 suspend the plummet from the hook1 which will be found inside the head of the tripod4 ,if the ground be solid and level1 then by shifting the toes of the tripod slightly1 and firmly pressing them down one by one1 the centre of the plummet may be brought easily within about #be of an inch of its true position4 ,the theodolite is then placed on its tripod1 observing that the telescope is in a position easy to be used4 ,the centre of the picket-hole1 when this is used for a station1 is generally taken by guess-work1 which is considered near enough4 ,it may be taken with a little more refinement by placing1 in the same hole1 a short false picket of nine inches or so in length1 but of the same diameter as the ordinary picket1 the top of which is cut off smooth and polished1 and has lines sawn across its centre inlaid with ebony1 described in ,chapter ,,xvii4 ,the false picket is carried about with the theodolite4 ,with ,everest's and many other forms of theodolites the hook is fixed under the axis of the instrument4 ,in this case it is usual to set the theodolite before adjusting it to the station1 as there is no separate hook to the tripod1 which also occurs with all framed stands4 #dfe4--,where there is no hook to the tripod an excellent plan is to have a false centre1 which may be a piece of turned wood with a hole through it1 to fix on the top of the tripod head4 ,the plummet cord adjusts through the hole4 ,this false centre is also convenient where the axis adjusts to position by a mechanical stage4 ,fig1 #aid shows a false centre formed of a piece of ivory with two slots to permit the cord to loop over and yet hang centrally4 #dff4--;,it may be observed that if the tripod be set up out of level1 which it must necessarily be in many cases1 the hook1 if attached to the stand and following its inclination1 will not hold the cord at a truly vertical position to the axis4 ,surveyors commonly allow a little for this inclination4 ,it is much more accurate to have the cord suspended directly from the axis of the instrument when it is constructed to admit this4 ,then if a false centre be used the plummet should be suspended a second time from the axis hook4 ,with the kind of runner shown in the figure this need take little time1 as it is instantly detached and replaced4 ,illustration3 ,fig4 #aid4--;,false centre for a tripod head4 #dfg4--;,after the tripod is fixed with the theodolite upon it1 the readers are set to exact focus4 ,the horizontal circle is then brought to zero by the vernier plate clamp and tangent1 and the compass brought to magnetic north1 if all angles are taken in reference to this as a check1 by means of the lower clamp and tangent4 ,the vernier plate clamp is then released4 ,the eye-piece is correctly focussed upon the webs1 lines or points against the northern sky1 or upon a piece of white paper held obliquely if this is preferred4 ,the telescope is then ready to be directed towards a picket or other station mark to be observed1 and set correctly to focus this1 after which the eye is moved to the right and left1 to the extent of clear vision in the eye-piece1 to see that the object appears to remain fixed upon the intersection of the upper ,v of the webs1 or does not dance1 as it is sometimes termed4 ,the observation1 if of a picket1 should be taken as near the ground as possible1 as it may not be set quite upright4 ,if the telescope is directed to objects where the sun's rays would enter it1 the ray shade should be pulled out sufficiently to quite shield the object-glass4 ,the initial reading to be recorded is always taken on the face of the instrument1 in which position the upper tangent screw is always on the right-hand side4 ,when the observation is clear and satisfactory1 it is recorded in the field-book4 ,if the sight lines taken are to be measured by the chain1 the amount of inclination is taken by the vertical circle reading to the top of the picket if this is the #f-;feet ordinary length1 or to a marked band if this is longer4 ,the inclination may be taken exactly to angle by vernier1 or roughly by scale of difference of hypotenuse and base if this is engraved on the vertical circle1 or by both of these--the one as a check upon the other4 ,it is common to take the upper inclination as a plus 77 and the lower as a minus 7-74 ,inclination observation is recorded at the same time as the horizontal position4 ,other observations of the various positions or pickets are taken in a similar manner at the same time4 ,when a stadia or tacheometrical diaphragm is used the angle is recorded and the stadia reads the distance4 ,it is thought well when the theodolite is in position to take as many exact observations as possible in all directions of intended stations4 ,it is also convenient to take a number of observations1 which from the circumstances present may be inexact1 such for instance as the angles subtended by trees1 gates1 rough buildings1 or even sometimes the corners of fields1 as from such observations these objects may be placed nearly enough for ordinary plotting by the angles they subtend from this and another station upon the plan4 ,in any case they form a check to positions if taken with pickets afterwards more definitely4 ,these may be marked in the field-book inx4 for inexact4 #dfh4--;,field ,book4--,this book is generally made #h inches by #d inches1 covered with red leather1 with elastic closing band and sheath for pencil1 as an ordinary pocket-book4 ,it contains about #ajj pages of good stout writing-paper4 ,two lines are ruled in red ink1 inch apart1 vertically down the centre of each page4 ,the column between the lines is used for distances measured by the direct chain line at which hedges are crossed1 stations1 offsets1 or other measurements are taken4 ,in the right and left columns observations are made of objects desirable to be recorded or triangulated4 #dfi4--;,for superior triangulation1 definite and prominent fixed objects are taken at as great distances as possible1 so as to include the details of measured triangles within a superior triangle4 ,a church steeple1 for instance1 is a favourite sighting object4 ,this cannot1 however1 generally be made1 a station for future triangulation unless a scaffold is built up around it4 ,generally the most convenient method on fairly level ground1 if the survey is large1 is to have an ordinary scaffold pole1 #bj feet or so in length1 carefully straightened by a village carpenter with a stretched chalk line and then painted white4 ,this may be squared at the end and fixed vertically in a socket formed of crossed boards to a depth of about #c feet in the ground1 with long crossing tail pieces rammed firmly with the soil to keep it steady4 ,when this is used for a triangulating station1 the pole is taken out of its socket and its exact position is centred for placing the theodolite4 ,flags are sometimes used to indicate stations3 their defect is that the wind may blow them from or to the observer and thus render them invisible4 ,other methods will be found in practical works on surveying4 ,this subject will also be reconsidered in ,chapter ,,xvii4 ,illustration3 ,fig4 #aie4--;,diagram bisection of circle4 #dgj4--;,elimination of ,instrumental ,errors during ,triangulation--,changing ,face4--,it is generally advised to change face with the theodolite after angles are taken in the ordinary way1 that is1 to take first the initial angles reading from the face vernier with the tangent screw on the right hand1 and then to take the same angles with the back vernier1 the telescope being transitted4 ,this1 of course gives a reading on a different part of the circle and corrects the error of position of the vernier1 or centring1 in the following manner3--,in ,fig4 #aie let a be zero 7#cfj71 the reading of the face vernier4 ,let the opposite reading 7#ahj7 be at a4 ,suppose at #ahj on the left-hand side of the instrument the #ahj reads at b1 then observe by the telescope an object that cuts this reading1 or place a picket to do so4 ,change face2 then the same arc will come to c1 and the telescope must traverse cb to come to the first direction4 ,the instrumental error is half bc1 which bisected in a gives #ahj exactly4 ,the same principle of repetition with changed face may be made an any part of the circle1 and the mean will be the correct reading4 #dga4--,repeating ,angles4--,this is performed by taking all parts of the circle for reading a given angle1 so that errors of division and centring of the instrument are eliminated4 ,the process is as follows3--,take the angular positions of two objects in azimuth1 commencing with the zero of the horizontal circle1 say the two objects subtend from the centre of the instrument #cf #aj2 then turning the telescope back from its advanced position at #cf #aj by releasing the lower or axis clamp1 we may bring the first reading to the original zero position4 ,now clamp the lower clamp and release the vernier plate clamp and take again a forward reading4 ,if this reads #cf #aj #cf #aj #gb #bj1 the circle and centring appear so far correct2 but it will probably read #gb #ba1 and the corrected reading would be the mean #cf #aj #cj4 ,if we continue this system round in ten pairs of readings the whole circle will be embraced1 then the mean of the sum of the minutes divided by the number of pairs of observations will give the true reading of the minutes4 ,by taking the readings of two opposite verniers separately1 the circle would be encompassed by five readings4 ,this plan is followed in all important triangulations where the work is submitted to calculation4 ,such refinement is scarcely necessary for direct plotting with the protractor4 #dgb4--;,it may be observed that if the horizontal circle is placed with its zero constantly to magnetic north--not necessarily for taking angles in reference to this--that the same part of the circle will always be used in the same direction2 so that the sum of errors of the whole circle must necessarily tend to tie1 even if the division is to a certain degree imperfect1 provided also that the protractor used in plotting is also kept in one direction4 ,this plan has otherwise no inconvenience1 as any arc or angle may be taken by the difference of the circle reading in any position in which it may happen to fall4 ,this does not mean that it is advisable to survey above ground by the needle--it is quite otherwise4 ,it is best to have some distinct1 sharply defined object to which all angles are referred1 and therefore called a referring object1 as the general index4 ,the magnetic bearing need only be the initial position of the horizontal circle of the instrument4 #dgc4--,with larger1 what are termed geodetic instruments1 to be described in the next chapter1 constructive errors are not permissible2 but these instruments are observed under altogether different conditions1 which are suitable to the precision demanded4 ,a large theodolite is generally fixed upon solid rock1 or masonry with good foundation1 or upon a very firm solid framed stand1 and is protected from wind1 sun and rain4 ,where it is necessary on level ground to elevate the instrument for more extensive view1 a proper structure is built1 in which the theodolite is isolated from the outer walls or enclosure carrying the stage upon which the observer works1 so that no vibration or deflection of this1 caused by the wind or the weight of the body1 affects the instrument4 ,under such conditions angles are read on various points of the circle by micrometer microscopes so as to obtain a sufficient number of means1 that personal and instrumental errors may be reduced to a minimum4 ,,chapter ,x4 ,,large ,,theodolites ,,used ,,only ,,for ,,geodetic ,,surveys--,,stanley',s #aj- ,,and #ab-;,,inch--#ad-;,,inch ,,altazimuth--,,colonel ,,strange',s #cf-;,,inch ,,theodolite4 #dgd4--,large theodolites employed upon geodetic surveys4 ,where the complete survey of a country has to be made1 a system of large triangles is formed over the country from convenient positions which are naturally or artificially elevated so as to obtain distant views with the telescope4 ,these triangles are correctly measured by angles subtended from a very carefully measured base or bases set out upon approximately level planes1 which are generally of a mile or more in length4 ,where measurements are derived from such bases by constant intersection of angular positions extended therefrom to large triangles or other polygons1 it becomes important that the theodolite employed should measure such angles with great accuracy4 ,in this case the vernier reading does not possess sufficient refinement1 and the divisions representing the degrees have to be magnified to appear wider apart1 so that they can be more finely subdivided for the reading to be taken by means of a micrometer microscope capable of subdividing the divisions made upon the instrument even to single seconds of arc4 ,the theodolites used for the superior triangulation of ,great ,britain were ,ramsden's #cf-;inch and #ah-;inch1 which1 although constructed in the last century1 remain excellent instruments4 #dge4--,the construction of large theodolites is varied very considerably according to the conditions present in the country to be surveyed4 ,this subject if carried into detail would extend much beyond the intended limits of this work4 ,this chapter will therefore be limited to the description of a #aj- or #ab-;inch instrument1 and to two historical instruments which have been used successfully for geodetic work4 ,illustration3 ,fig4 #aif4--,stanley's #aj-;inch transit theodolite4 #dgf4--aj- or #ab-;inch ,theodolite4--,these instruments approach the limit in size of portability for movable stations in triangulation4 ,the illustration1 ,fig4 #aif1 is of the author's latest #aj-;inch model1 the patterns of which were made for a theodolite with vernier readings to be used for the construction of a spiral tunnel through the ,andes1 now completed4 ,the object in its construction was to obtain great rigidity with moderate weight4 ,to this end the gun-metal of which it is made is shaped out from castings as comprehensive in unity of parts as possible4 ,it has a framed mahogany stand 7not shown7 which is braced in every way and provided with a very rigid head4 ,in general construction of the instrument illustrated it has a mechanical sliding stage and an extra powerful clamp and tangent arrangement for the lower limb1 the adjusting screws being all covered to exclude dust4 ,the circles are divided to #e minutes1 and are read by micrometers to single seconds of arc4 ,two vertical arcs are used1 the second one carrying the clamp and tangent arrangements1 which also serves to balance the trunnion4 ,the #aj-;inch instrument carries a #af-;inch telescope with #b-;inch object-glass1 and the #ab-;inch instrument an #ah-;inch telescope with #b-a_/h-;inch object-glass4 ,the tangent screws all act against springs to avoid loss of time4 ,illustration3 ,fig4 #aig4--ad-;inch altazimuth theodolite4 #dgg4--ad-;inch ,theodolite4--,for this description a modern instrument is taken which ,colonel ,a4 ,r4 ,clark selected for illustration in his excellent article on ,geodesy in the ninth edition of the ,encyclopdia ,britannica1 to the publishers of which the author is indebted for the illustration1 ,fig4 #aig4 ,the instrument is a combination of a transit theodolite with special arrangements as an altazimuth instrument with fixed base1 one side of the vertical circle being divided to place the zero in a direction coincident with the polar axis4 ,the construction as a simple fixed transit theodolite for support upon a pedestal in stone wherein the axis remains permanent for a principal geodetic station1 and therefore requires only a single setting to bring it to true north and south for zero1 renders change of position of horizontal limb unnecessary for a permanent station4 ,for this the instrument is well adapted1 and will be discussed here4 ,the telescope is of #ah inches focus1 with #b inches clear object-glass4 ,the axis pivots are of hard steel3 one is perforated for illumination by a lamp4 ,the vertical circle is placed almost directly upon the side of the telescope1 and the tangent arm on the opposite side is of nearly equal weight1 so that there is no counterbalance necessary4 ,there are three ,ramsden eye-pieces giving powers of #ag1 #ce1 and #ed1 and one diagonal eye-piece4 ,a level is attached inside the standard1 divided to read #aj of arc3 this has cemented ends1 art4 #agg1 and is enclosed in an outer tube for protection4 ,two other exactly similar levels are attached to the exterior axis of the instrument4 ,the circle is divided to #e of arc and reads by two micrometer microscopes to single seconds4 ,the vertical axis of the instrument is of steel4 ,it is placed with the apex of the cone upwards1 and terminates on a triangular spring with three adjusting screws by which any portion of the weight of the upper part of the instrument can be relieved from the axis1 so that the whole instrument moves quite freely4 ,the horizontal circle reads with three micrometer microscopes on the upper circle to single seconds4 ,originally the light was thrown down on the divisions by three ivory cones placed over the fronts of the microscopes1 as shown in the illustration2 but these have been changed in the present instrument for concave swivelled reflectors1 which may be set to any angle convenient to throw sufficient light upon the circle4 ,the microscopes are supported from the body of the instrument upon hollow conical arms upon the same excellent plan originally used by ,ramsden4 ,the microscopes have adjustments in three directions1 so as to bring them exactly into place for trisection of the horizontal circle4 ,the clamp and tangent motion is placed directly upon the divided circle1 and has adjustments to secure freedom from strain2 but this is not perfect--it is perhaps the worst feature in the instrument1 some modification of the plan shown1 ,fig4 #aif1 being much better for large instruments4 ,the whole instrument is mounted on a tribrach frame1 which is adapted to stand upon a portable table or upon masonry4 ,the screws have lateral adjustment to prevent loss of time by wear4 #dgh4--;,it is a common custom with this class of instrument to make the axes of hard steel4 ,this plan is no doubt very satisfactory as it leaves the optician's hands1 but the author very much prefers good hard bell-metal4 ,when he saw the above described instrument at ,southampton1 there was quite sufficient evidence of rust on the pivots to destroy all perfection of centring1 and this could scarcely have occurred with bell-metal4 ,of course the brittleness of bell-metal would be objectionable where the instrument might be subjected to severe jar in carriage from place to place2 but the author has obviated this by a plan he would strongly recommend for general adoption--of having the axis of good gun-metal1 and to silver-solder a ring of bell-metal thereon where the fitting surfaces occur4 ,if the gun-metal is pure it will bear the average reliable strain of hardened steel1 which in hardening and tempering is not with certainty always free from flaws2 and the average wear of pure bell-metal is perhaps quite as good as steel4 #dgi4--cf-;inch ,theodolite1 ,fig4 #aih1 was designed by the late ,colonel ,a4 ,strange and constructed by ,messrs4 ,troughton ,simms for the ,great ,trigonometrical ,survey of ,india4 ,it is probably the most complete and perfect theodolite ever constructed4 ,the leading characteristics of this important instrument only will be given4 ,it has a horizontal circle #cf inches diameter1 and a vertical circle #bd inches diameter4 ,the telescope has a focal length of #cf inches3 the aperture of the object-glass is #cbe inches4 ,illustration3 ,fig4 #aih4--cf-;inch theodolite--,great ,indian ,survey4 ,from a photograph4 #dhj4--,the ,stand has three massive mahogany legs ,,aa braced together with horizontal and oblique wrought-iron bars ,b4 ,each leg is divided vertically1 and contains a long1 gun-metal1 square-threaded screw ,c which is made to rotate by means of a worm-wheel and endless screw worked by a winch handle ,d1 and capable of being firmly clamped after adjustment at points about #ae inches apart ,e4 ,the upper ends of these screws are conical1 and fit into three inverted radial grooves formed in the lower side of a cast-iron circle or table1 which is thus supported by the three screws without being attached to them1 and is therefore free to accommodate itself to expansional changes without restraint4 ,the upper surface of the cast-iron circle is turned flat and true to receive the tribrach of the instrument4 ,the three screws ,f which pass through the side of this circle are intended to adjust the centre of the instrument over the station mark4 ,a lever ,g also passes through the side of the circle and actuates three rollers1 which1 when in action1 support the greater part of the weight of the instrument1 and so enables the horizontal zero to be set without difficulty4 ,as the instrument weighs over #djj lbs41 it will be seen that some such arrangement is absolutely necessary to enable it to be moved on the cast-iron circle4 ,when the correct position has been obtained1 the lever is thrown out of action1 and the instrument remains immovably seated upon its circular frame4 #dha4--,the ,foot ,screws are tapped through the ends of the tribrach arms in the usual way1 but have a range of motion not exceeding #a_/aj inch4 ,this range may appear small1 but is really much more than is required1 as the upper surface of the cast-iron circle can be levelled by the long screws in the mahogany legs before the instrument is placed on it1 so that not more than about #a_/ajj inch of motion is required4 ,the foot screws do not rest directly on the cast-iron circle1 but on the extremities of an intermediate three-armed plate1 securely bolted to the centre of the instrument1 the distance between the tribrach and the plate being about #a_/aj inch4 ,the object of this arrangement is to obviate the disturbance of level and azimuth which arises from clamping foot screws of the ordinary construction after adjustment1 as well as that due to looseness of the foot screws in the tribrach arms4 ,the arms of the spring plate1 being of considerable width1 have great horizontal rigidity1 but being comparatively thin are easily bent vertically4 ,the outer ends of the arms rest on the cast-iron circle or stand2 the foot screws pass through the tribrach arms1 but not through the spring arms4 ,it is evident therefore that when the foot screw is turned inwards with the screwing motion1 the solid end of the tribrach will be raised and the slit between the two arms widened2 but since the end of the screw does not rest on the stand1 but on an intermediate arm1 which is actually a portion of the tribrach itself1 it is clear that if a lateral pressure be applied to the tribrach no motion will be caused thereby1 however loose the screw may be1 so long as the pressure is less than the lateral rigidity of the intermediate arm4 ,the lateral pressure caused by turning the instrument in azimuth when taking observations is greatly within this limit4 ,this plan is perfectly successful1 but it is only available where a moderate range of vertical movement is needed4 ,in the present instance1 as the cast-iron ring or stand on which the instrument is supported is always first made practically level1 the vertical range of the foot screws need not be more than a small fraction of an inch4 ,another point with regard to the foot screws is their delicacy and certainty of action4 ,this is attained by applying to them a clamp and tangent screw arrangement ,h very similar in principle to that sometimes applied to circles4 ,although the foot screws themselves are rather coarse1 having only about eight threads to the inch1 the arrangement is such that one entire revolution of the slow motion tangent screw alters the level only about one second of arc4 ,hence the foot screws in this instrument1 though coarse and strong enough to bear great weight are probably for the first time made in keeping1 in point of refinement1 with its most delicate parts4 #dhb4--,the ,horizontal ,circles4--,the inner or working circle is #cf inches in diameter4 ,it is very finely divided on silver to #e minutes1 and is read by five equidistant micrometer microscopes to tenths of a second of arc4 ,it is fixed at the centre to the tribrach1 but everywhere else is perfectly free4 ,the outer or guard circle consists of a second horizontal circle exterior to and concentric with the inner circle4 ,there is a space of about #a_/aj inch all round between the two circles1 and the upper plane of the outer circle stands about the same quantity above that of the inner or principal circle4 ,the guard circle is supported by radii of its own1 quite independent of those of the inner circle4 ,this circle has several functions4 ,it protects the working circle from accidental injury2 it helps to distribute changes of temperature uniformly over the circumference of the working circle2 it receives the clamp and tangent screw1 leaving the working circle absolutely free from contact at all times2 and it bears a strongly-cut set of divisions1 more visible to the naked eye than those of the working circle1 which are exceedingly fine1 and therefore would be inconvenient for setting the instrument approximately in azimuth4 #dhc4--,the ,horizontal ,tangent ,screws4--,it will be seen at ,,ii that there are two clamps and two tangent screws to the horizontal circle4 ,it is necessary to have both1 on account of the large size of the circle4 ,in use1 of course1 they are not both used at the same time4 ,in the present position of the instrument the clamp and tangent screw on the left-hand side of the illustration would be employed2 but on reversing the telescope this clamp would be released and the one on the opposite side made use of4 ,it is necessary with this1 as with smaller instruments1 to avoid loss of motion in the tangent screws4 ,many methods have been employed to obviate this loss of motion1 but while they are suitable to small instruments they are not so effective with large ones1 such as that under consideration4 ,the plan adopted in this case is that known as the divided nut principle4 ,the block into which the tangent screw is tapped is divided transversely and the two halves are forced asunder1 and therefore act against the contrary sides of the screw threads by four internal spiral springs4 ,the tension of these springs is necessarily constant1 and therefore not subject to the disturbance and slow recovery of elastic force unavoidable in an external spring4 ,means are supplied for regulating the tension of the four springs1 which must be a little in excess of the force necessary to move the revolving mass1 without taking the parts to pieces4 #dhd4--,the ,vertical ,axis is a truncated cone of steel with its base downwards4 ,it is about #fe inches high and #cc inches and #b inches in diameter at the base and summit respectively1 the flange being about #de inches in diameter and constructed on the isolated principle4 ,the vertical axis socket and the five horizontal microscopic arms are cast in one piece of aluminium bronze1 the elliptical table carrying the telescope supports being bolted to the central boss in which the socket of the vertical axis is formed4 ,the vertical axis and the elliptical table are both perforated in the centre so as to allow of a look-down telescope being employed in adjusting the instrument accurately over the station mark4 #dhe4--,the ,telescope is furnished with two separate eye-ends1 carrying respectively a vertical and a horizontal parallel wire micrometer ,j4 ,it is also supplied with both bright and dark field illumination1 the latter being employed when faint stars are observed4 ,the vertical circle ,k is divided on silver similar to the horizontal circle1 and is read by two opposite micrometer microscopes when the instrument is used for terrestrial work3 but when required for astronomical purposes four micrometers can be used1 and they can be shifted to any part of the circle on which they are clamped4 ,in the illustration the four micrometers are shown in position4 ,the two rods or handles seen parallel with the telescope at ,,ll are attached to the middle of the transit axis where the telescope passes through it1 and are intended to raise or depress the telescope without touching it by hand4 ,these rods are also used for carrying adjustable counterpoises1 the instrument being so balanced in every part that the equipoise is as nearly perfect as practicable through any diametrical section of the vertical axis4 #dhf4--,the ,spirit ,levels1 both horizontal ,m and vertical ,n1 are very delicate4 ,they are constructed so that the divisions on their scales represent as nearly as possible one second of arc4 ,the scales are divided to twenty per inch4 ,the glass bubble tubes are mounted on ,v bearings1 and are kept in position by light springs in such a manner that they are free to adapt themselves to changes of temperature with perfect freedom4 ,they are also enclosed in external cylindrical glass covers to protect them from sudden changes of temperature4 ,the arrangements for adjusting the levels are such as to obviate strains without risk of shake1 and to ensure delicacy of action4 #dhg4--,the ,five ,micrometer ,microscopes ,o for reading the horizontal circle are carried by the same number of equidistant radial arms branching from the central boss which carries the whole of the instrument above the horizontal circles4 ,these micrometers are made on ,robinson's principle1 ,fig4 #aii1 that is1 with a short bow spring ,s having a central nut tapped through it to keep the tension between the bearing of the micrometer screw on the end of the outer box and the slide which carries the webs constant with whatever part of the screw may be in use4 ,the radial arms each carry a vertical socket which is bored out cylindrically to receive the microscope4 ,these sockets are slotted vertically1 and have three clamping screws at the side to hold the microscopes firmly in position when they are once adjusted4 ,the two webs in these micrometers are placed parallel to one another1 and at such a distance apart that when in proper adjustment they are a trifle wider apart than the width of one line on the circle1 as shown in ,fig4 #bjj4 ,the micrometer heads are divided into sixty parts1 and the whole is arranged so that in practice ten revolutions of the micrometer screw traverse the webs over ten minutes of arc or two divisions on the circle4 ,each division therefore on the micrometer head represents one second of arc2 and as the divisions are clearly cut on silver and about one-tenth of an inch apart1 there is no difficulty in reading to the tenth of a second1 which1 on a circle of #cf inches in diameter1 is equal to the #jjjjjhgb of an inch1 or the three-thousandth part of one division of the circle2 this1 as before stated1 is equal to five minutes of arc1 or the #jbfaf of an inch4 ,the illumination of the microscopes1 or rather of the divisions of the circle1 is a most important matter4 ,when such exact measures are to be taken it is effected by means of perforated silver reflectors attached to the micrometer arms and mounted quite independently of the micrometers themselves4 ,the axis of each reflector coincides with the axis of its microscope4 ,all the reflectors have both vertical and horizontal movements1 and are therefore readily adjustable to the best position for securing effective illumination under the varying conditions in which the instrument may be employed4 ,illustration3 ,fig4 #aii4--,robinson's micrometer4 ,illustration3 ,fig4 #bjj4--,webs of micrometer4 #dhh4--,relieving ,apparatus4--,it will be readily understood that the moving parts of so large an instrument must necessarily be very heavy4 ,in this case the telescope1 vertical circle1 pillars1 elliptical table1 horizontal micrometer arms1 and vertical axis socket weigh nearly #cjj lbs4 ,it would of course be impossible to take horizontal angles with so much friction on the flange of the vertical axis as this weight would produce1 hence the necessity for some form of relieving apparatus4 ,that employed in this case is a system of forty spiral springs1 each of a definite length1 which when adjusted support about #fbe lbs4 ,the spiral springs are mounted on a flat ring in two circles with projecting pins to keep them in position4 ,the upper ends of the springs support a steel ring with a circular groove on its upper surface1 between which and a corresponding groove in the outer part of the vertical axis socket three equidistant1 nearly frictionless steel rollers run2 so that by this means about #bej lbs4 weight is taken off the flange of the vertical axis1 the remaining weight being sufficient to allow of the instrument moving with the necessary freedom1 and at the same time giving all the stability requisite for accurate levelling4 ,,chapter ,,xi4 ,,mining ,,survey ,,instruments--,,circumferentors--,,plai n ,,miner',s ,,dial--,,sights--,,tripod ,,stand--,,adjustments--,,henderson',s ,,dial--,,lean',s ,,dial--,,adjustments--,,hedley',s ,,dial--,,additional ,,telescope--,,improved ,,hedley ,,tribrach ,,and ,,ball ,,adjustment--,,reflectors--,,continenta l ,,forms--,,theodolite ,,souterrain--,,tripod ,,tables--,,stanley',s ,,mining ,,theodolite--,,pastorelli',s ,,and ,,hoffmann',s ,,adjustable ,,tripod ,,heads-- ,,mining ,,transit ,,theodolites--,,stanley',s ,,prismatic ,,mining ,,compass-- ,,hanging ,,dial--,,hanging ,,clinometer--,,semi-,,circumferentor--, ,mining ,,lamps4 #dhi4--,miner's ,circumferentor4--,in the original form of theodolite1 as it was at first designed by ,digges1 open sights took the place of the telescope4 ,the sights in this case were extended on arms4 ,the compass-box1 afterwards added1 was placed over the axis and made as free from obstruction as possible1 so that the needle1 upon which general surveying formerly depended1 could be read correctly by placing the eye vertically to the plane of the horizontal circle of division against which the needle read4 ,after the introduction of the telescope to the theodolite this old form of instrument took the general designation of the circumferentor2 and subsequently1 being best adapted to underground surveying1 it became1 with some slight alterations1 the miner's dial4 #dij4--,upon this original circumferentor improvements have been made in the various mining dials we possess1 in all of which the large open compass is still preserved4 ,this prominence of the compass does not indicate that the modern scientific mining engineer has any desire to depend upon it for taking horizontal angles1 but that in close and tortuous workings it provides the nearest and often the only possible means of taking angles having regard to the extreme difficulties of observation of any kind4 ,where workings are open and fairly plane the telescope and circle with vernier reading can be used1 so that at the present time the better instruments possess the means also of taking observations of angular direction by vernier reading4 ,several other very important factors specialize mining from ordinary surveying instruments1 which may be stated as follows3--#a4 ,that there shall be means of shortening the tripod for work in strata of small depth4 #b4 ,that the instrument shall be low and compact in itself1 that the head of the surveyor may be placed above it if possible1 even in shallow workings4 #c4 ,that great extent of adjustment of the compass-box to horizontality shall be given in the fittings of the instrument1 on account of the difficulty of extending the legs at all times for tripod adjustment and from the extreme inclination of the floor of the working in some cases4 #d4 ,that it is desirable in mining survey instruments that the telescope1 if there is one1 shall take sights at all angles upon the surface of the earth in the locality in which the instrument is used1 as also about a vertical position1 so as to be able to sight lines from the top to the bottom of the shaft1 or vice versa1 to set off angles in the same azimuth as those taken at the surface by direction of stretched wires or otherwise4 ,this last contrivance will also give the means of sighting a perfectly vertical point beneath the centre of the instrument placed at the top of the shaft1 to make a concurrent station below during ventilation1 when the plummet would be disturbed4 ,the devices by which these various requirements have been met more or less perfectly will go far to explain the specialities of construction found in mining surveying instruments1 which will now be described1 commencing with the oldest and most simple specialised form upon which improvements have been made in many directions4 #dia4--,plain ,miner's ,dial4--,the original simple form of specialized miner's dial is shown in ,fig4 #bja4 ,it consists of a compass1 divided to single degrees1 read by a finely pointed edge-bar needle mounted on a jewelled cap4 ,the needle has a sliding rider placed upon it1 art4 #acj1 so that it may be carefully balanced to horizontality in any locality in which it is used4 ,the divided compass is raised on a step1 and the upper surface of the needle is made to be quite level with the division when the compass is horizontal4 ,in erecting the instrument with the needle correctly balanced1 the compass may therefore be brought to horizontality by the coincidence of the upper surface of the needle with the plane of the divisions1 without the necessity of having spirit levels4 ,illustration3 ,fig4 #bja4--,mining dial4 ,illustration3 ,fig4 #bjb4--;,cover to the same4 ,illustration3 ,fig4 #bjc4--,sight4 ,illustration3 ,fig4 #bjd4--,section of ball and socket joint4 #dib4--,the compass-box is extended in one meridian1 north to south1 by strong arms that carry a pair of sights hinged to turn down to the surface of the cover for portability4 ,the compass-box and arms together are termed the limb4 ,the limb of the instrument is mounted upon a ball and socket joint to be described4 ,the socket is slotted down on one side to permit the limb to be turned to a vertical position4 ,in this position the level shown on the front of the instrument is used for levelling by means of the sights3 this level is not1 however1 put on all plain dials4 #dic4--,the cover of the compass-box1 ,fig4 #bjb1 is fixed on the box to a given position by a stud and slot4 ,it has an arc divided upon its outer surface1 which is centred from a small hole placed near the outer edge4 ,a line from the centre of the hole to the zero of the arc is made perpendicular to the central indices of the sights4 ,a piece of silk or a horse-hair carrying a small plummet is fixed to hang from the hole4 ,by this means when the limb is turned down in the slot of the socket and the silk or hair stretched by the plummet to permit it to hang in front of the arc1 it will then cut the divisions1 and thus form a reading index to the arc1 giving thereby approximately the vertical angle at which the sights are set to degrees4 #did4--,the instrument is mounted on a simple jointed tripod to be described4 ,it will be seen by the above description that this instrument is cheaply made1 and is not designed for very exact work4 ,it is now giving way for more exact instruments1 but it forms the groundwork on which mining survey instruments are most generally constructed4 ,the height of this dial with sights erect is #aa inches2 weight1 #f lbs4 ,some of the separate parts above enumerated1 which are common to many other forms of mining instruments1 will now be more particularly described4 #die4--,sights1 one of which is shown separately1 ,fig4 #bjc1 are common to mining instruments4 ,they are constructed essentially in two parts1 technically termed the slit and the window4 ,the slit ,a is a narrow parallel cut made through the metal upon the inner surface of the sight1 which is turned towards the centre of the instrument4 ,the thickness of the metal is hollowed away on the outer side which comes next the eye1 so as to present a thin edge only for the sighting slit1 as shown in section at ,a4 ,in some instruments the slit is formed of two thin plates fixed to the sight by screws in slots1 which render it adjustable both to width and position2 this is the better way if machinery be not used for cutting the slit4 ,the window ,b is an oblong opening1 across which a hair wire or a thin plate placed edgewise is fixed in line with the slit4 ,the hair or wire is laid in a deeply engraved line1 so that it is in the same plane as the centre of the slit4 ,the ends of the hair are held firmly by drawing them through small holes and fixing them therein by means of dry1 conical1 pinewood pins pressed tightly in the holes4 ,when a thin plate is used edgewise1 this is soft-soldered into the top and bottom of the window4 ,in the pair of sights the window of one sight is placed at the lower position and the slit in the upper4 ,in the fellow sight the positions of these parts are reversed1 the observation being always taken from the slit through the window4 ,the duplication of parts in each sight permits it to be used in either direction4 #dif4--;,in the use of the ,sight the point or object to be observed from the slit should appear to be bisected by the hair in the window at the same time that it appears to the eye to stand in the centre of the slit4 ,for this reason it is not necessary that the slit should be very narrow4 ,it is generally more comfortable to take the sight with the eye at the distance of #aj to #ab inches in front of the slit to obtain clear vision of it4 ,in this case if it be made too narrow it shuts out the field of view4 #dig4--;,it is not quite certain that the old slit and window is the best form4 ,many mining engineers prefer a pair of equal slits1 one of which replaces a window4 ,in this case1 instead of the wire covering the object sighted in the use of the instrument1 the object is made to appear in the centre of the forward sight slit4 ,in this construction the sight apertures are made much narrower so that they do not cover too much of the field of view4 ,excellent work is done with this open form of sight1 and its construction is much more solid than that of having loose hairs4 #dih4--,universal ,sight1 termed technically hole and cross sight1 consists of a small hole ,c1 ,fig4 #bjc1 on the inner side of one sight that is hollowed away on the outer side which comes next the eye1 so as to present a thin edge of the hole only4 ,the fellow sight ,c has a hair cross placed centrally in a circular window4 ,this is of occasional use for sighting angles approximately in altitude and horizon simultaneously2 but the cross occupies so much of the sight space that observation with it cannot be depended upon4 #dii4--;,ball and ,socket ,joint4--,this is shown in elevation ,fig4 #bja at ,f1 and in section ,fig4 #bjd ,f1 ,d4 ,it is one of the oldest forms of adjustment1 and is common to many dials4 ,when the clamping screw ,g is released the ball is free in its socket ,f to move about its centre1 to the extent of the opening at the top of the socket1 in any direction4 ,a plug ,e1 which really forms the lower half of the socket1 is screwed into the part ,f at the lower part of what is technically called the socket-piece4 ,the plug is turned upwards by its screws so as to tighten the ball by means of a tangent screw ,g which works in a rack thread cut in a part of the circumference of the plug1 thus forming a screw and cross screw1 which1 as the construction indicates1 clamps the ball with great rigidity4 ,there are several other ball and socket arrangements2 these will be discussed in describing the special instruments to which they are affixed4 ,the only objection to this form is that it elevates the dial very much more than others4 #ejj4--,the ,tripod ,stand of an ,ordinary ,miner's ,dial4--,the upper part is shown in ,fig4 #bje4 ,this form of tripod is common to many dials4 ,the legs are made about #a inches in diameter4 ,the heads of the legs are fitted directly without brasswork between the book-plates ,a1 to which they are held by cross screws or bolts which form the joint on which the legs move for extension4 ,unless the head be worked out of the solid1 the book-pieces are screwed to a plate that carries a male plug centre to which the dial is fixed by a milled-headed screw shown at ,fig4 #bja ,l4 ,the plug is grooved at the position of the point of the screw so as to permit rotation of the instrument when the screw is slightly released4 ,this tripod head remains permanently fixed to the legs4 ,each leg is jointed to part in its centre by unscrewing1 to present when disjointed a metal point to hold the surface of the ground1 to form a short stand4 ,the usual height of the full tripod legs is #e feet2 the upper part only #b feet #f inches4 ,the usual form of joint is shown in detail in section ,fig4 #bje4 ,c the male screw1 which is fitted to the woodwork by a socket and cross pinned to it4 ,this piece has a point at its lower end4 ,d the socket-piece is screwed over the point to extend the leg when the tripod is required of full length4 ,the woodwork of this lower piece has a conical metal point to bite the ground when it is set up in use4 ,occasionally for close work shorter legs are provided1 or the legs are jointed in three parts4 ,in the common dial shown1 the legs are left exposed when out of use2 with superior instruments they are packed in a deal case that protects the socket fitting to which the instrument is attached4 ,another much better form of tripod will be discussed further on with the instrument to which it is attached4 ,illustration3 ,fig4 #bje4--;,jointed tripod legs of a miner's dial4 #eja4--;,examination and ,adjustment of the ,plain ,miner's ,dial4--,the tripod should be first set up to full length and each length separately twisted to right and left to see that its socket fittings are good and free from shakiness4 ,the legs should each be separately pressed in and out at its centre to see that the screws clamp the parts firmly and are free from shakiness4 ,the instrument should then be set up and its socket fitting be felt to see that it is free from shake1 and also be turned round to see that it moves freely4 ,the ball fitting should be clamped and its rigidity be tested by fair pressure on the two ends of the limb separately4 ,the sights should be examined to see that they are quite linear with hair and slit4 ,the compass-box should be levelled by the coincidence of the upper surface of the needle with the plane of the division1 and be reversed in every direction by turning the compass-box1 the reading being observed with the ,n4 point of the needle at ,n4 ,e4 ,w4 ,s4 to see that it bisects the graduation by angles #ahj apart4 ,the compass-box being level1 the sights should be ranged with an external object at a distance--a plumb-line is best--a piece of string suspending a stone answers--to see that they are vertical1 and that they cut the same line with the position of the sights changed fore to back4 ,if the sights are coincident1 but do not range with the plumb-line1 the needle is out of balance1 and this may be corrected by shifting the rider4 #ejb4--;,henderson's ,dial4--,this is an improvement upon an old form of circumferentor1#ai in which four sights are centred in opposite pairs so as to revolve about the vertical axis1 so that one pair of sights may take any angle to the other pair4 ,in ,mr4 ,j4 ,henderson's dial the improvement consists in making the compass larger1 the needle being made to read by a vernier placed upon one end to #c of arc4 ,mr4 ,henderson prefers plain slit sights instead of slit and window sights1 as before stated1 which avoids the accidental derangement of the horse-hair4#bj ,the instrument combines some of the parts of ,lean's dial1 to be next described4 ,illustration of this instrument is given in ,mr4 ,b4 ,h4 ,brough's ,mine ,surveying4 #ejc4--,lean's ,dial4--,the inventor of this instrument was ,mr4 ,joel ,lean1 a ,cornish mine manager1 who was well known at the end of the #ahth century for his important improvements in mining apparatus4 ,this dial is still popular in ,cornwall and other mineral districts4 ,in general construction the sights and limb on which they are mounted are the same as in the plain dial just described1 art4 #dia4 ,the legs are also the same--other parts are additional or modified4 ,in the engraving1 ,fig4 #bjf1 the sights and vertical arc with its telescope are shown mounted together on the limb4 ,this is done to show the relative position of these parts3 they could not in practice be used simultaneously upon the instrument4 ,they are separately attached to the limb by the same pair of milled headed screws4 ,as a general rule the telescopic arrangement1 which will be described further on1 is used above ground and the sight arrangement below4 ,the details of construction are as follows3-- ,illustration3 ,fig4 #bjf4--,mining circumferentor or ,lean's dial4 #ejd4--,the ,tripod--of the mining circumferentor1 in common with many other forms of dial1 has the legs fitted directly between book-pieces1 which are fixed to the lower parallel plate1 as shown ,fig4 #bjf1 thus dispensing with the separate tripod head1 common to levels and theodolites4 ,otherwise the parallel plates are similar to those described for levels and theodolites1 art4 #aic1 and are used in the same manner4 ,the upper parallel plate in this dial carries the male axis1 which fits into a socket attached below the centre of the limb in the manner just described for plain dial4 ,the tripod stand1 with its parallel plates attached1 is generally packed in a pinewood case when out of use4 ,the reason for attaching the legs directly to the lower parallel plate instead of having a tripod head is that it saves the extra elevation of the instrument by the depth of one screw fitting4 ,at the same time it must be observed that it exposes the axis to the air by separating the instrument at this part when it is put by1 which renders the axis difficult to be kept lubricated and in smooth working order4 ,on the ,continent and in ,america it is general to detach the legs only1 on a plan shown1 ,fig4 #he1 p4 #adj4 ,this keeps the axis attached1 and is probably the better plan1 although it may be found a little more troublesome to erect the instrument4 ,illustration3 ,fig4 #bjg4--,section of compass-box and axis of ,lean's dial4 #eje4--,revolving ,compass forms a part of ,lean's dial and many other dials4 ,it is shown in section ,fig4 #bjg4 ,as the axis is constructed in this instrument1 the socket-piece ,a is ground to fit the male axis ,s1 and at the same time it is shouldered to fit the surface of the parallel plate ,t to prevent excess of friction on the axis fitting1 so that it may move easily to set the needle to magnetic north of the compass-box if desired4 ,the socket-piece is attached to the compass-box through a collar4 ,the compass has a step ,d which is divided to degrees on its inner edge to read to the point of the needle1 and similarly to degrees on its outer edge to read with a vernier scale1 shown ,d to #c4 ,the vernier is set off on each side of the zero line in ten divisions1 which are figured #cj1 #de1 #j1 #ae1 #cj1 art #cbb1 p4 #ahd4 ,the upper surface of the needle is made level with the upper surface of the step4 ,the bottom plate of the compass-box is divided to #aj3 in some difficult positions in the use of the instrument this last is the only reading that can be sighted4 ,the compass-box1 which carries the vernier ,b1 is fixed centrally on the arm plate4 ,the arm plate is centred upon a step fitting between the compass and the socket-piece1 so that it carries the whole superstructure of the instrument around the compass1 its relative position being read by the vernier4 ,the edge of the compass plate is formed into a toothed wheel1 as shown in section in the figure on the right-hand side1 into which a small wheel or pinion ,r is fixed in a box upon the arm plate that works by means of a large milled-head screw ,p4 ,by means of this milled head the instrument may be rotated about the compass1 so that the line of division on the compass step reading into the vernier performs the functions of the horizontal limb of a theodolite4 ,in this manner angles may be taken by means of the vernier1 quite irrespective of the reading of the needle4 ,when the compass is set to the zero of the vernier at north 7#cfj7 it may be fixed in this position by means of a pin fitting in opposite holes to the arm plate and bottom plate of the compass1 not shown2 and when thus fixed the needle only is used as in the plain dial4 ,between the collar-piece ,c and the socket-piece ,a a wedge-shaped lift raises the needle off its centre by pressing in a slide shown at ,l4 #ejf4--,the ,vertical ,arc is erected upon the limb as close as possible to the compass-box1 so as to leave room for a level to be placed between the seatings of the arc and sights4 ,the axis of this arc is a simple hinge joint1 brought down nearly to the surface of the cover which protects the glass of the compass-box3 this is done to keep the instrument as low down as possible4 ,the telescope1 which is of the same kind as that used for the theodolite1 traverses the arc tangentially1 permitting it to be adjusted for reading the arc by its vernier by means of a clamp and tangent motion at any position4 ,the arc is divided on one side into degrees1 and reads by the vernier to #c in the same manner as the horizontal circle4 ,on the opposite side it is divided with a percentage scale of difference of hypotenuse and base which reads to an index line4 ,a spirit level is placed under the telescope1 in line with its axis1 to which it is adjustable by means of capstan-headed screws4 ,the telescope when fixed is placed just sufficiently above the arc to permit it to be brought to a vertical position at #ij1 or a degree or two over this1 with the full aperture of the object-glass beyond the extreme edge of the horizontal circle4 ,by this construction a bearing may be taken of any object upon the surface from the top of a shaft1 and a line may be sighted to the bottom of the shaft in exact azimuth with this without changing the horizontal adjustment of the instrument4 ,in the same manner1 if the vertical axis be perfectly adjusted by the level on the vernier plate1 the telescope at #ij n will indicate a perfect vertical to the station of the instrument above1 the n being the allowance to be made for the eccentricity of the telescope1 provided the collimation is perfect4 ,if this is not perfect1 the vertical may still be taken accurately by means of three observations taken from equal division of the entire horizontal circle1 say at #cfj1 #abj and #bdj4 #ejg4--;,it will be noticed that the vernier to the compass circle comes directly under the vertical arc1 therefore it can only be read obliquely when this arc is mounted3 with open sights the vernier can be read directly4 ,this is a defect in this instrument1 as the vernier is mostly required for exact work when the telescope is used4 #ejh4--,lean's dial possesses the qualities #a and #d1 pointed out in art4 #dij as important to dials2 in #d the power of setting the telescope to the vertical with great facility being the most important4 ,this quality has kept the dial a favourite with many mining engineers in mineral districts for many years4 ,otherwise for general work the compass is most inconveniently obstructed by the arc above it1 and the instrument1 although1 of course1 of less height than the theodolite1 some of the functions of which it performs indifferently1 is too high to be used in shallow workings4 ,the height of a #e-;inch ,lean's dial to the central apex of the telescope is #i inches2 to the top of the sights placed in a level position1 #h inches2 weight of instrument only1 #f lbs4 ,the #f-;inch instrument is about #a inch higher1 and weighs #a lb4 more4 #eji4--;,a number of variations have been made in ,lean's dial2 but none that the author is aware of has proved successful4 ,in an instrument of this class1 designed by ,mr4 ,j4 ,whitelaw1#ba the vertical arc is brought down to the compass-box by placing pivots on each side of the box after the manner of ,hedley's dial1 to be next described4 ,this lowers the instrument about an inch1 and is an improvement2 but this is effected at the expense of placing a striding bar across the compass box1 which is a great impediment to the clear sighting of the compass4 ,messrs4 ,newton ,son have made the telescope to detach from the arc of ,lean's dial to be placed directly upon the limb4 ,in this way they claim for it that it combines a miner's dial and dumpy level4 ,the arrangement appears to the author to make the instrument top heavy as a dial1 and to give too little power for a good level1 added to which it costs about the same as the two separate instruments of equal quality4 ,of course any telescopic dial may be used as a level by clamping it at zero4 ,practical surveyors generally object to compound instruments that entail many loose pieces4 ,these were a fashion in the middle of the nineteenth century4 #eaj4--;,examination of ,lean's ,dial4--,as regards the stand1 sights and parallel plates1 particulars have been given upon the plain dial just described4 ,the revolving compass should be turned round by the milled head ,p1 ,fig4 #bjg1 of the pinion wheel ,r to see that the compass-box revolves steadily at all points without disturbance of the needle4 ,it may also be particularly observed that the needle does not oscillate at any part of the circle1 to be sure that the compass-box is quite free from iron4 ,the vernier should be examined at four opposite positions of the needle to see that the needle is truly centred and is in accord with the vernier4 ,the lifter should be tried to see that it lowers the needle gently on the centre1 and that it holds the needle firm off the centre4 ,the telescope should be set up and directed to an object1 and all parts of the instrument clamped and the needle observed4 ,the telescope should then be detached and the sights set up1 to see that they range fairly with the telescope4 ,if they do not do so the difference should be noted and treated as a constant in any case of change from telescope to sights on the same survey4 ,the difference ought to be very small1 otherwise the instrument should be returned to the maker4 #eaa4--,the ,adjustment of ,lean's ,dial is the same as that of the plain theodolite1 so far as this can be carried out2 but generally the adjustment is depended upon as it leaves the manufacturer4 ,for the general use of this and other dials some notes will be made further on1 but as regards vertical position and the taking of azimuth angles1 for which this dial is specially adapted1 notes may be made here4 #eab4--,to set a line in ,azimuth with one taken above ,ground4--,this is necessary where there is local attraction to the needle below1 or there is a suspicion of this1 so that the needle cannot be depended upon with certainty4 ,the instrument is placed on staging over the pit and a vertical is taken to its centre either by the means briefly discussed art4 #ejf by the instrument1 or by suspending a plummet1 a ball1 or a bullet from the centre of the instrument by a thread and burning the thread when the ball is free from vibration4 ,the ball is allowed to fall upon a smooth horizontal surface formed of earth or otherwise1 in which it makes a dent which will be vertical to the axis of the instrument if the ball has not been deflected by ventilation currents4 ,two lights1 as distant as possible to be seen to range in line with the dent1 are placed at the bottom of the pit4 ,the lights1 if thought desirable1 may range north and south with the needle2 but in whatever direction this may be set the correct azimuth of this may be taken by cutting them by the webs of the nearly vertical telescope of the dial2 and this azimuth may be correctly set out on the surface by a pole or other station mark1 or its true direction by a pair of these1 one on each side of the pit's mouth1 the second station mark being set out after a shift of the horizontal vernier exactly #ahj on the circle4 ,a straight-edged flooring board painted white may be made to cut the line from light to light1 which is more definite for bearing than the lights themselves4 #eac4--;,hedley's ,dial1 the invention of ,john ,hedley1 ,h4,m4 ,inspector of ,mines1 in #ahej1 has now become the most popular form of miner's dial1 modified1 however1 from its original form in various ways4 ,the peculiar feature of this form of dial is that the sights move upon a framework centred upon a horizontal axis1 so that they may by a rocking motion take horizontal angles within a wide azimuth without obstruction to the sight of the compass4 ,illustration3 ,fig4 #bjh4--;,hedley's dial4 #ead4--;,for consideration of the general features of ,hedley's dial1 the tripod and the ball and socket are the same as that described for the plain dial2 but the socket is not cut down on one side to change the position of the axis1 as the compass-box in this instrument is required to be kept uniformly level4 ,the general appearance is shown ,fig4 #bjh4 ,for districts in which the working strata are fairly level1 parallel plates are put to this instrument in place of the ball and socket joint4 ,the compass-box revolves1 as that described for ,lean's dial2 but it is more general in this instrument to have a clamp and tangent motion1 as in a theodolite1 than the rack and pinion motion4 ,two levels for setting the compass horizontal are sunk into the plate of the compass-dial low enough to miss the edge-bar needle4 ,the step of the compass is divided into degrees and the plate of the dial to #aj4 ,the vernier1 which is placed on the opposite side of the box to the vertical arc1 reads to #c1 as described for ,lean's dial4 #eae4--,the ,rocking ,centre forms the peculiar feature of ,hedley's dial4 ,from opposite points of the under side of the compass two pivots are projected4 ,these are set perpendicular to the vertical axis1 which is placed above the ball and socket4 ,the pivots are placed central with the vernier and in line with ,e4 to ,w4 of the compass when this is set to zero 7#cfj74 ,the pivots form the axes of a stout ring--rocking ring--which surrounds the compass-box1 with space sufficient to clear it when the ring is rocked about its axis4 ,the ring has two extended arms which carry sights as shown4 ,these turn down upon the compass-box when out of use4 ,one of the pivots is prolonged for about inch beyond the outer circumference of the ring4 ,the prolongation is made generally of triangular section4 ,this forms a fitting to the vertical arc1 which is attached by a milled-headed screw when required1 the arc being an encumbrance when this dial is used for making horizontal plans only4 #eaf4--,the ,vertical ,arc1 with its index arm1 forms a separate piece4 ,the arm is centred upon the arc with a ground fitting1 which is retained in its position by a collar fixed with three screws4 ,the arm-piece forms the axis1 through the centre of which a triangular hole is made to fit the triangular prolongation of the pivot1 so that the index arm remains fixed1 and the arc moves with the rocking ring1 to which it is held by a pair of dowels4 ,the arc is divided into degrees on the outer edge of its surface1 and a scale of difference of hypotenuse and base upon its inner edge4 ,the graduations read to a single index line upon a fiducial edge carried down from an opening in the index arm4 ,hedley's dial can be locked by a pin1 which is attached to the under side of the compass-box1 so as to work by the compass only4 ,the ring can also be locked level with the compass by a sling latch-piece so as to convert it into a plain dial4 #eag4--,the great merit of ,hedley's dial is that the rocking centre permits a greater range of open sighting than any other2 and the instrument is very low1 permitting its use in shallow workings4 ,further1 that it is a very strong instrument to resist accidents1 and is very portable4 ,the height of a #f-;inch ,hedley's dial above the tripod head1 in a level position1 is #i inches to the top of the sights4 ,weight of instrument1 #g to #aj lbs4 ,illustration3 ,fig4 #bji4--;,hedley's dial with ball clamp4 #eah4--;,in the author's simple dial1 ,fig4 #bji1 which is of a modern form1 the ball is clamped by a capping-piece over it moved to clamp by two stout pins4 ,this form gives a little less height and still holds the dial firmly4 ,the horizontal axis moves rather stiffly1 so that no clamp to the arc is required4 ,it is a very cheap form of dial1 but substantially made4 ,it answers for a small mine survey4 #eai4--,there have been many variations made and proposed for ,hedley's dial4 ,mr4 ,casartelli1 of ,manchester1 places the arc over the centre of the compass-box4#bb ,this plan is intended to make the rocking centre firm2 but the arc interferes a little both with the sights and the view of the compass box4 ,messrs4 ,davis and ,son connect wheel-work with the arc1 so as to magnify the scale of motion4 ,other less important variations in ,hedley's dial are common4 #ebj4--;,examination and ,adjustment of ,hedley's ,dial4--,the general examination of the stand and of such parts of the instrument as correspond with ,lean's dial is the same as just given4 ,the rocking ring should be lifted and pressed down at each end alternately to see that there is no loss of time on the axis4 ,the arc should be examined in like manner4 ,the dial should be set up in front of a plumbed line to see that its sights range properly when the instrument is set level by its bubbles4 ,a point should be observed1 say through the hole and cross webs at the top of the sight2 and with this point kept in view the rocking ring should be moved upwards or downwards so that the point traverses the plumb-line to the extent of the rocking motion4 ,if it does not do so1 possibly the transverse level in the plate of the compass-box may be adjusted to make it do so2 but in this adjustment it must be particularly observed that the balance of the needle remains so that it still reads the graduation with its upper edge1 and that the sights traverse the same plumb-line when turned about1 as it is possible to set the level right with one pair of sights and throw other parts out4 ,there are no simple means of adjustment provided1 so that if the instrument is not accurate it should be returned to the maker for correction4 #eba4--;,improvement in ,hedley's ,dial1 by ,addition of ,telescope4--,surface work being generally performed with the theodolite1 surveying with open sights following this cannot be effected with sufficient accuracy2 therefore there becomes a necessity for the use of the telescope1 which was first placed on this instrument by the author at the suggestion of ,mr4 ,w4 ,preece1 ,c4,e4 ,in mines1 also1 although sights present often the only possible means of directing angular positions in cramped and tortuous workings1 on the other hand1 better work can very often be done and the telescope be conveniently used4 ,under these conditions1 this addition forms an important improvement in the instrument1 to be at hand to apply when desired4 ,the telescope of this instrument detaches exactly as with ,lean's dial1 but the sights are made with an angle piece1 so as to extend them to a distance of about #ab inches apart for sighting4 ,fig4 #baa is of one cranked sight4 ,the instrument illustrated ,fig4 #baj has parallel plates1 art4 #aic1 p4 #ii1 suitable for fairly level workings4 ,a ball and socket joint is sometimes fitted to this instrument in place of these4 ,illustration3 ,fig4 #baj4--;,hedley's dial with telescope4 ,illustration3 ,fig4 #baa4--;,bracket sight4 #ebb4--,the ,telescope is placed on ,y's1 and is of exactly the same form as that described for a plain theodolite4 ,the ,y's in this instrument offer a great convenience for reversing the telescope for back sights in range when the vertical axis is fixed4 ,the level under the telescope is sufficiently good to convert this instrument into a level for drainage1 etc41 when the rocking ring is locked with the compass4 ,its examination and adjustment are the same as those last given1 except for the telescope1 which is the same in all particulars as that of a #e-;inch plain theodolite4 ,illustration3 ,fig4 #bab4--;,improved miner's dial4 #ebc4--;,improved ,miner's ,dial4--,the illustration given1 ,fig4 #bab1 is of the form of dial introduced by the author1 a part of the arrangement only being of his own design4 ,the telescope with ,y supports is the same as that just described1 and the sights1 not shown1 are cranked in the same manner as shown ,fig4 #baa4 ,the horizontal circle1 instead of being in the interior of the box1 is placed on the exterior rim1 and reads with two verniers--not for correction1 but for convenience of reading in different positions4 ,the compass is divided upon the upper surface of the step to degrees1 and in the same manner on the interior cylindrical surface of the step4 ,this last often permits the compass to be read in a close working when the upper surface could not either be lighted or sighted4 ,this plan was used on old circumferentors4#bc ,the plane of the compass is divided to #aj as usual4 ,the compass adjusts by clamp and tangent motion4 ,the axis of the instrument is supported upon a ball and socket arrangement designed by the author for roughly bringing the compass to level1 and a parallel plate adjustment for final setting4 ,the ball is fixed by clamping a pair of plates together by a thumb-screw4 ,each plate is hollowed in the centre to hold nearly half the ball4 ,when fixed1 the instrument is found to be very rigid4 #ebd4--;,a plan of clamping designed by the author to meet the conditions of the tribrach system of adjustment of equal rigidity to that above described1 is shown in elevation1 ,fig4 #bac ,b4 ,in this the upper half of the socket is screwed down outside the lower half socket by means of three projecting handle pins4 ,this is a somewhat neater arrangement than that shown in ,fig4 #bab4 ,either of the above-described ball arrangements elevate the instrument1 and are better omitted for close working if there is a special adjustment in the tripod attached to the instrument1 as that to be described presently1 which will be found sufficient in most cases4 ,the height of the instrument from the tripod is about #f inches2 weight1 #aa lbs4 for both parallel plate and tribrach adjustments4 #ebe4--;,adjustable ,tripod for ,dials4--,the author's improved form of tripod is adjustable to all heights between #cj inches and #eg inches1 ,figs4 #bac1 #bad4 ,each leg is formed of two stiff bars of mahogany1 shown in detail1 ,fig4 #bad ,g of section1 about #a inches by #e_/h inch1 and a third bar or leg ,g of about #a inches square1 which slides between the other two4 ,the sliding surfaces are grooved and tongued together in ,v grooves in the solid4 ,two strap-pieces of brass ,,ss are fixed near the ends of the bars4 ,one of these ,s is firmly soldered to a boss-piece that takes a thumb-screw1 which has quite sufficient power to hold the leg ,g firmly at any position of extension4 ,it is a rigid stand1 which may leave the tripod head nearly vertical upon any inclination of the floor surface4 ,illustration3 ,fig4 #bac4--,the author's adjustable ball joint and socket tribrach stand4 ,illustration3 ,fig4 #bad4--;,adjustment to leg of tripod4 #ebf4--;,hedley's ,dials1 with ,pastorelli's and ,hoffmann's ,ball ,arrangements4--,by either of these arrangements the ball and socket is brought down close into the parallel plate adjustment so that the dial is of less total height4 ,hoffmann's is now becoming the most popular system1 as practice has shown it to be the most perfect for mining survey4 ,by either of these arrangements the ball and socket is clamped by the same screws that bring the instrument to final position4 ,in ,pastorelli's arrangement#bd the socket is drawn down upon the ball by the adjusting screws4 ,in ,hoffmann's#be the ball is pressed up into the socket1 which is the exact mechanical equivalent4 ,when the screws are lightly clamped the ball can be moved with moderate force1 or even quite loosely by careful adjustment2 and in either case1 when the ball is once set1 care must be taken to keep pressure constantly upon it during the final adjustment by the screws4 ,the general arrangements are shown in two ,figs4 #bae1 #baf1 which are taken from the drawings of the respective patents4 ,in ,fig4 #bae1 va1 the axis of the instrument terminates in a ball e which works in a cup f4 ,the axis has also a portion of a ball of greater radius b concentric with the lower ball e4 ,the upper parallel plate d is cupped over this ball4 ,when the parallel plate is moderately free on b1 the axis va may be set to any angle within the range of the central opening of d2 and as the friction upon bd is greater than that upon fe1 the axis moves by the adjustment of the parallel plate screws aa4 ,in ,fig4 #baf the action is precisely the same1 except that the pressure is upwards instead of downwards4 ,in ,fig4 #bae there are springs s under the parallel plate screw heads to keep contact when the screws are loosened4 ,in ,fig4 #baf the spring is a plate under the screws s1 the action being the same in both cases4 ,illustration3 ,fig4 #bae4--,pastorelli's ball and socket adjustment4 ,illustration3 ,fig4 #baf4--;,hoffmann's ball and socket adjustment4 #ebg4--,some objections have been made to this class of arrangement1 over the simpler one of clamping the ball independently and then adjusting by the screws1 as being more complex4 ,on the other hand this compound arrangement has the merit in underground instruments of being lower and more compact1 which is very important4 ,the author has somewhat modified the arrangements of ,hoffmann's head1 as shown in the engraving on next page1 to render it still more compact for mining instruments4 ,illustration3 ,fig4 #bag4--;,improved ,hedley's dial1 mounted on ,hoffmann's head4 #ebh4--;,in ,fig4 #bag an improved ,hedley's dial is mounted upon an improved form of ,hoffmann's head4 ,the whole arrangement is very compact1 rigid1 and rapid in action4 ,the height of this dial is #i inches2 the weight #h lbs4 for a #f-;inch instrument1 in aluminium #e lbs4 ,illustration3 ,fig4 #bah4--;,improved ,hedley1 with cradle ring4 #ebi4--;,hedley's ,dial with ,cranked ,rocking ,centre4--,one defect of the ,hedley's dial1 which in certain cases makes ,lean's preferred1 is that with the rocking ring the sights cannot be brought vertical for looking up or down a shaft4 ,the author has devised a means of getting over this difficulty by making the ring of cradle form1 thus throwing the bearing surfaces to sufficient height to cause the ring1 when the arc is raised to about #ij1 to fall under the compass-box and its adjustments1 ,fig4 #bah4 ,this dial presents possibly the greatest refinements of the ,hedley principle at the time of its patent1 ,no4 #iacd1 #ahih4 ,since this date the reviser has introduced a few further refinements as illustrated at ,fig4 #bai4 ,illustration3 ,fig4 #bai4--,stanley's improved dial4 ,this instrument has tribrach levelling with quick-setting spherical lower plate1 a sliding tribrach for centring over any desired spot1 and full clamp and tangent motions to both horizontal centres4 ,the dividing is upon silver on a #f-;inch covered limb reading by two verniers to single minutes1 folding sights interchangeable with telescope ,y's1 and this dial may be used upon any staging without its stand4 ,the somewhat peculiar shape of the cranked rocking ring is necessitated by the movement of the sliding tribrach1 which it has to clear in all positions for reading vertical sights4 #ecj4--;,accessories ,common to ,hedley's ,dials are a vertical reflector and a diaphragm illuminator4 ,reflecting ,cap4--,one of the disadvantages of ,hedley's dials over ,lean's was pointed out to be the impossibility of vertical sight where the two last described dials are not used4 ,some years ago the author devised a plan of obtaining this vertical sight by reflection by means of a reflecting cap1 ,fig4 #bbj1 placed over the end of the telescope4 ,the cap is formed of a tube which fits the outer surface of the object end of the telescope4 ,this is prolonged sufficiently to lock it by a dowel in correct position against revolution when the points that are used for index in the diaphragm of the telescope are vertical4 ,the tube is cut in two and hinged to turn up1 as shown in two positions ,h and ,h4 ,when turned up it leaves the tube open for direct vision4 ,a reflector ,r is placed in the cap1 and there is an opening below it equal to the full aperture of the telescope4 ,it is easy to see that by this means a pair of lights or a line may be sighted up or down a shaft1 and the azimuth of its direction be reflected to follow a line by slightly rocking the telescope upon its pivots4 ,this may be done1 however1 with more refinement if there is a clamp and tangent motion to the vertical arc1 which is placed only on first-class instruments4 ,illustration3 ,fig4 #bbj4--,reflecting cap to miner's dial4 #eca4--;,illumination of the ,diaphragm for observing the webs or a point1 may be conveniently effected underground by employing a conical ring reflector in front of the object-glass4 ,the aperture through the cone leaves the field of the object-glass nearly free1 as it is only necessary that the cone should project in front of this for a very small distance4 ,this reflector is placed over the object end of the telescope when it is required1 just the same as the ray shade4 ,the vertical reflector1 ,fig4 #bbj1 goes on the same fitting4 ,the reflector ,fig4 #bba ,r may be made of silver or platinum4 ,a light placed anywhere opposite this1 and perpendicular to the axis of the telescope will throw sufficient light to show the webs or point4 ,sometimes a simple1 plain mirror placed on an arm bent over to the centre of the front of the object glass1 in which the mirror stands at #de to the axis1 is used2 but this plan is not so good as that shown ,fig4 #bba1 as the light has to be brought to face the mirror quite perpendicular to the axis of the telescope1 and this process is frequently difficult to accomplish underground4 ,illustration3 ,fig4 #bba4--;,conical reflector to illuminate axis of telescope4 #ecb4--;,continental ,forms of ,miner's ,dials4--,on the ,continent generally sights have been abandoned for miner's dials4 ,the telescopes are usually of short form1 with large object-glass and wide field of view4 ,the telescope is generally placed eccentrically1 which permits the instrument to be made of very low form4 ,there is a certain amount of disadvantage in the eccentricity of the telescope1 as angles cannot be taken direct from the centre of the instrument but this is compensated for in the plotting by making each station a small circle equal to the amount of the eccentricity of the instrument to scale1 and setting off angles tangentially to this1 which may be done with a little more trouble than that of plotting the angle from a point4 #ecc4--;,french ,miner's ,compasses4--,fig4 #bbb shows the simpler form of this instrument4 ,the needle is open and quite free from obstruction4 ,the telescope is centred about level with the compass-box4 ,the vertical axis has clamp and tangent adjustment4 ,the transverse axis is set entirely by hand as with the plain dial4 ,the instrument is set up level by its tribrach adjustment4 ,the height with #e-;inch needle in a level position1 without tripod head1 is about #e inches2 weight about #aa lbs4 without the tripod table4 ,the extremely squat form of the instrument permits its use in very close workings1 with a short tripod1 if the workings are fairly level4 ,it is used also as a cheap form of surface surveying instrument1 consequently it is not generally very carefully made4 ,as a good instrument of the class it cannot compete with that to be next described4 ,illustration3 ,fig4 #bbb4--;,french form of miner's dial4 #ecd4--;,it will be seen by ,fig4 #bbb that the instrument has no direct connection with its stand or tripod4 ,this is general with all ,french and ,german instruments1 even with theodolites and surveying levels1 it being the rule that the top of the tripod should form a kind of table upon which the instrument is set up4 ,the table is almost uniformly made of wood1 and is somewhat bulky and clumsy in construction1 therefore not very well adapted to mining surveying1 particularly in wet mines4 ,neither is the tribrach system of adjustment1 unless it is supplemented by some form of ball and socket arrangement1 or with adjustable stand4 ,this subject will be further discussed in the description of superior instruments presently4 ,illustration3 ,fig4 #bbc4--;,french miner's transit survey instrument4 #ece4--,miner's ,transit ,instrument4--,this is the thodolite souterrain of the ,french1 and is of a construction very general throughout the ,continent--,fig4 #bbc4 ,the compass is placed clearly in view4 ,the vertical axis has a clamp and tangent motion to bring the compass to exact bearing if desired1 or to permit surveying with the compass only4 ,the axis has also a clamp and tangent screw to the exterior divided circle1 which reads with two verniers4 ,the telescope is placed on the side of the instrument1 and has clamp and tangent motions to read the vertical circle which the vernier traverses in transit4 ,all the divisions are made strong to be read clearly by lamp-light1 either to #a or #c by the vernier1 as desired4 ,a second level is generally placed on some part of this instrument at right angles to the one shown4 ,the instrument is balanced by a counterpoise weight to keep its vertical axis in equilibrium4 ,the height of an instrument with #e-;inch needle is about #f inches2 the weight without the tripod table is about #ad lbs4 ,the tripod table is constructed in various ways by different makers4 #ecf4--,the value of the transit principle applied to mining instruments1 for taking back and fore sights for hanging lines in undulating strata1 by simply turning the telescope over on its axis1 cannot be overrated for exact work such as the telescope alone can perform4 ,further1 with this construction the inclination and difference of hypotenuse and base for correction of the chain measurements may be taken4 ,but it is important in the use of this instrument to observe the side upon which the telescope is situated at the time of observation1 right or left4 ,for this a column should be placed in the field-book4 ,as a rule fore sights are taken with the telescope left2 back sights with the telescope right1 remembering that in plotting all angles are taken eccentrically from the axis of the instrument1 that is1 tangential to a small circle which represents the eccentricity of the telescope according to the scale used in plotting4 #ecg4--,the ,tripod ,table of a superior class of ,continental instruments1 whether this is used for surface or mining surveying1 is usually made with some form of adjustment to bring the upper surface approximately level before setting up the instrument4 ,in this case the table is made a combination of wood and metal2 and the only difference between mine and surface tables is that in the former case there is a jointed arrangement for shortening the legs1 but not in the latter4 ,the table surface for superior work is generally adjusted to approximate level either by a ball and socket joint or by a pair of knee joints placed at right angles to each other1 with clamps to hold it firmly when adjusted4 ,radial ,v-grooves are commonly made for the points of the tribrach1 and a hole is sometimes made in the centre of the table for suspending a plummet from the axis of the instrument4 ,there are many forms of tripod table in use1 a modified form of one of which in metal will be described further on in the chapter on plane tables4 ,there are certain merits in this table arrangement over connective stands1 as the table is convenient to set up fairly level1 and the instrument need not be exposed until the operation is complete4 ,on the other hand there is more risk of upsetting and injuring the instrument by accident when loosely placed on the table4 ,there are1 however1 schemes more or less complicated to prevent this1 as by a screw fixed in the tripod head acting against a spring which draws the instrument constantly down when attached1 and other contrivances1 none of which is perhaps equal in simplicity to ,everest's arrangement for the tribrach1 ,fig4 #aia1 p4 #bgc1 on this particular point4 ,illustration3 ,fig4 #bbd4--,stanley's improved mining survey transit4 ,illustration3 ,fig4 #bbe4--,stand for the same4 #ech4--;,improved ,mining ,survey ,transit4--,the author has modified the form of instrument last illustrated1 retaining the general principles4 ,in ,fig4 #bbd the compass is made larger and reads in the inside of the step as well as upon the surface1 which is the only way in many cases that it can be read in a close working4 ,the reading of the horizontal circle is placed nearly vertical1 so that it may be seen clearly when the instrument is near the roof of the mine4 ,the vertical circle is made smaller than the horizontal1 as this circle1 as a rule1 is of less importance1 and it can generally be read more exactly from its convenient position4 ,the arrangement also permits greater freedom for the use of the tribrach4 ,the telescope is made with a much larger object-glass than is usual1 to take a wide field of view2 therefore it forms a good level4 ,illustration3 ,fig4 #bbf4--,stanley's miner's dial sight4 #eci4--,two pairs of sights are placed upon the telescope1 either for roughly sighting an object or station1 or to be used in difficult positions4 ,these are made on a new principle1 shown ,fig4 #bbf4 ,the sights are placed in two windows1 each of which is formed of a needle point of platino-iridium4 ,in sighting1 the points are brought over each other1 the distant lamp or object appearing between them4 ,a sharp point gives much clearer definition than a hair1 as it subtends of itself no angle to the axis of the eye4 ab represent the pair of sights1 c as they appear superimposed4 ,this instrument is very conveniently fitted with subtense points in the telescope1 by which distances may be taken with the author's staff1 ,fig4 #aje1 p4 #aeh1 without actual measurement1 for the particulars of which see next chapter4 ,the subtense points are arranged to measure the staff either vertically or horizontally4 ,as a rule it will be found with this instrument better to take rough positions first with the points1 and afterwards by the telescope4 ,the instrument cannot be recommended universally for underground surveying1 but it is valuable under certain conditions in close strata4 ,its height is #f inches and weight #ac lbs4 ,fig4 #bbe is an ordinary tripod1 like that used with a level4 ,this is preferred by many mining engineers as being firmer than any jointed arrangement1 and is sufficient for working in a seam of fairly equal thickness4 ,the legs vary from #i inches to the full height1 #e feet #d inches4 ,an ordinary set of three tripods would be #a foot #f inches1 #c feet #f inches1 and #e feet #d inches4 ,illustration3 ,fig4 #bbg4--,stanley's underground theodolite4 #edj4--,mining ,theodolite4--,this theodolite is of the most convenient form for underground railways1 ,fig4 #bbg4 ,the telescope transits on its axis to be brought to a vertical position4 ,the vertical axis is pierced so that about #aj of angle may read below the vertical most conveniently by means of a diagonal eye-piece4 ,the centre is supported upon a sliding fitting so that it may be displaced about #a inches about the centre of the tripod and be clamped to its position4 ,the horizontal axis is pierced to permit the diaphragm to be illuminated by a lamp4 ,the tripod stand is fitted with sliding legs1 if it is to be used for mine survey1 to adjust for irregularity of surface of the ground and for low workings4 ,the form of the instrument is very compact1 rigid1 and portable4 ,illustration3 ,fig4 #bbh4--,stanley's prismatic mining compass4 #eda--,prismatic ,mining ,survey ,compass4--,this arrangement is designed by the author for very close workings4 ,the entire depth of the instrument being only #d inches1 any reading may be taken from one point of view simultaneously with the observation4 ,the #e-;inch compass1 ,fig4 #bbh1 has a floating ring divided to half degrees1 and the reading of this is reflected through a prism so that it appears directly under the fore sight1 to be seen at the same time4 ,the prism has a slight magnifying power1 so that by estimation a bearing may be easily taken to degree or nearer4 ,the principle of the compass is described art4 #adh1 the prism art4 #ee2 but in this case the prism is raised and has a second lens under it1 so that it forms a kind of prismatic ,ramsden eye-piece4 ,this elevation of the prism permits sighting under a certain amount of downward inclination1 regulated by the height of the prism and the length of the back sight1 as well as the upward inclination which is common to the use of prismatic compasses4 ,the most important feature in this compass is the mode of lighting1 which is effected by means of a large prism1 ,fig4 #bbi ,r1 placed under the compass-box in a square tube1 and a small movable lamp to throw light into it1 ,fig4 #bbh ,l4 ,the floating ring1 ,fig4 #bbi ,c1 is made of celluloid1 quite transparent1 so that the divisions upon it are clearly read through the small window in the cover of the compass-box4 ,the fore sight ,w is jointed in two folds jj1 so that it extends the distance of sights to about #aj inches apart in use1 and yet folds away closely to the compass for portability when out of use4 ,on the near sight a cut is made transversely to the slit4 ,a second similar cut on the fore sight is made level with this to take levels roughly4 ,about #bj are set off on each side of the cut on the fore sight1 so that angles of altitude may be approximately taken--although the instrument is not well adapted to this4 ,two levels set at right angles to each other1 to be used in setting up the instrument1 are fixed under the compass-box4 ,weight of instrument1 #d lbs4 without the tripod stand4 ,illustration3 ,fig4 #bbi4--,section of prismatic mining compass4 #edb4--;,hanging ,compass4--,a very general method of underground surveying in mineral districts upon the ,continent is by means of the hanging compass2 this instrument is therefore generally found in catalogues of surveying instruments in ,france1 ,germany1 and ,italy4 ,the original hanging compass was invented by ,balthasar ,rssler about #affj4bf ,it appears to the author to be a valuable instrument for surveying in tortuous mineral veins where sighting is difficult4 ,the measuring line upon which it is used is either a hempen or copper cord or a chain4 ,the compass is hung upon the cord or chain1 which may be stretched to any point out of sight1 and the compass will then indicate the bearing of the line4 ,in ,germany two instruments are used simultaneously--the hanging compass for taking the bearing1 and a clinometer1 composed of a light brass semicircle graduated to degrees1 with a small plummet for taking the inclination4 ,illustration3 ,fig4 #bcj4--,stanley's hanging dial4 #edc4--;,hanging ,dial4--,fig4 #bcj represents a modification of the hanging compass designed by the author1 by which inclination may be taken simultaneously with bearing1 if the dial can be suspended near the centre of the line or chain where the catenary curve is parallel with its points of support4 #edd4--;,in the construction of the instrument a circle of brass about #f inches diameter1 inch wide1 and #a_/h inch thick1 has two arms extended to #ab inches at the upper part1 on the end of each of which a hook is formed for hanging the instrument upon a cord or chain4 ,upon the lower part of the circle a fork-piece1 with a bearing clipping the circle1 is attached by two screws4 ,the fork-piece is constructed to support two axes concentric to the vertical circle1 in which the compass-box is suspended much above its centre of gravity1 so that it falls by its own weight in use to a level position4 ,upon the edge of the compass-box an index is brought up nearly to the interior surface of the vertical circle1 which reads into graduations upon this circle into degrees and half degrees4 ,illustration3 ,fig4 #bca4--;,hanging clinometer4 #ede4--;,a ,light ,hanging ,clinometer1 ,fig4 #bca1 shows the kind that is used in ,germany1 of #e inches diameter1 graduated to degrees1 made of thin brass4 ,it is packed in the case with the hanging compass1 described art4 #edb4 ,the ends of the semicircle are formed into hooks for hanging on the line4 ,the plummet has a horse-hair line1 which cuts the degrees4 ,the clinometer may be used only when the hanging dial ,fig4 #bcj cannot be suspended near the centre of the line1 in which case this light semicircle will cause less deflection of the line1 and give the inclination approximately4 ,for further details of the use of the hanging compass the reader is referred to ,mr4 ,b4 ,h4 ,brough's admirable work on ,mine ,surveying4 ,illustration3 ,fig4 #bcb4--;,french semi-circumferentor4 ,illustration3 ,fig4 #bcc4--,tripod head4 #edf4--,semi-circumferentor4--,this simple instrument can scarcely be enumerated with mining surveying instruments1 as it is much more used for surface work2 but being of the class of circumferentors to which miners' instruments generally belong1 this is the most convenient place for its description4 ,it has very general use on the ,continent4 ,its construction is very simple1 ,fig4 #bcb4 ,it is supported on a ball and socket joint4 ,the socket is formed in two pieces1 which are clamped together to hold the ball by a winged-headed screw4 ,one pair of sights is mounted upon the extreme ends of lugs upon the limb4 ,the limb is divided to half degrees4 ,when the ball is loosely clamped the fixed pair of sights may be adjusted to cut any desired object4 ,a second pair of sights is jointed upon an axis to move centrally between the first pair4 ,these are made shorter to pass within the first pair to any angle around the arc1 except the small angles with which the sights themselves interfere when they are superimposed4 ,the movable sights carry verniers to read on the limb to #b4 ,there is a small compass attached to the limb4 ,as a cheap instrument for taking angles approximately it is very useful1 particularly for workmen employed in carrying out work from drawings plotted from a survey by a better instrument4 ,the weight of the instrument with #f-;inch circle is about #b lbs42 height above tripod1 #g inches4 #edg4--,the tripod of this instrument is made of wood4 ,the head is shown ,fig4 #bcc4 ,the legs are simply extensions of the upper parts1 which are shown attached with bolts4 ,the point of each leg has a steel shoe to prevent it slipping in use4 ,the head is turned to a cone1 which fits into the socket-piece of the instrument and permits it to be rotated with moderate friction4 ,the head is made of triangular section that the legs may be clamped firmly to it4 ,when used for underground work a separate set of short legs is provided1 which attach to the head by the same bolts4 #edh4--,lighting ,underground4--,the old underground station1 formed of a lighted candle or lamp1 is not now considered good in practice where surface land is exactly defined by boundaries held by legal clauses and rights4 ,the system of underground surveying now very generally followed is that first recommended by ,mr4 ,thomas ,baker1 ,c4,e41 and afterwards fully developed by ,mr4 ,h4 ,mackworth1#bg by which a station taken for angular directions is formed by the position of the centre of a tripod4 ,for this system three tripods are provided for each instrument1 with head adjustment complete4 ,these tripods are made in such a manner that the instrument can be placed on any one of them in a level position4 ,two lamps are provided1 the flame of either of which will take the position of the vertical axis of the instrument when the lamp is placed upon the tripod formerly occupied by it4 ,it is easily seen that by this system fore and back sights or angular positions can be extended with all the accuracy that the uniformity of the flame of the lamp will permit4 #edi4--,mining ,survey ,lamp4--,the author constructed this lamp from an idea given to him by ,mr4 ,geo4 ,kilgour1 ,c4,e41 ,fig4 #bcd4 ,it is somewhat different from the ordinary form4 ,its accuracy does not depend upon the regularity of the flame4 ,a vertical axis is formed under the lamp1 which is made to the same fitting on which the mining survey instrument is placed4 ,the lamp is placed entirely eccentric to the vertical axis in such a manner that a vertical line formed by a wire upon its face may stand central and linear with the axis4 ,a cross line is also placed at the same height above the tripod head as the centre of the axis of the telescope or cross sight4 ,by this means1 although the lamp throws its light broadly in one direction only1 the cross is a perfectly defined object1 easily picked up and brought to exact bearing in the instrument when placed upon another tripod4 ,in converting this lamp from a fore to a back sight it has simply to be turned half round on its axis1 which is done without any displacement of the relative position of the cross in vertical or horizontal directions4 ,where this lamp is required in mines liable to fire-damp1 it is made on the safety principle of the ,davy lamp4 ,illustration3 ,fig4 #bcd4--,mining survey lamp4 ,electricity has been applied to lamps for surveying4 ,this plan has been found successful where a secondary battery is used that can be charged by a dynamo upon or in the mine1 or with some of the modern dry batteries4 ,illustration3 ,fig4 #bce4--,stanley's complete mining outfit4 #eej4--,mining ,targets4--,the three tripod system has been much improved by the introduction of accurate targets made specially for the instrument used1 and interchangeable with the instrument on either stand4 ,the reviser has designed several forms of these4 ,they are generally used with a mining theodolite for high-class mine surveying1 and the lower part is similar to the lower part of the theodolite they are used with4 ,instead of a horizontal circle1 they simply support a plate carrying cross levels1 and a pillar carried up to bring the target level with the optical centre of the telescope of the theodolite2 this part is made to fit the outer centre of the lower part into which it is held by a special clamp4 ,the theodolite is made with a double outer vertical centre1 and this is held to the lower part similarly clamped1 so that the theodolite and targets all lift out of their centres and interchange with each other4 ,a complete mining set of this description is shown at ,fig4 #bce4 ,this forms a very complete mining outfit4 ,it consists of a highest-class tacheometer with quick setting spherical lower plate1 mechanical centring stage1 auxiliary top and side telescope1 illuminated axis1 striding level1 also two targets with quick setting spherical lower plates1 mechanical stages1 cross levels1 and swivelled sighting crosses4 ,all three are made with lift-out centres1 which are interchangeable1 and all have base plates permitting their use on any staging or fixing without their stands4 ,the targets are sometimes made to hold candles instead of the swivelled cross1 and sometimes with plain steel points only4 ,the auxiliary telescope is the special form designed by ,mr4 ,dunbar ,scott1 and it embraces all the advantages and eliminates all the disadvantages of all other types4 ,the particular feature is its interchangeability with top or side positions1 and the means provided to ensure perfect adjustment with the minimum of trouble1 thus forming a mining transit which will perform with exactness all the complex functions in mine surveying and requiring no correction for eccentricity4 ,the auxiliary telescope is provided with a centre that may be screwed to the threaded extension of either the transverse axis or the vertical pillars of the main telescope4 ,in either position it is clamped firmly and ranged quickly into alignment with the main telescope by two opposing screws4 ,the diaphragm of the auxiliary telescope has one web only1 so placed that it is vertical when on the top and horizontal when at the side4 ,illustration3 ,fig4 #bcf4--,stanley's ,dunbar ,scott auxiliary4 ,the observation of steep horizontal angles is made only with the auxiliary on top1 and of precipitous vertical angles with the auxiliary on the side4 ,a counterpoise is provided1 which exactly balances the auxiliary1 so that there is no strain upon the instrument4 ,for vertical sighting it is also most useful and accurate1 as by transferring the lines of both positions of auxiliary two lines are transferred down a shaft1 at right angles to each other1 which1 if produced1 will intersect each other exactly under the centre of the instrument1 and no allowance or calculation whatever has to be made to ascertain the centre4 ,the whole attachment adds very little to the weight1 the greater part being of aluminium1 and it is packed separately in the case so as not to interfere in any way with the instrument when not in use4 ,in ,fig4 #bce the auxiliary telescope is shown at top2 ,fig4 #bcf shows it attached at the side4 #eea4--,pocket ,instruments4--,a very light pocket instrument has been designed by ,mr4 ,d4 ,w4 ,brunton1 which will be found useful2 he terms it a pocket mine transit1 but of course it has nothing to do with a transit4 ,it is designed for roughly taking horizontal and vertical angles1 and answers the purpose of a prismatic compass1 clinometer and ,abney level1 and is very portable1 made in aluminium1 and weighing only #h oz4 ,it is shown at ,fig4 #bcg4 ,illustration3 ,fig4 #bcg4--,pocket mine transit4 ,the cover is provided on its inside with a mirror1 and this acts as a back sight2 it is opened out to an angle which reflects the fore sight1 and the object sighted and the reading of the needle is then taken4 ,it is necessary to hold the instrument firmly against the body and see that it is level sideways by placing the spirit level across the box and bringing the bubble to the centre of its run1 while any turning movement should be made by turning the body from the hips4 ,for vertical sighting the fore sight is used as the back sight1 and the mirror in the lid moved to reflect the bubble1 the back sight being formed by the hole in the mirror seen at the bottom of the centre line1 the clinometer bubble is then moved till the air bell is seen in the centre of its run and the vernier reading taken4 #eeb4--;,dip ,compass4--,this consists of a magnetic needle suspended between centres so as to move readily in a vertical plane1 and is shown at ,fig4 #bch4 ,when in use the ring is held in the hand and the compass-box by its own weight takes a vertical position2 it must then be held in the plane of the meridian4 ,in this position the needle when unaffected by the attraction of iron assumes a horizontal position4 ,when brought over any mass of magnetic iron ore it dips1 and thus detects the presence of such ore with certainty4 ,illustration3 ,fig4 #bch4--;,dip compass4 ,if held in a horizontal position it serves as an ordinary pocket compass and thus indicates the magnetic meridian in the plane of which it should be held when used to ascertain dip4 ,,footnotes3 #ai ,plate xiv41 fig4 #e4 ,geometrical ,essays1 ,geo4 ,adams1 #ahjc4 #bj ,proc4 ,min4 ,inst41 ,cornwall1 #ahhc1 vol4 i4 p4 #cag4 #ba ,patent ,no4 #aeib1 ,april #ahgh4 #bb ,patent ,no4 #aheg1 ,j4 ,l ,casartelli1 ,may1 #ahgd4 #bc ,illustrated plate xv4 ,fig4 #a41 ,geometrical ,essays1 ,john ,adams1 #ahjc4 #bd ,pastorelli's patent1 ,no4 #bgad1 #ahfc4 #be ,hoffmann's patent1 ,no4 #bjhd1 #ahgh4 #bf ,geometria ,subterranea1 ,voitel1 #afhf4 #bg ,subterranean ,surveying1 ,thos4 ,fenwick1 ,lockwood4 ,,chapter ,,xii4 ,,instruments ,,to ,,measure ,,subtense ,,or ,,tangential ,,angles ,,to ,,ascertain ,,distances--,,historical ,,notes ,,of ,,the ,,method--,,principles ,,involved-- ,,stadium ,,measurement1 ,,direct ,,and ,,by ,,the ,,ordinary ,,telescope--,,corrections ,,for ,,refraction ,,of ,,the ,,object-,,glass--,,stanley',s ,,subtense ,,diaphragm-- ,,anallatic ,,telescope ,,of ,,porro--,,tacheometers--,,stadium--,,fi eld-,,book-- ,,omnimeter ,,and ,,its ,,field-,,book--,,bakewell's ,,subtense ,,arrangement4 #eec4--;,direct ,subtense ,measurement of ,distances1 by an ,instrument1 depends upon our powers of measuring the image of a distant staff or stadium1 or the divisions marked thereon as they appear at the focus of the telescope4 ,if the stadium is placed at right angles to the direction of one of two sight lines which subtend a given angle1 the number of units divided upon the stadium cut by these lines will be proportional to units of length of base or cotangent for a constant focus of the telescope2 so that if we can measure at a fixed angle the number of equal units of measurement of a stadium correctly1 we can obtain its exact distance2 and whether this method is more or less exact than chain measurement will depend entirely upon the perfection with which either of these operations may be practically performed4 #eed4--,the ,origin of the ,invention of ,subtense ,surveying was thought to be due to ,wm4 ,green1 an optician of ,great ,moulton ,street1 ,london1 who was awarded a premium for its invention by the ,society of ,arts in #aggh4 ,he published a pamphlet giving a description of his method in #aggh4bh ,this subject he pressed upon the notice of professional men at the time1 and his method has continued in use in this country ever since4 ,his refracting telescope1 which alone has remained in use1 formed part of the theodolite4 ,a micrometer was placed in the focus of the eye-piece of the telescope1 which revolved a quarter turn in its axis to read angles vertically or horizontally4 ,he constructed his micrometer with lines fixed at a given distance apart1 and by a second method with the lines adjustable4 ,for this adjustment a fine line was ruled upon one side of two pieces of glass4 ,the ruled sides were placed face to face1 so as to be at the same focus4 ,one of the lines was adjustable by a micrometer screw4 ,his staff was #bj links in length by #d inches in width1 divided decimally into #ajjj4 ,his description of the manner of using his instrument will give a general idea of working the others which have been derived from it--tacheometers1 omnimeters1 etc4--and this is worthy of note1 as the invention1 though generally attributed to him1 was not his3-- #eee4--,to find the contents of a field with either of the instruments described1 let the telescope be placed so that the observer may see all its angles from his station4 ,if near the centre of the field the better4 ,the person who carries the scale 7staff7 is to go all round the field1 stopping at every angle1 and to place the scale at right angles to the axis of the telescope 7passing7 from corner to corner 7from right to left if required7 with the help of a signal by the observer4 ,after the distances all round the field are taken 7by measurement of the image of the micrometer7 and all the angles included betwixt them1 with the theodolite1 plot it out in the usual manner1 e4g41 with a nonius protractor4 ,describe a circle1 and on this circle set off all the angles from the centre through each point upon the circumference4 ,set off the length of every line by a scale of equal parts4 ,these points will give the limits of the field1 which may be laid out in trapeziums1 triangles1 etc41 and measured from the same scale of equal parts4 ,the surveyor will comprehend how easily the contents of the field are found by trigonometrical calculation1 since by this method there are two sides and one included angle given4 ,the common method of measuring with the chain1 besides the inaccuracies to which it is liable1 does only give the length of the surface of the ground between two objects1 and therefore not its proper distance1 unless the surface be straight and no object to hinder its being measured from one end to the other4 ,how often this is practicable ,i leave to the consideration of those who are most accustomed to measure lines1 and doubt not that upon the whole they will find the telescope method has besides ease1 accuracy1 and universality1 necessity itself to recommend it4 ,he points out the utility of the system for levelling1 as both distance and inclination may be taken at the same time4 ,he finds by experiment that the accuracy of the method exceeds that which he could reasonably expect by calculations deduced from theory1 by several circumstances in its favour being inseparable from it4 ,the observer's station is the centre of circle whose radius is the distance required1 which is obtained by measuring the length1 that is1 the tangent or subtense1 of the small arcs whose limits are defined by viewing their image in the focus of a telescope between two points there placed1 and moving them up and down until they appear to touch the very extremities of said limits exactly4 ,the manner of seeing is natural and by practice will become habitual1 and therefore continually approach nearer to perfection4 ,thus may any surveyor in less than two hours take all the dimensions of an irregular polygon necessary for obtaining its area1 if it be as much as #hj or #ajj acres and limited by twenty or thirty unequal sides4 ,green points out that if the subtense angle is taken horizontally1 atmospheric refraction error is eliminated4 ,he proposes to use both reflecting and refracting telescopes4 ,with the reflector he possibly obtained accurate results1 but with the refracting telescope he does not appear to have recognised a constant correction which is necessary and important4 ,it has since been found that in #aggh the ,danish ,academy of ,sciences awarded a prize to ,g4 ,f4 ,brander for a similar device1 which he had applied to his plane-table1 six years before4 ,its real discoverer was ,james ,watt1 who used it in #agga for measuring distances in the surveys for the ,tarbert and ,crinan ,canals4 ,in ,james ,patrick ,muirhead's ,life of ,james ,watt1 he gives a statement by ,watt himself that he constructed his instrument in #aggj and showed it to ,smeaton in #aggb4 #eef4--,subtense ,instruments1 as that originally made by ,green1 are of some form of theodolite1 the telescopes of which are constructed to measure either the angle subtended by the chord of a small arc or the tangent of the same4 ,for convenience the tangent is more generally taken upon a graduated stadium or staff1 which is erected for measurement perpendicularly to the horizon1 the principle of which is shown in the following scheme3-- ,illustration3 ,fig4 #bci4--;,diagram of tangential angle measurement4 ,let ,,ac1 ,fig4 #bci1 be a horizontal line2 ,,bc a stadium set up vertically4 ,then if the angle ,,bac and the height ,,bc are known1 the distance of ,,ac can be easily calculated4 ,for any intermediate distance between ,a and ,c a vertical will be in length proportional to this distance4 ,let de be at one-third the distance from ,a2 then the line de will be one-third the length of ,,bc4 ,if we divide ,,bc into three parts and place the stadium at fg two-thirds the distance from ,a1 the angle d,ae given by an instrument subtending a fixed angle will cut the staff at the second division1 equal to two thirds the staff1 which demonstrates the principle of all tacheometers1 ,cleps1 etc4 ,if the tangent be made a constant equal to the length of the stadium ,,bc1 and this stadium be placed at another position1 say de or fg2 then the angle subtended by its entire length will vary in a manner that can only be estimated by trigonometrical calculation4 ,in case of reading two distant marks on the stadium only for the subtense1 the single central web of the telescope being directed first to one and then to the other of these webs1 the distance is calculated as follows3-- ,given the tangent ,,bc and the angle ,,bac1 required the distance ,,ac4 ,let the angle ,,bac be represented by ,d2 then-- ,,ca _/ 7,,cb7 cotan ,d1 or ,,ca ,,cb cotan ,d4 ,reducing by logarithms1 we have-- log ,,ca log ,,cb ,l cotan ,d - #aj4 ,for example1 make ,,cb #ad feet1 and the angle ,d #b #de #ej1 thus3-- log ,,cb #aadfabh ,l cotan ,d - #aj #acafbfe ---------- log ,,ca #bdfbcic1 or ,,ca #bij feet4 ,the above gives the principles followed with instruments of the theodolite class simply2 but arrangements are made in omnimeters and similar instruments to read the tangent directly and determine the height ,,cb in equal parts1 so that observation of the heights ,,bc gives rectangular co-ordinates and thus saves reduction from degrees of arc4 ,in practice the staff or stadium is made of the greatest length convenient for portability4 ,with a telescopic staff1 #ad or #af feet is commonly used4 ,if a unit tangent be not employed1 the foot is divided into #ajj parts1 each of which parts1 with the tacheometer1 represents #a foot of the base1 and the whole staff #adjj or #afjj feet4 ,the ordinary ,sopwith staff1 art4 #bfc1 answers the purpose1 but art4 #bfh better4 #eeg4--,measuring ,distances by the ,ordinary ,telescope by ,measurement of its ,focal ,image4--,when we apply a refracting telescope to measure a subtense angle by webs fixed in the diaphragm1 vision is not direct as in the scheme ,fig4 #bci1 but subject to bending caused by the refractive quality of the lens1 art4 #eh1 the telescopic focus varying with the distance from the staff4 ,thus with a #ab-;inch telescope there will be a difference of about #be inch in the focus1 whether the staff is held at #ej or #ejj links from the telescope2 and this difference of focus is equal to a difference of base or cotangent between the points ,a and ,c in the last figure1 so that these distances do not remain proportional to the fixed unit of the tangent or stadium4 ,it is important to go carefully into this subject of the use of subtense webs in the ordinary telescope1 as the necessary correction does not appear to have been recognised by ,english writers on instruments1 and no doubt this is the principal reason that subtense measurement has not been more practised in this country4 #eeh4--;,at the commencement of the last century1 ,riechenbach1 a ,bavarian engineer1 pointed out a method still in use on the ,continent4 ,the author is indebted to the kindness of ,lord ,rayleigh for the following demonstration of ,riechenbach's formula3-- ,illustration3 ,fig4 #bdj4--,subtense diagram4 ,let ,fig4 #bdj ,,ab s1 ab i1 ,,oa d1 ,ob r4 ,o is the optical centre of the object-glass2 ab a pair of webs at variable distance r from ,o according to telescopic focus2 f focus for parallel rays4 ,then by similar triangles s_/d i_/r or d rs_/i1 r is found by optical laws to vary in the proportion of #a_/r #a_/;d #a_/;f4 ,we may therefore eliminate the variable r by substituting its value r fd_/7d - f71 by which we find d sf_/i f1 which gives the true correction2 and the distance from the axis of the instrument will be d sf_/i f c where c is the constant distance of the object-glass from the axis of the instrument4 ,it is usual to place the vertical axis of a theodolite central between the object-glass and the diaphragm at solar focus1 so that the constant c becomes f_/#b4 ,it is seen that sf_/i represents the direct subtense1 whereas the refraction1 which is a constant1 gives f and the position of the object-glass f_/#b4 ,riechenbach's formula being true for parallel rays is evidently also true for any subtense with refraction for the staff at any distance4 ,we may therefore adopt a plus constant of #a;f1 which added to the apparent subtense is found to produce no error4 ,thus with a telescope of #a foot solar focus1 and using the decimal system of notation1 as before mentioned1 if a stadium or distinct scale be placed at #cja feet distance from the centre of the instrument1 and the webs or points of the diaphragm be adjusted to read #c feet #cjj divisions1 every subtense may afterwards be taken as number of divisions read #a feet for distance in feet4 ,if the subtense is to be taken in links or metres the dividing of the stadium will be to these measures1 but the constant remains the same #a feet always4 #eei4--,when the line of sight is inclined from the horizon and the stadium is held erect--a convenient method commonly followed upon the ,continent--the reading becomes in excess of the true reading1 in the ratio of the cosine of the angle of the stadium1 represented by a line tangent to the sight-line subtended to the foot of the stadium1 as shown in the following diagram4 ,illustration3 ,fig4 #bda4--;,diagram of vertical stadium on an incline4 ,thus1 ,fig4 #bda1 let the portion cut by the lines ,,ab1 ,s be the reading of the stadium2 then ,s7cos a7 ,s4 ,the inclined distance is then equal to 7f_/i7,s7cos a7 f c and the horizontal projection of that distance or a 77f_/i7,s7cos a7 f c7cos a2 or as f c is small and the angle generally small also1 f c may be taken equal to 7f c7 cos a4 ,then a7f_/i7,s cos#b a f c4 ,illustration3 ,fig4 #bdb4--,stanley's patent subtense diaphragm4 #efj4--,the ,subtense-diaphragm of the author1 ,fig4 #bdb1 forms the eye-piece of a theodolite4 ,it has movable indices which are separated according to a scale formed by calculation upon the data of the above formul4 ,by this1 distances may be taken in the horizontal plane for land of any inclination without after calculation4 ,this result is obtained by observing the angle of inclination upwards or downwards on the theodolite and setting the micrometer to this angle before reading the subtense distance4 ,the reading is taken by points which are arranged to measure the subtense #a to #ajj1 so that the ordinary ,sopwith staff may be used4 ,the diaphragm at zero appears as an ordinary subtense-diaphragm4 ,it may be observed that this diaphragm may be used as a good check1 as distances may be taken over any irregularities of intervening incline and give the true base for the entire distance4 #efa4--;,if the mean contour distance is required from station to station1 this may be taken directly by subtense from the staff-reading held at right angles to the axis of the telescope4 ,the means of doing this1 devised by the author1 is to place a sight director of a special form upon the side of the staff1 ,fig4 #bdc4 ,this small piece of apparatus is shown attached to the staff4 ,it consists of a small telescope three inches long attached at right angles to the staff by means of a dovetail slide fitting when in use as shown4 ,the staff-holder sights the tacheometer through the short telescope1 which can only be seen to appear therein by moving the staff until it is approximately at right angles to the direction of the tacheometer4 ,illustration3 ,fig4 #bdc4--,sight director for stadium4 #efb4--,the ,anallatic ,telescope4--,in this telescope the focus is constant1 and consequently the tangential measurements indicated by the numerical qualities subtended by a constant angle are directly proportional to the base1 so that there is no constant to be added4 ,the invention of this instrument and its modern application to subtense measurement was due to ,professor ,j4 ,porro1 of ,milan1 who put it to practical test in #ahbc1bi in an instrument termed a tacheometer4 ,the telescope will be best understood by the following details3-- ,the object-glass ,o1 ,fig4 #bdd1 is made of a focus that falls well in front of the axis of the instrument ,,cc1 so that the rays cross before falling upon the anallatic lens ,a1 the optical arrangement being such that if the rays fell direct without any refraction they would reach the axis and subtend angles therefrom inversely proportional to the distance of the stadium4 ,the object-glass and anallatic lens are of the same focus1 so that the rays after crossing from equal refraction may emerge parallel in the space ,a to ,m4 ,the stop at ,s and at the axis ,,cc cuts off eccentric rays that would otherwise give internal reflections from the telescope tube4 ,the eye-piece1 represented by ,,mf1 may be made to pick up the image of the stadium in front of it upon an ordinary webbed diaphragm or upon ruled glass4 ,the diaphragm webs are fixed1 or the glass surface engraved with three or five horizontal lines and one vertical4 ,the outer horizontal lines are used generally as the subtense lines1 and the central line for levelling and taking altitudes4 ,the vertical line is used for triangulating on the surface of the ground4 ,illustration3 ,fig4 #bdd4--;,diagram of anallatic telescope4 #efc4--,there is an adjustment made by sliding tubes to bring the object-glass and anallatic lens within mutual focus to ensure the parallelism of the emergent rays and to adjust magnification4 ,this is commonly effected by means of a rack and pinion1 moved by a separate key kept in the instrument case1 but which should not be touched after the instrument is once adjusted by the maker1 except in the case of accident4 ,it is much better made without this rack adjustment and permanently fixed by the maker1 as if it has the adjustment it is likely to be tampered with and thus defeat its object4 ,the eye-piece adjusts to distance from the object-glass in the ordinary manner of the surveying telescope--by rack and pinion4 #efd4--,the eye-piece of the anallatic telescope is generally made of much higher power than those ordinarily employed for levels and theodolites--#be to #cj diameters is usual4 ,where a diaphragm is used the subtense lines are commonly placed on a slip of glass in two or three sets1 so that greater magnitude of image may be taken for objects at distances of from #b to #g chains with the #ad-;feet staff1 or that the staff may be read at greater distances than #ad chains4 ,this series of lines is distinguished as #ej1 #ajj1 and #bjj1 ,figs4 #bde1 #bdf and #bdg2 so that with this as great a distance as #bh chains with a #ad-;feet staff may be estimated1 but this is beyond the safe power of the instrument4 ,the intermediate line1 as shown ,fig4 #bbj1 is valuable in all cases for levelling4 ,the advantage of the increased power of the eye-piece is more than neutralized by the loss of light4 ,illustration3 ,figs4 #bde1 #bdf1 #bdg4--,subtense lines ruled on glass4 ,illustration3 ,fig4 #bdh4--;,adjustable point diaphragm with stadia points4 #efe4--,while many civil engineers are satisfied with a single percentage pair of subtense lines the author much prefers using the point system1 arts4 #bcg to #bci4 ,in this case the diaphragm1 as made by the author1 possesses two systems of adjustment2 that shown ,fig4 #bdh at a for the single point for altitudes1 and the pair of points separated by the spring ss for subtense angles4 ,these points adjust by separate screws top and bottom with a milled-headed key f4 ,the two verticals are fixed permanently4 ,these points are all made of platino-iridium1 which possesses the hardness and elasticity of spring steel1 and is at the same time1 as far as is known1 perfectly non-corrosive4 ,in case of any light dust or moisture resting upon the points1 it is perfectly safe to brush them lightly with a soft camel-hair brush to clean them4 ,where the #bjj factor is required1 a mean may be taken of two observations above and below the central point4 ,where #ej is required1 the vertical points may be adjusted to this4 #eff4--;,in adjusting the lines1 webs1 or points to a given subtense1 the anallatic lens may be moved to give more or less angular displacement or magnification of the image4 ,greater accuracy is obtainable when the staff is held normal to the line of sight instead of vertical4 ,if the staff be held incorrectly in the inclined position at great angles of elevation or depression1 the resulting error is very much smaller than in the case of an equal variation of the staff from the true vertical position4 ,when adjustment is made upon a distant stadium at small angles of elevation or depression1 the subtense of the small arc will vary so little from a tangent to one of its radii that the one or other may be taken without sensible error4 ,the plan originally proposed by ,green of placing a sight tube through the stadium at right angles to its face1 as a means of keeping it in the chord of the arc1 is as good as any other1 but is more cumbersome than that described art4 #efa4 ,if the vertical stadium be preferred1 this may be set up by the small level1 ,fig4 #aji1 p4 #afc4 #efg4--;,it is well to note that with the anallatic telescope the stadium must not be so near that the rays from the object-glass do not cross in front of the anallatic lens or the subtense will appear much increased1 so that there is a fixed nearness at which this form of telescope can be used1 say #ej feet4 ,for this reason engineers generally prefer an ordinary telescope1 making use of the addition of a constant4 ,the author also prefers the plain telescope1 as being more correct according to his experiments where the constant is correctly allowed4 ,there are many advantages in the use of a plain open telescope instead of the anallatic telescope for tacheometers1 among them the following may be mentioned4 ,more light reaches the eye because there are fewer lenses2 there is no intermediate lens requiring adjustment and which becomes dirty and bedewed and is inaccessible for cleaning1 and for the same dimensions of the telescope greater power can be obtained4 ,a larger telescope and of higher power is of great advantage in subtense measurement1 but the full advantage is not obtained in the anallatic telescope4 ,the idea which appears to be still common that an ordinary open telescope will not give accurate results at all distances by means of stadia readings1 plus the distance of the anterior principal focus of the object-glass from the axis of the instrument1 is entirely erroneous4 ,when a staff is held at any distance in front of the object-glass of an open telescope1 an inverted image of the staff is formed at the conjugate focus which subtends an angle at the corresponding nodal point of the lens1 equal to that subtended by the staff at the other nodal point4 ,if a diaphragm with two stadia points or webs be placed at this conjugate focus the ratio i_/f the ratio l_/,d2 where i is the space between the stadia points1 l the height on the staff which these points appear to intercept when viewed through the eye-piece accurately focussed on them1 ,d the distance of the staff from the object-glass1 and f the distance of the diaphragm from the object-glass4 ,now in this equation i is a fixed space1 l is the observed height on the staff1 and both f and ,d are variables1 of which it is desired to find the value of ,d4 ,from the laws of optics it is also known that #a_/;f #a_/;,d #a_/;,f where ,f is the principal focal length of the lens4 ,therefore f ,,fd_/7,d - ,f7 for all values of ,d4 ,substituting this value of f in equation 7#a7 we get i 7,d - ,f7_/,,fd l_/,d2 and multiplying both sides by ,d1 i 7,d - ,f7_/,f l4 ,d - ,f 7,f_/i7l and ,d 7,f_/i7l ,f which is true for all distances4 ,but this distance is measured from the object-glass1 and the distance ,s required by the surveyor is that from the axis of the instrument1 and it is therefore necessary to add that of the object-glass from the axis d4 ,s ,d d 7,f_/i7l ,f d1 and ,f d is the constant of the instrument c4 ,s 7,f_/i7l c4 ,when the range is greater than that at which the divisions of an ordinary levelling staff can be clearly read with the stadia points1 target stadia rods or targets fixed to a levelling staff are used4 ,it is usual to use plain targets fixed with their centre lines at exactly #aj or #bj feet apart or other convenient distance1 and the angle subtended by these is measured by a micrometer diaphragm4 ,the reviser1 in conjunction with ,mr4 ,c4 ,w4 ,scott1 ,b4,a4,i41 ,a4,m4,i4,c4,e41 has designed a micrometer diaphragm which has been proved to give very accurate results4 ,it is made to revolve1 so that either horizontal or vertical stadia rods may be measured1 and it is fitted with fine fixed platino-iridium points1 which are much more satisfactory than webs or lines engraved on glass4 ,these are fixed on one side of the diaphragm1 two each #a_/bjj part of the principal focal length of the object-glass above and below the axial point4 ,on the other side of the diaphragm is a movable point which can be traversed over the fixed points by a micrometer screw1 every complete turn of which moves the point over a distance equal to #a_/ajjjth of the principal focal distance and the head of the micrometer being divided into #ajj parts1 it reads to the one hundred-thousandth part of the same2 while a small star-wheel records the number of complete revolutions1 five of which cover the space between any two of the fixed points4 ,in using this micrometer with say a #aj-;foot target1 let the lower target cross-bar be clamped to the level staff at #b feet1 and the upper target cross-bar at #ab feet4 ,direct the axial point to the centre between the targets at #g feet and read the angle1 then bring the nearest fixed point to the top or bottom mark by means of the tangent screw1 and bring the micrometer point to the other mark by the micrometer screw4 ,the micrometer reading is the reading on the divided head plus the hundredths indicated on the star-wheel plus #ejj for each included complete space between the fixed points4 ,see whether the micrometer reads up or down1 and set the fixed point to the lower or upper mark on target accordingly4 ,to obtain the distance from the axis of instrument1 divide #ajj1jjj1 multiplied by the length of the target by the micrometer reading1 and add the constant of the instrument ,s #ajj1jjjl_/x c where x is the micrometer reading1 and l the length of the target4 ,the tacheometer which the author has lately made has a plain open telescope1 but this is of the same size as that used upon the ,porro system1 and consequently it gives much more light and better definition4 #efh4--,tacheometers consist essentially of any form of theodolite that is provided with means for reading distances by its telescope4 ,stadia work is simply another name for tacheometry1 which is derived from the ,greek tacheos 7quickly71 and metreo 7,i measure71 and signifies the art of measuring rapidly4 ,the graduation of the arcs and circles of these instruments is sometimes made upon the centesimal system1 the circle reading #djj grades1 which are subdivided to half grades to read with the vernier or micrometer to centigrade minutes of #ja grade4 ,the centesimal system facilitates calculation1 and permits a free use of a logarithmic slide rule of a special kind4 ,in ,france1 where working with this system at one time became more general1 we have very complete centesimal trigonometrical tables adapted to the tacheometer published in stereotype1#cj but it has not gained favour1 and very few instruments are now so divided4 ,a compromise which has found a certain amount of favour is the decimal division of the ordinary degree of #ij to the quadrant2 this greatly facilitates the calculation compared with what is necessary with the sexagesimal division into minutes and seconds and the reading of the verniers is much simpler and less liable to errors4 ,moreover1 the mental conversion of the sexagesimal division into decimals of the same degree is much simpler than the conversion into the centesimal degree of #ajj to the quadrant4 ,any instrument divided sexagesimally can be converted by simply changing the vernier if the divisions on the limb are degrees or half degrees4 ,the theodolite1 ,fig4 #afi1 the author made specially for a tacheometer4 ,any theodolite may be converted into a tacheometer by fitting it with a subtense diaphragm4 ,a modern tacheometer should be a high-class theodolite in which every possible refinement is included4 #efi4--,the tacheometer1 although manufactured for many years for export1 has been very little used in this country4 ,the instrument to be described1 shown ,fig4 #bdi1 is the author's latest pattern4 ,it is made with sexagesimal division or ingrades1 to read by the verniers to #bj or to centigrade minutes4 ,the telescope is of much larger and of higher power than that of the ordinary theodolite4 ,for a #f-;inch instrument the telescope is of #aa inches focus1 with an object-glass of #a inches aperture4 ,the eye-pieces are of the ,ramsden form of powers #ah and #be4 ,the points in the diaphragm are set to cut #ajj divisions of the stadium at #ajj units constant of the measurement intended to be taken1 links1 feet1 or metres4 ,this precludes distant measures1 say of over #ae chains1 where a #af-;feet stadium is used1 but they are made adjustable so that they may be set1 if desired1 for any other subtense1 although this is not recommended4 ,it is doubtful whether the subtense method can be considered as reliable at a distance of over #aejj links2 or at any rate we must assume that much greater accuracy can be obtained by dividing distances greater than this into two by an intermediate station for observation1 independently of the additional convenience of having the staff-holder within easy distance of communication4 ,illustration3 ,fig4 #bdi4--,stanley's #f-;inch tacheometer4 #egj4--,where points are not used in the diaphragm or where lines are preferred1 these may be divided upon glass in fine lines as ,fig4 #bdf2 or spider webs may be used1 but these are more difficult to set exact for stadia4 #ega4--,stadium4--,any accurate levelling staff will answer for the stadium1 but the ordinary ,sopwith1 ,fig4 #ii1 is slightly confusing4 ,a more open reading is generally recommended--that shown ,fig4 #ajb1 p4 #aee1 which the author designed for the purpose1 answers perfectly4 ,it is better to read the stadium low1 as there is less vibration2 but it is not often possible or at any time advisable to read it from the bottom--#a foot up is generally most convenient4 ,readings are taken and recorded of each subtense web1 or point1 separately1 and the difference of reading subtracted for the subtense of tangent4 ,with a point diaphragm for taking the subtense angle a fair certainty of accuracy of measurement of distance within #jjb may be assured1 which is much nearer than can be attained by average chaining1 taking six times the labour4 #egb4--,the ,general ,system of ,working the ,tacheometer1 with sufficient detail for practice1 would take too much of our limited space to be given here4 ,we now have several good works published in ,great ,britain1 in addition to the able paper by ,mr4 ,brough before mentioned1 such as ,the ,tacheometer3 ,its ,theory and ,practice1 by ,mr4 ,neil ,kennedy2 ,surveying1 by ,whitelaw2 ,aid to ,survey ,practice1 by ,l4 ,d',a4 ,jackson1 c4 ,there is a small work published in ,new ,york giving some details4#ca ,there are complete works in ,french1 ,italian1 ,german1 and ,spanish4 ,in ,french1 ,leves de ,plans a la ,stadia1 by ,m4 ,j4 ,moinot1 engineer to the ,paris1 ,lyons1 and ,mediterranean ,railway1 gives very complete instructions for all conditions of country1 upon surveys which he has personally carried into practice with this instrument4 ,there are several tacheometers made upon the ,continent1 of more complicated forms than those herein described1 but they do not produce better work4 #egc4--;,field-books for the tacheometer are ruled in various ways in columns1 which vary in number in different books from twelve to twenty4 ,the ,french generally have fourteen columns1 giving the number of the station1 time1 heights of line of collimation above point levelled1 numbers of points selected1 horizontal and vertical angles observed1 reading of subtense webs and their differences1 height of staff by reading central web1 and columns for calculations and remarks2 most ,english forms are more simple4 ,illustration3 ,fig4 #bdi;a4 #egd4--;,a convenient protractor in which the equivalent of surface reading is taken from a scale upon its lower part directed from the centre of the protractor is here shown4 ,illustration3 ,fig4 #bej4--,perspective view of #e-;inch omnimeter4 #ege4--,the ,omnimeter is one of the class of instruments in which the tangent to a radius proceeding direct from the axis of the telescope is represented by the stadium made of constant length1 the subtense angle varying with the distance4 ,the omnimeter is the invention of ,chas4 ,a4 ,c4 ,eckhold1 a ,german engineer1 described in the provisional ,british patent#cb as a person living in ,alexandria4 ,the instrument as originally devised consisted of a kind of theodolite to which the subtense tangential system was added as an entirely separate part4 ,the important part of the provisional specification shows that the principle of the invention consists in the use of two sights to the instrument1 one a telescope to sight the object1 and the other a powerful compound microscope to read divisions upon a tangential scale4 ,the telescope and microscope are firmly united together in parallel position with their axes exactly crossing the transverse axis of the theodolite1 so as to move together through the same angle by the motion of the telescope in traversing the azimuth4 ,a delicate level is placed upon the telescope1 and when the bubble is in the centre of its run the scale is truly at right angles to the axis of the microscope4 ,the scale in the early instruments stood vertically at the extreme edge of the instrument in a position lateral to the object-glass of the telescope4 ,it was finely divided to millimetres1 and read the intervals of the divisions by means of a micrometer screw with a vernier4 ,illustration3 ,fig4 #bea4--;,details of omnimeter1 showing section of microscope and scale4 #egf4--,with the instrument as originally constructed1 it was found that the delicate scale1 protruding vertically to the extreme edge of the instrument1 was very liable to injury unless supported by heavy metal work1 which rendered the instrument cumbersome4 ,a great improvement was made in this instrument1 which brought it to its modern form1 by placing the tangent scale in a horizontal position1 where it could be firmly fixed upon the vernier plate as shown ,fig4 #bea ,s1 and reading the scale by means of a reflecting prism ,p in the eye-piece of the microscope4 ,in this improved instrument1 as the microscope and telescope are still united on one axis so that they move at equal angles to each other1 it is clearly indifferent whether the scale be placed vertically or horizontally1 provided it is placed truly at right angles to the microscope when the axis of the telescope is horizontal4 ,the scale1 which is #d inches long1 is placed in a sliding fitting to adjust longitudinally to its position by means of a micrometer screw4 ,in the ,english instrument the scale is divided into #ajj parts for calculation4 ,the divisions are subdivided by shorter lines1 making the actual division #bjj4 ,the micrometer screw has #ej threads to the inch1 and moves over one of the divisions of the scale only4 ,the micrometer head is divided into #ajj1 numbered at the tens2 a vernier placed against the head subdivides each of these divisions into #e1 making the total micrometer #ejj for one complete revolution4 ,the total division of the #d-;inch scale therefore becomes3 #bjj 7divisions of scale7 #ejj 7micrometer7 #ajj1jjj in #d inches4 ,the scale is placed centrally to the instrument1 so that when the telescope is level the microscope is vertical1 and reads #ej1jjj when in perfect adjustment4 ,illustration3 ,fig4 #beb4--;,details of prismatic eye-piece4 #egg4--,the general appearance of the instrument resembles the transit theodolite1 already described art4 #cfh1 in every way except for the addition of the microscope and scale1 shown in perspective in ,fig4 #bej4 ,the details of construction of the microscopic apparatus may be followed in ,fig4 #bea4 ,t telescope with sensitive level ,b mounted upon it2 ,r body of microscope connected solidly upon the same axis as the telescope1 shown in half section4 ,the eye-piece is placed at right angles to the microscope and telescope1 and reads through the reflection of a prism ,p to the face of the instrument4 ,the details of the eye-piece are shown in section ,fig4 #beb4 ,the tangential scale is shown in section ,fig4 #bea ,s with the micrometer with edge reading vernier at ,m4 ,the compass of the instrument ,c is of the trough form1 and placed on the opposite side to the level to be used after transitting the telescope from the position in which it is shown in the figure4 ,the axis of the connected telescope and microscope is exactly #f inches above the surface of the tangential scale ,s4 ,illustration3 ,fig4 #bec4--,omnimeter webs2 a telescope1 b microscope4 #egh4--,the telescope diaphragm is generally webbed with one horizontal and two vertical webs1 ,fig4 #bec a1 the altitude reading being taken from the top of the horizontal web1 and the horizontal angular position from the centre of the interval between the vertical webs4 ,the microscope diaphragm b has two horizontal webs1 and reads from the centre of the interval1 which is judged by the eye4 ,observed in this manner1 there is no error due to covering angle subtended by the webs themselves4 ,the most exact reading is obtained with a fine point4 #egi4--,reading of the ,tangent ,scale4--,as the micrometer divides half a principal division into #ejj1 the complete figured divisions are therefore divided into #ajjj4 ,this is done for the sake of decimal notation4 ,in reading it is only necessary to observe that the shorter or half division is #ejj1 which must be added to the micrometer reading when it is past this division2 as for instance #fe reading is #fe1ejj1 and say the micrometer reads #bcd past this1 the reading is then clearly #fe1ejj #bcd #fe1gcd1 just as before described for reading half degrees with the vernier4 #ehj4--,value of the ,scale taken in ,rectangular ,coordinates4--,the radius from the transverse axis of the telescope to the tangent surface of the scale is exactly #f inches4 ,the scale is #d inches divided into #ajj1jjj parts1 as it is read with the aid of the micrometer and vernier4 ,the radius therefore in terms of the scale would be at #f to #d1 that is #aej1jjj4 ,by this we see that the divisions of the scale by the angle subtended give tangents1 the value of each division of which is the reciprocal of this on #aej1jjj of the radius or base to any unit we may select4 ,if we make the unit #a foot1 then one division represented by a unit of change of position of the vernier reading1 and consequently of equal angular change in the direction of the axis of the telescope1 would give a tangent of #a foot upon a stadium placed at #aej1jjj feet distance4 ,if the stadium were made #aj feet1 as is usual1 the same angular magnitude would be traversed in ten times this distance1 or over #bhj miles1 making the value of the units of the vernier #a1ejj1jjj4 ,this will give a general idea of the delicacy of the instrument so far as constructive principles are concerned1 and not its performance4 #eha4--,the ,stadium is marked off in a number of feet1 links1 or metres1 according to the unit taken for measurement of the surface of the land4 ,the ,english stadium is generally formed of a #ad-;feet levelling staff1 with the surface painted with a ground of plain white4 ,at #aj feet apart two black bands about #b inches wide are painted in1 leaving in the centre of each band a clear white line of about one-tenth of an inch in width4 ,these white lines are carefully set to #aj-;feet standard centre to centre4 ,but a better plan is to have two equilateral triangles painted1 with their apices meeting to the centre4 ,an intermediate #e-;feet line is drawn in black1 which is found convenient for near measurements1 to avoid too great angular displacement of the telescope4 ,when the measurement is in chains1 #ae links or #bj links may be taken for the distance of the lines apart to give the tangent4 ,for metre measurement #c metres are commonly taken for the stadium division4 ,these are in each case subdivided4 ,the lowest stadium reading should be #a foot at least from the ground to avoid grass and other obstructions4 ,illustration3 ,fig4 #bed4--,ruling of omnimeter field-book4 #ehb4--;,field-book4--,the field-book as shown above1 ,fig4 #bed1 was recommended by the inventor4 #ehc4--,mode of ,operating with the ,omnimeter4--,carefully set the instrument up at its station in perfect adjustment as a theodolite1 noting the departure point upon the scale reading through the microscope4 ,place the stadium in a vertical position at the point to which measurements are required4 ,direct the telescope so that the horizontal web cuts the upper line of the stadium1 and lightly clamp it4 ,now read the microscope and record the reading as observed in the field-book4 ,unclamp the telescope and take the reading of the lower point of the staff and record this4 ,record the bearing of the instrument on the horizontal circle as with a theodolite4 #ehd4--,to ,determine the ,horizontal ,distance in ,feet4--,divide the constant radius of #a1ejj1jjj given before by the difference of the two readings of the stadium mark1 which are #aj feet apart4 ,for example3-- ,first reading of scale #fg1ejj1 micrometer #bce #fg1gce ,second #fd1jjj1 #dej #fd1dej ,difference #c1bhe2 then #a1ejj1jjj_/cbhe #deff feet distance4 ,the process is somewhat simplified by logarithms1 as we have only the log4 of the difference to subtract from the constant1 the #a1ejj1jjj mantissa of which is #a1gfj1iac4 ,thus-- log4 #a1ejj1jjj #fagfjiac log4 #c1bhe1jjj #ceafeced --------- #bfeieeei #deff feet4 #ehe4--,to ,determine ,horizontal ,distance in ,chains the stadium should be marked as just described for feet1 but at #bj links distance from line to line4 ,then the radius #aej1jjj #bj gives #c1jjj1jjj4 ,taking for example1 readings as before with difference of #cbhe we have-- #c1jjj1jjj_/cbhe #iacb1 or #i chains #acb links distance4 ,to ,determine ,horizontal ,distance in ,metres1 the stadium is divided to #d metres4 ,then radius #aej1jjj #d #fjj1jjj4 ,taking1 for example1 difference of reading as before #cbhe then #fjj1jjj_/cbhe #ahbfd metres4 #ehf4--,levelling--,taking ,altitudes4--,to take the elevation of the staff above the level of the instrument1 subtract the reading of the scale1 when the axis of the telescope is level1 from the lower reading of the staff on the scale1 and divide by the distance difference1 as found by the method discussed before1 then multiply this by #aj feet4 ,thus taking the lower reading as before #fd1dej and the constant for the level position of the instrument1 say #ej1jaj1 we then have-- ,lower reading #fd1dej ,level #ej1jaj ------ ,difference #ad1ddj then #ad1ddj_/cbhe #aj #dcif feet nearly4 ,the heights1 in relation to the position of the instrument1 are positive or negative according as the scale readings are greater or less than the constant level reading or departure point4 #ehg4--,work of the ,omnimeter4--,the perfection of the principles of the omnimeter would lead anyone to infer that work might be done with it of the highest degree of accuracy4 ,the testimony of the greatest authorities show by comparison that it is unable to compete in this respect with the best made tacheometers4 ,a large number of these instruments are employed in ,india4 ,colonel ,laughton reports upon it--,it has been found to give very accurate heights of buildings1 etc41 also to be wonderfully accurate when used as a levelling instrument2 but it is not so accurate for measuring distances over #fjj feet1 and even at this distance the error sometimes amounts to as much as #a foot4 ,it is recommended as admirably adapted for city surveys and traversing1 also in hilly and jungly countries1 and for railway and similar purposes4#cc #ehh4--,wherein the instrument fails to give exact results is no doubt in the difficulty of its manipulation4 ,for taking two readings1 which are necessary for every operation in distance1 the instrument has necessarily to be set twice1 the hand being placed upon the micrometer for the second observation while the attention is upon the sighting of the telescope2 and even when the readings are taken by the telescope1 the microscope has to be separately adjusted to read the micrometer scale4 ,in the repetition of these processes it is almost impossible to avoid some slight disturbance of centre by pressure4 ,in distant readings atmospheric changes giving difference of refraction occur quickly1 so that there is more risk of error from two separate observations than if the observations of the subtense webs are taken simultaneously1 as with the tacheometer4 ,further1 any defect in workmanship or wear tells seriously against the readings of the instrument4 ,its advantages are theoretically that a wide angle is subtended by the stadium with the omnimeter in short distances which must be in every way an advantage4 ,further1 since the early general use of the omnimeter1 the tacheometer has been greatly improved1 particularly in providing it with a larger and better object-glass so as to obtain greater field of view1 that fairly near stations may be taken with it that were formerly only possible of reading with the omnimeter4 ,the manufacture of omnimeters is now very limited2 the subject is only retained in this edition because there are still some hundreds of these instruments in use4 #ehi4--;,improvement in the ,omnimeter4--,one improvement in this instrument by ,mr4 ,w4 ,n4 ,bakewell1 ,m4,inst4,c4,e41 consists in turning the body of the microscope to a right angle at the position of the transverse axis of the omnimeter1 and placing a reflecting prism at the angle4 ,by this means the eye-pieces of the telescope and the microscope are brought side by side1 greatly facilitating the joint readings4 ,a second improvement is in making the scale #a1jjj1jjj instead of #aej1jjj1 which much facilitates calculation1 but it is doubtful if these improvements will stay the declining popularity of the omnimeter4 ,illustration3 ,fig4 #bee4--;,bakewell's tangential arrangement to a theodolite4 #eij4--;,bakewell's ,tangential ,arrangement to a ,theodolite for ,measuring ,distances4--,this arrangement1 which gives the distances by direct reading without calculation1 was devised by ,mr4 ,w4 ,n4 ,bakewell to extend the power of an ordinary #f-;inch transit theodolite fitted with subtense webs4 ,the observations are made on marks at #c feet and #ac feet on an ordinary ,sopwith staff--a #aj-;feet base1 as is usual with the omnimeter4 ,any other base may be used if the distances registered are proportionally altered1 or the scale may be divided to suit4 ,it was first applied by the author to a theodolite that had been in good service1 without the necessity of making any structural alterations in the instrument4#cd ,the measuring apparatus consists of a tangent screw impinging upon a radial plane1 with micrometer and vernier4 ,the details will be readily comprehended from the engraving1 ,fig4 #bee1 and the following full description4 #eia4--,the transverse axis of a theodolite1 upon the opposite side of the telescope to that upon which the vertical arc is fixed1 is turned down to a cylindrical surface true with the pivots4 ,a collar ,a1 which fits the cylindrical surface1 is slit up on one side to enable it to be clamped firmly to any position of the axis by a clamping screw ,b4 ,the collar is connected in the same gun-metal casting with the radial arm ,c that terminates at ,t in a plane1 which is made truly radial with the transverse axis of the telescope4 ,this radial arm ,c has a long ,german-silver spring ,s at the opposite side to the radial plane1 which keeps it up firmly in contact with the point of the micrometer screw4 ,a screw is cut on the drum of the micrometer ,d2 on the spiral the scale of distances is engraved2 and readings are taken from a line on the index ,i which slides on the bar ,e4 ,the scale being one of reciprocals the divisions are at unequal distances1 so a vernier cannot be used2 consequently at long ranges where the divisions are close1 the subdivisions must be estimated4 ,where this is too rough a method1 resort must be had to calculation4 ,the outer end of the drum ,d is divided into #bjj1 and reads by vernier ,v carried by the arm ,e in #e or thousandths of a revolution4 ,the micrometer screw has twenty-five threads to an inch1 and the radius of the arm ,c is #d inches4 ,one complete revolution of the screw is one-hundredth of the radius1 and using a base of #aj the radius factor is #ajjj #ajj #aj or #a1jjj1jjj2 consequently ,barlow's or any other table of reciprocals can be used1 and the distances obtained1 by inspection with comparatively little labour4 ,this additional part has not range sufficient for altitudes1 being available for about #b degrees only4 ,the distance may be taken as a subtense or small tangential angle at a radius which1 with the azimuthal angle taken by the vertical arc of the theodolite1 will give altitude by its sine and horizontal distance by its cosine in the usual manner4 ,the principle is that of the omnimeter1 and it possesses the same objection for perfect performance1 that the theodolite has to be handled twice for the two observations necessary4 #eib4--,the ,gradienter ,screw4--,this is no doubt a simplified copy of ,bakewell's tangential arrangement and is shown at ,fig4 #bef4 ,illustration3 ,fig4 #bef4--;,gradienter screw4 ,it is a micrometer screw fitted to a tangent arm1 which can be clamped to the trunnion of telescope when the latter is in any position4 ,the screw is cut of a value that causes the web of the telescope to move #ej_/ajj of a foot at #ajj feet distance for each revolution1 and the head of the screw is divided into #ej parts1 consequently each division upon the head represents a movement of the cross web of the telescope of #a_/ajj of a foot upon a scale placed at #ajj feet distance4 ,the scale on the arm over the gradienter screw indicates the number of complete revolutions of the head1 therefore1 if the screw be revolved two whole revolutions the two divisions covered on this scale indicate #ej_/ajj #b #a foot to the #ajj feet4 ,to establish any grade with this screw4--,set the gradienter head to zero1 then level the telescope and clamp the gradienter arm4 ,suppose grade required be #age4 ,turn the gradienter head through three whole revolutions1 which will equal #aej1 then go on turning through #be of the divisions on the head and the total movement will be #age1 the required grade4 ,for ,measuring ,distance4--,first with a staff for moderate distances4 ,any space on the staff covered by two complete revolutions of head is #a_/ajjth part of distance1 thus1 if the difference between the two readings be #cdge feet the staff is distant #cdge feet4 ,second ,method4--,for long distances with any rod of known length1 such as a #bj-;foot stadia rod4 ,send out a man with the rod which he holds vertical at place to be measured4 ,then measure its length with the gradienter screw2 say it takes #b revolutions and #de divisions over1 thus #b revolutions #ajj and #de extra divisions #ade4 ,then-- #bjjj feet_/#ade #ajj #acgic feet4 ,another instance4--,suppose the man at a distance has no stadia rod4 ,he simply holds up any stick1 say a walking stick4 ,measure this in telescope4 ,say it subtends #a revolution and #bh divisions4 ,this #gh4 ,when your man comes in with the stick1 measure its length4 ,say it was #cbe feet4 ,then-- #cbe feet_/#jgh #ajj #daff feet4 ,the above illustrations are for readings taken approximately level4 ,if there be much elevation or depression the angle must be read and the difference of hypo and base calculated and the stadia rod or staff must be inclined so that its face is at right angles to the line of sight from telescope4 ,this can be done by the rod man inclining the staff or rod until the shortest reading is given if a staff be used1 or the longest measurement is recorded by the gradienter screw head if a stadia rod be used4 ,it is better in this case to have the staff fitted with a director 7see art4 #efa71 so that the person holding the staff may sight into the telescope of the instrument1 thus ensuring the staff being exactly at right angles to the line of sight4 ,no constant should be added with either this1 ,bakewell's1 or omnimeter measurements1 as the angles are taken from the centre of the instrument4 ,this gradienter screw has the same fault as mentioned for the two foregoing1 viz41 that all readings are taken by two movements of the instrument4 ,,footnotes3 #bh ,description and use of an ,improved ,reflecting and ,refracting ,telescope and ,scales for ,surveying1 by ,william ,green1 #aggh4 #bi ,la ,tachomtre1 ou l',art de ,lever les ,plans et de ,faire les ,nivellements1 ,paris1 #aheh4 #cj ,tables ,trigonomtriques ,centsimales1 by ,j4 ,l4 ,sanguet1 ,paris4 #ca ,manual of the ,theory and ,practice of ,topographical ,surveying by ,means of the ,transit and ,stadia1 by ,j4 ,b4 ,johnson4 ,new ,york4 #cb ,patent1 prov41 ,no4 #ahei1 ,june1 #ahfh2 patent ,no4 #cgei1 ,dec41 #ahfh4 #cc ,report on ,omnimeter1 by ,major ,g4 ,a4 ,laughton1 ,superintendent1 ,bombay ,revenue ,survey4 #cd ,proc4 ,inst4 ,c4,e41 vol4 xcii4 part ii4 p4 #bdh1 #ahhg-ahhh4 ,,chapter ,,xiii4 ,,instruments ,,constructed ,,especially ,,for ,,offering ,,facility ,,of ,,taking ,,inclines--,,inclinometer--,,theodolite --,,gradiometer--,,clinometers--,,abney' ,s1 ,,troughton',s1 ,,de ,,lisle',s1 ,,stanley',s1 ,,barker',s1 ,,burnier',s1 ,,watkins'-- ,,clinometer ,,sights--,,rule ,,clinometers--,,road ,,tracer4 ,certain instruments are constructed specially with the object of taking inclines1 where this is the predominant work to be performed with them4 ,they form an important branch of surveying instruments1 and for their special kind of work present many time-saving capabilities4 #eic4--,lister's ,inclinometer ,theodolite4#ce--,this instrument is the invention of ,mr4 ,james ,lister1 ,c4,e4 ,it was originally designed to set out upon the surface of land the widths of slopes or batters by pegs1 as required in the execution of railway1 canal1 and other earth works4 ,in general construction it resembles a theodolite as before described1 arts4 #cgj to #cia1 with the addition of an extra vertical axis to the telescope piercing the horizontal axis at right angles1 ,fig4 #beg4 ,in this construction the telescope upon the horizontal axis can be set by the vertical supplementary axis to any inclination1 so that if the vertical axis be set to the slope of a railway cutting1 any number of points or pegs may be set out continuously with the same setting by direct observation through the telescope across any irregularity or inclination of the land surface4 ,in this operation an immense amount of labour is saved over the ordinary system of pegging by calculation with the aid of a theodolite1 where each peg requires a separate setting of the instrument4 ,when the inclinometer theodolite is used for surveying purposes1 the telescope is fixed by a spring catch which places it firmly true to the reading of the ordinary vertical arc4 ,illustration3 ,fig4 #beg4--,lister's inclinometer theodolite4 ,the instrument is also fitted with a mechanical device for repeating the tangential angles when operating on curves1 which obviates the necessity of reading them on the horizontal arc1 thus facilitating the work4 ,this will be referred to in the following explanation of the manipulation of the instrument as the angle repeater4 ,the main difference between the method of taking cross sections by the level and by the inclinometer theodolite is in substituting inclined bases for horizontal ones1 which will be clearly understood by reference to the following diagrams1 which illustrate somewhat extreme surface inclination4 ,illustration3 ,fig4 #beh4 ,illustration3 ,fig4 #bei4 ,fig4 #beh shows the levelling method and ,fig4 #bei the method by the inclinometer theodolite4 ,in the first it will be seen that each section requires to be taken singly with repeated changes in the position of the instrument at each section1 involving numerous readings on the staff1 booking1 and reduction of the levels for changes only4 ,also the sectional measurements require to be taken in short horizontal lengths with the plumbing of the end of the tape at each length4 ,by the inclinometer method this unnecessary labour is avoided1 there being no changes in the position of the instrument1 as from one setting a series of sections may be taken on either side of it4 ,there is no reduction of levels1 and the sectional measurements are taken on the surface to which the base line is always approximately parallel4 ,the saving of labour is even more marked in the setting out of slope pegs than in the taking of cross sections1 for in addition to the transference of level from the centre pegs to the outcrop of the slope several approximate calculations have to be made before the exact position of the slope peg can be found1 while by using the inclinometer theodolite it is only necessary to put in normal slope pegs at intervals of a quarter of a mile1 or at such distances apart that a ranging rod may be seen from one point to the other1 and by setting up the instrument at each alternate peg1 or at half mile intervals1 the whole of the intermediate pegs for a quarter of a mile on each side of it can be boned as simply as ranging a straight line1 the telescope being inclined to1 and revolving in the plane of the slope4 ,in this manner as much work may be done in a few hours as will take a week with the levelling method1 and this without the slightest physical or mental strain to the operator4 #eid4--;,explanation of the ,method of ,operating with the ,inclinometer ,theodolite4--,for setting out a centre line of railway1 etc41 and putting in level pegs the instrument may be used as an ordinary theodolite1 or even as a level1 and the work performed in the usual manner4 ,it may also be used as a level when setting out the normal slope pegs on slightly inclined ground surfaces1 but when the inclination is considerable it may be used in a special manner with advantage as hereinafter explained4 #eie4--,to take ,cross ,sections when the ,line is ,straight4--,it is unnecessary to explain the use of the instrument when the ground surface is comparatively level1 so as to require no change in position and resetting of the instrument1 it being obvious that in this case it may be used simply as a level with advantage2 but when the surface is inclined in the direction of the centre1 and also at a right angle thereto in the direction of the section lines1 the method of procedure is as follows3-- ,assuming that it is desired to take a series of #ae sections 7and this is within the limit of the number that can be taken from one setting of the instrument71 set up the inclinometer1 preferably over the centre peg of the series1 in such a position that the two front legs of the tripod stand across the centre line1 and the back leg 7which has a distinguishing mark7 rests upon the centre line4 ,set the lower limb of the tribrach stand upon which the instrument is supported to a level condition in its lateral direction by manipulating the back leg1 and at the same time observing the bubble on the stand4 ,this will enable the instrument to be subsequently tilted to a certain extent in a perfectly vertical position4 ,clamp the horizontal arc to zero and direct the telescope to the centre line4 ,clamp the lower limb and bring the arc round to an angle of #ij4 ,the vertical arc is now at right angles to the centre line and parallel with the section lines4 ,now release the telescope from the vertical arc and turn it again on the centre line1 and by working the back adjusting of the instrument 7or in case of necessity manipulating the back leg7 tilt the instrument until the cross web of the telescope is elevated to a short distance above the seventh or most distant peg of the sections1 or site of the first section to be taken4 ,now tilt the vertical arc until the cross web assumes a position parallel to the general inclination of the ground surface laterally4 ,clamp the arc to this inclination and note the angle thereon1 for this will be the angle of the inclined base from which the whole of the sections will be taken and subsequently plotted4 ,commencing at the seventh peg at this side of the instrument1 the sections may now be taken consecutively to the seventh peg on the other side by taking readings on a level staff held in an inclined position at a right angle to the cross web or base1 as shown in ,fig4 #bei1 and oscillated that the lowest reading may be taken4 ,a reading must be taken on the centre peg at each section to establish the height of the base above the peg4 ,the base may be raised or lowered at any section1 or part of a section1 to meet any excessive elevation or depression of the ground surface which might prevent the staff being read1 but a separate reading on the centre peg at each variation of the base must be taken1 thus3--,fig4 #bfj4 ,illustration3 ,fig4 #bfj4 ,the bases being parallel the angle of inclination remains the same4 ,the tilting of the instrument produces a variation in the angle of the vertical arc1 but this is only to such an infinitesimal extent that unless the tilt be excessive it may be disregarded4 ,the correction1 however1 may be simply made after the instrument has been adjusted for any operation by ascertaining or simply noting approximately the angle of the tilt1 and setting off this angle on the horizontal arc towards the tangent line1 thus varying the chord or base line to this extent1 or it may be found by referring to a table of natural sines1 etc41 and multiplying the cosine of the angle of the tilt by the tangent of the vertical arc angle1 the result being the tangent of the corrected angle1 thus3--if the angle of the tilt be #aj1 and the vertical arc angle #be--,referring to tables1 cosine #aj #ihdha1 tangent #be #dffca4 #dffca #ihdha #deibd tangent #bd #dj1 the corrected angle making a variation of #bj4 #eif4--,to take ,cross ,sections when the ,line is on a ,curve4--,this operation is similar to that explained above for taking cross sections when the line is straight1 except that being on a curve a variation of the tangential angle must be made at each peg or section4 ,as this is performed mechanically by a single movement of the angle repeater and no reading of the angle is required1 the work is just as readily performed4 ,to more clearly elucidate the method1 we will take a case in point and assume that the number of sections to be taken is #ae and that the radius of the curve is #ej chains1 which the accompanying diagram illustrates4 ,diagram 7,fig4 #bfa7 showing the adjustment of the instrument for taking sections on curves and the variation of the tangential angles for each section4 ,illustration3 ,fig4 #bfa4 ,if the centre pegs be taken as slope pegs1 the diagram applies to illustrate the setting out of half widths4 ,having set up the instrument at ,a1 ,fig4 #bfa1 over the centre peg of the series in the manner before described1 ascertain the tangential angle for the first chain of the curve by dividing the constant1 #agai1 by the radius of the curve in chains1 which gives the angle in minutes or #agai #ej #cd #bd1 and set the angle repeater to give a movement of double this angle or #a #h #dh1 ready for application at each change of section4 ,set the horizontal arc to the tangential angle for the seventh peg from the instrument at which the first section has to be taken1 or #cd #bd #g #d #j #dh1 and direct the telescope to the peg4 ,zero is now on the chord line ,,ad1 which is parallel to the tangent at the seventh peg1 and at an angle of #h #a #cf1 from the tangent line ,,ab1 which divided by #g gives the variation of the tangential angle at each section1 or #a #h #dh1 to which the angle repeater has been set4 ,release the horizontal arc and bring it round to an angle of #ij from zero1 and the vertical arc will be at a right angle to the line ,a ,d and parallel with the section line at the seventh peg4 ,release the telescope from the arc and turn it at right angles thereto in the direction of the zero line ,,ad4 ,now1 by working the back adjusting screw of the tribrach1 tilt the instrument until the cross web comes somewhat above the seventh centre peg1 then tilt the vertical arc until the cross web is parallel with the lateral inclination of the ground surface4 ,clamp the arc and note the angle thereon to determine the inclination of the base to plot the sections from1 and the instrument is then in adjustment for taking the first section at the seventh peg in the manner already described1 being careful that the lateral bubble on the instrument is in a perfectly level condition4 ,to take the second section at the sixth peg1 one movement of the angle repeater must be made and the lateral bubble adjusted1 which operation must be repeated for every succeeding section4 ,the movement of the angle repeater brings the vertical arc parallel to the section line at each peg1 and the adjustment of the bubble maintains the angle of the inclined base uniform throughout4 ,when the sections are all taken on this side of the instrument1 the telescope is turned to the other side and the operation continued until the whole fifteen are completed4 ,from the above detailed description it may be thought that the adjustment of the instrument for the operation is somewhat complicated1 but in practice it is not so4 ,after the first experience and the method is understood1 it is only a matter of two or three minutes1 and once in position the sections may be taken as rapidly as on level ground1 and the saving of labour is practically the same as in taking sections when the line is straight4 #eig4--,to set out ,half ,widths or ,slope ,pegs when the ,line is straight4--,in commencing this operation it is necessary in the first instance to set out two or more half widths1 according to the length of the cutting or embankment4 ,these may be a quarter of a mile apart1 or so far as a ranging rod may be clearly seen from one point to the other4 ,the pegs put in at these points act as normals from which to bone or range in all intermediate pegs by sight simply1 without further recourse to levelling measurement or calculation4 ,if the ground surface be comparatively flat1 these normals may be put in in the usual way by using the instrument as a level1 but if the surface is much inclined and the slope deep1 a simpler method may be adopted1 which will be hereafter explained4 ,illustration3 ,fig4 #bfb4 ,assuming that the normals have been put in1 set up the instrument at any intermediate peg in such a position that the telescope when set to the angle of the slope shall line with the top of the peg1 as per sketch1 ,fig4 #bfb4 ,then release the telescope from the vertical arc and direct it to one or other of the nearest normals1 adjusting the cross web to cut the top of the peg by turning the instrument on its axis4 ,clamp in this position and the telescope will revolve in the plane of the slope1 and any point on the intermediate surface intersected by the cross web is the outcrop of the slope and the position of the peg4 ,when all the pegs on the one side of the instrument are put in1 turn the telescope to the other side to cut the next normal and proceed in the same manner4 ,when all the pegs have been put in for this half mile distance1 the instrument may be moved to the next half mile normal and the operation repeated1 until the whole cutting or embankment is completed1 the last normal point being in all cases the formation width at the ends4 ,in speaking of half-mile distances we are assuming the most favourable conditions of surface and application of the method1 but in practice where the surface is undulating the positions of the normals should be at the most elevated points from which a considerable range of sight may be obtained4 ,in fixing the points for the slope pegs1 a rod should be held in an inclined position and be brought to line exactly with the cross web of the telescope1 the pegs should then be driven level with the ground surface where the foot of the rod has rested4 #eih4--,to set out ,slope ,pegs when the ,line is on a ,curve4--,the operation is similar to that described above1 except as explained for taking cross sections on a curve4 ,a variation of the tangential angle must be made for each peg1 and if the centre peg shown on the diagram accompanying that explanation be taken as one of the slope pegs1 it will also serve the purpose of illustrating the present one1 and a brief recapitulation of the manipulation of the instrument to bring it into adjustment for the operation is all that will be required4 ,the normal slope pegs having been set out and the instrument set up at an intermediate one1 as before explained1 instead of directing the telescope in the first instance to intersect one of the next normals1 set the angle repeater to double the tangential angle for the first chain in the curve1 and the horizontal arc to the tangential angle for the distance in chains that the normal is from the instrument4 ,then turn the telescope to cut the normal peg and clamp the lower limb4 ,now bring the horizontal arc round to an angle of #ij from zero and clamp4 ,release the telescope from the vertical arc and turn it at a right angle thereto in the direction of the zero line ,,ad1 and by working the back adjusting screw tilt the instrument until the cross web cuts the normal peg again4 ,adjust the lateral bubble on the instrument to a level condition and it is in adjustment for the operation4 ,to put in the first peg from the normal1 make one movement of the angle repeater and adjust the bubble4 ,to put in the second one1 make another movement of the repeater and adjust the bubble1 and so on until the whole is completed4 ,it will thus be seen that by a simple mechanical operation a vast amount of work can be done in an incredibly short space of time as compared with the levelling method1 and that with little or no effort on the part of the operator4 #eii4--;,alternative method of setting out the ,normal ,pegs4--,let the diagram1 ,fig4 #bfc1 represent the section of a cutting at the point opposite which the normal has to be set out1 when the section depth may be assumed to be #af feet1 the formation width #cj feet1 and the slope #a to #a1 or at an inclination of #ef #ah4 ,the distance bc for a #a to #a slope is one-third the formation width1 or #aj feet4 ,the data required for the operation is the distance ad from the centre peg to the plane of the slope1 which is found by multiplying ac by the natural sine of the slope angle #ef #ah1 thus3 #bf #hca #bafj feet4 ,the operation when the line is straight is to set up the instrument at a centre peg some distance away from the normal in the manner previously described1 viz41 with the front legs set across the centre line1 the back leg on the centre line1 and the bubble on the tribrach set level before adjusting the instrument1 which manipulation produces a perfectly vertical tilt4 ,after adjustment1 set the horizontal arc to zero and direct the telescope to the centre line1 clamp the lower limb1 set the vertical arc to the angle of the slope1 and bring the horizontal arc round to an angle of #ij1 or a right angle to the centre line4 ,liberate the telescope and direct it again to the centre line1 and by working the back adjusting screw tilt the instrument until the cross web intersects the top of the centre peg at the normal4 ,the telescope will now revolve in the line ag parallel with the plane of the slope and at a distance of #bafj feet from it4 ,therefore any point on the surface in the line of the slope where #bafj can be read on the staff is the outcrop of the slope and the position of the peg4 ,in this example1 when the required reading is higher than the ordinary staff1 lower the tilt and take an intermediate reading1 as at f in the diagram1 ,fig4 #bfc1 which may read1 say1 #abjj1 when the required reading on the peg will be reduced to #ifj4 ,illustration3 ,fig4 #bfc4 ,in setting out normals on a curve by this method the only difference in the operation to that above described is that instead of in the first instance clamping the instrument with zero on the centre line1 it must be clamped with zero on the chord line1 i4e41 at double the tangential angle for the distance the instrument is from the peg1 as before explained in detail for operations on curves4 ,by this method two normals may be set out at least #bj chains apart from one setting of the instrument1 or several slope pegs may be set out in like manner1 which under certain contingent difficulties of ground surface is an advantage of considerable importance4 ,in this connection there is also an alternative method of putting in the slope pegs after the normals have been set out1 which1 under certain conditions1 may be employed with advantage4 ,instead of setting up the instrument at the back of the normal with the telescope set to line with the plane of the slope1 and to range the pegs in by means of a rod or staff held at the inclination of the slope1 as before described1 it may be set up in any position in the line of slope where a reading can be taken on the peg1 as at a on the sketch 7,fig4 #bfd71 and at the point read1 as at b1 a disc should be clamped to the staff1 as this can be much more clearly seen than the staff graduations when sighting long distances4 ,the staff should then be transferred to the next normal and held on the peg4 ,if the telescope be now turned in this direction and the cross web adjusted to cut the disc1 any point on the intermediate surface where the disc can be intersected is the outcrop of the slope and position of the slope peg4 ,illustration3 ,fig4 #bfd4 ,it is necessary to observe in the setting out of slope pegs that when there is a change of gradient the operation must cease1 but if the point where this occurs be made the position of a normal the operation may be proceeded with1 if the instrument be set up at this point4 #fjj4--,to set out ,slope ,pegs on both sides of the ,line simultaneously without moving the ,instrument from the ,centre ,line4--,,conditions4 ,single ,line4 7ab7 ,formation #ae feet4 7cd7 ,depth of cutting #ad feet4 ,slope #a to #a4 ,the point e1 ,fig4 #bfe1 is the extension of the slope lines to cut the centre line1 and its depths below formation for #a to #a slope is half the formation width1 or #g #f4 ,illustration3 ,fig4 #bfe4 ,,operation4--,the instrument being set over a centre peg with the telescope at the slope angle1 turn the telescope to any other peg and adjust the cross web to line therewith 7on line c f74 ,take the section depth cd 7#ad feet71 to which add de 7#g #f7 #ba #f4 ,this multiplied by #gjg1 the natural sine of the slope angle 7#de7 will give the distance from the axis of the instrument to the slope line1 thus3 #baej #gjg #aebj feet1 and the point on the surface at g where #aebj can be read on the staff is the position of the slope peg4 ,this is similar to that described in the last paragraph1 but if the telescope be now changed to the angle of the slope on the other side of the line ch1 the peg i is instantly found by the same reading 7#aebj74 #fja4--,the ,use of the ,inclinometer in ,mining4--,a lode having been discovered1 it is required to mark out on the ground the general line of the outcrop4 ,hitherto the method employed has been to find the strike and drift of the lode and to level and survey the surrounding country and plot on a contour plan4 ,lines parallel to the strike and spaced according to the trigonometrically calculated bases are ruled in4 ,the points of intersection of the contour line with that of the parallel line to the strike of the same height above datum will be a point of outcrop4 ,the bearings of these points are read1 and their distances scaled from the plan1 the theodolite is then taken to the field1 and the points found are marked out on the ground4 ,this entails a considerable amount of labour and careful work both in the field and office1 and then only points at intervals are obtained and not a continuous line4 ,the inclinometer1 having an adjustable axis at right angles to the horizontal1 enables the line of sight to be made to revolve in any plane4 ,if at the spot where the lode has been discovered the instrument be set up in line with the strike1 and the movable axis adjusted to the angle of dip1 it is evident the line of sight lies wholly in that plane1 and a continuous line of outcrop may be pegged out on a flat or undulating country1 which can be produced to any length required by taking the instrument to a fresh station4 ,this feature of the instrument is equally1 if not more1 important than its use for rapidly pegging out railway slopes4 #fjb4--,the ,gradiometer4--,this instrument1 while performing all the duties of a first-class level1 is designed also for taking vertical inclines at small fixed angles for railways1 drainage works1 steep incline levelling1 etc41 etc41 and also telemetrical readings up to great distances4 ,in general construction1 as regards telescope1 stand1 etc41 it resembles a level1 and when set at zero is equal in every way to one of the best1 with the additional advantage that it may be used for rapid work without the trouble of setting up by the levelling screws1 as the telescope may be levelled at any sight by means of the gradienter drum milled head4 ,the gradiometric arrangement is effected by the telescope being mounted in trunnions1 one pair being adjusted vertically2 the amount of elevation or depression is indicated by a drum carrying an open extended scale graduated to read rise or fall1 from #a in #ab to #a in #a1bjj1 which may be conveniently and distinctly read without the use of a vernier4 ,the additional parts do not increase the bulk of the case and add very little to the weight4 ,illustration3 ,fig4 #bff4--,stanley's gradiometer4 ,by its use a great saving of work is effected4 ,for instance1 for a town drainage in which it is desired to work out an inclination1 say the levels indicate a fall of #aj feet between the extreme points3 if the line the drainage is intended to take be measured1 however angular or zigzag it may be1 and the length of that line be divided by the amount of fall1 this will give the gradient2 say the line of streets measures #e1jjj feet1 this1 divided by #aj feet1 gives a gradient of #a foot in #ejj4 ,therefore if the drum be set to that proportion1 all the pipes may be laid directly without further setting4 ,the gradients for any railway may be instantly found by merely turning the drum until the telescope sights1 up or down the incline to be measured1 a reading on the staff equal to the height of the instrument1 and taking the reading of the drum at the position of the indicator4 ,for levelling steep inclines it also saves a great number of settings up1 as1 instead of levelling for1 say every #ad feet rise or fall1 the gradient of the total distance can be taken and also the distance measured by stadia reading1 when the incline is not too great for taking one reading with telescope level1 or by gradient reading when this cannot be done1 and by adding the staff reading to the distance divided by the gradient1 and deducting the height of the instrument the difference of level can at once be ascertained4 ,example3 ,sighting a staff at a gradient which falls conveniently upon it1 say #a in #ce and this reads #hg feet4 ,distance measured1 as explained later1 say #gce feet1 then #gce_/ce #ba feet #hg feet #big feet2 deduct the height of instrument1 say #di feet1 difference of level #bdh feet4 ,for measuring long distances beyond the range of the stadia lines or points in the diaphragm1 or for measuring distance on inclines1 the gradiometer will also be found very useful1 as by taking the difference of any two suitable gradients1 the base distance is given without calculation for difference of hypo and base4 ,if the gradient be not very steep or below the height of the staff1 the simplest method is to sight the staff with the telescope level and take the staff reading2 say this is #abde feet1 then set the gradient drum to #a in #ajj and again take the staff reading and1 say this is #dcj feet1 the difference between these readings #hae feet4 ,strike out the decimal point which multiplies it by #ajj and we have the base distance #hae feet4 ,for shorter distances a larger base upon the staff may be taken1 thus giving greater accuracy2 for instance1 if the gradient drum after taking the level reading be set to #a in #ej and the resulting difference divided by #b1 any error in taking exact readings is reduced by one half1 or #a in #cc-a_/c and divide difference by #c2 or #a in #be and divide difference by #d3 or #a in #bj and divide difference by #e1 etc4 ,any error of reading would be reduced by one third1 one fourth1 one fifth1 etc4 ,the difference of readings obtained by either of the following two gradients will also give base measurement without any calculation whatever3 #ajj and #ej #fc-b_/c and #dj #fj and #cg #ej and #cc-a_/c #cc-a_/c and #be #be and #bj #bj and #af-b_/c #ab and #aa-a_/i #aa-a_/i and #aj4 ,example3 ,suppose the top of staff is below level altogether1 turn the drum until the top of staff is sighted in the telescope2 say the gradient of this is #bg go on turning until gradient #be is indicated and take the staff reading2 say this is #abge1 then move the drum until gradient #bj is indicated and take the staff reading3 suppose this to be #cdj1 then #abge - #cdj ------ #ice ,omit the decimal point and the measurement reads #ice feet1 which is the horizontal distance4 ,the two most suitable gradients would of course be used according to the position4 ,distances may be set out with equal facility with the gradiometer by the subtense method1 by working out a subtense suitable for the distance4 ,this is easily done by dividing the distance required by any two numbers having a difference of the required subtense1 the result being two gradients1 which1 when worked with1 will give that subtense at the required distance4 ,example3 ,if the distance required to be set out be #fej feet1 a suitable size for an object to be plainly visible at this distance would be #aj feet4 ,then take as divisors two numbers having a difference of #aj1 say #aj and #bj4 #fej #aj #fe #fej #bj #cb ,these two gradients will give a subtense of #aj feet at a distance of #fej feet1 and all that is necessary is to send a man out in the required direction with a #aj-;feet rod 7preferably having ends1 thus 1 for long distances1 to facilitate distinct reading71 and signal him to move farther off1 or nearer until the length of the rod1 held vertically1 is exactly covered by the movement of the telescope caused by revolving the drum between gradients #fe and #cb4 ,illustration3 ,fig4 #bfg4--,stanley's gradioplane4 ,it is always preferable to make the subtense as large as possible1 as the larger it is the more accurate the result will be4 ,all distances set out by this method are base distances1 no matter what the difference of level may be1 and such figures for divisors should be used as give the gradients below #ajj4 ,gradients between #ab and #fe are the best and quickest to work with1 and with care more accurate results are obtained than with chaining4 ,thus1 at one time1 a distance may be set out or measured1 the difference of level taken1 and also the gradient ascertained1 and the drum can instantly be set to zero and all ordinary levelling operations continued4 ,if preferred the gradient drum can be divided to percentage gradients #jja to #h instead of ordinary gradients #a in #ab to #a in #a1bjj4 #fjc4--;,gradioplane4--,this is a new instrument1 specially designed by the reviser for very accurate underground surveying1 such as is required for large sewage work or water works1 long tunnels1 or any work requiring a very rigid and accurate instrument1 with a very powerful telescope for measuring all horizontal and small vertical angles4 ,the horizontal circle is #f inches diameter1 and reads by two verniers to #bj seconds of arc1 or it is fitted with micrometer microscopes reading to five seconds of arc if desired4 ,in the former case it carries a floating bevelled aluminium ring compass divided to degrees1 reading by microscope1 and in the latter a long trough compass4 ,vertical angles are measured by a very accurate form of gradiometer screw carrying a drum with open extended scale in exactly the same manner as the foregoing instrument1 and the remarks regarding that and its working apply equally to this instrument4 ,the telescope1 which is #ad inches long and carries a #a inch object glass is so mounted that it will revolve in the plane of any inclination set by the gradiometer drum1 and is provided with a locking arrangement for fixing it absolutely true for fore or back sight1 and it carries a long sensitive spirit bubble to enable it to be used as a most accurate level and for rapid levelling2 this may instantly be set level by the drum at any sight without troubling to level the instrument4 ,the diaphragm is fitted for subtense measurements4 ,a further refinement is fitted to the telescope when desired1 by which any grade may be instantly divided into any desired number of parts2 this is effected by means of a horizontal circle fitted to the stage under the telescope1 which is read by a vernier attached to the telescope4 ,this circle is divided from #j when the telescope is fixed at zero round each way to #ij degrees into #ajj parts1 the vernier divided to read #ajjths or #ajths of each division4 ,it will be seen that when the telescope is in line with the gradient drum1 that is at zero1 it will be raised or depressed to whatever grade is indicated upon the drum1 and is then capable of being revolved #ahj degrees for taking a back sight1 when it sights the opposite grade to that which it does when at zero4 ,when it has revolved #ij degrees only the telescope becomes level at any grade1 and therefore at any position it is set between zero and #ij degrees it sights a part of that grade2 supposing the telescope at zero is set by the gradienter drum at #a #a1jjj then by revolving the telescope from that to level1 it passes over #ajj parts of that grade1 each of which may be subdivided by the vernier to #ajj parts again1 consequently #ajj #ajj #a1jjj which equals #a in #aj1jjj1jjj or any desired number of #aj1jjj1jjjths may be readily set by means of the clamp and tangent fitted to the telescope1 or if the grade be set by the gradient drum to #a #ajj then #ajj #ajj #ajj equals #a in #a1jjj1jjj1 or any other grade which is set by the gradient drum may1 with equal ease1 be divided by #aj1jjj or any other proportion that the horizontal circle vernier may be divided to give4 ,a sliding lower plate is provided for accurately centring the instrument1 the levelling screws are adjustable for wear1 and the tribrach is fitted with quick-setting spherical joint4 ,this instrument will also be found of great utility in mining work1 to mark out the general line of the outcrop when a lode has been discovered4 ,this1 by the ordinary method1 entails a considerable amount of labour and careful work both in the field and office1 and then only points at intervals are obtained1 not a continuous line4 ,with this instrument the line of sight may be made to revolve in any plane1 so that if it be set up in line with the strike at the spot where the lode has been discovered and the gradient drum adjusted to the angle of dip1 it is evident that the line of sight will be wholly in that plane1 and a continuous line of outcrop may be pegged out on a flat or undulating country and can be produced to any length required by taking the instrument to a fresh station4 ,illustration3 ,fig4 #bfh4--,stanley's gradioplane4 ,the above illustration1 ,fig4 #bfh1 shows the gradioplane fitted with a horizontal circle to the telescope for subdividing the grades of the gradienter drum1 and when thus fitted forms the most exact instrument for setting out or ascertaining gradients that has been devised4 #fjd4--;,abney's ,clinometer4--,this very popular little instrument1 the invention of ,captain ,abney1 ,fig4 #bfi1 embraces the same form of sighted level with reflector as that shown in section1 ,fig4 #hg1 p4 #adb1 but the level instead of being fixed in line with the tube is placed above it upon an axis which forms the centre of a divided arc4 ,the axis with the bubble is turned to any angle by means of a light milled-edged wheel placed in front of the arc4 ,it carries an index which reads on the arc the angular position of the level to the centre of the instrument by a vernier to #aj4 ,there is also a scale placed upon the arc giving gradients from #a in #a to #a in #aj4 ,as the bubble of the level in its course passes the centre over the axis its reflection is made to become coincident with the sight line through the tube only when it is quite level4 ,therefore whatever the inclination of the tube1 the bubble may be brought level by turning the milled head until it appears centrally in the sight axis of the tube1 and the angle at which this occurs can be clearly read afterwards upon the arc4 ,the size of the instrument in its case is #e by #b by #a inches2 weight1 #h oz4 ,illustration3 ,fig4 #bfi4--;,abney's clinometer4 ,illustration3 ,fig4 #bgj4--,troughton's clinometer4 #fje4--,troughton's ,abney's ,clinometer4--,in the ,troughton form1 ,fig4 #bgj1 the arc is toothed1 and it is moved by a pinion similar to the movement of the box sextant1 so that the bubble moves slowly in relation to the motion of the fingers when adjusting4 ,the arc is read by a single index line instead of by a vernier4 #fjf4--,telescopic ,hand ,clinometer4--,the author has recently added a telescope to the ,abney form of clinometer1 as shown ,fig4 #bga4 ,the arc is moved by rack and pinion and reads by a vernier to single minutes1 therefore good reading within one minute of arc may be made with it4 ,captain ,east1 ,r4,e41 suggested a mode of steadying the instrument for observation which appears to answer admirably for hand observation4 ,he puts the hook-end of his walking-stick into his waistcoat pocket and clutches a part of the stick by his right hand at the height of his eye4 ,then holding the instrument in his right hand supported by the stick it is kept quite steady for observation4 ,illustration3 ,fig4 #bga4--,telescopic ,abney clinometer4 #fjg4--;,de ,lisle's ,reflecting ,clinometer4--,there have been several arrangements made for converting the ,burel level1 ,fig4 #hi1 into a clinometer2 that devised by ,general ,a4 ,de ,lisle1 ,r4,e41 with modifications by ,colonel ,bell and ,mr4 ,alfred ,cooke1 as represented in ,fig4 #bgb1 is the most popular4 ,in this a heavy arc is constructed upon the lower part of the instrument4 ,this is jointed upon a vertical axis at ,c so that it may be revolved to bring the mass of the arc either forward or backward1 to take inclines upwards or downwards1 or to rest at an intermediate position to make the instrument flat and portable in its case1 it takes the position shown in the figure4 ,the arc has a stiff centre axis with a radial bar1 the edge of which forms the index4 ,a sliding weight is placed on the radial bar1 which is sufficiently heavy when at its greatest extension to exactly counterbalance the weight of the arc in a horizontal position and to make the mirror quite vertical4 ,in this position it forms a simple ,burel level4 ,a set of graduations are made upon the arc1 which are numbered #a to #ej to #a to #a4 ,the radial bar index set to one of these numbers gives the amount of inclination that will result from the coincidence of the reflection of the centre of the pupil of the eye cutting the object to be observed4 ,the length of this instrument is about #f inches2 its weight about #aj oz4 ,illustration3 ,fig4 #bgb4--;,de ,lisle's reflecting clinometer4 #fjh4--,prismatic ,clinometer4--,this instrument was originally devised by the author about #ahfj4 ,the form of the instrument1 ,fig4 #bgc1 is that of a prismatic compass1 art4 #aee4 ,a similar metal or card and talc dial to that of the prismatic is used1 but this is centred upon a transverse axis which is pointed at the ends to fit into hollow centres4 ,this card is weighted on one side1 so that when the sights are in a truly horizontal position the prism will show the zero of the card cutting the sight line4 ,if the instrument be inclined upwards or downwards1 the degrees of elevation or depression will be indicated by the card retaining its pendulous position4 ,this is a very convenient instrument for use with the box sextant1 and as it is only of about half an inch in thickness1 and of the same diameter1 it will pack conveniently in the case with that instrument--weight1 #h oz4 ,illustration3 ,fig4 #bgc4--,stanley's prismatic clinometer4 ,illustration3 ,fig4 #bgd4--;,barker's clinometer4 ,in ,using this ,form of ,clinometer the prism is raised or lowered in its sliding fitting until the divisions of the card are sharply defined4 ,then in looking over the edge of the prism through the slot above it1 the hair in the window of the back sight will appear to cut the divisions of the card2 and the object seen in the distance1 in front of the hair to which the instrument is directed1 will appear coincident with the number of degrees of inclination indicated by the card4 ,this clinometer is sometimes fitted upon a prismatic compass1 so that inclines may be read by the same prism and sight arrangement4 ,this is1 however1 done more neatly by the arrangement next described1 if the instrument is intended to be used with the prismatic compass only1 and is not wanted separately for use with the chain4 #fji4--;,barker's ,combined ,prismatic ,compass and ,clinometer1#cf ,fig4 #bgd4--,the prismatic compass of this arrangement is that of ,hutchison's form1 art4 #aee4 ,the clinometer is of the same kind as that just described1 but this1 instead of being a separate part of the instrument capable of detachment1 remains permanent4 ,to effect this arrangement the clinometer card is mounted over the compass card on a pin axis instead of centres4 ,a part of the clinometer card is cut away so as to permit the compass card to be read beneath4 ,this cut-away part is held by a stop to a position out of the field of the prism when the instrument is to be used as a prismatic compass4 ,when the stop is released and the instrument is held with its face vertical1 the pendulous clinometer card comes into view1 and cuts by its reading through the prism the sight line1 as before described for the prismatic clinometer4 ,the prism is focussed to the upper or lower dial by a long1 sliding fitting4 ,it is used as the instrument last described4 ,illustration3 ,fig4 #bge4--;,continental form of clinometer 7,burnier74 ,illustration3 ,fig4 #bgf4--,section of the same4 #faj4--;,continental ,form of ,clinometer4--,hand clinometers on the ,continent are generally made on ,captain ,burnier's plan1 ,fig4 #bge1 which was explained for the prismatic compass1 art4 #aef4 ,indeed this instrument is more generally combined with the prismatic compass4 ,the graduation is set up on a plated ring vertical to the plane of the swing of a pendulum1 shown in section ,fig4 #bgf4 ,the reading index is a hair which is read on the graduation by means of a cylindrical lens1 ,b1 when this is brought coincident with the sights ,d,w as described for ,burnier's compass4 ,when the clinometer and compass are combined the vertical rims stand opposite to each other1 ,,ac4 ,a lifter1 ,fig4 #bge1 ,l1 is provided to take the working parts out of bearing1 and a stop ,s to prevent oscillation4 ,the illustrations show the combined instrument3 ,b cylindrical lens reading the drums2 ,a clinometer2 ,c compass2 ,,dd fore sight2 ,,ww windows1 both of which fold down on the top of the instrument4 ,illustration3 ,fig4 #bgg4--,major ,watkins clinometer4 #faa4--,major ,watkins' ,clinometer4#cg--,the vertical plane of division is adopted1 as in that of ,captain ,burnier1 but the reading1 instead of being taken on the exterior of the ring by a magnifier1 which entails a projection1 is placed on its interior4 ,this reading is magnified by a concave reflector1 shown ,fig4 #bgg at ,r1 which reads to a line on a slip of ivory placed just beside the eye-hole ,e shown in the engraving4 ,the pendulum is stopped by a pin1 upon which it springs when the box is rotated vertically to prevent wear when out of use4 ,there is much less work in making this instrument than ,burnier's1 and the round form is more portable4 ,the only point on which it does not bear comparison is in that the concave mirror represents a uniform distance sight which makes the reading indistinct to persons of weak sight1 whereas ,burnier's admits of adjustment by placing the instrument nearer to or further from the eye1 the cylindrical lens being made large to admit of this form of adjustment4 ,this instrument could be improved by the mirror being made adjustable4 ,weight1 #f oz4 ,illustration3 ,fig4 #bgh4--;,compass with clinometer sight4 #fab4--;,clinometer ,sights4--,a clinometer sight is often attached to a light pocket compass1 as shown ,fig4 #bgh at the upper part of the engraving1 consisting of a pin hole and hair cross4 ,this1 used in the manner shown by the position of the eye in the engraving1 can only be made to take sight inclines by another person reading the pendulum index1 which marks the inclination in the degrees to which the compass is divided4 ,this portable pocket instrument is1 however1 useful in other ways4 ,standing face to the instrument it will measure inclines directly very fairly by looking over the top edge and bringing this to the visual rate of inclination at which the pendulum index can be read in front view4 ,geologists commonly use it in this way to take the dip of strata4 ,it can also be used by putting it on or against any inclined surface4 ,the case is generally gilt or nickel plated1 and is about #b inches diameter1 and the instrument weighs about #c oz4 ,illustration3 ,fig4 #bgi4--,rule form clinometer4 #fac4--,rule ,form ,clinometer4--,this is made in the form of a stout #ab-;inch1 one-fold boxwood rule1 ,fig4 #bgi4 ,it is much used by civil engineers as a working tool1 and intended to be applied directly to an inclined surface1 either placed on a straight-edge or otherwise1 generally to take the inclination of earth work4 ,it may be placed upon a picket laid upon the ground to take natural slope4 ,when used in this manner the lower surface is placed on the straight-edge or picket1 and the rule is slowly opened until the bubble in the level in the upper limb becomes central4 ,the arc of the head joint will then indicate the inclination4 ,it may be used in another way3 the lower limb may be set level on the dumpy level compass or on any flat plane1 and the inclination may be sighted through the pin-hole and cross-hair sights shown at the ends of the upper part of the instrument4 ,its size is #f by #a by inches2 weight #i oz4 ,there are several varieties of this instrument4 ,illustration3 ,fig4 #bhj4--,road tracer4 #fad4--,the ,road ,tracer is a balanced clinometer much used by natives in ,india and ,china for road making1 ,fig4 #bhj4 ,it consists of a pendulum1 supported upon a stand that carries a sighted tube which indicates the level of the ground when the weight is carried in the axis of suspension4 ,the weight is adjustable to a scale by a screw4 ,the scales read inclines1 by displacement of the weight1 up and down in percentages or gradients1 to which it may be divided4 ,illustration3 ,fig4 #bha4--;,bellamy's road tracer4 ,this instrument has been improved by ,mr4 ,c4 ,v4 ,bellamy1 ,m4,i4,c4,e41 ,m4,i4,m4,e41 ,f4,g4,s41 c41 ,director of ,public ,works1 ,lagos1 ,west ,africa1 a civil engineer who has had great experience in the colonies1 and it will be found much more accurate1 less liable to get out of order and far more convenient to use than the old forms4 ,it is shown at ,fig4 #bha4 ,the chief feature of this pattern lies in the adoption of the arc of a circle instead of a straight scale1 and a pendulum weight actuated by a rack and pinion in place of the screw and sliding weight4 ,this admits of greater nicety in the divisions and allows a stronger and lighter construction4 ,the sighting tube is provided with reversible sliding shutters1 so that back readings may be taken without unclamping the instrument or altering the vernier or index4 ,a powerful clamp is provided for locking at any desired grade4 ,a recent further improvement by ,mr4 ,bellamy has been made by making this instrument in a form to give readings in degrees of arc as well as in gradients4 ,fig4 #bhb4 ,illustration3 ,fig4 #bhb4--;,bellamy's improved road tracer4 ,,footnotes3 #ce ,lister's ,patent1 ,no4 #bcge1 #ahfd4 #cf ,francis ,barker's patent1 ,no4 #aibf1 #ahha4 #cg ,british patent1 ,no4 #bag1 #ahhd4 ,,chapter ,,xiv4 ,,instruments ,,of ,,reflection--,,octant ,,or ,,quadrant--,,reflecting ,,circle--,,sextant--,,principle--,,para llax--,,construction--,,examination-- ,,adjustment--,,artificial ,,horizon--,,sounding ,,sextant--,,box ,,sextant-- ,,supplementary ,,arc--,,improvements ,,upon ,,this--,,optical ,,square--,,optical ,,cross--,,apomecometer4 #fae4--,the ,octant or ,quadrant measures angles within #ij by an arc of #de4 ,this instrument is generally termed an octant on the ,continent from the space of the divisions2 a quadrant by ,english-speaking races1 from the extent of angles it takes4 ,the idea of bringing the reflection of an object from a mirror in line with the direct sight line from another object1 to measure the angle at the position of the observer subtended by the two objects1 was originally proposed and worked out in a manner by ,hooke1#ch and also by ,newton4#ci ,newton's invention was the more simple and important4 ,this was communicated to ,dr4 ,halley1 then ,astronomer ,royal1 but it was left unpublished until after his death1 when it was found in ,newton's own handwriting among ,dr4 ,halley's papers4 ,newton employed two mirrors to obtain the reflection of an object placed at any angle of less than #ij to the axis of the telescope or sight tube1 to throw an image directly through the tube4 ,one of these mirrors was placed at an angle of #de to the axis of the telescope and covered half its field aperture1 so that a direct image of an object could be received by the eye from the open uncovered part of the telescope at the same time as the reflected image of another object from the mirror4 ,the second mirror was placed so as to throw its reflection into the mirror on the end of the telescope without giving any obstruction to the open aperture4 ,this side mirror was fixed with the centre of its plane over the axis of a movable arm which read upon an arc the amount of its angular displacement to #ij4 ,the mirrors were so arranged that their faces should be parallel to each other when the movable arm was placed at the zero of the arc4 ,the graduation of the arc was of double the closeness of the ordinary arc reading1 so that the angular positions of the two mirrors in relation to each other was indicated according to the following law3-- ,that the angle between two reflections in the same plane is equal to twice the inclination of the reflecting surfaces to each other4 #faf4--;,hadley's ,quadrant4--,in ,newton's quadrant the arc was brought most inconveniently in front of the face4 ,by ,hadley's arrangement the telescope or sight line is brought in a direction about parallel with the chord of the arc1 producing the very convenient form of instrument now in use4 ,this instrument was exhibited at the ,royal ,society1 #acth ,may1 #agca4dj ,it was tried experimentally by the ,astronomer ,royal1 ,august1 #agcb1 in a yacht excursion1 when readings were taken satisfactorily within a minute of arc4#da ,it afterwards came into general use4 ,the quadrant was at first held to be sufficient for measuring the sun's altitude for obtaining latitude1 but ,hadley1 as early as #agca1 saw the advantage of extending the arc so as to be able to observe the opposite horizon if the direct one was obscured4 ,it was also found that measuring the moon's angular distance from a star beyond #ij was serviceable in determining longitude4 ,he therefore proposed by a duplicate system of reflections to extend the arc by what is termed a back sight to #bbj4 ,the means he suggested1 which were commonly carried out in instruments of the period1 were found to be too complicated for practice4#db ,in the meantime the construction of these instruments1 originally framed of a combination of wood1 ivory1 and metal1 was much improved by making the frame entirely of metal4 ,there were also great improvements made in the optical parts1 by which the arc of #ij was extended4 ,in #ageg ,captain ,campbell had an instrument constructed of metal of #fj of arc which therefore read to #abj4 ,this instrument1 with details of improvement1 principally by ,ramsden1#dc became the modern sextant4 #fag4--,reflecting ,circle4--,as soon as the success of the sextant was assured there appeared to be a general desire to complete the circle by reflections1 many inventors thinking this would possess great advantages over the arc of #abj1 and we find therefore no lack of inventions to this end1 even by eminent men4 ,reflecting circles1 as they are termed1 that were of sufficient merit to come into limited use1 were designed by ,mayer1 #aggj2 ,borda1 #aghg2 ,mendoza1 #ahja2 ,hassler1 #ahbd2 ,fayrer1 #ahcj4 ,troughton's circle of about this period was no doubt the best instrument of the class4#dd ,we have also meritorious reflecting circles by ,pistor and ,martins1 and by ,amici4#de ,although these instruments were used at sea to a limited extent1 particularly on foreign ships1 they were also used on land1 where indeed they were more manageable4 ,as no further reference to these reflecting circles will be given1 anyone interested in the matter may refer to the books mentioned in the notes1 where very full particulars of their structure are given4 ,it was felt necessary to mention the subject here1 as the same ideas are constantly cropping up as assumed advantages where previous experience is forgotten4 ,reflecting instruments at sea are tedious to use when the angle to be taken exceeds that taken in by the eye without movement of the whole body4 ,on land1 when the angle exceeds #abj1 a theodolite is better2 but supplementary angles may be taken with the sextant conveniently on land1 where the portability of the instrument is of great consideration4 ,this will be again brought forward in discussing box sextants with supplementary arc4 #fah4--,the ,sextant1 of the invention of which some particulars have just been given1 is only used as a surveying instrument for the exploration of new countries1 for which employment--it may be used with or without a tripod or stand--it is found to be a most convenient1 light1 and portable instrument for the traveller for ascertaining longitude1 latitude1 and time with the aid only of an artificial horizon4 ,triangulation may also be taken with it of terrestrial objects1 even for the complete circle1 by repetitions from station to station in angles within #abj4 ,the same principles which are followed in the construction of the nautical sextant are followed also in the manufacture of two modified forms of this sextant which are used for surveying only1 the sounding sextant and the box sextant4 ,as the nautical sextant is most open to observation of its parts it will be more convenient to discuss the construction and general arrangements of this instrument first4 #fai4--,optical ,arrangements of the ,sextant4--,newton in the description of his instrument placed the mirrors parallel to each other1 that is1 to zero of the arc1 in his illustration for the demonstration of the principle4 ,in this position he showed that the direction of the reflected ray is coincident with the direct ray entering the eye from the same object or star4 ,this scheme the author has generally found the clearest for illustrating the principle to persons not well acquainted with optics1 there being some difficulty in explaining the law just given1 art4 #fae1 from a more complicated scheme4 ,illustration3 ,fig4 #bhc4--,reflection in direct line from two plain mirrors4 #fbj4--;,if two mirrors be placed with their faces parallel to each other in such a manner that a ray of light may continue after two reflections from them1 the ray will continue its path parallel in its direction to its incidence upon the first mirror4 ,let ,,mm1 ,fig4 #bhc1 be two mirrors placed with their faces opposite and parallel to each other4 ,let the incident ray ,,im fall on the mirror ,m whose normal is a4 ,then1 as the angles of incidence and reflection are equal1 art4 #ed1 it will be reflected at equal and opposite angle to the normal to ,m4 ,let the normal of ,m be a4 ,then again1 the incident line ,,mm will be reflected at equal angles to the normal to ,d1 that is1 as shown by the diagram1 it will continue parallel with the incident ray and in such a position that an object at ,p would appear to the eye1 placed at ,d1 as though it were at ,p in the direct line of sight4 #fba4--,parallax4--,it will be seen by the figure that the point ,p does not appear to the eye at ,d in its true position but at ,p therefore with the mirrors ,,mm quite parallel1 the points ,p and ,p appear coincident1 and would read as one point with the index of the sextant set at zero1 that is1 at the position when the mirrors are parallel to each other2 whereas the points ,p and ,p really subtend a small angle if direct lines be drawn from them to ,d4 ,it is therefore clear that the angle read by coincident reflection and direct or1 as it is sometimes called1 visual image is less than the true angle at about the position shown4 ,this difference is called the error of parallax4 ,when the object is distant this error is immeasurably small4 ,the parallax error varies proportionately to the distance of the mirrors apart and with their angular position4 ,if the mirrors are in such an angular position that the rays proceeding from an object impinging upon the centre of the first mirror would1 if continued1 reach the eye1 there would be no error of parallax4 ,this occurs in the nautical sextant at about #fj1 and the parallax error increases on either side of this point4 #fbb4--;,in the practice of surveying this small error is neglected4 ,when the box sextant is used the mirrors are placed at a very small distance apart1 and the parallax error therefore is extremely small even for near objects4 ,where two objects are to be triangulated1 the one near and the other distant1 the parallax error is much decreased or eliminated by taking the near object by direct vision1 and the distant object by reflection4 ,in this case1 if the near object be towards the right hand1 the sextant must be used in an inverted position4 ,if the two objects be both near1 a distant object may be sighted in the direction of one of them for the reflected image4 #fbc4--;,it is readily seen that if the parallelism of the glasses shown in the figure be disturbed1 say by a change in the relative angular position of ,m so that the planes ,m and ,m continued to subtend an angle to each other1 then the normal of ,m must also be changed in direction equal to this2 but the ray ,,mm remaining constant1 as there is no movement of ,m1 this ray will therefore be displaced in its reflection from ,m an amount equal to the angle of incidence on ,m from its normal1 plus the angle of reflection from the opposite side of the normal1 that is1 to double the amount of angular change of the position of the mirror or of its normal1 which is the same thing4 ,the sextant therefore reads1 by change of position of one of its mirrors1 half the angle of reflection upon its arc2 and to make it read to the angular value of its reflection the divisions on the arc are made twice as close1 that is1 half degrees are made to read as degrees4 ,this will be better explained by the following scheme4-- ,illustration3 ,fig4 #bhd4--,principles of reflection of the sextant4 #fbd4--,the above scheme1 ,fig4 #bhd1 is taken from ,captain ,magnaghi's admirable work before mentioned1 which gives a very clear geometrical demonstration of the value of angular positions in compound reflection4 ,a ray of light ,,sr directed to a plane mirror ,r is reflected therefrom to a plane mirror ,r1 following a plane of reflection perpendicular to the intersection of the two mirrors4 ,the direction ,r,t of the ray reflected by the second mirror falls into the same plane of reflection1 and makes with the direction ,,sa of the incident ray an angle double that which is comprised between the two mirrors4 ,the two planes of reflection ,,sab and ,,abt unite in one because they both contain the line ,,ab and the normal ,,bp to the mirror ,r4 ,in prolonging the normals of the mirrors to their point of intersection ,p we find that-- ,,bts ,,bas - ,,abt2 but as ,,bas - ,,abt ,,bpa ,,bda1 therefore ,,bts #b ,,bda4 #fbe4--,the mirrors being placed in the position shown in the figure1 if we look through a telescope whose visual axis is placed in the line ,,et1 with its objective to the mirror ,r1 we see in the centre of the field of view the image of the object ,s reflected consecutively by the mirrors ,r and ,r4 ,we also see in the telescope whether the mirror ,r is only a certain height above the plane of reflection1 so as to permit half of the object-glass to receive the rays coming from the point ,e situated in the prolongation of the line ,,tb1 also the image of ,e which is necessarily coincident with that of ,s1 because the rays by which each image is formed enter the telescope in the same direction ,,bt4 ,therefore when the images of the two objects ,e and ,s appear superimposed or coincident in the middle of the field of view1 we have an index given that the mirrors form an angle with each other which is half that which is made at the point ,t from the same objects1 and when one is known the other is easily deduced4 #fbf4--,nautical ,sextant4--,the ordinary construction of this instrument1 ,fig4 #bhe1 consists of a cast gun-metal frame1 forming approximately in outline a segment of a circular disc ,,aa including within its extreme radii about #aee4 ,illustration3 ,fig4 #bhe4--,nautical or astronomical sextant4 #fbg4--,the ,limb ,g1 which is made only about #a_/ab inch in thickness1 has generally a face of about inch in width1 which is inlaid with silver or platinum1 as ,fig4 #abg1 p4 #ahf1 to take the graduation to about #adj4 ,the limb is stiffened by a deep1 thin rib about inch wide1 supported by a corner hollow4 ,the exterior radial arms and interspace framing1 ,fig4 #bhe ,,mm1 which vary very much in design according to the taste of the maker1 is made generally of about #a_/ad of an inch in width upon the face of the bars1 with a depth of #c_/h inch4 ,this arrangement of the bars placed edgewise gives great stiffness to the surface of the arc with little weight4 ,a handle ,l1 made generally of ebony1 is supported on two standards or brace-pieces ,n1 which are carried off to about #b inches from the back of the frame to hold the handle parallel with the face4 ,the handle has sometimes a hole bushed through it with metal1 to support the sextant upon a corresponding pin forming part of a stand or tripod when the instrument is used for taking observations on land4 ,three feet are placed at the corners of the frame of the sextant1 one shown at ,q1 to support it conveniently on a table to take the reading of an observation just made4 #fbh4--;,at the centre of the arc a female axis of about #a inches in depth ,e is attached by three screws to the frame perpendicular to the plane of graduation4 ,this carries the male axis1 which centres the vernier on the vernier arm ,m4 ,the axis is covered by a protecting tube which forms one of the three feet upon which the instrument rests when laid down4 ,the vernier arm is made of gun-metal of about #a_/af inch in thickness and from #a inch diminishing to inch in width4 ,this is stiffened by a light rib on its upper side4 #fbi4--,the ,vernier ,v reads upon an #h-;inch sextant1 that is1 one of eight inches radius1 to #aj1 the graduations being to #bj and the vernier taking #abj divisions4 ,a description of the vernier reading was given1 art4 #cah4 ,the vernier falls upon the arc on the plan shown ,fig4 #abg1 p4 #ahf4 ,it is clamped near to position by the milled-headed screw ,h1 and is adjusted by the tangent ,i4 ,a magnifier ,j is placed on a jointed sling-piece ,k which traverses the vernier4 ,this is sometimes provided with a ground glass shade to dull the silver for reading4 ,the sling-piece moves the magnifier opposite to any division of the vernier4 #fcj4--,over the axis of the vernier arm a large1 oblong mirror1 termed the index glass1 ,a1 is fixed with its face in a plane cutting the centre of the axis4 ,the index glass is placed with its longest sides approximately in line with the vernier arm4 ,this mirror is placed in a metal tray and is sometimes made adjustable by three screws2 but it is better fixed by the maker by screwing the flange-piece1 which forms one end of the tray1 hard down4 ,the index glass moves with the index arm and gives the first reflection of sun1 moon1 or star which falls thence upon the horizon glass ,b4 #fca4--,the ,horizon ,glass ,b is placed upon a spur-piece formed in the same casting as the frame4 ,this glass1 which is worked perfectly parallel1 has the lower half of its surface next the frame silvered4 ,the silver is cut to a sharp line against the plain part4 ,the horizon glass placed in its metal tray has adjustments given to it by means of capstan-headed screws in a manner that will be presently described4 #fcb4--,the ,telescope screws into a ring fitted at ,r1 which stands upon a bar erect from near the edge of the frame4 ,the female screw by which the telescope is held is formed of two rings which adjust for the amount and direction of separation1 so that the telescope may be directed coincident with the horizon glass4 ,the bar or standard supports the ring fitting and is made of either square or triangular section1 fitted accurately in a deep socket fitting1 in which it slides to raise or lower the ring by means of a milled-headed screw placed on the end of the bar4 ,this permits adjustment only sufficient to bring the axis of the telescope opposite the line of division between the plain and silvered parts of the horizon glass4 #fcc4--;,four ,circular ,shades1 carried in square frames fitted with dark bluish-grey glasses1 are jointed to the frame at ,c4 ,these have nib-pieces at the upper corners1 so that one or more of the shades may be turned up at a time by the finger-nail to intercept any surplus amount of light from a luminous body reflected from the index-glass2 or the whole of the shades may be turned up when observation is made of the mid-day sun4 ,three other similar shades1 but placed in circular frames are fixed at ,d1 which hinge over and back1 to be thrown in or out of interception1 and are used to subdue the light from the horizon if required4 #fcd4--,the ,telescopes used as a part of the sextant are generally two in number4 ,one for direct vision is a short tube of about #c inches in length1 focussing at about #d inches4 ,the optical arrangement is the same as that of an opera glass1 consisting of an achromatic object-glass of about #d inches focus and a concave eye-glass of about #b inches negative focus1 ,fig4 #ad4 ,the second telescope is about #g inches to #h inches in length4 ,this has two ,huygenian eye-pieces1 which have each a wired diaphragm at the mutual focus of the eye-piece and the object-glass4 ,one of these has two fine wires placed parallel for use in adjusting the telescope1 and the other has two pairs of crossed wires to indicate the centre of the field of view4 ,there is also a plain pin-hole sight provided for open vision4 #fce4--,the ,case in which the instrument is packed is generally made of well-seasoned mahogany1 dovetailed together at its corners4 ,the fittings are made to put the instrument back in its case as it was last used within a wide range4 ,a tommy-pin for adjustments and a hand magnifier are supplied with the instrument4 ,the case is generally ,french polished inside as well as out to prevent absorption of moisture from sea air4 #fcf4--,manufacture and ,examination of the ,nautical ,sextant4--,besides the general good work that this instrument demands1 the important points to be observed are1 that the glasses should be of hard crown glass worked perfectly parallel from face to face2 they should also be well polished4 ,these observations apply to both the reflecting glasses and the shades4 ,the silvering of the mirror should be protected with a good coating of copal varnish4 ,the mirrors should be held by three points only1 and be quite free from strain4 ,the upper of the three points should detach1 so as to be able to remove the glass at any time for resilvering4 ,the axis should be fitted with all the care necessary for a theodolite1 and be placed truly central to the arc4 ,the extremity of the vernier arm when free of its clamp should traverse the arc at equal distance from its face and move with very light friction4 ,the extreme lines of the vernier should cut equal divisions all along the arc #j to #adj1 observations being taken particularly at both ends and in the centre of the arc4 ,the vernier should lie flat on the limb from end to end of the arc4 ,the standard or stem-piece for elevating the telescope should move upwards and downwards stiffly but equally by the motion of its milled-headed screw4 ,the division lines of the limb and vernier should be cut fine but very deep3 they should be cut on the dividing engine from the axis of the sextant to ensure true centring of the arc1 and not as in the usual plan of having the axis adjusted to the divisions4 ,illustration3 ,fig4 #bhf4--,section of axis and index glass of sextant4 ,illustration3 ,fig4 #bhg4--,section of limb and clamp and tangent4 #fcg4--;,axis4--,this is the most important part of the instrument1 and requires the greatest care in construction4 ,fig4 #bhf represents this to a scale half size4 a the axis1 made of hard gun-metal1 has a collar by which it is attached to the index arm4 ,the axis is ground and burnished carefully into ,s the socket-piece1 which is fitted into the frame and held down by three screws4 ,at the end of the socket there is a collar-piece ,b attached upon an angular or tight conical fitting by the screw ,d1 which prevents the axis rising out of its socket4 ,the axis is covered by a cap ,l which protects it from injury1 and this at the same time forms a leg to the instrument as before mentioned4 ,the index glass ,i is mounted in a tray ,t shown in section4 ,there are two points of contact at the lower part of the back of this glass1 formed by pins1 and one point of adjustment pressing against the clip ,g by a spring ,c in front1 acting contra to a screw at the back ,e1 which adjusts only a small distance to bring the index glass to perpendicularity4 ,the flange-piece ,f is adjusted in the manufacture so as to leave very small separate adjusting to the index glass necessary4 #fch4--,section of the ,limb and ,clamp and ,tangent4--,the general arrangement is shown in ,fig4 #bhg4 ,m arms of the frame2 ,j section of the limb2 ,c clamp attached to the tangent ,n for clamp and tangent motion1 described art4 #cdf2 ,o milled head to clamp2 ,n milled head to tangent4 ,the vernier is shown at ,v1 reading through an opening on the face of the index arm ,p4 ,the rib to stiffen this arm is shown at ,r4 ,illustration3 ,fig4 #bhh4--,vertical section of horizon glass4 ,illustration3 ,fig4 #bhi4--,plan of section ,a to ,b4 #fci4--,the ,adjustment ,arrangement of the ,horizon ,glass4--,this most important adjustment is constructed in various ways4 ,the plan now generally thought to be the best is for the maker to fix the horizon glass frame firmly in its true position perfectly perpendicular to the surface of the frame1 and to allow a small amount of adjustment to the glass only4 ,a convenient plan of doing this is shown in the vertical section full size in ,fig4 #bhh4 ,the frame ,,ff is made in one casting1 which has its base collar firmly fixed to the frame of the sextant4 ,fig4 #bhi is a cross section ,a to ,b4 ,h the horizon glass is held upon its face by three points1 one of which is shown at ,l1 which is placed in the centre of the top4 ,the lower front points are the exterior corners of a plate which is cut away between4 ,this plate is held by the screw ,g4 ,the screw ,g forms a kind of hinge which1 together with the elasticity of the plate1 gives a slight pressure directing the glass hard upon the points of the screws ,j and ,q4 ,the screw ,j resists this pressure lightly and permits adjustment of the horizon glass ,h to angular position in relation to the plane of the index glass to a small extent1 by means of a pin placed in the capstan head ,j4 ,the perpendicular position of the horizon glass1 ,h1 is secured by slight adjustment of the capstan head ,k1 which moves against a spring ,l in the vertical centre of the top of ,h4 ,this piece1 with screw and spring1 is attached to the horizon glass frame ,,ff by the screw ,m1 so that it may be easily removed to replace or resilver the glass4 ,the silver on the glass is cut to a sharp line at about the point ,h with a razor4 #fdj4--,testing the ,parallelism of the ,surfaces of the ,glasses4--,the best method is to firmly fix a telescope provided with webbed or pointed index diaphragm so that the webs or points cut a distant1 sharply defined object1 or its edge only1 quite clearly4 ,if the glass to be tested be now placed in four directions agreeing with its four sides in front of the object-glass of the telescope1 and it is worked perfectly parallel1 and is free from stri1 the distant object will not appear to be displaced by its presence in the slightest degree at any position4 ,if the glass be not mounted and is quite square1 should there be any very small error1 the thickest or thinnest edge should be placed towards the frame2 but in this case only a very small error is permissible4 ,the coloured glasses require the same test as the white ones4 ,where the parallel glass to be tested is small1 the object-glass of the telescope may be covered by a paper cap1 with a small hole only left through its centre1 sufficient to take the glass4 #fda4--,the glasses1 when fixed in the sextant1 may be examined for parallelism approximately by setting them end up singly to the sun1 with the sextant set at an angle that the direct and reflected images of the sun's limb appear just to touch1 the eye-piece of the telescope being constantly covered by the sun-glass4 ,if there be a want of parallelism1 the image will be disturbed4 ,one reason that the telescopic plan first proposed is better to be followed in the construction of the instrument1 is that the telescope is fixed and that there is no indistinctness from unavoidable motion of the body1 such as occurs when the sextant is held in the hand4 #fdb4--,the ,quality of the ,surfaces of the ,glasses may be examined1 both for flatness and brightness and for equality of density1 by holding them so that the reflected image of a straight body1 as for instance a stretched thin string placed at a distance1 may be observed by reflection in glancing over the surfaces with the eye nearly parallel with its plane4 ,if the glass be imperfect the image that reaches the eye will appear to be wavy4 ,if the reflection appear misty1 this is generally due to want of parallelism of the glass2 but this mode of observation is altogether somewhat technical and difficult to attain without skill4 #fdc4--,to ,silver the ,index or ,horizon ,glass with ,mercury4--,clean the glass thoroughly by boiling it in water containing an alkali 7potash or soda71 and then polish it off with whiting and water1 using a clean piece of old linen or perfectly clean wash-leather4 ,do not touch the surface with the fingers4 ,take a piece of clean tin-foil freshly opened from the roll and cut out a piece slightly larger than the glass to be silvered4 ,lay this upon a smooth pad--an old leather book-cover answers4 ,place a single drop of clean mercury about the size of an ordinary shot upon the tin-foil and rub this gently over the surface until it is entirely silvered4 ,now pour very gently sufficient mercury upon the foil till the surface appears to be flooded4 ,take a sharply cut straight-edge formed of stiff writing-paper1 and draw this over the surface of the mercury to clear it4 ,take a slip of clean smooth writing-paper very little wider than the foil and of about one and a half times its length3 spring the paper to a slight curve and place one part of it over the silvered foil so that when it springs open it will cover it and exclude the air from the surface4 ,now give the glass a final polish and lay it upon the paper over the foil4 ,hold the glass down with slight pressure with the left hand1 and slowly and steadily draw out the slip of paper in the linear direction of the surface of the glass with the right hand4 ,this will take out the air between the foil and the glass1 so as to bring the mercury in contact and leave a perfect mirror4 ,it must now be set aside with the glass turned face downwards in an inclined position1 so that the surplus mercury may drain off from the foil4 ,small slips of foil should be put at its lower edge1 which1 by their attraction for the mercury1 will accelerate the draining4 ,the mirror should not be touched after setting it up to drain for twelve hours at least1 after which the surplus foil may be trimmed off4 ,after another thirty hours or more it may have any varnish or other protection applied to the back of the silver4 #fdd4--,where instruments are taken abroad mercury silvering may become spotted1 so that a small store of mercury and tin-foil should be taken out with the sextant for resilvering4 ,but it should be particularly observed that the mercury should never be placed in the same case with the instrument1 as the smallest particle1 if it touch the frame1 will eat into the brass and destroy its strength4 ,sealing-wax dissolved in spirit answers for a varnish at the back of the foil fairly well after resilvering if proper varnish be not at hand4 ,it is advisable before attempting to silver a sextant mirror to practise on a few slips of ordinary glass in order to get into the way of doing it4 ,in modern practice base silver is deposited1 and no mercury is used1 but the process requires special skill4 #fde4--;,adjustment of the ,index ,glass4--,hold the sextant clamped to about #fj in a horizontal position with the index glass near the eye4 ,look nearly along the plane of the glass in such a manner as to be able to see one part of the plane of the arc by direct vision1 and another part by reflection of it at the same time4 ,if the direct view and the reflected join in one line1 and the arc appears as the continuity of a single plane1 the index glass is perpendicular to the plane of the sextant4 ,if this be not the case it can be adjusted by turning the set screw placed at the back of its upper centre1 ,fig4 #bhf ,e1 very gently4 #fdf4--;,adjustment of the ,horizon ,glass to ,perpendicularity4--,place the vernier at zero4 ,hold the plane of the sextant parallel to the horizon and observe if the image of the horizon seen by reflection at the edge of the silver line coincides exactly with the image received directly through the plain part of the glass4 ,if it does so the horizon glass is perpendicular to the plane of the instrument1 that is1 assuming the index glass is also perpendicular4 ,in this adjustment it is well to rock the plane of the instrument say #bj1 to see that the horizon is cut as a clear line about its horizontal position for this amount of angle4 ,if the mirror be not perpendicular adjust gently by the single screw at the top of the horizon glass frame4 ,if the horizon be not water1 the sharp outline of any distinct distant object will answer1 or a piece of fine string placed at a distance and stretched straight4 #fdg4--;,adjustment for ,index4--,this is the adjustment for parallelism of the two mirrors at the zero of the arc4 ,the sextant is clamped at zero as before3 the arc of the instrument is turned in a vertical position and the horizon again observed4 ,if this appears to cut a clear line through the plain glass and the mirror there is no index error1 and the planes of the glasses are truly parallel to each other in this position4 ,if the line is not continuous adjust gently by the lower screw1 ,fig4 #bhh1 at ,g4 #fdh4--;,adjustment of the ,horizon ,glass by the ,sun4--,this is a better adjustment than that given above1 except that it introduces any error that may be due to the imperfection of the shades2 and it is more difficult particularly for the first approximate adjustment4 ,arrange the telescope and shades so that a clear outline of the sun's limb may be observed without distressing the eye4 ,place the vernier at zero4 ,observe the sun1 which will be most conveniently sighted at about #dj elevation1 first with the plane of the frame vertical1 and then horizontally perpendicular to this4 ,if the sun presents a round disc in both these positions the sextant is in adjustment4 ,if in the vertical position there appears to be a small notch at top and bottom of the sun's limb1 the glass is not perpendicular to the plane of the instrument1 and this requires adjustment by the screw at ,fig4 #bhh ,k4 ,if notches appear at the sides of the limb when it is held horizontally there is an index error1 which may be adjusted at ,g if it be small4 #fdi4--;,index ,error after ,adjustment ,allowance4--,the limb of the sextant is graduated #e beyond the zero position when the glasses are parallel to each other4 ,this is called the arc of excess4 ,the vernier is also divided three lines beyond its zero position1 which is marked by an arrow4 ,these extra divisions are placed on the instrument for correcting the index error by measurement of the angle subtended by the diameter of the sun's disc alternately on one side and the other of the zero line1 in which observations1 if the two readings agree1 the sextant must be in perfect adjustment2 when they do not agree half the error may be adjusted by the horizon glass4 ,the same observations may also be made with a bright star by setting the index alternately on one and the other side of zero4 ,when the sun is used the reflected and direct images are brought together1 so that the two suns that appear in the instrument just touch limb to limb1 first upon direct reading and then upon the arc of excess4 ,when the division is adjusted very nearly1 any small error1 plus or minus1 may be allowed as a constant for all readings4 ,in observations of the sun care should be taken that the eye is protected1 both by the sun-glass cover to the telescope and by sufficient use of the shades4 #fej4--;,adjustment of the ,telescope to ,set its ,axis ,parallel to the ,plane of the ,sextant4--,in fixing up the instrument after manufacture1 the ring standard which carries the telescope is set at a measured distance from the plane of the frame1 so that the centre of the ring coincides with the height of the silver line cut on the horizon glass4 ,this is necessarily a primary adjustment4 ,for final adjustment the long1 inverting telescope is screwed home in the ring1 and the eye-piece which has two parallel wires across its diaphragm placed in it4 ,the telescope is brought to focus on any distant object1 the eye-piece being turned at the same time to bring the wires parallel with the face of the instrument4 ,two objects are taken subtending an angle of #ij or over1--as the sun and moon1 or the moon and a bright star1--and the index is moved so as to bring the objects1 say the limbs of sun and moon1 in contact with the wire nearest to the sextant1 and fixed there4 ,then by changing the position of the instrument a little1 the images are made to appear upon the wire furthest from the sextant4 ,if the limbs of the sun and moon still remain in exact contact as they appeared before1 the axis of the telescope is truly adjusted4 ,if the limbs of the two objects appear to separate at the wire furthest from the sextant1 the ring-adjusting screw furthest must be loosened a very little and the screw nearest the sextant tightened the same amount4 ,if the reverse1 and the images appear to overlap1 adjust in the reverse direction4 ,by repeating this operation a few times the contact will appear to be the same at both wires1 and the axis of the telescope will be in collimation1 that is parallel with the plane of the instrument4 ,after the telescope is truly adjusted it may be raised or lowered a little to make the reflected and direct images appear equally clear4 #fea4--;,final ,examination of the ,sextant4--,it will be readily seen that an instrument1 although correct in theory but depending upon perfection of workmanship in centring1 division1 surface and parallelism of glasses1 and also in its adjustments1 can scarcely be brought to perfection4 ,the errors generally increase from the zero point1 where adjustments are possible1 and are greatest at #adj4 ,in the ordinary commercial sextant of the dealers the errors of centring alone are commonly #c minutes to #e minutes1 with like errors in other parts4 ,it is therefore better1 where the sextant has to be absolutely relied upon1 to subject it to actual trial4 ,the zero point can be readily fixed by rules already given2 besides this the meridian altitude of several bright stars subtending angles of about #cj1 #fj1 #ij1 and #abj should be measured either from a clear horizon or from a mercury artificial horizon1 to be described presently1 for angles under #fj1 and the errors plus or minus tabulated4 ,the data for the meridian altitudes of certain stars upon any night may be taken from the ,nautical ,almanac1 which will require correction for the latitude and longitude of the observer4 ,this subject is too complicated to be entered upon in detail here4 ,at the present time the ,national ,physical ,laboratory undertakes the examination of sextants for a moderate fee4 ,this is effected by means of fixed collimators1 art4 #bbi4 ,for angles distributed over the arc the parallax error is eliminated by placing the collimators in pairs4 ,the ,n4,p4,l4 certificate may now be had with good instruments when purchased4 ,it may be noted that an originally well-made instrument retains its qualities for all time1 the wear of such instruments being inappreciable4 #feb4--,to ,use the ,sextant the right foot should be placed nearly #b feet in advance of the left and directed at right angles to it4 ,in this position the body is firm4 ,the instrument is supported by the right hand1 the elbow being brought down firmly upon the body4 ,the clamp screw first and then the tangent screw are moved by the thumb and finger of the left hand4 ,some practice is required to make a steady observation4 ,to bring two objects into apparent juxtaposition1 methods of observation for terrestrial objects will be reconsidered in discussing the box sextant further on4 ,as regards celestial observations reference should be made to works on practical astronomy1 as the subject would take too much space to be entered upon here4 ,the whole subject1 with many refinements of correction of parallax1 etc41 which fall beyond the limits of practical surveying with the sextant1 is ably discussed in ,chauvenet's ,spherical and ,practical ,astronomy4 #fec4--;,artificial ,horizon4--,for ascertaining the latitude of a place from the observation of a celestial body by means of a sextant1 it is necessary to have some means of estimating the position of the horizon4 ,a method of doing this1 originally proposed by the elder ,george ,adams1 optician1 #agdh1df was to float a parallel disc of glass upon a basin of mercury1 and to receive the reflected image of a star from the mercury by the sextant simultaneously with its direct image4 ,the angle then given by the reading of the arc is double the angle at which the true horizon is placed relatively at the same time4 ,this idea1 carried out in a practical form in an instrument henceforth called the artificial horizon#dg is due to ,wm4 ,jones1 a well-known optician at the end of the #ahth and beginning of the last centuries1 who arranged convenient means of making the instrument portable1 and to keep the mercury from disturbance of the air by covering it with a glass roof4 ,the form of artificial horizon that he invented has been in common use ever since4 ,he also invented another simpler form1 which was that of taking the reflection from a piece of silvered1 or of black1 glass4 ,the performance of the artificial horizon depends in any case entirely upon means of obtaining a reflection from a perfectly horizontal surface4 ,illustration3 ,fig4 #bij4--;,diagram of artificial horizon4 #fed4--,theory of the ,artificial ,horizon4--,a ray ,m ,fig4 #bij1 from a luminous body1 at infinite distance will have its image reflected from a level reflecting surface ,,ss at an angle equal and opposite to the incident ray1 the angles ,m,,as and ,,eas being equal4 ,let ,e be the place of the eye or the sextant3 this will receive a ray from the same distant body in direction ,,me1 which is sensibly parallel with ,m,a4 ,the angle ,,mea being double the angle of incidence ,m,,as1 the half of this angle will therefore produce the horizontal line ,,eh at the height of the observer's eye if the plane of reflection ,,ss be level4 ,therefore if we take half this angle ,,mea as it appears in the sextant1 it will give an angular position of the object in relation to the horizon at the height of the eye1 or be tangential to the surface of the earth4 ,if ,m,,as be #cj1 the angle ,,aem will be #fj1 showing the elevation of object half this or #cj4 ,the sextant takes #abj with certainty2 therefore #fj will be the limit of meridian altitude the artificial horizon will measure4 ,illustration3 ,fig4 #bia4--;,artificial horizon of black glass4 #fee4--;,artificial ,horizon in ,black ,glass4--,this instrument is the most portable1 packing in a close pocket case4 ,it is made of both circular and square form in plan4 ,fig4 #bia is the ,admiralty pattern4 ,the black glass should have a truly plane surface4 ,it is fixed over a brass tray by being floated on plaster of ,paris to avoid strain4 ,a light rim of brass is screwed down over the glass to keep it in position4 ,there are three adjusting screws ,,aa,a4 ,it is adjusted to level by a loose level tube ground on its under face ,p4 ,the level tube shown in detail ,fig4 #ea1 p4 #id1 is placed on the surface lineally with the two screws1 ,fig4 #bia ,,aa1 and afterwards at a right angle to its first position with one end of the tube towards ,a4 ,it is finally tested by traversing at the position shown in the ,fig4 #bia1 and at right angles to this direction4 ,there is a great risk of getting a strain on the glass in fixing it in its frame4 ,the author therefore prefers the circular form that leaves the glass quite free except at its fixings at three equidistant points only4 ,in this kind of artificial horizon there is only one surface of glass to be worked true2 therefore1 there is perhaps less risk of error on this account than in other forms4 ,on the other hand the mercury presents a more perfectly level plane4 ,the circular artificial horizons are commonly made #c inches diameter2 weight1 lb42 the oblong1 ,fig4 #bia1 #d inches by #c inches2 weight #b lbs4 ,illustration3 ,fig4 #bib4--;,artificial horizon1 mercury4 ,illustration3 ,fig4 #bic4--,mercury bottle to the same4 #fef4--;,artificial ,horizon of ,mercury1 ,fig4 #bib4 ,this instrument consists of an oblong tray of about #f inches by #c inches by inch in depth made of wrought iron4 ,it is covered by a roof with two sloping sides at about #de to the plane4 ,the sides of the roof are glazed with worked parallel glass fixed by screws at three points4 ,the mercury when out of use is contained in an iron screw-stoppered bottle1 ,fig4 #bic4 ,it is poured into the open tray for use1 and the tray is afterwards covered by the roof to prevent currents of air disturbing the level of the surface4 ,after use the mercury is poured back into the bottle from the corner of the tray4 ,it should be particularly observed that it is perfectly drained1 as any free particles in the case in which all parts of the instrument are packed would be certain to attack the roof1 which is made of brass and simply varnished4 ,the instrument is packed in a mahogany case1 size #g inches by #f inches by #e inches2 weight1 with #a lb4 of mercury1 about #d lbs4 #feg4--,the ,bottle1 ,fig4 #bic1 is made of cast iron4 ,it has a screwed plug stopper with a leather collar and a covering cap with a small hole through its apex4 ,to pour out the mercury the cap and stopper are unscrewed1 the plug is taken away1 and the cover is screwed on again4 ,the mercury then issues from the small hole in the cap4 ,to return the mercury the cap is reversed and screwed upon the bottle4 ,it then forms a funnel4 ,the tray has a covered corner at which there is a small hole4 ,this permits the mercury to be poured into the funnel without splashing4 ,both plug and cap are then screwed down firmly1 and the bottle is placed in a secure fitting in the case4 ,illustration3 ,fig4 #bid4--;,captain ,george's artificial horizon4 #feh4--;,captain ,george's ,artificial ,horizon1#dh ,fig4 #bid4 ,this is a great improvement on that last described4 ,the instrument being made entirely of iron there is no risk of getting it injured by escape of the mercury4 ,it is also much more portable and convenient4 ,two chambers ,e and ,m are connected together by a tube through a stem-piece in which there is a strong iron cock at a4 ,the chamber ,e is cored out and form a bottle into which about #a lb4 of mercury is introduced by removing a screwed stopper at ,b4 ,the chamber ,m is an open tray with a cover formed of a piece of parallel glass placed in an iron rim which screws down upon it4 ,a milled-headed screw at ,c forms an air plug4 ,the cock moves very stiffly by the leverage given by a tommy-pin1 shown a1 which is inserted in the hole at a4 ,the chamber ,e is slightly elevated to cause the mercury to flow from it to ,m1 the cock being turned on at the same time and the air screw ,c released a little4 ,by the same arrangement1 ,m being raised1 the mercury flows back into the bottle for storage4 #fei4--;,for ,using this ,artificial ,horizon1 when the mercury is poured out in the tray ,m1 it is levelled by the three screws ,,aa,a so that it covers the bottom of the tray and presents a clear1 level surface4 ,a separate disc of parallel glass1 which fits the tray ,m very loosely1 is provided with the instrument4 ,this floats on the surface of the mercury and keeps it quite still1 even when the covering glass is removed4 ,this arrangement is useful also in case of an accident to either of the glass covers4 ,the disc is kept when out of use in a soft leather bag which fits in the tray ,m4 ,this artificial horizon is generally carried in a solid leather case with sling to go over the shoulder4 ,its weight complete is about #d lbs42 size1 #i inches by #d inches by #a inches4 ,the surface of mercury is a circle of #c inches diameter4 #ffj4--;,improved ,captain ,george's ,artificial ,horizon4--,mr4 ,s4 ,a4 ,ionides1 ,c4,e41 has devised an improved form of the foregoing instrument shown at ,fig4 #bie4 ,illustration3 ,fig4 #bie4--;,ionides's artificial horizon4 ,in this the container is formed beneath the horizon box with a plug tap fitted in the thickness of metal between the two2 this form makes the whole much lighter and less than half the size of the usual ,captain ,george's pattern4 #ffa4--;,in ,using the ,artificial ,horizon with the ,sextant it is generally placed on the ground at such a distance in front of the observer that he can conveniently see the required reflection of the star or sun1 the observer moving about until the reflection is obtained4 ,this is a tedious process and requires some practice4 ,it is much more easily effected if the sextant be mounted on a tripod or other stand4 ,when a stand is used it has generally a universal joint1 so as to be able to take surface angles also from the fixed position4 ,when the altitude of objects on the earth is taken1 the observation requires reduction for refraction1 which becomes an important factor1 although this is variable with atmospheric conditions2 but upon the whole it always tends to make the object appear higher than it really is4 ,commonly one-seventh of curvature is used as an approximate correction4 ,for solar and stellar refraction1 works on astronomy should be consulted4 ,the index error of the sextant is corrected before refraction1 when the natural horizon is employed4 ,when the artificial horizon is used the index error is allowed before taking its half as a single measure4 ,the artificial horizon is used also with the theodolite4 ,it forms the most perfect means of adjusting the transverse axis by taking an observation of the pole star with the telescope1 first directly and then by its reflection from the artificial horizon4 ,if the images cut the centre of the webs in the two positions by the movement of the transverse axis only from the one to the other1 this axis is proved perfectly level4 #ffb4--,various schemes for obtaining the horizon by some system of levelling apparatus attached to the sextant have been devised1 none of which are very practical1 as they all depend upon a pendulum or a gravitation surface of a liquid or a gyroscope1 and are all unstable as hand instruments4 ,there have been numerous patents taken out with this object from that of ,winter 7#agfj7 downwards1 which anyone interested in the subject may consult4#di ,the matter is mentioned here as the recurrence of the idea appears to be frequent4 ,illustration3 ,fig4 #bif4--,sounding sextant4 #ffc4--,the ,sounding ,sextant4--,this instrument is used for coast surveys4 ,angles are taken with it of objects1 buoys1 etc41 from the land and also from a boat on the water for such objects or for others upon land4 ,it is constructed upon the same principle as the ordinary nautical sextant2 but as it is to be used as an all-day working instrument1 and not for a few diurnal observations only1 it is made much more solid1 and its optical parts take a more extended field of view4 ,the graduation is also stronger1 such precision of reading only being required as may afterwards be plotted on a chart4 ,this instrument is shown in perspective1 ,fig4 #bif4 ,the index glass is large--about #b inches by #a inches4 ,this is secured on all sides by a firm rim to the tray in which the glass is held at three points4 ,the adjustment of the index glass is left under control1 as it may occasionally be necessary to remove it from effects of spray upon and about it4 ,the horizon glass is made about #a inches in width and inch in depth4 ,this is entirely enclosed in a tray1 the whole surface being a mirror without any plane part to the glass as with the ordinary sextant1 so that it is entirely protected by the metal4 ,by this arrangement the eye receives the direct ray from the object immediately before it1 and the reflected ray from an object whose angular position is desired to be taken with it3 but these images do not come exactly into contact1 as the narrow frame interposes4 ,it is1 however1 sufficiently near for terrestrial observations4 ,the adjustment of the horizon glass to the perpendicular of the plane of the arc is the same as that shown in detail for the box sextant further on4 ,the adjustment of the horizon glass to the index is by a stiff arm extended from the sole-plate projected into a loose opening1 where it is held firmly by two opposing capstan-headed screws1 as before described4 ,the arc of the sextant is of #f inches radius1 graduated upon silver to #bj1 and reading by the vernier to single minutes only by the microscope4 ,the clamp and tangent are the same as those described for the nautical sextant4 ,the frame is straight braced4 ,the telescope has a wide field1 with achromatic object-glass of #d inches focus1 the clear aperture being #a-a_/h inches4 ,the supporting ring of the telescope has no rising stem or collimating adjustment1 but is solidly fixed in its true position by the maker4 ,the ring carries a plain disc pin-hole sight1 which takes the place of the telescope for near observations4 ,the instrument in use is held in the hand by a firm oblong handle4 ,the instrument rests1 if required for reading1 upon three legs as the ordinary sextant4 ,its weight is about #b lbs41 or when packed in its case1 #e lbs4 ,its examination and adjustment are of the same kind as those just described for the nautical sextant4 #ffd4--;,box ,sextant4--,this very neat and portable instrument was invented by the late ,william ,jones4#ej ,it is used for taking angles within #abj upon the surface of the land to within a single minute of arc4 ,it has become deservedly popular with ,british surveyors as a land surveying instrument1 and is equally so as a military one4 ,it is the same in principle as the nautical sextant already described1 but it possesses the great merit--as a surveying instrument constantly in hand--that all its glasses and delicate parts are securely protected from accidental injury by being covered2 whereas the nautical sextant1 made for one or two diurnal observations only1 has all these parts exposed4 ,and it is not only that all parts are protected when the instrument is in use1 but they are all doubly protected by the covering box when carried about out of use2 so that it is found that a well-made box sextant set originally in perfect adjustment will retain this adjustment in average use for very many years4 ,the author has seen an instrument twenty years in use still in perfect adjustment4 ,the box which covers the instrument out of use forms also a most convenient handle or support for it when in use by attaching it in a reversed position underneath1 as it appears in ,fig4 #big4 ,this attachment is made either by a screw cut entirely round the body of the instrument1 or1 what is much better1 by a bayonet fitting1 for the reason that large screws of this description are liable to cross thread4 ,the general description of the outer parts is as follows3-- ,illustration3 ,fig4 #big4--,perspective view of the box sextant ready for use4 #ffe4--;,c a covering box which inverts from the position shown in the figure and covers the instrument4 ,this has a diameter of #c inches and a depth of #a inches4 ,b box containing the optical and moving parts of the sextant4 ,a axis of index glass4 ,this axis also carries a toothed segment fixed close under the front of the box1 by which both the index glass and index are moved by means of a pinion to be described4 ,the index carries a vernier divided into #cj1 which reads into the arc to single minutes2 the arc is divided to half degrees on silver4 ,the magnifier is centred by a swivel hinge joint over the axis1 so as to permit it to be brought to focus upon the arc at any position4 ,this magnifier is held down on the front of the box when out of use by a nib catch at a position of about #hj of the arc4 ,o a milled head1 the axis of which carries a pinion which works into the segment above described under the index glass4 ,the pinion is about #a to #i of the segment1 so that the index traverses the arc of #fj 7reading #abj7 by one-and-a-half turns4 ,this gives a conveniently slow motion to the index glass1 and enables this sextant1 if it be well made1 to be set rapidly with great precision4 ,s two nibs1 part of two levers for putting the shades in or out of action4 #fff4--;,in the closed form of sextant the shades block the reflecting position between the index and the horizon glass4 ,for surface surveying they have therefore to be opened out1 through an opening closed by a slide shutter which moves by a stud in a slot on the under side4 ,the shades consist of one green and one dense red glass which must be worked parallel1 as before described for the nautical sextant4 ,these are used for taking altitudes of the sun1 for adjustments only4 #ffg4--,the ,key ,k is a milled head which screws out1 and carries a watch-key pipe at the end of its stem by which adjustments may be made from three square-headed screws fitting its pipe1 two of which are close to b1 the axis of the horizon glass4 ,these adjust perpendicularly to the plane of the arc4 ,one screw at a adjusts the parallelism of the index and horizon glasses when the index is at zero4 #ffh4--,the ,telescope is achromatic1 with draw tube for focussing4 ,it magnifies about #b diameters4 ,it has a concave eye-glass1 and therefore gives an erect image1 ,fig4 #ad4 ,a sun-glass ,e screws over the eye-glass when it is required for sun observations4 ,the telescope is attached to the sextant by means of a crank-piece upon the telescope which is fixed by the mill-headed screw ,t and two steady pins4 ,the crank-piece screws in reverse position upon the telescope for portability before putting it by in its case4 #ffi4--;,by some makers the telescope is made to slide into the body of the sextant and thus become quite portable4 ,this plan is a very neat one1 but it requires care to see that the shades do not interfere before it is put by4 ,the weight of the entire sextant with its solid leather case is about #ah oz4 only4 ,for close work the telescope is not generally used4 ,a sliding shutter pierced with a small hole covers the telescope opening into the sextant1 which is used as a sight hole4 ,illustration3 ,fig4 #bih4--;,box sextant under the face4 #fgj4--,the ,interior or ,optical and ,mechanical part of the ,sextant is shown ,fig4 #bih4 ,i index glass1 fixed over the toothed segment on the same axis4 ,the pinion is shown working into the segment moved by the milled head ,o of ,fig4 #big on the face of the sextant4 ,fig4 #bih3 horizon glass1 cut by ,,ed1 adjusts to the vertical by screws ,,cc1 which have square fittings on the face of the instrument1 shown ,figs4 #bii and #cjj full size4 ,the differential adjustment between horizon and index glasses is made by a screw with a square fitting at ,p4 ,this adjustment acts by screwing against a helical spring1 shown at ,q4 ,the reflected rays enter by a wide window in the side of the box1 ,fig4 #bih d1 the direct rays by a small window f4 ,the path of a ray is shown by fine lines from ,r to ,e1 for the positions in which the index and horizon glasses are placed4 ,the pin-hole opposite which the eye is placed is shown white4 ,s shades with their axis are shown cut off1 to prevent confusion of other parts4 ,they are simply round discs of parallel glass on arms which rise from the back of the face by pressure of the nibs at ,s4 ,illustration3 ,fig4 #bii4--,plan of horizon glass4 ,illustration3 ,fig4 #cjj4--,section of the same4 #fga4--,the ,construction of the ,box ,sextant may be fairly inferred from inspection of the engravings4 ,the face-plate is made of a casing in brass #a_/h inch thick1 which should be well hammered to harden and stiffen it4 ,the axis1 which has a wide collar1 is fitted into a hole in the plate1 first by turning it as exactly as possible1 and then by burnishing it in by friction1 the hole being broached slightly conical with a ,d-broach4 ,the careful fitting of the axis is an important part4 ,the horizon glass frame1 ,fig4 #cjj1 is held down by a central screw which fits tightly both in its fore hole and thread4 ,the flange of the tray ,f is cut to an angle on its under side to permit adjusting to verticality by rocking over this angle1 by tightening and loosening the adjusting screws cc which protrude in square heads to the face of the instrument4 ,the horizon glass1 ,h1 which is half silvered1 is fixed in a tray-piece which has two narrow fillets turned to the face of the glass1 and a spring-piece at the back brought up by a screw a4 ,this glass is entirely open at its unsilvered part4 ,the toothed segment should be cut upon its own axis1 and although fitted to the pinion without any looseness1 it should not press the index axis4 ,the silver is inlaid in the arc on the plan shown ,fig4 #abg4 ,the vernier is soldered closely on the index and should read down to a fine clean edge4 #fgb4--;,examination of the ,box ,sextant4--,the glasses should be cleanly silvered1 with a sharp1 clear cut between the silver and the clear glass of the horizon glass4 ,the pinion should move softly and equally in causing the index arm to traverse the arc4 ,if the pinion be moved in little jerks backwards and forwards there should be no shake1 but the index should follow every slight motion4 ,the magnifier rising joint should move rather stiffer than the traversing joint1 so that the focus is not changed by traversing across the arc4 ,the magnifier should have about #a inch or less focus1 and should stand square to the plane of the sextant when in focus4 ,the graduation should be deep and fine1 and the vernier should read #cj #bi at the two ends and the centre of the arc4 ,if there be a small excess or defect of vernier to arc1 this should be noted and allowed for1 either at the time of reading or as an index error4 ,the sliding fittings of the pin-hole sight1 shades1 and under shutter should move firmly but not stiffly4 ,the telescope should fit without shake4 ,the covering box should fit well in both positions of cover or hand-hold4 #fgc4--;,adjustment4--,the box sextant is best adjusted by the sun upon the plan described art4 #fdh4 ,the adjusting screws1 as already stated1 are moved by the key1 which unscrews from the face of the sextant1 ,fig4 #big ,k4 ,the adjustment is made permanently by the maker1 except only that of the horizon glass1 which is at the command of the user4 ,the adjustment to perpendicularity of face is made by the two screws upon the face near b2 adjustment to zero of arc by the screw at the side a4 ,in defect of appearance of the sun1 the sextant may be adjusted to any clear1 sharp line1 as that of a stretched piece of twine1 for perpendicularity of plane1 and to any object of clear outline sufficiently distant1 say at half a mile1 to avoid error of parallax for index zero1 art4 #fba4 #fgd4--,use of the ,box ,sextant4--,the sextant has its under shutter opened by pressing the stud attached over in its slot4 ,the nibs of the shade levers1 ,fig4 #big ,s1 are then raised and the shades depressed4 ,the cover is then screwed1 or slid on if it fixes with bayonet notches1 upon the under side of the sextant to form the hand-hold4 ,the pin-hole sight is pressed over for use if not already in its position1 unless it be intended to use the telescope4 ,the box sextant is held in the left hand1 with the right-hand thumb and forefinger constantly holding the milled head1 and turning this so as to bring the two objects1 of which it is desired to obtain the angular position1 from the observer1 exactly in apparent juxtaposition1 the one over the other4 ,in turning the milled head it is better to let all the other fingers of the right hand clutch and steady the instrument4 ,to take angles objects should be observed that cut sharp1 erect outlines1 as buildings1 posts1 trees1 etc41 if possible4 ,in open country it is necessary to use pickets1 to be described further on4 ,with pickets the reflected image of the upper half of one picket should form a continuous outline with the direct image of the lower half of the other picket in the eye1 so that the pair of pickets appear as one4 ,where an angle greater than #abj is required an intermediate picket is set up1 and angles taken to the right and left of this are added together4 #fge4--;,it must always be remembered that the sextant takes angular positions actually1 whereas plans are made in azimuthal angles4 ,there are some not very satisfactory means of approximate correction for this1 for which books on surveying may be consulted2 but altogether the sextant is not very useful for taking angles for plans on other than fairly level ground1 wherein it has proved a most valuable and sufficiently exact instrument4 ,where ground is undulatory fairly good work may be done with it by taking stations for exterior triangles at equal heights on the hillsides1 as ascertained by a hand level or clinometer to be described1 or sometimes from hilltop to hilltop where these are of fairly equal heights4 ,for sketch plans of very hilly or mountainous districts the prismatic compass1 art4 #adh1 is better1 as this gives1 although with less precision than the sextant1 its angles in azimuth4 ,illustration3 ,fig4 #cja4--;,interior construction of box sextant with supplementary arc4 #fgf4--;,box ,sextant with ,supplementary ,arc4--,this sextant is preferred by many because of its more extended use4 ,it is complete as an ordinary sextant for angles up to #abj2 but if it be thought desirable to extend the angles to #bbj--;by a single observation this may be done4 ,the ordinary arrangement of the box sextant just described is left intact and forms the upper part of the instrument4 ,this arrangement1 as in the box sextant1 is attached entirely to the face or arc plate1 the only difference being that the index glass is made of less depth4 ,for the supplementary arc arrangement a mirror is fixed upon the lower or sole plate exactly under the position of the index glass4 ,this mirror is termed the supplementary index glass4 ,the position of the face of the index glass is at right angles to the face of the ordinary index glass when the index is at zero4 ,the arrangement of glasses is shown ,fig4 #cja3 ,,mm index glasses4 ,the supplementary angle is read through a separate pin-hole sight which is placed at about #ij from the pin-hole sight of the proper sextant and a little lower down on the rim4 ,the arc of this sextant reads in the ordinary manner1 left to right1 to an inner circle of figures for angles from #j to #acj4 ,the supplementary arc reads by the same vernier1 and is figured in the same manner at the tens2 but it reads into an outer circle of figures which progress in the reverse direction1 that is1 right to left4 ,the readings of the supplementary arc are from #ij to #bbj1 so that for a certain range1 that is1 for angles from #ij to #acj1 these may be taken either by direct arc or by supplementary arc4 ,the supplementary angle is taken by means of the coincident images of two reflections1 one from the index glass and one from the supplementary index glass1 and not by one direct and one reflected image as in the sextant proper4 ,illustration3 ,figs4 #cjb1 #cjc4--;,diagram of supplementary arc sextant4 #fgg4--,theory of ,supplementary ,angles to the ,sextant4--,for the measurement of these angles we have to consider direct reflections only of two reflecting planes placed one above the other nearly in contact1 so that the images projected from both planes may reach the eye superimposed4 ,let ,fig4 #cjb ,,ii be the surface of a mirror 7index glass7 which is movable to any angle in relation to the face of the mirror ,,ss 7supplementary index74 ,for demonstration of the principle these mirrors are shown in this diagram at #ij to each other2 therefore coincident reflections will be at #ij #ij #ahj4 ,let the lines ,,fc and ,,bc form a right line 7#ahj72 ,f fore sight and ,b back sight4 ,an object at ,f would be reflected from the mirror ,,ii to the eye at ,e1 the angles ,,fci and ,,eci being equal4 ,another object at ,b reflected from the face of the mirror ,,ss would also reach the eye at ,e1 the angles ,,bcs and ,,ecs being equal4 ,and as the angles ,,fci and ,,bci are equal in crossing a right line1 the line ,,fcb must be also a right line 7#ahj7 which is indicated by the angle of coincidence of the two reflections to ,e4 ,the positions of the reflections are shown as angular measurements upon the graduated arc4 #fgh4--;,in ,fig4 #cjc let ,,ss remain as before1 angle ,,bce will remain as shown in both figures4 ,move the index glass from the position ,,ii of ,fig4 #cjb to the position ,,jj of ,fig4 #cjc1 so that after this movement the eye at ,e would receive the image of an object at a new position ,f as reflected from the mirror ,,jj1 ,f,,cj and ,,ecj being equal4 ,in this process1 as the reflector ,,jj in the angle ,,icj would have moved half the angle ,,jcf1 the record of this movement upon the index1 which moves with ,,jj1 is at the same time double the true angular difference1 as with the sextant proper fully described1 the graduations being in both cases the same pro rat4 ,the increase of angle is taken supplementary to the angle given by the first reflection1 by addition to this angle in a direction right to left from the right line of the former sight ,,ec2 consequently this increase is read backward on the sextant1 that is1 right to left1 and is indicated by the outer line of numerals4 #fgi4--,manufacture4--,the general structure of this instrument is nearly the same as the ordinary box sextant1 except the parts just referred to4 ,the supplementary index glass is an ordinary mirror similar to the index glass but of only inch in depth3 it is mounted in the same way4 ,its adjustments are similar to the horizon glass in kind1 but there are no exterior screws1 this glass being permanently fixed by the maker4 ,opposite the supplementary index glass a wide window is cut through the rim of the case near the sole plate to take sight of the object at angles exceeding #abj1 so that in this sextant two large windows are cut out opposite to each other4 ,the diameter of this sextant is #c inches2 the exterior depth about #a-e_/h inches1 that is1 #a_/h inch deeper than the ordinary box sextant4 ,it weighs about #bj oz4 ,it is carried in a solid leather case with strap to pass over the shoulder4 #fhj4--;,examination and ,adjustment4--,examination will be nearly the same as for the common box sextant4 ,the most important point is that the readings taken within both arcs should be alike1 assuming1 which is necessary1 that the part comprising the sextant proper is perfectly adjusted4 ,thus there is a #ij on both direct and reverse arcs4 ,the #ij may be measured by any pair of objects on the direct arc1 and afterwards compared by shifting the index to the #ij1 on the supplementary arc4 ,if no object be found at #ij1 then #ie #cj or any other quantity may be compared4 ,it is also well to compare readings at or about #abj on both arcs4 ,the #ij and #abj fall in the same position in the reading1 and this checks any error in either4 ,if the adjustment be not fairly perfect1 the instrument should be returned to the maker4 ,indeed1 this sextant would be better without any external means of adjustment1 leaving these to be made by the optician in such a permanent form that they will not be liable to change4 ,it is1 as the plain box sextant1 exceptionally protected from accident4 #fha4--;,in using this instrument the arc up to #abj is taken exactly as with the plain box sextant4 ,beyond #abj the sextant is shifted to take sight through the supplementary pin-hole1 being particular to observe that the pinion is now turned the reverse way to increase the angle1 and that the vernier reads for the supplementary arc right to left4 ,it is in this reversing1 if not carefully performed1 that a little difficulty is experienced in using this instrument4 #fhb4--;,box ,sextant1 with ,continuous ,arc to #bdj4--,this instrument is an improvement by the author upon one originally designed by ,mr4 ,w4 ,franklin4 ,the reading is taken continuously from the same sight-hole and by the same arc1 and in a direct manner without any reversal for part of the arc4 ,this sextant reads with certainty to #bdj4 #fhc4--;,in the construction of this sextant there are two horizon glasses superimposed one above the other and crossing each other1 with faces which are adjustable for perpendicularity at an angle of #abj4 ,the horizon glass is divided top from bottom by a clear band cut through it1 as in the old form of back-sight nautical sextants4 ,one of the wide glasses reflects into the upper1 and the other into the lower mirror of the horizon glass4 ,the pin-hole sight or the telescope is placed in the same position as in the plain box sextant described4 ,the horizon glass is fixed and both the index mirrors adjust to angular positions1 or one index glass only and the horizon glass is adjusted1 this arrangement being optional4 ,the arc is graduated as the plain box sextant1 but it reads with two rows of figures from #j to #abj1 and from #abj to #bdj1 the #j of the under line being under #abj of the upper4 ,when the arc is set to zero the index glasses are in such a position that the direct vision and the reflection as seen in the upper mirror of the horizon glass are coincident for direct images1 as at the zero of the plain sextant1 but at this point the lower mirror of the horizon glass reflects to the eye an object at #abj4 ,when the index is moved forward the angles continue onward1 reflected from both glasses1 so that the upper reads on #aj1 #bj1 #cj1 etc41 whereas the lower read #acj1 #adj1 #aej1 etc42 so that if the objects desired to be triangulated are under #abj the coincidence is seen in the upper mirror1 and if over this in the lower1 the great distance of #abj apart of the angles preventing the risk of accidentally taking the one for the other4 ,in the compact form of a box sextant this instrument embraces the uses of the ordinary reflecting circle of double the diameter1 due to the entire circle graduation2 and the range is sufficient1 as beyond #bdj the head materially interferes with observation4 ,the size and weight of the instrument are generally but little over that of the plain box sextant4 ,the adjustments are made permanently by the maker4 ,the use of this instrument is fully inferred from the description given4 ,the construction is shown in ,fig4 #cjd1 ,e place of the eye with direct ray through the horizon glass ,h to ,o4 ,the index glass ,i is that of the ordinary sextant1 shown by dotted lines1 throwing the image of an object at ,p to the upper horizon glass and thence to the eye at ,e4 ,b is the fixed supplementary glass with its surface at #fj to the lower horizon glass at ,a4 ,the sight lines from an object at ,q are reflected from ,b to ,a and thence to ,e4 ,a spring arrangement shown ,,ss with a milled head underneath permits the lower glass ,a to be drawn down to convert the instrument into a simple box sextant4 ,illustration3 ,fig4 #cjd4--,stanley's continuous arc box sextant4 ,illustration3 ,fig4 #cje4--,section of supplementary horizon arrangement4 #fhd4--;,details of ,spring ,arrangement to the supplementary horizon glass are shown in ,fig4 #cje full size in section4 ,the springs ,,ss in ,fig4 #cjd and ,s ,fig4 #cje form two points of support to the horizon glass1 the silvered face of which is shown at ,a4 ,a third point of contact is near ,d1 placed in the centre of the end of the supporting plate for the horizon glass4 ,when the screw ,r1 which is placed in a loose fitting1 is released1 the springs bring the supporting plate tight up to ,d and hold the horizon glass firmly in an elevated position4 ,when the screw ,r is tightened it brings this glass down4 ,the horizon glass is adjusted over a rocking centre by the screws ,,cc4 ,a screw and collar b prevent the loss of the screw ,r4 ,by this arrangement the horizon glass is brought in or out of the field of view1 in order to use the supplementary arc or for leaving it as a plain sextant4 ,illustration3 ,fig4 #cjf4--,stanley's portable surveying sextant4 #fhe4--,open ,surveying ,sextants1 similar to nautical sextants but generally smaller and of stronger construction1 preceded the box sextant1 and are still used to a limited extent upon the ,continent1 particularly with some form of supplementary arc1 or arrangement to produce a large part of the reflecting circle4 ,these forms are also occasionally revived by the opticians of our own country4 ,the reason of this is easily seen4 ,to the optician who lives in a town1 moves on a level surface1 and has comfortably warm hands1 even in the winter1 to hold and move the separate parts of an instrument1 the open sextant appears the most perfect1 as he can get at every part of it easily to clean and adjust4 ,the surveyor takes another view of the subject4 ,he is exposed in the open country to all weathers and all difficulties of movement over the land2 therefore that form of instrument which is best protected and least liable to injury by a fall will be sure to be popular with him4 ,it is upon these conditions the box sextant of some form is generally preferred4 ,a handy form of portable surveying sextant has been devised by the author and is shown at ,fig4 #cjf4 ,the arc is of #d inches radius and is divided on silver to read #bj1 is complete with shades and telescope and packs into a case #g #f #b inches4 ,illustration3 ,fig4 #cjg4--,optical square4 ,illustration3 ,fig4 #cjh4--;,double optical square4 #fhf4--,optical ,square4--,this extremely handy little instrument is invaluable for taking offsets in chaining for any irregularity or obliquity to the right line in the boundaries of fields1 hedgerows1 fences1 streams1 etc41 giving as it does instantly at sight a right angle to any object that may be sighted on either hand4 ,the instrument is optically constructed exactly as a box sextant2 but the glasses are fixed with their faces permanently at the angle of #de to each other1 by which means the reflection of #ij is truly given on principles fully discussed at the commencement of this chapter4 ,this instrument being made very small1 that is1 #b inches or less in diameter1 it is found most convenient for manipulation to place the adjustments to the larger glass1 that is1 the index glass4 ,the horizon glass1 ,fig4 #cjg1 h is therefore fixed firmly1 like the index glass of the box sextant1 by two screws to the sole plate4 ,the index glass i is held and adjusted in exactly the same manner as the horizon glass of the box sextant1 as shown in detail1 ,figs4 #bii1 #cjj1 the only difference being that the frame which holds the glass is made of the entire height4 ,the rim of the case of the optical square is formed of a short length1 #c_/h inch to #e_/h inch1 of a pair of telescope tubes which slide easily together4 ,one of these is attached to the sole plate and the other to the cover1 so that at first they close together as a box and lid4 ,all the openings required for sight1 as ,fig4 #cjg at ,q for horizon sight1 o for index sight1 and e for pin-hole or eye sight1 are cut through the two tubes4 ,illustration3 ,fig4 #cji4--,optical square4 #fhg4--,the inner case is cut in the plane of some part of the circumference of the instrument from a pin-hole into a bayonet notch1 made with a horizontal slot for the two cases to revolve upon each other upon a pin1 sufficiently to close and open the sight holes4 ,this plan secures the instrument from any intrusion of dust when it is closed and out of use4 ,an adjusting key is placed in the case1 held by a tube or stud at the position k4 ,the weight of the entire instrument is about #d oz4 if of ordinary make2 but smaller ones are made in ,german-silver or silver1 #a inches diameter1 #c_/h inch thick1 weighing under #b oz4 ,these latter are very convenient for the waistcoat pocket1 and are equally as exact as the larger instruments4 ,fig4 #cji shows the general outward appearance of the optical square4 #fhh4--;,examination and ,adjustment of the ,optical ,square4--,place two pickets in an open space at a distance apart1 the further the better4 ,range an intermediate short picket in right line with these or the top of a stake the height of the eye1 or what is better still1 if at hand1 the top of a tripod stand4 ,place the optical square over the intermediate station or tripod4 ,place another picket1 which we will distinguish as the #ij picket1 at a distance1 and make this appear in the optical square coincident by reflection with the direct sight of one of the pickets in the right line from our station4 ,turn the optical square right over on its place1 and looking in the opposite direction take a sight at the other right line picket and observe the #ij picket4 ,if this still appears coincident with the direct line in reflection the optical square is in perfect adjustment4 ,if it does not appear so1 half the difference must be adjusted by means of the key taken from the interior of the case and placed on the square at k1 ,fig4 #cjg1 and this observation repeated until the #ij is correct4 #fhi4--;,in ,using the ,optical ,square it is customary to walk along the chain line at about the desired position for taking an offset1 looking by direct vision through the plain part of the horizon glass h at a fore sight object until the required object is sighted by reflection at right angles to this1 where it appears by coincidence of image with the fore sight4 ,the heel of the forward foot in stepping indicates fairly the vertical position of the optical square2 but some surveyors prefer the use of a drop arrow to fix the point4 ,the offset is then chained in the line4 #fij4--;,double ,optical ,square4--,this instrument is exactly what its title indicates1 that is two optical squares1 the one placed exactly over the other1 the one reflecting to the right hand and the other to the left4 ,a simpler name1 however1 would be an optical cross4 ,this arrangement of reflectors greatly extends it use4 ,first1 as regards the #ij1 this need not depend in any way upon the position of the observer1 as two objects may be observed1 one to the right and one to the left1 to appear to cut the direct forward line of sight1 and therefore to cut the base line at the exact position of the instrument at right angles to it4 ,secondly1 an intermediate station can be found in direct line between any two points1 as the #ij #ij forms this line4 #fia4--,the arrangement of the optical part of the instrument is shown ,fig4 #cjh4 ,the two index glasses ,,cd are fixed at equal angles to the direct line of sight ,,eo4 ,the two horizon glasses ,,ab are superimposed with the interval of a small space1 #a_/af inch1 between them4 ,the horizon glasses are each separately adjusted so that their reflecting planes are respectively #de to the index glass from which they receive the reflections4 ,the diameter of the instrument as usually made is about #b inches2 its depth #g_/h inch4 ,the weight is about #i oz4 ,it is generally carried in a light1 solid leather1 sling case4 ,total weight with instrument1 #ab oz4 #fib4--;,examination and ,adjustment of the ,double ,optical ,square4--#a4 ,place the instrument1 as already described for the optical square1 at a station intermediate between two pickets4 ,examine the right angles1 first looking towards one picket and then towards the other from the same position1 as with the optical square1 turning it over for this examination4 #b4 ,turn the instrument half round and examine it this way also by turning it over again in like manner4 ,adjust either horizon glass if required4 #c4 ,now take the position for the eye of the former #ij and see whether the extreme pickets appear in true position by the exact coincidence of their images at #ahj4 #d4 ,do this again1 facing the opposite way and turning the instrument half round4 ,if the extreme pickets still range in line from the central station the adjustment is perfect4 ,if they do not do so half the error must be corrected by returning to the first and second adjustments to find out between which pair of mirrors it lies4 ,for this adjustment the instrument is much better to be placed upon the top of a tripod1 as the position of the axis should remain fixed after turning it over or changing the direction of the instrument4 ,it is only from severe accident that the maker's adjustment will be disturbed4 #fic4--;,apomecometer4--,this little instrument1 the invention of ,mr4 ,r4 ,c4 ,millar1 is intended to measure the height of buildings1 trees1 etc41 by measuring the distance from the vertical upon the surface of the ground4 ,it performs one of the functions of the box sextant in the same manner as the optical square1 that is1 to measure a single angle by reflection4 ,the angle measured is #de1 consequently by measuring a space upon level ground up to a vertical1 the vertical will be known1 this being equal to the horizontal4 ,of course this will always be approximate1 as the ground will seldom be truly level2 but by taking a position1 even on an incline1 as nearly as possible level with the object1 a very fair estimate may be made4 ,horizontal distances may be measured in the same manner from a perpendicular to any line4 #fid4--,the instrument is constructed in exactly the same manner as the optical square just described as regards its mirrors and its adjustments1 but the faces of the mirrors are fixed at the angle of #bb #cj1 so as to give a reflection of #de1 upon principles fully discussed4 ,in ,fig4 #caj1 ,a is the index glass1 ,b the horizon glass1 ,e the pin-hole sight4 ,there is a window opposite the index glass1 and one behind the horizon glass1 each sufficient to take in a wide field of view at about #de and in the direct line ,e to ,h4 ,these windows close by rotation of the casing of the box1 which is made as the optical square4 ,when closed the instrument is dust-tight and may be carried in the waistcoat pocket loose1 or in a light snap leather case4 ,its size is #a inches diameter1 #c_/h inch in thickness1 weight #b oz4 in ,german silver4 #fie4--,the ,use of the ,apomecometer4--,to measure the altitude of a building the open side nearest level is selected1 and a station for observation is taken which is at a distance thought to be approximate to the height4 ,the instrument is held edgewise with the pin-hole sight to the eye1 and the reflection of a point of the building about level with the eye is observed by direct vision through the instrument4 ,at the same time there will appear a reflection of the summit of the building4 ,if we now walk backwards or forwards1 as the case demands1 keeping sight of a level object1 as for instance in ,fig4 #caa the plinth of a building1 then at a certain point the summit of the building will appear by coincident reflection4 ,the height of the object will be the same as the distance plus the height of the observer's eye4 ,this distance may be measured on the ground1 or if a rough estimate is sufficient it may be stepped1 the principle of which is shown by ,fig4 #caj in the line ,,oh1 being equal to ,,fh4 ,if a part of an object is required to be measured such part may be taken on the horizontal plane1 as for instance the height of the figure in ,fig4 #caa1 by ab being ed1 as the base ab can easily be measured4 ,an approximate may be found by dropping a small pebble at a and at b and then measuring the distance apart of these pebbles4 ,illustration3 ,fig4 #caj4--,optical details of the apomecometer4 ,illustration3 ,fig4 #caa4--,scheme for measuring heights4 #fif4--,the distance of an inaccessible object may be measured1 as for instance a buoy at sea1 by measuring in any straight line double the distance and taking equal angles thereto by the apomecometer on any direct line4 ,an approximate idea may be formed by walking over measuring points4 ,as for instance1 b being a buoy at sea1 ,fig4 #cab1 walk from e1 at which a walking-stick may be set up1 towards an object o4 ,at ,e the buoy and object o will appear to be coincident4 ,then drop a stone or make a mark directly under the instrument4 ,walk on till beyond ,e and turn to face e4 ,now in returning1 the buoy and the object e will appear coincident at ,e4 ,the distance ,,ee is double that of the intermediate a to b4 ,illustration3 ,fig4 #cab4--,scheme for measuring distances4 ,,footnotes3 #ch ,posthumous ,works1 p4 #ejb2 also ,animadversions to the ,machina ,clestis of ,helvetius1 p4 #di4 #ci ,phil4 ,trans41 vol4 xlii4 p4 #aee4 #dj ,phil4 ,trans41 vol4 xxxvii4 p4 #adg4 #da ,ibid4 p4 #cdj4 #db ,see ,nicholson's ,navigator's ,assistant4 #dc ,pearson's ,practical ,astronomy1 p4 #ecg4 #dd ,ibid4 p4 #egg4 #de ,gli ,strumenti a ,reflessione per ,mesurare ,angoli1 by ,g4 ,b4 ,magnaghi1 #ahge4 #df ,description of a ,new ,quadrant1 by ,george ,adams1 #agdh4 #dg ,adams' ,geometrical ,essays1 edited by ,william ,jones1 #ahjc4 #dh ,prov4 ,patent ,no4 #bfbd2 ,christopher ,george1 #ahfh4 #di ,see ,british patents--,winter1 #agfj1 ,no4 #geb2 ,ould1 #agia1 ,no4 #ahdb2 ,nugent1 #agid1 ,no4 #aihj2 ,wright1 #agif1 ,no4 #bjha2 ,cook1 #agif1 ,no4 #bjhg2 ,roxby1 #ahbb1 ,no4 #dfie2 ,glover1 #ahci1 ,no4 #hbef2 ,lane1 #aheg1 ,no4 #affi2 ,rahill1 #ahfj1 ,no4 #ahde1 etc4 #ej ,adams' ,geometrical ,essays1 p4 #bfd1 #ahjc4 ,,chapter ,,xv4 ,,graphic ,,surveying ,,instruments ,,and ,,appliances ,,connected ,,therewith--,,plane ,,tables--,,alidades--,,telescopic ,,arrangements--,,subtense ,,measurements--,,various ,,devices ,,for ,,holding ,,the ,,paper--,,continuous ,,papers--,,adjustment ,,of ,,tripod ,,heads--,,method ,,of ,,using--,,edgeworth',s ,,stadiometer--,,sketching ,,protractor--,,sketching ,,case--,,camera ,,lucida1 ,,etc4 #fig4--,plane ,tables4--,these instruments have been used for filling in the greater number of topographical surveys in all countries4 ,they possess the merit that any intelligent1 untrained person can be readily brought to comprehend their manipulation in the work to be performed1 as angles of position of objects are taken directly by drawing lines pointing to them from a point upon a sheet of paper stretched upon a table4 ,in new countries natural objects without very marked outline are conveniently defined for position4 ,the objection to this method1 from a point of view of the practical surveyor1 is that the work which can be done with equal facility in a comfortable office from the field-book is with this instrument performed in the open air1 under risk of rain1 dust1 and other atmospheric discomforts affecting both the person and the material on which he works4 ,but for countries where the climate can be depended upon1 the facility with which surveyors with little experience can map details for filling in superior triangulations made with the theodolite1 its use has gained much favour4 ,natives can be easily taught to use it1 and the check on their work through the previous triangulation is perfect4 ,the subject of plane tables will in these pages be considered only in its general aspect1 with the examples of a few good instruments1 referring the reader who cares to follow the subject further to an excellent paper by ,mr4 ,j4 ,pierce1 ,jun41 read before the ,institute of ,civil ,engineers1 ,february1 #ahhh4ea #fih4--,the ,plane ,table in its simplest form consists of a small drawing-board mounted upon a firm tripod stand1 and is shown at ,fig4 #cac4 ,illustration3 ,fig4 #cac4--,simple plane table4 ,a rule termed an alidade1 with sights placed at its ends1 gives the direction of any object from a given point on the sheet of paper stretched upon the table1 to which a fine line is drawn by an ,,hh pencil to point the direction4 ,the alidade sometimes carries a trough compass fixed upon it1 but this is generally a separate instrument which is placed against its fiducial or ruling edge to give a magnetic north to south line1 to which all other lines are assumed to take angular direction4 ,a loose spirit level is also provided1 by means of which the board may be set level by shifting the legs of the tripod4 #fii4--,plane ,table with ,telescope4--,where greater refinement of observation is required than is possible with sights1 a telescope is mounted on the alidade1 which moves in the vertical plane upon an axis1 so that it may be directed in a linear direction with the fiducial edge of the rule to any point in azimuth4 ,the telescope sometimes carries a level1 so that the table may be set level by means of the alidade4 ,illustration3 ,fig4 #cad4--,plane table4 ,illustration3 ,fig4 #cae4--,tripod stand4 #gjj4--;,a class of plane table which meets all necessary refinement for ordinary filling in of field work is shown in the illustration1 ,fig4 #cad4 ,this nearly resembles those made by the author for filling in details of the great trigonometrical survey of ,india4 ,the drawing surface of this table consists of a loose panel which stretches the sheet of paper by pressing it into its frame1 where it is afterwards held by a pair of ledges which fit at their ends into long slots4 ,the panel of the board1 shown in detail ,fig4 #caf1 is mounted upon a firmly braced tripod stand4 ,the head of the tripod stand1 shown ,fig4 #cae1 is secured to the board with a central screw 7not shown7 which permits the board to be set in any direction1 it being the rule that the edge ,w should always take a north to south direction4 ,three screws sss at the corners of the triangular head can be raised or lowered by milled heads from the under side4 ,these screws permit about #ae of adjustment to the table without any unsteadiness1 as the centre screw clamps it finally hard down upon them when all adjustments are made4 ,a small trough form of magnetic compass a is placed upon the rule to strike the magnetic north to south line1 to which all angles are referred in transposing the work of the plane table4 ,the diaphragm of the telescope is provided with a platino-iridium point fixed vertically at the mutual focus of the object-glass and the eye-piece4 ,a pair of points to subtend an angle to measure a staff for distance1 ,fig4 #cai1 is a convenient addition4 ,illustration3 ,fig4 #caf4--,panel board of plane table4 #gja4--,the ,telescopic ,arrangement of the alidade is varied in different countries4 ,in some cases it is placed near to one end1 which is perhaps better than in the centre of the rule1 as it is more easily read4 ,in the modern ,french military alidade a prismatic eye-piece is used1 so that observation is made by looking directly down upon the eye-piece of the telescope4 ,in the ,prussian alidade adjustment is made to the standard of the telescope so as to bring the horizontal axis upon which it moves level1 that the telescope may move in azimuth1 however irregular or uneven the surface of the paper on the board may be4 ,this is necessary for any great degree of refinement in the plane table1 as the surface of a piece of wood upon which the paper is stretched will be almost certain to warp if exposed to all weathers1 and this1 added to the small width of the alidade1 can scarcely retain the axis in exact horizontality1 placed as it is high above the surface of the table4 ,some plane tables made by the author for ,general ,robinson for ,indian service were of papier-mach to remedy the defect of warping1 but even this material warps upon exposure4 ,plane tables have been made in ,germany of metal and of glass1 but in this case the weight is a great objection4 ,the author has found surfaced slate very good1 but it has the same objection of too much weight for a portable instrument4 ,illustration3 ,fig4 #cag4--,stanley's plane table4 ,illustration3 ,fig4 #cah4--;,alidade to plane table4 #gjb4--,lateral ,adjustment to the ,alidade4--,the author's plan of obtaining this is to increase the practical width of the rule by giving it an extended point of support on one side so as to set the telescope in azimuth4 ,for this construction the telescope is mounted upon a plate with an arm extending outwards upon the back of the rule4 ,this has a milled-headed screw placed at the near extremity of the arm4 ,the screw is inserted in a deep bush for wear2 this attachment is shown in section ,fig4 #cah4 ,the adjusting screw ,a has a collar fixed upon its point which is centred upon a tight screw tapped into the milled head4 ,this collar1 as it does not turn with the milled head1 does not abrade the surface of the paper by contact with it4 ,a small cross level ,b is put upon the arm between the milled head and the standard of the telescope4 ,the under side of the rule is cut away or placed obliquely to the surface1 so that it bears on the outer ruling edge only4 ,the milled-headed screw being at its normal position and the table level1 less than half a turn one way or the other will bring the small cross bubble to its centre in a few seconds for any average irregularity of the surface of the table1 and by this means cause the telescope to move correctly in azimuth4 ,illustration3 ,fig4 #cai4--,subtense points4 #gjc4--,the ,telescope ,arranged for ,subtense ,measurements4--,where a stadium1 art4 #eef1 is to be used for estimating distances from station to station1 when an ordinary telescope is used1 the author places two platino-iridium points vertically from top and bottom of the diaphragm1 and adjusts these by a screw until a subtense angle upon the stadium of #a foot cuts the point at a distance of #ajj feet1 or according to the measurements to which the land is taken4 ,in this case it is necessary to have an altitude arc to the telescope1 as shown upon the alidade in ,fig4 #cag4 ,this has a degree scale reading by vernier to about #c minutes4 #gjd4--,various ,devices for ,fixing the paper on the ,surface of the ,table have been made4 ,many prefer simply pinning it with drawing pins on a quite plain pinewood surface4 ,in this case the table is better slightly sunk round the edges with a rabbet of the depth of the thickness of the head of the pin1 so that the alidade may rest firmly even over the pin heads4 ,the ,french plane tables have very generally rollers at each end of the table1 upon which a long slip of paper is rolled1 sufficient for twelve or more stations4 ,the rollers for small tables are made of brass tube about #e_/h inch in diameter4 ,they commonly move with a turn-key which is inserted in a square fitting in the end of the roller4 ,the rollers keep the paper tight by means of ratchet wheels and spring pawls at their ends4 ,this plan is very convenient for topographical work1 as for instance a river may be followed from station to station right down its course and appear on a single slip1 its bearing being indicated by the compass north line4 ,fig4 #cbj shows the manner in which the author has made this plane table4 ,illustration3 ,fig4 #cbj4--,plane table with rollers4 ,illustration3 ,fig4 #cba4--;,gurley's plane table adjustment4 #gje4--;,adjustment of the ,plane ,table4--,there are a great many devices for this4 ,mr4 ,pierce1 in the admirable paper already mentioned1 gives illustrations of the different plans4 ,some of these have all the complication of the adjustment of the stage of a theodolite1 and one has superadded to this a slide-rest motion4 ,these things of course are necessary if the field work is made to take the place of finished office work4 ,one general feature of plane table tripods is some means of adjustment of the table to uneven ground1 when the tripod-head cannot be brought nearly level4 ,gurley's plane table adjustment is perhaps the simplest of any of these devices1 and appears to the author to be as good as any other4 ,fig4 #cba1 ,d the table top2 ,a a ball fitting turned inside and out1 and attached firmly to the table top2 ,c a socket fixed firmly in the head of the tripod2 ,b a bolt with globular head fitting the interior of ,a1 and carried through the head to a winged nut which clamps it firmly4 ,a spring is placed to act against the winged nut1 so that when this is slightly loosened the ball fitting ,a may move between ,b and ,c with moderate firmness when the table is being set to an angle4 ,illustration3 ,fig4 #cbb4--,stanley's high-class plane table4 ,to meet all conditions the revisor has designed a high-class plane table shown at ,fig4 #cbb4 ,this has a ball and socket rough levelling arrangement and parallel screws for fine levelling1 circular motion to table with clamp and tangent1 spring rollers for taking any length of paper and instantly clamping it1 alidade with extra powerful telescope with vertical circle divided on silver reading by two verniers to minutes with clamp and tangent motion1 cross levels1 diagonal scale1 and adjustment for setting telescope to revolve in vertical plane1 circular compass with cross levels and plumbing bar4 ,the board is generally made #cj #bd4 ,the telescope is stadia reading and is made with long sensitive bubble mounted upon it or upon the verniers if preferred as shown at ,fig4 #cbc4 ,illustration3 ,fig4 #cbc4--,stanley's high-class alidade with bubble on verniers4 #gjf4--,method of ,using the ,plane ,table4--,the table is first set and levelled up at a commanding position to observe the extent of country it is intended to plot from observation from a single station4 ,let ,fig4 #cbd #a be the first station for plotting the enclosure abcdef4 ,draw lines by the alidade pointing to these angles represented by the letters from a point near #a4 ,set up a picket or stadium at the station #b where it is intended that the plane table shall next be set up1 and draw the line #a #b distinctly on the paper4 ,measure the line #a #b either by its subtense on the stadium or by direct chain measurement1 and plot this from station #a on the paper according to the scale to be worked to in making the plan4 ,on removing the table set up a picket or distinct land mark vertical with the position of station #a occupied on the paper4 ,move the table to station #b at the measured distance and set the direction of the board by means of the alidade so that the line #b #a cuts the picket left at station #a4 ,now draw lines from station #b to all the points abcde1 cutting the former lines as represented by dotted lines in the figure1 and the intersections of these lines will give the true positions of abcde1 according to the scale selected for the base #a #b1 and these may be tied up to represent the boundaries1 as shown on the plane table #b4 ,it will be readily seen that the line #a #b represents a bearing in azimuth2 so that if the edge of the table be set1 say truly ,n4 to ,s41 in both positions the line on the paper #a #b will agree in both these positions of the table2 but the check by the alidade of this line is valuable to save risk of error4 ,illustration3 ,fig4 #cbd4--;,diagram of plane table work4 #gjg4--,where an extent of land is to be surveyed by the plane table1 longitudinal bands of a mile or so in width are taken4 ,where the roller plane table with continuous paper1 ,fig4 #cbj1 is used1 the forward points of observation are lined in and the backward ones simply tied up1 being certain by observations written in pencil upon the paper that identical objects are tied up from the positions of both stations4 ,where an object cannot be seen from both stations its position may be indicated by the stadium from a single bearing1 or it may possibly be tied up from a further advanced station4 #gjh4--;,edgeworth's ,stadiometer4#eb--,the general construction of this instrument is given in the inventor's specification of patent1 from which the engraving1 ,fig4 #cbe is taken4 ,the vernier plate of an ordinary theodolite is extended to a plate of about #aj inches in diameter4 ,this is adjusted to level by means of parallel plate screws4 ,the plate or plane table is divided on its edge 4 ,the part representing the limb of a theodolite is carried out from its axis by two arms only3 upon these the standards ,,rr of the telescope are mounted4 ,these standards leave a striding space near the plate1 into which any scale ,s of equal parts with a zero centre is introduced1 which is intended to be used for the plotting1 the striding space being so arranged that the fiducial edge of the scale shall pass exactly over the axis of the instrument4 ,the standards unite in the same casting to form the horizontal axis bearing of the telescope4 ,this axis permits the telescope to move in azimuth4 ,the telescope carries a vertical arc divided to degrees1 also a scale of centesimal differences of hypotenuse and base1 with the ordinary clamp and tangent adjustment of a theodolite4 ,it is also fitted with a level above it which is used in setting up the instrument4 ,stadia webs are placed in the diaphragm and are made adjustable to subtend upon the stadium a percentage of arc agreeing with the unit to which the land is measured4 ,the inventor does not appear to have known the optical error of the system proposed for measuring distance1 art4 #eeh4 ,neither does this appear to have been recognised by others writing upon the instrument1 who have generally followed the late ,j4 ,f4 ,heather's description4#ec ,illustration3 ,fig4 #cbe4--;,edgeworth's stadiometer4 #gji4--,to ,use ,edgeworth's ,stadiometer4--,after it is set up1 a circular disc of paper of about an inch less diameter than the table is held down upon it by four spring clips4 ,the telescope is directed consecutively from object to object1 the positions of which it is desired to take4 ,it is clamped by the screw below the plate during the observation4 ,the stadium is placed against the object and the distance taken by the subtense of the webs in the diaphragm1 which may be exact if a constant be added after proper adjustment1 art4 #eeh4 ,if the stadium be above or below the horizontal plane it is inclined by means of a sight-hole through it1 as originally proposed by ,green1 so that the subtense is equal under all conditions4 ,the horizontal distance is taken by the difference of hypotenuse and base1 as shown on the vertical arc1 so that the record of a complete observation appears for calculation as-- stadium reading constant - altitude correction4 ,this distance is at once set off from the centre of the instrument by the scale on a line drawn upon the disc of paper1 and observations are written against the line4 ,in making a number of observations from one station two or more discs of paper may be employed to save confusion of lines and interference of descriptions4 ,these papers are separately used in plotting as protractors by pricking holes through the stations defined in the field from the centre of the disc which represents the station of observation4 #gaj4--,the ,sandhurst ,protractor1 ,fig4 #cbf1 is a military protractor adapted especially for topographical delineation1 which is commonly used with the plane table4 ,it is different from many instruments of its kind in having only useful matter upon it4 ,it is made of boxwood1 upon which the protractor is cut1 and has also one scale of #f inches to a mile in yards1 at the lower edge1 the tens of which are carried across to make parallels of #ij in the manner of an ordinary military protractor4 ,over the back of the protractor is a scale which gives a standard for shading slopes of land upon topographical maps1 ,fig4 #cbg1 from #b to #ce1 also lines for contour shades4 ,a small plummet1 the cord of which is passed through a hole in the centre1 from which the degrees are protracted1 is supplied with the instrument4 ,when the protractor is held up1 degrees downwards1 the cord of the plummet will pass over the degrees and indicate the angle at which it is held4 ,by looking over the edge the angle of inclination of the land may be taken directly1 as with a clinometer1 or by looking along the edge by a second person reading the plummet the angles of altitude may be taken more exactly4 ,illustration3 ,fig4 #cbf4--,sandhurst ,sketching clinometer protractor4 ,illustration3 ,fig4 #cbg4--;,example of scale of shades for slopes4 #gaa4--,military ,sketching ,board4--,this sketching board1 ,fig4 #cbh1 the invention of ,mr4 ,graham ,f4 ,hodgson1 will be found a very great improvement upon the old pattern boards4 ,it is designed to meet the requirements of military and other officers not conversant with the higher branches of surveying1 and it will also be found of great use to surveyors1 explorers1 and other travellers4 ,it consists of a mahogany board revolving on a circular metal plate attached to a handle held in the operator's left hand4 ,mounted on the metal plate is a compass1 which is visible through a glass plate flush with the face of the board and the tracing paper or cloth on which the map is made2 the paper being stretched tightly over the board by means of rollers4 ,a magnetic north line is drawn on the paper over the centre of the compass4 ,the operator invariably has his board in its relatively correct position by always keeping the magnetic north line immediately over the top of and aligned with the compass needle when his sights are taken4 ,illustration3 ,fig4 #cbh4 ,top view4 ,under view4 ,the sights are taken by means of an alidade moving along a slotted bar1 which itself slides along a bar fixed at the side of the board4 ,the object aimed at is sighted in a mirror attached to the end of the alidade and aligned with a point at its other end1 and the alidade is clamped into position by a thumb-screw on the slotted bar4 ,the advantages of this instrument are many and will only be fully realised when it is in practical use4 ,no backsights are necessary4 ,sights can be taken with one hand4 ,the operator is always in a comfortable position and the object aimed at is always immediately in front of him4 ,the alidade remains in position by means of the clamp screw along the ray drawn till the object sighted at is reached and the distance known1 which is merely marked off by means of the scale on the alidade4 ,it is invaluable when sketching rivers from launches or canoes when backsights are often impossible4 ,it is light and portable1 being easily carried slung over the shoulder in a canvas case4 #gab4--,the method of using is simple and ensures a great degree of accuracy with a minimum amount of time and trouble3-- 7#a7 ,the tracing cloth is first fixed by means of the rollers over the board4 7#b7 ,a magnetic north line is then ruled across the paper and passing immediately over the centre of the compass visible under the paper4 7#c7 ,the operator then1 holding the board by the handle underneath1 proceeds to make his map and first brings the magnetic north line immediately over the top of and aligned with the compass needle4 7#d7 ,he then from some point1 marked as his starting point on the paper1 proceeds to take sights to any objects he may wish to delineate on his map4 ,these sights are taken by means of the alidade fixed above the board4 ,the sighting rule is pushed along a slotted bar1 which itself slides along a bar at the edge of a board until the edge of the alidade is against the starting point and is sighted on the object aimed at4 ,the object is sighted in a small mirror fixed at the end of the alidade and aligned with the point at its other end4 ,the alidade is then clamped into position with the thumb-screw on the slotted bar and the operator draws his ray corresponding with the direction of the object aimed at4 ,the distance is then marked off on the scale on the alidade4 7#e7 ,when the operator moves to the next station no back-sight is necessary4 ,he at once puts the board into its relative correct position by merely revolving it until the magnetic north line is again lying over the top of and aligned with the compass needle and he then proceeds to take all necessary sights at that station4 ,illustration3 ,fig4 #cbi4--;,cavalry sketching case4 #gac4--;,cavalry ,sketching ,case4--,this forms a very convenient exploring sketching board1 permitting sketches to be made on horseback while en route4 ,the pattern shown in ,fig4 #cbi is that of ,captain ,w4 ,vernier4 ,it consists of a small board #i inches by #g inches1 at two sides of which there are small rollers to hold paper #g inches wide and from #c feet to #f feet in length1 according to its thickness4 ,two stout indiarubber bands1 which hold a small straight-edge to scale in any position on the paper with sufficient firmness to be able to draw a line against it1 are passed over the board4 ,a small compass on one side of the board indicates direction4 ,after one sketch is made1 a new part of the paper is rolled forward4 #gad4--;,camera ,lucida--,optical ,compass4--,in new countries where landmarks are not clear a sketch of the general aspect of the country will make the points of triangulation more clear4 ,where the plane table is not used these sketches may be made with accuracy as to positions by the use of the photograph camera1 the camera lucida1 or points of observation may be taken in correct bearing by the optical compasses4 ,these latter instruments are described in the author's ,treatise on ,drawing ,instruments1 seventh edition4 ,,footnotes3 #ea ,proc4 ,inst4 ,civil ,engineers1 vol4 xciii4 part iii4 paper ,no4 #bcjh4 ,see also ,military ,surveying in the ,field1 by ,major ,the ,hon4 ,m4 ,g4 ,talbot1 ,prof42 ,papers ,royal ,engineers1 vol4 xiv4 p4 #be4 #eb ,patent ,no4 #abjb1 ,d4 ,r4 ,edgeworth1 ,april #ahff4 #ec ,heather's ,surveying ,instruments1 #ahgj1 p4 #he4 ,,chapter ,,xvi4 ,,instruments ,,for ,,measuring ,,land ,,and ,,civil ,,works ,,directly--,,chains--,,various ,,tellers--,,standard ,,chains--,,arrows--,,drop ,,arrow--,,vice ,,for ,,adjusting ,,chain--,,caink',s ,,rule ,,for ,,inclines--,,steel ,,bands--,,wire ,,land ,,measures--,,compensation ,,systems--,,linen ,,tapes--,,offset ,,rods--,,pine ,,standard ,,rods--,,rods ,,with ,,iron ,,core--,,beam ,,compass ,,rods-- ,,coincident ,,measurements--,,compensated ,,rods--,,base ,,line ,,apparatus--,,coast ,,survey ,,lines--,,perambulator--,,pedometer--,, passometer--,,sounding ,,chains-- ,,sounding ,,lines--,,telemeters--,,hand ,,rods--,,rules4 #gae4--,the ,instruments ,generally ,employed for ,measuring ,land are chains1 steel bands1 and tapes4 ,where roads are roughly measured1 pedometers are commonly used4 ,where very exact measurements are required1 rods have been used4 ,rough approximate measurements are obtained by stepping1 with the use of the passometer to count the steps4 #gaf4--,land ,chains4--,although these are made in many qualities the forms vary very little4 ,they are too well known to need much description4 ,in the ,british ,isles and some of our colonies the chain of #ajj links1 equal to #ff feet1 the invention of ,edmund ,gunter about #afbj1 is generally used1 #aj square chains 7#ajj1jjj square links7 giving the statute acre1 presenting a decimal system of measurement much in advance of any other at the present time4 ,the best land chains are made of steel1 which is afterwards hardened and tempered to spring temper1 in the process of which the surface is burnt off with asphalt varnish in order to produce a covering to resist the rusting effects of moisture4 ,steel chains are made light and strong4 ,the light chain1 of ,no4 #ab ,birmingham wire gauge1 weighs under #e lbs4 ,the strong chain1 of ,no4 #h ,b4,w4,g41 weighs about #ab lbs4 ,a light chain of #ej links1 of weight under #c lbs41 is sometimes used with the complete chain of #ajj links for taking offsets4 ,illustration3 ,fig4 #ccj4--,land chain and arrows4 ,all the best chains1 whether of steel or iron1 are made with long links formed by turning up the ends of a length of wire4 ,three small oval links are placed between each pair of long links4 ,these three interval links are found to cause the chain to kink less than when only two are used4 ,each oval link is sawn through at the meeting line1 which is brought up on one flat side of the oval in bending it from the wire4 ,the saw-cut forms the point of adjustment4 ,the small link is afterwards re-sawn and closed to shorten it1 or forced open to lengthen it4 ,there are generally four swivels in the length of the chain1 two of which are at the handles3 these prevent the chain from becoming twisted in turning the handles over in use4 ,a swivel is shown ,fig4 #cca at ,s4 ,iron chains are sometimes galvanized to prevent rust4 ,this process1 however1 makes the chain much more brittle1 and cannot be recommended4 ,it may be noted that all link chains lengthen with use4 #gag4--,tellers are small pieces of brass suspended to the chain by a spare link placed at every ten links4 ,they divide the chain decimally from either end equally4 ,proceeding from one end of the chain the tellers read #aj1 #bj1 #cj1 #dj1 #ej1 and the other end they read by subtraction from the complete chain3 #ajj - #aj #ij1 #ajj - #bj #hj1 #ajj - #cj #gj1 and #ajj - #dj #fj4 ,fig4 #cca shows detached pieces of chain with value of the tellers figured under4 ,s inserted swivel4 ,the #ej teller shows the link attachment4 ,a shows the position at which the arrow or other mark is placed to commence or finish the chain measurement1 the handle being included in the first link4 ,these tellers are liable to catch and get dragged off in chaining4 ,when this chain is used abroad1 or far from home1 it is well to have an extra set of tellers to repair losses4 ,illustration3 ,fig4 #cca4--;,gunter's land chains4 #gah4--;,inserted ,tellers4--,this form of teller is preferred by many1 ,fig4 #ccb4 ,it is much less liable to get dragged off1 but it is not considered quite so distinct1 and it is a little liable to get clogged with grass and weeds4 ,illustration3 ,fig4 #ccb4--;,inserted tellers4 #gai4--,the author's design for inserted tellers is shown ,fig4 #ccc4 ,these are perhaps quite as distinct as the last4 ,the holes in wet weather fill up with mud and the surfaces keep bright1 so that they remain very readable4 ,there is much less drag1 and the chain therefore wears longer4 ,illustration3 ,fig4 #ccc4--,stanley's inserted tellers4 #gbj4--;,feet ,chains are usually made #ajj feet1 more rarely #ej feet4 ,they are generally made in foot lengths1 but sometimes for flexibility are preferred in #f-;inch lengths4 ,they are commonly made of ,no4 #h ,b4,w4,g4 steel or iron4 ,the weight of #ej feet is #f lbs42 #ajj feet1 #aa lbs4 ,if made of light steel1 ,no4 #ab ,b4,w4,g41 the #ajj feet weighs #f lbs4 #gba4--,mining ,chains used in mineral districts are made generally #aj fathoms1 or #fj feet1 #f-;inch links counted off by tellers in fathoms4 ,they are made entirely of brass4 ,the weight is about the same in brass as steel--,no4 #h ,b4,w4,g41 #i lbs4 ,occasionally they are made extra strong1 ,no4 #g ,b4,w4,g42 weight #ab lbs4 ,in coal mines ,gunter's chains are generally used4 #gbb4--,metre ,chains are made #bj or #be metres long4 ,they are marked with tellers at every two metres with a plain ring at the metre4 ,the tellers are generally of the inserted kind1 ,fig4 #ccb4 ,in taking measurements the sign of the teller is doubled3 thus the ordinary #a or #aj is counted #b metres2 the #b1 #d1 and so on4 #bj-metre chains in light steel1 ,no4 #ab ,b4,w4,g41 weigh #d lbs42 strong1 in ,no4 #h ,b4,w4,g41 #i lbs4 #be-metre1 light1 #f lbs42 strong1 #aa lbs4 ,a land chain is generally secured for carrying by a leather strap with a buckle4 ,occasionally it is carried in a sailcloth bag with a strap over the shoulder4 #gbc4--,standard ,chains4--,these are of the same form as the ordinary steel chain1 but all the links are hard soldered after being adjusted link by link4 ,they are not intended to be used for regular chaining1 except it be for laying down rough base lines4 ,their special employment is to test chains1 or to set out with two pegs on a straight piece of ground a standard length or station where the common chains in use may be tested daily4 ,a standard chain is commonly enclosed in a box with a lock to prevent its accidental use for an ordinary chain4 #gbd4--;,arrows4--,these are sometimes called pins4 ,ten form a set4 ,they are shown with the chain in ,fig4 #ccj1 and are commonly made of the same wire as the chain--,no4 #h ,b4,w4,g4 ,they are much better made one gauge stouter 7equal to about #a_/g inch71 and preferably of hardened steel than of iron4 ,the common length is #ae inches4 ,where heath1 stubble1 or woodlands prevail #ah-;inch are better for use1 and in some exceptional cases even #b-;feet are very convenient4 ,surveyors going to new countries are recommended to take the longer arrows as well as those supplied with the chain4 ,it is common either to tie a short length of scarlet webbing upon each ring of the arrow or to sew a piece of red flannel or bunting upon it to find it easily in long grass4 ,arrows are sometimes carried in a quiver with a strap over the shoulder1 ,fig4 #ccd1 which leaves the hands of the fore chainman free to remove obstructions where they occur4 #gbe4--;,drop ,arrow1 ,fig4 #cce4 ,where ground is very hilly it is common to roughly level the chain by holding the lower position shoulder high1 either by guess work or by using any kind of rough hand level or clinometer to ascertain this4 ,the arrow is then dropped1 and the point1 held at first lightly in the ground1 is pressed hard down or another arrow supplanted for it4 ,the chain in this case is used in odd multiples of links as they occur1 of which record is taken separately at each station4 ,in going downhill a drop arrow answers very well4 ,in going uphill a plummet to the last arrow is better4 ,some use the drop arrow as a plummet1 carrying for this purpose in the pocket a piece of fine whipcord1 with a bent hook tied to one end1 to be used when required4 ,illustration3 ,fig4 #ccd4--,quiver with arrows4 ,illustration3 ,fig4 #cce4--;,drop arrow4 #gbf4--;,examination and ,adjustment of ,chains4--,respectable makers send out chains tested to within half of one of the small links of standard1 that is1 within a quarter of an inch2 but in use this error may increase either by the bending of the long links of the chain1 when it becomes shorter1 or in the more general case of friction from wear and from strain1 by which it becomes longer4 ,in ,london1 standards are fixed upon the pavement in ,trafalgar ,square and at the ,guildhall4 ,these standards are also fixed at many municipal town halls4 ,surveyors very commonly lay down a standard on the pavement1 or by pegs on a level gravel path4 ,where a peg is used it should be driven home nearly to the surface4 ,it should if possible be made of a piece of heart of oak #ab inches long and about #b inches square4 ,the standard length1 which may be set off by a standard chain or new steel tape1 should be from a saw-cut across the centre of one peg to a similar cut on the other4 ,it is well also to have the centre space 7#ej links7 indicated by a smaller peg4 #gbg4--,the ,chain to be ,adjusted should be first examined and its long links set straight by means of a hammer on a flat1 hard stone or anvil1 after which the error will be1 if it has been much used1 that it is too long4 ,it should be then laid in direct line on the standard just described1 and stretched lightly with a pull of about #g lbs41 and then left to rest4 ,assuming it too long1 the centre of the chain should be observed to ascertain which half is of the greater length1 then short links should be taken out at distributed distances1 if more than one be required1 by twisting the link open in a vice1 and opening and closing another link to restore the chain4 ,illustration3 ,fig4 #ccf4--,stanley's vice for adjusting and repairing land chains4 #gbh4--;,chain ,vice4--,the links of steel chains can seldom be twisted open without breaking1 and broken links cannot be restored by steel links4 ,iron links answer1 but they are very stiff to twist open4 ,generally it will be found best for professional men to repair the chain with spare brass links4 ,these wear very well4 ,where a smith is near with his vice and a light hammer the links are readily opened4 ,it often occurs in open districts and abroad that no smith's shop is to be found4 ,to meet these cases the author has constructed a special vice1 as shown ,fig4 #ccf4 ,this vice is let into a piece of hard wood--an old oak post answers admirably4 ,in stone districts it is perhaps better to let it into a stone and fix it by pouring hot lead round it4 ,the part ,b is used for an anvil for straightening the links4 ,the vice ,v holds the link edgewise very firmly by bringing up the slide ,j by means of the screw ,s4 ,the link may then be knocked open by the pane end of a light hammer4 ,the link is closed again in the same manner4 ,if the vice be left out of doors the screw should be well greased and the whole covered with a leaden cover4 ,the weight of the vice is about #f lbs4 ,it is made of cast iron with chilled face1 or the jaws are faced with steel4 #gbi4--,opening and ,closing the ,chain for ,use4--,the chain is most readily unfolded by taking the two handles in the hand and walking away from it as it lies on the ground4 ,it is most convenient to place it about #de1 and half a chain length from the first station1 each chainman taking a handle and moving to his position4 ,the only danger in undoing a chain is from two chainmen taking one handle each and walking in opposite directions1 in which case1 if there happens to form a kink1 the opposite movement of the two men will probably stretch or break the chain4 ,in closing the chain it is taken by the middle links and folded up two links at a time till the handles are reached4 ,if the links be placed consecutively in position round the axis formed by the first links1 it may be folded up very compactly in a twisted form ready for the strap1 by which it is carried1 to be passed round it4 #gcj4--;,chaining is performed by two chainmen1 termed the leader and follower4 ,the follower1 having pressed a stake into the ground for a starting point1 then places the centre of the outside of the handle of the chain against it4 ,the leader takes ten arrows in his right hand and one handle of the chain in his left1 and walks directly towards a point which is to be the termination of the measurement1 stopping at nearly the length of the chain1 examining the chain to see that it is straight4 ,he then places an arrow lightly outside the centre of his handle4 ,the follower looks over this arrow to the distant station to see whether it is in direct line4 ,if it be not so1 he waves his right or left hand once1 twice1 or thrice for #a1 #b1 or #c inches for movement to right or left4 ,the follower picks up the arrows consecutively as left by the leader1 and when he has the ten1 #aj chains have been measured1 which is then recorded in the field-book1 or earlier than the ten if a shorter distance or object completes the measurement4 ,it is most important to observe that if an arrow be taken for the first station1 the follower having ten counts nine only for the first ten4 ,to prevent accident it is therefore safer to start from a stake or other landmark1 not one of the arrows4 ,some surveyors advise eleven arrows4 ,if eleven be used1 one should be distinctly marked from the rest so as never to be counted4 ,this may be done by omitting the red webbing tie1 or using a green tie for the odd arrow4 ,the ,french always make the drop arrow the eleventh arrow1 which is never counted in direct chaining4 ,illustration3 ,fig4 #ccg4--;,caink's rule for correcting inclines4 #gca4--;,caink's ,rule for correcting inclines in chaining is the invention of ,mr4 ,thos4 ,caink1 ,c4,e41 of ,malvern1 ,fig4 #ccg4 ,it is made four-fold1 each fold being one link4 ,the link is divided decimally along the inside of the rule4 ,on the outer edge of the rule there is a scale marked degrees1 a part of which is subdivided where the scale is open to read closer1 that is1 to #bj or #cj minutes4 ,these degree divisions1 which read up to #af on one side of the rule1 indicate the space from the end of the rule to be allowed in addition for the same degrees of inclination of the land up to #d links of measurement4 ,on the opposite side of the rule the inclination scale is carried from #af to #bb #aj4 ,for these higher numbers the length of the rule is first set off1 and then plus such part of the rule as is indicated by the position marked upon it of the required number of degrees4 #gcb4--,to ,use ,caink's ,rule4--,the follower has a clinometer of one of the kinds shown1 ,figs4 #bfj or #bfd4 ,he notes at starting the position upon the face or body of the leader that corresponds with the height of his own eye4 ,he takes the inclination of the land to this point of the leader's body while he is standing upright at one end of the chain and the leader standing at the other1 noting the number of degrees shown by the clinometer4 ,he then places the rule in the direction of the chain1 with the number of degrees indicated1 in front of the arrow1 and moves the handle of the chain to this position4 ,for the sake of verification1 if he has a second arrow he may place it in the new position1 which gives the true allowance4 ,in either case the leader moves the chain forward by the amount required and places his arrow ready to continue the work4 ,by this method it is seen that there is no after calculation or separate record necessary for undulating land1 but the true horizontal position is given correctly at each chain measured4 ,the same form of rule is made for feet and metres4 #gcc4--;,in mountainous countries the eight links of the rule is insufficient allowance for common inclinations4 ,such countries are measured much more accurately by some system of subtense measurement1 for which see ,chapter ,,xii42 but where a small piece of sudden steep inclination occurs half a chain may be taken1 and the number of degrees indicated upon the rule be doubled1 so that the full rule1 instead of taking #bb only1 will take #dd4 #gcd4--,steel ,bands for measuring1 termed steel band chains1 are made in various forms in this country1 and sold by nearly all opticians4 ,they are much lighter than chains of equal strength1 and are made of standard length4 ,they are also lighter to use1 being smooth and without any projection4 ,on the other hand the reading is less distinct than with the chain1 and they need more careful usage in chaining4 ,they also require oiling before being put by4 ,from the thinness of the metal they are altogether more delicate and less durable than the chains for hard wear2 but it is thought by many to be a compensation that they are always of true length4 ,illustration3 ,figs4 #cch1 #cci1 #cdj4--,steel bands and tapes4 ,illustration3 ,fig4 #cda4--,one link of steel band4 #gce4--,the bands commonly used for land measuring are made #c_/h1 1 #e_/h1 and inch wide1 of ,nos4 #bf and #bd ,b4,w4,g4 in thickness1 respectively4 ,the chain is divided into links by a small stud riveted through the centre of two small washers1 a large stud being placed at the fives and an oval plate held by two rivets at the tens1 which are numerically indicated in plain engraved figures1 as shown in detail1 ,fig4 #cda b1 or perforated with holes indicating the number of tens4 ,these band chains are made in links1 feet1 metres1 or to any foreign measure to order1 and of any length corresponding with land chains4 ,weights1 approximately--#ajj feet3 inch1 #g lbs42 #e_/h inch1 #d lbs42 inch1 #d lbs4 #ajj links3 inch1 #d lbs42 #e_/h inch1 #b lbs42 inch1 #b lbs4 #bj metres3 inch1 #e lbs42 #e_/h inch1 #d lbs4 #gcf4--,steel band measures are also made with divisions throughout1 etched upon them with acid in such a manner that the divisions and figures stand in relief up to the original surface1 whereas the new surface1 which is etched back to form the ground1 appears dull4 ,the brightness of the figures and divisions on the dull ground makes them easily read4 ,these bands are divided into links1 feet and inches1 metres and decimeters1 or closer quantities either on one or both sides of the band as required4 ,with the etched band there is perhaps a little risk of weak places from over-etching1 although these bands are most carefully made1 but perhaps this is not greater than in the inserted stud band1 where weak places are necessarily caused by the loss of width at the points where the holes are made for the studs1 wherein moisture hides after use in damp weather4 #gcg4--,the steel bands have handles the same as a land chain4 ,they are wound upon a steel cross1 ,fig4 #cdj4 ,they are commonly placed in a wind-up case similar to that of an ordinary measuring tape1 but in steel1 provision being made that one of the pair of handles may be secured about the position of the axis of the tape for winding it up4 ,in ,fig4 #cch the axis is made very large1 so that the handle may be pressed in from an opening in one side of it4 ,the newest idea is to cut a slit in one side of the plate up to the centre1 as shown1 ,fig4 #cci4 ,in this case the handle and band are put in from the side1 so that the axis is no larger than is necessary to take the handle4 ,a strap is placed on the side of the case for holding it4 ,this is shown cut off to admit sight of the handle4 #gch4--,the ,french make the handle generally ,t-shaped and hollow in the cross part1 which renders it very light and perhaps less cramping to hold4 ,the arrows are very commonly held by loops to the cross on which the band is wound4 ,this general arrangement is very portable and convenient to carry2 it is shown ,fig4 #cdb4 #gci4--,wire ,land ,measures4--,where long open stretches of new country are to be measured1 it is common to employ a steel wire chain1 of #e chains or of #ejj feet in length1 fitted with a pair of strong cross handles only4 ,illustration3 ,fig4 #cdb4--;,french land measure4 ,illustration3 ,figs4 #cdc1 #cdd4--,marchant's #ejj-;feet band4 #gdj4--,the author has made many chains of #ejj links2 in ,fig4 #cdd a part of one is shown full size4 ,this band1 as we may term it1 is wound upon a reel in an iron case1 ,fig4 #cdc4 ,a spring brake is placed at the position ,a1 which holds the reel and prevents the band from springing out into loose hoops when it is run out4 ,the #ej and #ajj links are indicated by short lengths of brass tube placed over the band--single at the #ej links1 but numerically indicated by number of bands as #b1 #c1 and #d chains4 ,in ,fig4 #cdd a #ej and a #cjj links are shown2 weight1 #c lbs4 ,this flat1 narrow1 steel band chain was unknown until introduced to the notice of the profession in the first edition1 #ahij4 ,it is now in very general use1 and lengths may be had from stock of #b1 #c1 #d1 or #e chains1 or #bjj1 #cjj1 or #djj feet wound upon a steel cross4 ,illustration3 ,fig4 #cde4--,richmond's tension handle4 #gda4--,richmond's ,tension ,handle4--,various devices have been employed for giving equal tension to chains and bands to ensure equality of measurements4 ,salter's spring balance has been very commonly used attached to one handle of the chain to give a uniform pull1 say of #ae lbs4 ,this appears to answer very well4 ,mr4 ,richmond1 surveyor1 of ,sydney1 has devised a very simple plan for tension of light bands1 which1 being lighter and attached1 is much more convenient than ,salter's balance4 ,this is shown ,fig4 #cde4 ,the band passes through a fitting in the centre of the handle1 and a spiral spring is fixed to this and the band at a short distance along it4 ,by pulling the handle a given tension can be applied1 which is shown by the mark it reaches towards the end of the band4 ,this is adjusted to standard length1 and a small notch is placed in the centre of the end1 from which a plummet may be suspended if necessary4#ed ,the engraving is of a slightly modified form by the author1 in which a thin tubular cap covers the free end of the band to save this exposed part from accidents4 ,illustration3 ,fig4 #cdf4--;,copper case thermometer for suspending to a band chain4 #gdb4--;,chain and ,band ,thermometer4--,where very great accuracy of chain or band measurement is aimed at1 temperature is taken to allow for expansion of the metal4 ,a thin plain glass thermometer of the clinical form is the most sensitive of any4 ,this is carried in a wooden pull-off case lined with indiarubber4 ,when it is used it is placed upon the ground by the side of the chain4 ,the delicacy of the clinical form of thermometer is often objected to by the practical surveyor1 hence there are several other forms with boxwood and ivory scales4 ,these are not very satisfactory1 as the boxwood and ivory retain the heat of the body1 from being carried in the pocket1 for a long time after exposure4 ,the author has enclosed the clinical form of thermometer in a copper case with open face1 ,fig4 #cdf4 ,the copper being a good conductor of heat1 this is very sensitive to the temperature of the air4 ,two turn-down hooks are placed at the ends of the tube to suspend it on the band4 ,the thermometer stem has two indiarubber caps1 so that it will bear dropping on grass4 ,it is contained in the same form of pull-off case as the clinical4 ,illustration3 ,fig4 #cdg4--,littlejohn's temperature handle4 #gdc4--,the coefficient of expansion for steel between #cb and #bab ,fahr4 is about #jjjjab1 which is less than #ja inch per degree per chain4 ,temperature corrections can therefore be recognised only upon very exact work1 appreciable only when long bands of the ,marchant type1 lately described1 of from #e chains to #aj chains in length are used4 #gdd4--,mr4 ,littlejohn has patented an adjustable handle for temperature4 ,this is divided for allowance for the #ajj-;feet or other band for every degree ,fahr4 or centigrade4 ,fig4 #cdg4 ,the handle is set to the temperature as it changes during the day4 ,it offers1 perhaps1 the highest refinement in ordinary land measurements4 ,illustration3 ,fig4 #cdh4--,stanley's repairing sleeve4 #gde4--,repairing ,sleeve for ,steel ,bands4--,the reviser has patented a sleeve which will be found useful1 as by its use a broken band can be immediately and permanently repaired in the field without the use of tools4 ,they are made to fit all sized bands1 but it is necessary that the correct sized sleeve should be used4 ,one of these sleeves is shown attached to a band at ,fig4 #cdh4 ,in order to effect a repair it is merely necessary to clean the broken ends of the band1 and insert them into the sleeve1 then hold a lighted match under it until the soldering material is melted1 when the repair is completed4 ,the central hole in the sleeve is to enable the user to see when the broken ends are in contact1 and the other two are to indicate when the soldering material is melted1 which takes place when it either bubbles up in or runs away from these holes4 ,illustration3 ,fig4 #cdi4--,linen ,tape4 ,illustration3 ,fig4 #cej4--,small steel pocket tape4 #gdf4--,linen ,tapes4--,this most useful implement1 ,fig4 #cdi1 is one of the most unsatisfactory measures the trader and user has to do with4 ,it consists1 as is well known1 of a tape oiled1 painted1 and varnished1 which is rolled up in a leather case when out of use4 ,when the weather is moist it shrinks1 and when dry it expands4 ,if it be too heavily painted it becomes brittle and rotten2 if it be lightly painted it remains more flexible1 but is more affected by moisture4 ,a good tape bears very well a stretching force of #g lbs4 to #ad lbs41 but if strained over this it is permanently stretched4 ,there is no plan known to the author by which these defects can be remedied4 ,numerous attempts have been made--often valueless or worse--some1 although popular1 mere claptraps1 such as the insertion of wire4 ,the best tapes for strength and permanency are made entirely of green1 hand-made1 unbleached flax4 ,the tape is said to come from ,holland to this country4 ,these are at first oiled with a drying oil 7boiled linseed oil71 and when seasoned for a month or so1 painted once or twice with white lead colour--not too thickly4 ,the printing is more permanent if done in oil2 but the tape is somewhat more flexible if the figures are stencilled in ,indian ink and the whole afterwards thinly varnished over with copal varnish4 ,the great secret for preserving the tape is to use it very carefully and only in fine weather4 ,in wet weather for taking offsets a light steel #ej-link chain is quite as convenient as the tape1 and safer4 ,tapes are divided into links1 feet and inches1 metres1 and all measures as required4 ,a decimal yard is commonly placed on tapes for measuring earth work4 ,for use with the chain a #ff-;feet tape is usually employed1 but many think a #cc-;feet better1 using the chain for dimensions above this4 ,for measuring buildings1 #ej-;feet or #ajj-;feet tapes subdivided to inches are employed4 #gdg4--,steel ,tapes4--,thin steel tapes1 #c_/h1 1 and #e_/h inch wide are in very extensive use4 ,they are more accurate and more costly than linen tapes1 but less flexible and less durable4 ,where dimensions are important they should always be used for short measurements4 ,in all cases it is advisable for a surveyor to keep a steel tape for examination of the lengths of linen tapes in use4 ,they are made to all the measurements of linen tapes4 #gdh4--,pocket ,steel ,tapes #f feet to #ab feet1 ,fig4 #cej1 are used more generally by mechanical engineers4 ,these tapes1 which are very light1 are held open by a catch1 and closed by a spring4 ,illustration3 ,fig4 #cea4--;,jointed offset rod1 top and centre4 #gdi4--,offset ,rods are generally made #aj links long1 either in one piece or jointed in the centre with a bayonet joint4 ,they are about #a-a_/h inches in diameter1 diminishing towards the top to #g_/h inch1 and made either of yellow pine or ash4 ,a hook is commonly put at the top1 ,fig4 #cea1 which takes the handle of a chain to draw it through a hedge or other obstruction4 ,the author's plan of making this is shown at ,h4 ,the lower end of the offset is shod with a steel or wrought iron socket point1 so that it may be set up in the ground and used if required as a picket4 ,bands are painted alternately black and white at every link4 ,square or flat rods are occasionally used for the same purpose1 but they are not generally so convenient4 ,the offset is ,used in the manner of an ordinary rule to take rectangular short measurements from the chain as it lies upon the ground1 commonly in order to obtain the contour of irregular outlines4 #gej4--,measurement by ,rods has become less general than formerly1 from the greater accuracy of ,konstat or ,invar steel tapes1 by which practically correct base lines may be laid down4 ,for geodetic works requiring the greatest accuracy the bases have been laid with rods of various forms4 ,these rods will be briefly described4 ,it is only in the construction of iron bridges1 roofs1 etc41 that rods are at present generally employed in the work of the civil engineer4 #gea4--,pine ,standard ,rods1 made of straight-grained pinewood seasoned five or six years and then well soaked in linseed oil1 make good standard rods4 ,the ordinary length in use is #aj feet by #a inches square4 ,if the rod be used for butt measurement the ends are tipped with gun-metal in which a turned steel stud is hard-soldered4 ,the stud is afterwards ground to true face in a lathe1 and left of standard length at #fj ,fahrenheit 7#aee centigrade71 ,fig4 #ceb4 ,a disc of brass #a inch diameter is inlaid at every foot for #e feet from one end of the rod1 with a line at the true foot4 ,these rods1 after the work upon them is finished1 are lightly ,french polished to keep them clean and to prevent the effects of moisture4 ,the effect of temperature upon deal was found by ,roy to be about the same as upon glass--#jjjjjhe1 average of total length per degree centigrade1 which is about three-fourths that of iron4 ,illustration3 ,fig4 #ceb4--,one end of a pinewood butt rod4 ,illustration3 ,fig4 #cec4--,s--,block square4 #geb4--,where butt rods are used for continuous measurement1 it is necessary that they be brought very carefully together4 ,in base line measurement three or four are used1 but for metal work or masonry two #aj-;feet only are generally employed4 ,it is necessary that the rods should lie upon a straight surface or be supported in a straight line4 ,in bringing them together1 a piece of indiarubber #a_/h inch or so in thickness temporarily placed at one end will prevent any palpable disturbance of the percussion if the fixed rod be well weighted4 ,one #e-;feet more fully divided butt rod is very commonly supplied with a pair of #aj-;feet rods for supplemental measurement4 #gec4--;,angle-piece4--,a solid angle-piece with two planes at right angles is very convenient for use with butt rods to give means of scribing the true length down to a surface1 ,fig4 #cec ,s4 #ged4--;,butt ,rods with ,iron ,core4--,where rods are to be used for preparing iron work it is better to have an iron core through the rod1 that may expand and contract with the metal on which they are used4 ,the rods that the author has designed for this purpose are made out of a length of seasoned pine #b inches square1 sawn down and turned cut sides outwards to prevent warping4 ,a #aj-;feet length of iron steam tube about inch diameter is painted several times and then bound round with paper soaked in paraffin4 ,this is placed in a pair of meeting grooves1 as shown in section ,fig4 #cee4 ,the two pine flitches are cross-tongued together and glued up with the inserted tube between them4 ,the tube has a turned steel cap placed over each end1 ,fig4 #ced1 and this is ground in a lathe to true standard at the temperature of #fj ,fahr4 ,a steel pin is placed through the centre of the rod to indicate #e feet4 ,the finished size of the rods is #b inches square4 ,the author has made these rods in sets1 consisting of two #aj-;feet and one #e-;feet packed together with an angle-piece1 ,fig4 #cec ,s1 in a deal case4 #gee4--,the #e-;feet ,rule is of steel1 inch by inch1 inlaid in a piece of dry pine1 altogether of only half the thickness of the rods1 so that it stands the correct height for central butt measurement1 ,fig4 #cef4 ,the rule is divided into feet and inches1 with one foot to eighths4 ,a centigrade thermometer is placed in one of the rods to indicate the prevailing temperature1 and a small piece of scale showing amount to be allowed in #aj feet per degree centigrade for temperature above or below #aee centigrade is engraved upon the thermometer scale4 ,the coefficient for the expansion of wrought iron is given by ,lord ,kelvin as #jjjjai mean per degree centigrade4 ,illustration3 ,figs4 #ced1 #cee1 #cef4--;,butt rods with iron core4 ,where a long length is laid down for a base line or other purpose1 it is better to take the thermometer reading at each measurement and defer correction to the completion of the work2 the temperature errors may then be added together as a total1 and the space allowance may become a measurable quantity4 ,for example1 say ten #aj-;feet lengths give by these united centigrade degrees1 plus and minus1 shown at separate readings #afg1 and that the standard of the rods is true at #aee4 ,then #afg - 7#aj #aee7 #ab per foot total allowance1 that is1 #ab #aj feet #jjjjai #jbbh feet or #bgcf inches to be added4 ,in measuring iron of course no correction has to be made4 #gef4--;,beam ,compass ,measurements are occasionally preferred for iron work4 ,in this case the beam is moved from centre punch mark to mark along a surface by the beam producing a scratch for the forward position in which to place the punch mark4 ,rods of pine are commonly employed4 ,figs4 #ceg1 #ceh will sufficiently illustrate the instruments4 ,illustration3 ,fig4 #ceg4--;,beam compasses4 ,illustration3 ,fig4 #ceh4--,standard scale4 ,illustration3 ,fig4 #cei4--;,coincidence rods4 #geg4--,the ,method of ,coincidence in measurements by rods has often been applied to measurement of base lines4 ,the plan consists in allowing one rod1 or a lighter continuous part of it1 to pass the other rod1 so that a line cut to standard on one rod may be read into one on the other4 ,the best plan to do this is to have a scale fixed along the face of one rod near its end1 as shown ,fig4 #cei1 and to have an extension from the other end of the second rod to pass alongside this scale1 so that two lines may be brought into coincidence4 ,the rod ,b has a fixed scale b placed on top of it at one end4 ,the rod ,a has a scale protruding from it4 ,this scale may be jointed with a good ground joint at ,j for portability4 ,the rods are laid lightly together1 and any final adjustment is given by light taps with a small hammer or mallet upon one or the other side of the stud ,p until exact coincidence of the lines shown at b is brought about4 ,this tapping operation appears a rather rough process1 but practically it is very exact4 ,illustration3 ,fig4 #cfj4--;,bessel compensated rod4 #geh4--;,compensated ,rods4--,the plan used by ,bessel for the measurement of a base upon the shores of the ,baltic in #ahcf is looked upon as a model of the most perfect work of its kind4 ,the rods were composed of two bars of iron having surfaces accurately planed1 with a similar bar of zinc placed between them4 ,the bars were laid one on the other1 but not in contact1 the surfaces being kept apart by glass plates1 upon which they could slide with little friction4 ,the linear expansion of zinc per degree centigrade is about #jjjjbib 7,fizeau72 that of iron much less than half this--about #jjjjaai 7,thomson74 ,the bars are attached to each other in such a way that the expansion of the zinc may act in the opposite direction to the expansion of the iron4 ,the form followed for the construction is shown in ,fig4 #cfj where ,,ii are the iron bars1 ,z zinc4 ,the length of the zinc required for compensation between the junctions is found in the equation-- 7,s ,z77#jjjjaai7 - ,z7#jjjjbib7 #j1 ,s being the total length of the standard rod in feet1 and ,z the length of zinc in feet required for compensation4 ,this plan is that adopted for the compensation of pendulums4 ,for the verification of a rod it may also be made to form the rod of a pendulum1 by which temperature expansion and contraction upon the system will be clearly indicated by difference of time rate in the change of temperature during night and day4 ,this test becomes important where great precision is aimed at1 as the expansion in metals varies according to their purity and state4 ,the standard lines in rods made upon this model are placed upon small inserted discs of platinum placed near the ends1 which are read by microscopes in coincidence upon a pair of rods4 #gei4--;,colby ,compensated ,rods1 the invention of ,major-,general ,t4 ,f4 ,colby1 who was for twenty-seven years superintendent of the ,ordnance ,survey1 upon which these rods were used4 ,each rod is composed of one rod of iron and one of brass1 which are so arranged in pairs that the difference of expansion of these metals shall act to diminish the amount of entire expansion at the points measured1 a quantity equal to its increase by temperature1 in a manner to be described4 ,the ,rods are each made #aj feet #ae inches long1 #e inches broad1 and #ae inches deep4 ,fig4 #cfb i is a side elevation of one rod1 ,fig4 #cfc ib plan of iron and brass rods1 ,fig4 #cfe ib perspective view4 ,by this it will be seen that the rods are placed edgewise4 ,the distance apart is #aabe inches4 ,they are supported in the middle upon rollers1 ,fig4 #cfb ,f4 ,they are firmly fixed together at their centres by transverse steel cylinders1 ,fig4 #cfc ,,rr #ae inches diameter1 each rod being left free to expand or contract from the neutral central point independently of the other4 ,the neutral point is formed of a ,t-piece ,e1 ,fig4 #cfc1 fixed firmly on the bottom of the box bx4 ,at the extremity1 and at right angles to each of these bars1 is a flat steel tongue1 ,figs4 #cfd1 #cfe ,a1 #fb inches long1 #aa inches broad1 and #jbe inch thick1 which projects #cbe inches from the side of the iron bar i4 ,the tongue ,a is jointed by double conical pivots at f and f1 which form axes perpendicular to the surface of the tongue1 allowing it to be inclined to slightly different angles to the direction of the bars according to the expansion or contraction the system experiences by heat4 ,the pivots are #je inch diameter1 and are placed at #bc inches from the end of the tongue next the brass bar4 ,on the tongue at ,p1 flush with its upper surface1 a small stud of platinum is inserted1 upon which a small dot is struck to form the point of standard measurement4 ,illustration3 ,colby ,compensated ,measuring ,rods4 ,fig4 #cfa4--;,end of rod mounted with microscopes1 trestles and ground plate4 ,the bars are placed in strong wooden boxes1 to the bottoms of which are fixed the plates that hold the brass rollers upon which the bars are supported1 ,fig4 #cfb ,f1 and the central stay ,e mentioned before prevents any displacement of the bars when the rods are held by the rollers ,,rr4 ,to protect the tongue ,a1 which projects beyond the boxes1 there is a special covering nozzle having a hole and cover over the dot4 ,a level is placed on one of the bars1 which is seen through a window in the lid of the box4 ,at the ends of the box plates are fixed for supporting the tripod of the double compensated microscope1 ,fig4 #cfa ,d1 employed to observe the standard points of one pair of rods brought by adjustment to true position ,,mm4 ,a pair of sight vanes which shut down are placed on the ends of the box for setting the rods approximately in line4 ,illustration3 ,colby ,compensated ,measuring ,rods4 ,fig4 #cfb4--,side elevation of point of support of rod4 ,fig4 #cfc4--,side elevation of centre1 with section of box bx4 ,fig4 #cfd4--,plan of rods and compensating arm4 ,fig4 #cfe4--,perspective view of the same4 ,two ,rigid ,tripod ,stands ,fig4 #cfa ,s are used to each of the rods placed under the rollers ,fig4 #cfb ,f upon which the bars are supported in the box4 ,the tripods carry a universal slide-rest by which the rod may be adjusted to position both in horizontal and vertical planes ,fig4 #cfa ,a4 ,six rods were used for the ,ordnance ,survey at one time1 and were designated by the letters ,a ,b ,c ,d ,e ,f4 ,the weight of each rod complete with microscopes in its case is #acf lbs4 ,compensated ,microscopes4--,the compound microscopes1 ,fig4 #cfa ,,mm1 used with the ,colby apparatus form a complete separate instrument1 consisting of two microscopes placed parallel to each other and united together for reading the rods when they are brought with their standard points the distance apart that separates the axes of the two microscopes4 ,in the intermediate space between the two microscopes1 and parallel with them1 a telescope ,t is fixed on the same piece of apparatus1 with adjustment for reading a point on the ground ,g perpendicular to the measuring rod4 ,the microscopes are held apart by two bars of brass and iron #g inches long1 #je inch broad1 and #jcge inch thick1 which are placed at #be inches apart and secured with the telescope1 which forms the fixed centre1 by collars to the bodies of the microscopes4 ,the difference of expansion of the iron and brass maintains the separation of the microscopes at their foci at one distance with every change of temperature of the air4 ,the object-glasses are of #b inches focus4 ,the microscopes are brought to adjustment and bearing by levelling on a tribrach whose base is fixed firmly to one of the rod cases1 and by lateral adjusting screws4 ,special microscopes are used with each of the six rods of the ,colby apparatus1 and are distinguished by the letters ,m ,n ,o ,p ,q ,r ,s4 ,the weight of each compound microscope is #e lbs4 ,very full particulars of the ,colby apparatus with engravings of all parts1 are given in ,the ,ordnance ,survey ,account of the ,measurement of the ,lough ,foyle ,base4 ,in measuring a base line a piece of nearly level land is selected1 and the rods are supported upon the trestles or tripod stands at about #c feet from the ground4 ,the heights of the upper surfaces of the tripods are ranged by a theodolite or level for all intermediate points between the two ends of the line4 ,generally twelve trestles are employed with these rods1 which are fixed firmly to the ground at every station by legs well rammed in1 ,fig4 #cfa ,,hh4 ,the cases containing the rods1 or the rods themselves1 are made sufficiently strong to be supported upon two points only without serious deflection4 ,the ,colby system of measurement of base lines varied in detail has been employed by nearly all the nations of ,europe and in ,america4 #gfj4--,modern ,base-line ,apparatus4--,the introduction of ,konstat steel 7highest grade ,invar7 tapes and wires has revolutionised the method of measuring base lines4 ,these tapes offer a means which is far superior to anything obtained by measuring bars1 because they combine the advantages of great length and simplicity of working1 with more precision than the shorter laboratory standards1 providing that suitable apparatus is used in applying them to their work4 ,base lines may now be rapidly measured with long ,konstat steel tapes so that much longer lines are laid down than was formerly the practice when measured with bars1 with the result that any errors that may be introduced do not affect the ultimate expansion so much owing to the greater length of the base4 ,the coefficient of expansion of ,konstat steel is under #jjjjjje per degree ,fahrenheit1 so that provided accurate means of suspending the tape and reading it and transferring the readings to a plate properly let in the ground are used1 we have a most exact and rapid method for this important work4 ,the tapes are usually #ajj feet or #cj metres long1 but #cjj feet or #ajj metres are often used4 ,the tapes are a few feet longer than these measurements1 so that the rings are well clear of the reading lines4 ,a silk cord is attached to these rings and passes over the end suspension supports1 one of which is shown at ,fig4 #cff4 ,these are made with two steel bars rigidly mounted on two tripods2 upon the bars a sliding carriage is mounted carrying a pulley running on ball bearings with a vertical motion for final adjustment of the tape for height4 ,a weight is attached to the other end of the silk cord to give the same tension as that under which the tape was divided4 ,illustration3 ,fig4 #cff4--,one of the two end supports of the band1 showing tension weight1 with cord running over the ball-bearing pulley4 ,to prevent catenery light intermediate stands1 as shown at ,b ,fig4 #cfg1 are used at about every ten feet2 these have a rising cross piece with guides which are adjustable for height and sideways to support the tape in perfect alignment4 ,having the tape properly suspended the reading instruments1 ,c ,fig4 #cfg1 are placed in position at either end4 ,these are mounted on rigid-framed stands and provided with levelling screws1 cross levels1 transverse screw motions and movement in azimuth1 with clamp and tangent motions and aligning telescopes4 ,a powerful microscope is rigidly fixed over a little table over which the tape passes and reads its division with great exactness1 coincidence with the division being made by the traversing screw4 ,by the side of the reading microscope1 and in exact collimation with it1 a plumbing telescope is rigidly fixed1 and this sights down to a transferring apparatus1 ,d ,fig4 #cfg1 which is over the plate let into the ground4 ,illustration3 ,fig4 #cfg4--,two reading and plumbing instruments1 ,c1 ,c2 transferring instrument1 ,d2 and one of the adjustable intermediate supports1 ,b4 ,the transferring apparatus is a spring centre punch rigidly mounted truly vertical on a supporting plate having transverse motions1 cross levels and levelling screws4 ,the top of the centre punch has a small platinum disc let in a recess1 and upon this disc very fine cross lines are marked4 ,this apparatus is placed on the ground over whatever has been let in to receive the mark1 it is then levelled and the cross lines upon the punch top brought by means of the transverse motion screws exactly to coincide with the spider web of the plumbing telescope1 and in this position the centre punch is lightly struck with a mallet which marks the plate let in the ground in the exact position of the centre of the cross lines at its top1 so that if now the transferring apparatus be removed the cross webs of the plumbing telescope would cut the dot marked in the plate by the centre punch4 ,this method is far more exact than any hanging plumb-bob1 as even if they are screened to prevent swinging very few hang with the point perfectly true4 ,in laying down a base line ,no4 #a reading and plumbing instrument is set up and levelled over the starting end block1 which is usually of hard stone or granite set on a firm foundation1 with a copper plate let in its top about the centre1 the line having been previously set out with a theodolite1 and the intermediate stations being roughly measured with an ordinary steel tape4 ,at each intermediate station or length of ,konstat tape used a teak post is driven into the ground and a zinc plate screwed upon its top2 the other end block is similar to the starting one4 ,the ,konstat tape is now mounted between the end suspension supports1 one being outside the starting end block and the other outside the first teak post which has been put in for the first length4 ,no4 #b reading and plumbing instrument is set up over this post1 and ,no4 #a and ,no4 #b are aligned upon each other by their aligning telescopes1 and the ,konstat tape adjusted over the little tables under the microscope of each2 the intermediate stands are then put in and adjusted for height to prevent catenery1 and the guide pieces are brought up to the tape on either side and clamped to prevent side deflection by wind4 ,the tape being properly suspended it can be easily moved with the fingers lengthways1 as it is suspended at either end by silk cords over ball-bearing pulleys4 ,it is brought in position with its starting end division somewhere under the microscope of ,no4 #a reading apparatus1 and the microscope is then brought into exact coincidence by the traversing screws4 ,the transferring apparatus is put on the granite block with the centre punch in the field of view of the plumbing telescope and then levelled2 the cross lines in the top of the centre punch are then brought to exactly coincide with the plumbing telescope webs by the transverse motion of the transferring apparatus1 the centre punch is struck and the mark thus made in the copper plate has a line engraved through it4 ,the transferring apparatus is then removed to the position under ,no4 #b reading and plumbing apparatus4 ,no4 #b microscope is made to coincide with the end division on the ,konstat tape by its traversing screws1 the centre punch of transferring apparatus1 brought by its traversing screws to coincide with the webs of the plumbing telescope and struck1 marks the first section4 ,no4 #a reading and plumbing apparatus is then transferred to the next post1 ,no4 #b remaining over the first section post1 the first end suspension stand is transferred outside ,no4 #b post and the tape mounted between as before1 the traversing motion of ,no4 #b reading apparatus must not be touched1 but the end division of the tape brought to coincide with its microscope web by shifting lengthways4 ,no4 #a microscope at the further end is adjusted to coincide by its traversing screws and the transferring apparatus as before1 and so on until the entire length is measured1 the last centre punch mark on the copper plate let in the further end block or stone having a line engraved through it4 ,a few #a-ajjth of an inch divisions1 or #a-ajths of a millimetre1 are divided on either side of one end division of the ,konstat tape so that any allowance for expansion or contraction may be made under the microscope at the time1 but with ,konstat tapes this is very small indeed4 ,with fairly level ground any slight differences of level can be allowed for in setting up the stands1 so that the tape remains level2 if the difference is too great for this the difference of hypo and base must be calculated4 ,thermometers are used1 generally one suspended on the tape at each end4 #gfa4--,perambulator4--,a very ancient instrument1 described by ,vitruvius as being among the effects of the ,emperor ,commodus2 it was used by hand1 or attached to a carriage to measure distances4 ,the instrument is at present used as formerly for measuring roads4 ,upon pavements and asphalt roads it measures accurately1 where by reason of traffic it is sometimes a difficult or very slow process to use the chain4 ,the plan of manufacture is varied considerably4 ,the author makes the felloe of the wheel in segments of well-seasoned mahogany in two rings1 ,fig4 #cfh4 ,these are rivetted together from side to side in such a manner that the grain of the wood is crossed as much as possible to prevent lateral warping4 ,the tyre1 which is #f feet in circumference1 is made of hard rolled brass #a inch by inch thick4 ,the spokes are light steel tubes covered with brass tube1 and screwed into a brass hub4 ,the axle of the wheel is placed in a steel fork which is formed by screwing1 by means of a winged nut1 two bars of about #ah by #a by #c_/h inches upon a boss formed at the end of the steel stem of the turned wood handle4 ,made in this manner the handle may be easily detached and placed flatwise upon the wheel1 so that the whole may be packed in a square deal case of moderate dimensions for transport4 ,illustration3 ,fig4 #cfh4--,perambulator4 ,illustration3 ,fig4 #cfi4--;,details of registering box4 ,illustration3 ,fig4 #cgj4--,section4 ,the ,registering ,part of the ,instrument1 ,figs4 #cfi1 #cgj4 ,the axle is protruded through the fork on the left-hand side1 and thence through the registering box supporting one of its ends4 ,the other end of the box is supported by a stud which fits into the side of the fork4 ,the axle in the part contained within the box is cut into a screw1 ,fig4 #cgj ,s1 of about sixteen threads to the inch4 ,the screw works in the edges of a pair of discs ,r1 placed one upon the other upon the same axis2 these are cut on their edges with teeth to form worm wheels in which the screw upon the axis of the wheel works4 ,the upper disc has #aaj teeth4 ,this therefore moves one revolution by #aaj turns of the wheel4 ,it is divided into #aaj divisions at its circumference1 but is figured #bj yards to #bbj yards or #a furlong1 so that each division represents #b yards1 corresponding with the circumference of the wheel1 ,fig4 #cfi ,o4 ,the divisions are read by a point attached to the side of the box shown at the top of the figure4 ,single yards are shown by the intermediate position of the pointer between the divisions1 but single feet may very well be estimated approximately4 ,the lower disc is cut with #aaa teeth4 ,the ratio #aaj to #aaa gives a differential displacement of one tooth only after #aaj revolutions of the wheel1 or of #bbj yards traverse4 ,the two discs take1 therefore1 by revolution over the surface #bbj #aaj #bd1bjj yards or #ace miles before they return to the same relative position as at starting4 ,this is1 therefore1 the space this perambulator will traverse without resetting4 ,to enable the lower disc to be read the upper disc is cut away for half the interior circumference of its circle4 ,a part of the upper disc is formed into a point1 to read direct from the centre into divisions on the lower disc1 in furlongs up to #ac miles4 ,the ,measuring ,box is covered with glass for protection4 ,the box can be taken off by removal of the milled-headed screw at any time to set it back to zero1 but in practice it is often found more convenient to spin the wheel round to zero or an even mile of the outer circle1 and record differences of reading1 if this can be done in the distance within the record of #ac miles of the lower disc4 ,the screw and axis1 which are of hard steel1 should be occasionally oiled with watch oil to keep the perambulator in good working order4 #gfb4--,the reviser has designed a light form of perambulator on the bicycle wheel principle4 ,it is shown at ,fig4 #cga1 and is very light and portable4 ,the rim of the wheel is of gun-metal and is usually made two yards in circumference4 ,it is fitted with a counter which denotes two yards to every revolution1 and the distance is given in number of yards only4 ,the handle is detachable from the fork for packing1 and the whole is contained in a light pine case4 ,the wheel is also made two metres and ten links in circumference4 ,illustration3 ,fig4 #cga4 #gfc4--,pedometer4--,used for roughly ascertaining distances passed over in walking4 ,this ingenious instrument was the invention of ,william ,payne in #ahca 7patent ,no4 #fjgh74 ,it is the size of an ordinary watch1 and has a similar face2 but between the figures1 which indicate miles #a to #ab1 there are four divisions only1 to indicate quarter miles4 ,the pedometer is slung up by a loop1 ,fig4 #cga1 ,h fixed upon the handle1 which in use is passed over the edge of the waistcoat pocket so as to keep the instrument in an approximately vertical position4 ,illustration3 ,fig4 #cgb4--;,construction of pedometer4 ,illustration3 ,fig4 #cgc4--;,face of passometer4 #gfd4--,the ,registering ,apparatus consists of a pendulum1 ,fig4 #cgb1 ,p placed horizontally by being supported by a delicate spring ,l to its highest position1 where it rests against a stud4 ,the action of the pendulum is caused by its following the motion of the body in stepping1 until stopped by the foot reaching the ground1 when the momentum attained by the pendulum carries it from its upper position of rest where it is sprung against the stop to its lower free position1 where it is stopped by a screwed adjustable stud ,s1 shown under it4 ,the axis of the pendulum is free upon the axis of the ratchet wheel ,r4 ,when the pendulum falls1 a fine spring1 fixed to its upper surface1 drops its end into the teeth of the ratchet1 moving over two or three teeth1 which are held against retrograde motion by the spring pawl ,d4 ,when the pendulum rises1 the ratchet is moved forward the number of teeth that the spring at first slipped over4 ,the ratchet is connected with a pair of geared wheels1 not shown1 the axis of the second of which forms the axis of the hand4 ,in this manner each oscillation of the pendulum is communicated to the index hand4 ,the ratchet is made with extremely fine teeth1 so that by adjustment of the screw stud ,s a greater or less number of these teeth may be taken by one beat of the pendulum1 and thus the mileage rate may be adjusted approximately to the step4 ,this is done1 however1 very imperfectly1 as the variation of the average steps of men amounts to one or two inches1 and the difference from the number of teeth taken will scarcely indicate less than three inches in the step4 #gfe4--,passometer4--,this instrument was originally invented by the author as an improvement upon the pedometer 7#ahfh74 ,the instrument1 ,fig4 #cgc1 is not intended to indicate miles or any distance1 it simply counts the number of steps taken4 ,the action is just the same as the pedometer1 but the ratchet teeth are larger and less liable to miss a tooth1 as it is made to take one tooth only at a single step4 ,the dial arrangement is entirely changed4 ,the steps are numerically indicated by a separate hand which reads into the graduations up to #ej steps upon a small dial4 ,each revolution of the small hand reads through gearing one division of the central hand1 which moves over the complete circumference of the dial1 reading up to #be1jjj steps4 ,this is the extent of indication4 ,it is necessary in continuation beyond #be1jjj steps to take a record of progression per #be1jjj where a greater distance is required to be measured4 #gff4--,the average step may be estimated perhaps within #a or #b per cent4 by training in walking several miles steadily1 counting the steps1 always remembering that we take shorter steps uphill and when we are tired4 ,but the mean step of the individual under all the different circumstances is the only rule that can be followed4 ,illustration3 ,fig4 #cgd4--,sounding chain4 #gfg4--,sounding ,chains used for coast surveys are generally made of iron1 but sometimes of brass4 ,they are usually made of #aj fathoms entire length4 ,the links are #a inch1 and the feet are indicated by tellers4 ,the form of teller designed by the author is shown in ,fig4 #cgd for the #c4 ,a leaden weight1 similar to that shown ,fig4 #cge1 is used upon the end of the chain--of #bh lbs41 for ordinary coast work1 or heavier if there are strong currents4 ,the chain is contained in a strong wooden box4 ,illustration3 ,fig4 #cge4--,sounding line and weight4 ,a very elaborate apparatus with steel wire line has been made for deep-sea sounding by ,lord ,kelvin and others2 but this subject is beyond the province of the present work4 #gfh4--,sounding ,lines1 used for survey of shallow coasts and harbours1 are made of water-laid line of fine green hemp1 about inch circumference1 ,fig4 #cge4 ,white tapes are inserted as tellers at every foot1 and red tapes at every fathom4 #c to #f fathoms are the ordinary lengths employed4 ,if the water is shallow the fathoms are easily counted1 but if thought necessary knots may be tied to indicate the number of fathoms on the red tellers4 ,the weight is about #g lbs4 for #ej feet line1 about #ae lbs4 for #ajj feet4 ,the under side of the weight is commonly recessed to take tallow when it is desired to bring up a specimen of the bottom1 if this is loose sand or mud4 #gfi4--;,coast ,survey ,lines4--,for surveying distances1 from point to point of soundings along a coast1 lines of fine copper wire rope marked with tellers at #ej and #ajj feet are commonly used4 ,the line is generally allowed to rest on the bottom of shallow water1 and is floated up by means of attached corks in deep water4 ,it is usually laid and picked up by means of a reel fixed at the stern of the surveying boat4 ,the lengths of line used vary from #ajjj to #ejjj feet4 #ggj4--,telemeters4--,these scarcely enter within the practical limits of surveying instruments1 but as several attempts have been made to introduce their use it is necessary to mention them4 ,the general attempt has been to measure a great distance1 #ajjj feet or more1 by means of the angles subtended from the ends of a short base to a distant point4 ,this base in the telemeter of ,piazzi ,smyth is #fj inches2 ,colonel ,clarke1 #gb inches2 ,otto ,struve1 #gce inches2 and ,adie1 #cf inches4 ,the angles are usually taken upon the principle of the sextant by coincidence of image4 ,very much greater success has been attained recently by ,messrs4 ,barr and ,stroud by means of their range-finder of #ed inches base4 ,the author1 as far as his information reaches1 is assured that no instrument of the class is satisfactory for surveying purposes4 ,further1 the subject is one to which he has devoted some study1 and designed two telemeters4#ee ,one of these appeared to him for a time satisfactory within certain limits4 ,the base in this instrument was #ej feet1 formed of a fine pianoforte wire stretched between two observing telescopes1 the tension of the wire directing the one telescope to a right angle1 and the other telescope to an arc which read either degrees and minutes or absolute distances in the eye-piece to the direction in which the telescope was pointed4 ,in first trials this instrument was found fairly satisfactory2 but subsequently in windy weather the deflection of the wire rendered the action of a pair of instruments quite unreliable4 ,there are some instruments1 as ,colonel ,gautier's telemeter used in the ,french army1 which depend upon combined reflectors placed normally at #ae to #de1 as in the apomecometer1 art4 #fic1 but with a tangent screw to give a small motion of displacement to one mirror which reads on a scale of calculated distances to angle from a certain base measured between two stations of observation4 ,a very similar instrument1 invented by ,labez1 has one reflector only at #de4 ,these instruments may be useful for measuring approximate distances for range in the army1 but can scarcely rank as surveying instruments1 the box sextant1 art4 #ffd1 being in every way a superior telemeter for the purpose when a measured base can be fixed and well-known trigonometrical calculation used4 #gga4--,the simplest and best telemeter for surveying purposes is the subtense telescope1 and all good1 up-to-date surveying instruments have their telescopes so fitted1 but for those who do not carry an instrument with a telescope the reviser has designed a small subtense telemeter1 ,fig4 #cgf1 which consists of a small telescope fitted with subtense points1 and mounted in a collar which has vertical and horizontal motions and a centre socket to fit a ,jacob's staff4 ,the stadia is set to read #a in #ajj4 ,the telescope has rack and pinion focussing and may be revolved in its socket so that the stadia rod may be read held either horizontally or vertically4 ,it is packed in a leather holster case1 and a four-fold #aj-;feet spring-pointed stadia rod is supplied with it divided into feet1 tenths1 and hundredths4 ,illustration3 ,fig4 #cgf4 #ggb4--;,hand ,rods1 although used more generally by building surveyors1 are extremely useful also to the civil engineer and land surveyor for town work among buildings and in mines4 ,they are made #e feet in length1 less generally #aj feet4 ,the #e-;feet are made of single blades of lancewood or of two jointed to fold4 ,the #aj-;feet are always jointed and made much stouter than the #e-;feet4 ,the #e-;feet are generally sold in pairs4 ,illustration3 ,fig4 #cgg4--,ordinary #e-;feet jointed rods--plan and section of joint4 #ggc4--,ordinary #e-;feet ,rods are divided to every #c inches1 with feet only stamped with numbers1 as shown ,fig4 #cgg4 ,where the rod is jointed the best form of folding joint is shown in the figure in section and plan4 ,the spring ,s is sunk into the face of the rod at the joint on one side1 and springs into a groove 7housing7 in the other side so as to lock the joint when it is either open or closed4 ,the most useful dimension for the rod is #a inch by #a_/f inch4 ,rods are nearly always made of lancewood1 but they are preferred dyed black for neatness by many surveyors4 ,a pair of rods is usually carried in a cowhide case4 ,they are also often carried in the stem of a walking-stick hollowed out for the purpose4 ,the rod or rods in this case are made much lighter1 generally inch by #a_/h inch for a pair of rods1 or #g_/af inch by #g_/cb inch for a single rod4 ,the single rod is to be preferred in this case for its extra strength4 #ggd4--;,fully ,divided ,rods4--,the author has made rods for many years divided to single inches4 ,these measure from both ends--one end direct as ,fig4 #cgh and the other end reversed by turning the rod over as ,fig4 #cgi4 ,by this plan the rod gives direct measurement in feet1 inches1 and parts from either end1 and the division is always placed outwards against the work1 so that measures may be taken from either end by turning the rod over sideways1 without turning it end for end4 ,illustration3 ,figs4 #cgh1 #cgi4--,stanley's surveyors' rods4 #gge4--;,connecting ,link for ,rods1 which weighs only #a oz4 and may be carried loose in the pocket1 is often found convenient for measuring heights1 as it permits the ends of a pair of rods to be brought together1 ,fig4 #chj4 ,by this means the arm will raise the rods about #g feet1 and with #aj feet1 the height of the pair of #e-;feet rods1 this will make #ag feet of measurement4 ,when the #aj-;feet is set against a wall1 its height1 if #bj or #cj feet1 may be guessed very approximately by standing at a distance from it4 ,illustration3 ,fig4 #chj4--;,connecting link for rods4 ,illustration3 ,fig4 #cha4--,slip jointed rod4 #ggf4--,slip ,jointed ,rod4--,this form is less general1 but it is a very convenient form of rod4 ,the jointing is effected by two loops which are fixed to the centre end of one part of the rod in such a manner that the other part may slide through the loops4 ,when the rod is extended to #e feet there is a stop which prevents further extension1 and a spring to keep it at this exact position1 ,fig4 #cha4 ,the outside of the rod is divided into feet and inches4 ,the inside is divided so that any addition to the half rod1 produced by extending it2 may give the measurement from end to end of the rod at this position1 thus3--,the half rod being #b feet #g inches closed1 if the loose side be drawn out #ai inches the rod from end to end will be #d feet #b inches1 which will be indicated by the division and figuring inside the rod4 ,this is very convenient for measuring openings such as doorways or passages4 #ggg4--;,brace-piece4--,a #aj-;feet rod is sometimes made with a brace-piece1 which folds up inside the rod4 ,this brace-piece is jointed to fix both half rods to #ij when it is desirable to use the rod as a square4 ,illustration3 ,fig4 #chb4--;,civil engineer's rule4 #ggh4--;,civil ,engineer's ,rule is made fourfold in both boxwood and ivory1 ,fig4 #chb4 ,the most convenient size is #a inch wide4 ,some of the profession prefer them narrow for lightness-- inch2 and some wide for strength--#a inches4 ,this rule is generally well made1 with ,german-silver joints and outside joint-plates4 ,the divisions placed on the rule outside are inches in eighths and tenths2 the inside1 the ordinary architects' scales1 #a_/h1 1 1 #a1 and four chain scales1 #bj1 #cj1 #dj1 and #ej4 ,a #aj is got by halving the #bj2 #fj1 by doubling the #cj4 ,a protractor reading to #e is divided on the head4 ,with silver joints and in fine ivory this rule is often made a presentation instrument4 ,,footnotes3 #ed ,the ,surveyor1 vol4 ii4 ,no4 #e4 ,sydney1 ,nov4 #ahhi4 #ee ,patent ,no4 #badb1 ,may1 #ahhj4 ,,chapter ,,xvii4 ,,stations ,,of ,,observation--,,pickets--,,false ,,picket--,,permanent ,,stations-- ,,referring ,,object--,,heliotrope--,,heliostat--,,h eliograph--,,signalling-- ,,morse ,,alphabet--,,night ,,lights--,,oil ,,lanterns--,,magnesium ,,light4 #ggi4--,stations of ,observation vary materially according to the extent of the survey and its purpose4 ,for geodetic works stations are raised at great expense1 often in masonry or solid woodwork4 ,for ordinary local or civil surveys the stations are commonly formed of single poles set up vertically1 which vary in dimensions according to the extent of survey and the difficulties which may be encountered by various obstructions to direct visions by woods1 lakes1 marshes1 etc4 ,the apparatus that may be useful in the work of the civil engineer in ordinary practice will only be considered here4 ,illustration3 ,fig4 #chc4--,ranging pole or picket4 #ghj4--,pickets or ,ranging ,poles1 ,fig4 #chc1 as the name indicates1 are used for ranging a direct line through a district1 either by a series of poles sighted from one to the other or by being placed in position convenient for triangulating by the theodolite where the country is open1 or free from many buildings1 trees1 or other convenient landmarks4 #gha4--,the picket 7,fr4 piquet7 is a straight1 slightly tapering pole shod with wrought iron or steel4 ,it is generally made of about #a-a_/h inches diameter1 and is painted in alternate feet red and white with an enamel paint that will not soil the hands or take dirt from them4 ,the shoes should be made with strap-pieces1 so that the picket1 which is generally made of yellow pine for lightness1 should not be liable to break off at the shoe in use4 ,fig4 #cha represents the lower part of a picket as made by the author3 ,b black1 ,w white1 ,r red4 ,it is usual to have six pickets at least out in use with a theodolite in open country4 ,illustration3 ,fig4 #chd4--;,false picket4 ,illustration3 ,fig4 #che4--,spur-shod picket4 #ghb4--;,false ,picket4--,for the placing of a picket it is usual to clear the sod with a small spade where possible1 so as to suspend the plummet from the theodolite into the hole made by the picket to triangulate from its position4 ,in marshy lands and under many conditions this is not easily done4 ,it will generally be found more expeditious to carry about one of the author's false pickets1 to place directly in the hole from which the picket is removed1 which saves the trouble of removing the grass4 ,this is shown in ,fig4 #chd4 ,it consists of a wooden peg1 upon the top of which a cross is sawn to represent the axis4 ,this cross is filled in with a veneer of ebony1 and the whole is polished over to keep it clean4 ,it will be readily seen that any picket accidentally broken will make a false picket4 ,in setting up the theodolite over it the plummet is brought to verticality with the centre of the cross4 ,in moving the false picket the original one is easily replaced1 if required1 in the same position for continuing the work4 #ghc4--,spur-shod ,picket4--,much stouter poles than may readily be pressed in by hand1 as for instance1 of #b inches diameter1 may be driven into the ground by having a spur or cross-bar of steel1 about #g inches long and about #c_/h inch diameter1 placed through the pole1 say at #a foot distance from the point1 a form which is much used on the ,continent4 ,this picket may be jerked down for a certain distance by pressure of the foot on each side1 and then jerked home to the ground by standing upon it1 to make a #aj-;feet or #ab-;feet pole stand sufficiently rigid for temporary work1 ,fig4 #che4 ,illustration3 ,fig4 #chf4--,socket for station pole4 #ghd4--,permanent ,stations are commonly constructed upon hilltops or other commanding positions4 ,a very general way is to set up a long pole of fir or other wood at command1 from #aj to #bj feet in height1 according to the circumstances4 ,occasionally it is desirable to remove the pole and place the theodolite centrally over its vertical position4 ,a very good way to do this is to have a slightly tapered wooden socket1 ,fig4 #chf ,s1 constructed of stout boards1 say #a inches thick1 made into a hollow square with a cross of boards1 ,,wwww fixed to it4 ,the socket is placed in a hole dug out entirely below the ground1 and is rammed in and fixed as an ordinary gate post4 ,the pole ,p is squared at the end to fit the tapered socket up to shoulders which are formed by leaving the other part of the pole round4 ,the socket for a #ae-;feet pole should be #ah inches deep2 for a #bj-;feet one1 #b feet deep4 ,where these poles are properly prepared they may be jointed together in two or more parts for portability4 ,bunting flags1 red and white1 about #ah inches by #i inches1 may be fixed at the tops of the poles4 ,in fixing the socket the pole should be erected in it to be able to keep it constantly vertical during the ramming4 ,a plummet suspended at arm's length1 at a distance from the pole in two positions at about right angles to each other from the centre of the pole1 will provide a means of keeping it erect during the fixing of its socket4 ,the socket hole1 upon lifting the pole out1 forms the centre for erecting the theodolite over its position4 #ghe4--,referring ,object4--,it is desirable that all arcs taken by the theodolite from an important station should contain one point in common1 for which the best defined object to be found at a distance may be selected4 ,colonel ,clark1 of the ,ordnance ,survey1 recommends as a referring object two rectangular plates of metal placed with their edges parallel to each other in the vertical plane1 at such a distance apart that the light of the sky seen through the opening appears as a vertical line of about #aj in width4 ,the best distance for this object is from #a mile to #b miles4 ,two pieces of board1 fixed a small distance apart by ledges screwed thereon1 answer the same purpose4 ,the description fully conveys the method without illustration4 ,stations ,visible at ,great ,distances are formed by means of reflection of the sun's rays or by artificial light4 ,illustration3 ,fig4 #chg4--,stanley's heliotrope4 #ghf4--;,heliotrope1 or heliostat as it is sometimes called1 may be any form of mirror to throw the sun's ray in a constant direction or to a distant station at a time of day fixed for making observation4 ,the instrument is uniformly constructed with a small glass mirror having a plane surface4 ,the angle of divergence of the extreme rays in the reflection is the same as that subtended by the sun's diameter at the position of the mirror1 that is1 of about #cb minutes of arc4 ,this divergence is sufficient to render the reflector visible at a great distance4 ,the plan upon which the author has constructed this instrument is shown in ,fig4 #chg4 ,it consists of a reflector ,m formed of a plain glass mirror of about #e or #f inches in diameter1 placed in a metal tray4 ,the mirror is centred vertically upon an axis to which a worm wheel ,b is attached upon one side that works into a tangent screw which is moved by a milled head so as to place the mirror at any angle to the horizon4 ,the mirror and its vertical adjustment just described are carried by a fork which is erected from the base board of the instrument upon a socket joint which permits the mirror to be turned about4 ,upon the lower part of the fork above its socket another worm wheel is constructed centrally to the axis4 ,this works into a tangent screw attached by fittings to the base board4 ,the tangent screw has a long shank leading to a milled head ,a4 ,by means of the milled heads the mirror may be set to any position1 so as to throw the reflection of the sun in any required forward direction4 ,a small hole is cut through the silver in the centre of the mirror to sight the position to which the sun's reflection is directed4 #ghg4--,the ,base ,board is of inch mahogany about #bj inches by #aj inches1 and is supported upon a very firm tripod stand1 like that described for a plane table1 art4 #gjj4 ,at one end of the board a sighting screen of mahogany1 #aj inches by #aj inches and inch thick1 is hinged1 so as to be held erect by means of a stay bar ,e4 ,in the centre of the screen an opening is turned out #c inches diameter1 and a frame-piece of half circle only is placed over this4 ,the frame piece is grooved out at the back so as to hold discs1 shown abc in the figure4 #ghh4--,the ,discs abc1 are of thin brass and have openings respectively 1 1 and #a inches wide1 so as to reduce the width of the line of light which appears through them when the reflection of the sun is thrown from the back4 ,these have each a fine wire stretched across them to indicate the centre4 ,a fourth disc1 not shown1 has a double cross of wires to indicate the centre only4 #ghi4--,to ,pack the ,instrument1 the screen is turned down the index frame1 falling into the opening ,f2 the mirror with its fork is lifted out and secured to the surface of the base board by buttons2 and the whole apparatus is put in a pine case4 ,its weight without tripod stand is #h lbs4 #gij4--,to ,use the ,heliotrope1 the station on which the sun's light is to be thrown is sighted by looking through the small hole in the centre of the mirror1 and adjusting the base board until the station appears in the centre space of the disc opening4 ,the mirror is then turned towards the sun by means of the milled heads until its image1 reflected upon the back of the screen1 appears central with one of the discs which is intended to be used4 ,all parts of the stand and fittings being made quite firm1 the attendant moves the milled heads1 as required1 to follow the apparent motion of the sun1 at intervals of five minutes or less4 ,it must be observed that the centre of the slit in the disc represents the station visible to the observer4 ,this point must therefore be plumbed to the station point in setting up the instrument4 ,a part of the screen at ,p is cut away to admit of the suspension of a plummet4 #gia4--,the heliotrope was much used in ,india for the great trigonometrical survey4 ,colonel ,h4 ,thuillier states from experiment that ,a heliotrope of #i inches diameter answers for #ij to #ajj miles4 ,for nearer distances it is much too bright to be observed through a telescope1 and the light must be diminished in the following proportion4 ,for distances of #b or #c miles 7the usual distance of a referring mark7 an aperture of #jbe of an inch will answer1 and for longer distances about #ja of an inch of aperture per mile of distance will suffice1 viz41 an inch for #aj miles1 #b inches for #bj miles1 and so on1 provided always the apparatus is carefully adjusted and the man who works is alert and skilful4#ef ,practically the discs here described will give all the variation required4 ,in less favoured climates than ,india more opacity will be found in the atmosphere1 and larger apertures required than those just stated4 ,signalling with the ,heliotrope4--,a thin wooden bat ,d is moved over and off the outside front of the open disc aperture1 following the rule of ,morse signals1 which will be presently described for the heliograph4 #gib4--;,heliostat4--,is a smaller instrument than the heliotrope1 in which the mirror or mirrors are moved by clockwork1 so as to keep the sun's reflection in a uniform direction throughout the day4 ,this instrument is delicate and not generally well adapted to field work4 ,illustration3 ,fig4 #chh4--;,heliograph4 #gic4--;,heliograph4--,this instrument is the invention of ,sir ,h4 ,c4 ,mance1#eg since improved by ,major ,macgregor1 ,colonel ,bonham1 and others4 ,it is used for a military signalling apparatus1 but it is also employed1 on account of its portability in place of the heliotrope for surveying1 where great precision by limiting the area of light reflection is not required4 ,the construction of the instrument is shown in ,fig4 #chh4 ,b is the back of a plain circular mirror of #e inches diameter1 supported upon pivots on a fork frame ,j1 the lower part of which forms a socket4 ,the socket is furnished with a thumb-screw to secure the mirror and its frame when placed upon a cone projecting from the apparatus connected with the base plate formed on the top of the tripod head4 ,the cone is erected upon a disc or wheel cut at its edge in teeth and centred upon the axis of the tripod head4 ,the wheel is revolved by means of a pinion connected with a milled head ,a which moves the mirror and the entire apparatus above in horizontal revolution4 #gid4--,the ,sighting ,arm ,l is attached to a collar fitting projected from the tripod head4 ,this may be fixed in any horizontal direction by means of the tangent clamping screw ,c4 ,the arm ,l has a supplementary extension by the piece ,sj1 which is jointed at the position of these letters and also by a socket fitting into the arm4 ,the termination of the extension is a sighting point ,i formed of a thin blade of metal4 ,the arm and its fittings permit the sighting point ,i to be set in any direction or elevation to follow the inclination of the land4 #gie4--,the ,sighting ,vane is a piece of white metal upon which there is placed a black dot termed the sighting spot4 ,a small circle1 about #a_/e inch diameter1 is left unsilvered in the centre of the mirror1 which does not reflect the sun's rays4 ,it therefore causes a small disc of shadow in the centre of the reflection of the mirror1 termed the shadow spot4 ,the shadow spot is made to appear upon the sighting spot when the instrument is adjusted to throw the sun's image upon a distant station4 #gif4--,the ,supplementary ,mirror ,m is similar to that already described1 centred also on pivots and placed in a forked frame4 ,this is mounted on a cone ,s which fits into a socket at ,s1 when the extension arm ,j is removed4 ,this mirror is intended to receive the image of the sun when placed towards the back of the pointing of the instrument to throw the sun's image from the mirror ,m to ,b1 to signal by double reflection1 when the sun is at a forward angle to the distant station4 ,the coincidence of reflection is taken with this mirror by the reflection of a piece of paper pasted on its centre of the same form as the index ,i4 #gig4--,telegraphing ,apparatus1 called technically flashing apparatus4 ,this consists of a rod ,r hinged to the top of the mirror at its upper end and also to a lever which forms a ,morse key at the lower end4 ,the rod is formed of a screw of about half its length1 which passes into a female screw tube so as to shorten or lengthen it as required to direct the reflection of the sun's rays by turning the milled head above ,r1 which forms a part of the tube4 ,the ,morse key is hinged at ,j to the stem of the instrument1 and is kept up to a fixed stop by means of a spring ,p extended by an arm from the stem of the instrument1 so that pressure upon the disc ,f moves the key down to its stop ,p1 and also tilts the mirror to throw its reflection off the observing station during the pressure4 ,the flashing described by the jar of its action is liable to displace the mirrors4 ,the use of the bat1 shown at ,fig4 #chg ,d1 is more certain for signalling words4 #gih4--,the ,tripod of the ,heliograph ,,tt,t consists of three circular mahogany legs #a-a_/h inches in diameter and about #d feet #i inches long4 ,the legs are capped with sockets carrying collar-pieces which are attached to the tenon-pieces of the head4 ,the head forms a box for the revolving apparatus and remains attached to it when the mirror apparatus and arm are removed4 ,the tripod head is protected when out of use by a leather cap attached by a strap to one of the legs4 ,the weight of the tripod is #f lbs4 ,in fixing the tripod for use it should have the legs extended nearly #fj1 and the toes should be firmly pressed into the ground4 ,at windy stations it is well to dig holes and sink the toes1 or to have a heavy stone suspended under the centre of the head4 #gii4--,the ,case for the ,heliograph is made of solid leather1 with separate divisions for mirrors1 arm1 and sight4 ,a spare mirror is sometimes packed in the same case that the instrument may not be made useless by accidental breakage4 ,a strap is provided with the case to go over the shoulder4 ,the instrument weighs #e lbs4 complete in its case4 ,great care should be taken to observe the arrangement and position of the parts of the instrument before taking it from its case1 as it is always packed closely4 #hjj4--,to use the ,heliograph with a ,single ,mirror4--,in this case the reflection is direct4 ,the instrument is approximately directed by looking through the mirror from behind1 moving the arm ,l and the sight ,i to cut the distant station1 and then clamping the screw ,c4 ,after this is done the exact position is found by placing the head nearly in front of the mirror1 with the back to the distant station with which it is intended to communicate4 ,then to adjust the mirror1 if required1 and move the eye until the distant station appears reflected in the exact centre of the mirror4 ,after this1 without moving the head1 finally to adjust the sight vane ,i until the reflection of the sighting spot is brought exactly in line with the centre of the mirror and appears reflected upon the image of the distant station4 ,the sighting spot is then in direct line between the distant station and the centre of the mirror1 in whatever direction or inclination the mirror may be afterwards placed to reflect the sun's image4 ,care should be taken not to disturb the stand nor arm in future movements of the mirror4 #hja4--,to ,adjust the ,mirror1 stand behind the instrument and adjust the vertical screw ,r and the horizontal pinion ,a until the black spot1 as it appears on the mirror from the reflection of the hole through it1 is seen upon the centre of the point of the sight vane surrounded by a ring of bright reflection from the silvered surface of the mirror4 ,the distant station will then receive the reflection1 which must afterwards be kept constantly upon it by gently moving the screw ,r and pinion ,a1 following the apparent path of the sun4 #hjb4--,to ,use the ,heliograph with ,two ,mirrors1 which is necessary when the sun is shining towards the distant station and its image can only be projected by double reflection1 the second mirror is placed upon the end of the arm in the socket ,s4 ,this has a white paper vane cemented upon it1 as shown at ,m4 ,the mirror ,b is placed roughly facing the sun4 ,the mirror ,m is turned towards the distant station upon which it is intended to direct the rays1 being careful at the same time to observe that the two mirrors do not intercept each other's rays4 ,now from the back of the mirror ,m we look into the mirror ,b1 moving the head until the centres of the two mirrors appear in a line with the eye4 ,then without moving the head1 adjust the direction and inclination of ,m until the reflection of the distant station appears in the centres of the mirrors4 ,now clamp the mirror ,m in this position1 from which it must not be moved so long as it is required to keep the same station in communication4 ,to keep the reflection following the sun a position is taken at the back of the mirror ,b1 and this mirror is worked as before described1 when it is used singly1 by the milled heads1 only that in the present case the paper vane ,m takes the place of the metal vane ,i4 #hjc4--,telegraphing by the ,heliograph4--,the communication is made by the alternate pressure and release of the ,morse key ,f1 each pressure throwing the reflected image of the sun off the observing station4 ,the ,morse alphabet1 which is universally used1 consists of rapid touches represented by dots1 and pressures of at least four times the time of a touch represented by dashes4 ,the following arrangement forms the alphabet3-- ,a - ,n - ,b - ,o --- ,c -- ,p -- ,d - ,q --- ,e ,r - ,f - ,s ,g -- ,t - ,h ,u - ,i ,v - ,j --- ,w -- ,k -- ,x -- ,l - ,y --- ,m -- ,z -- ,the time between the words is double that of a dash4 ,many other signs are commonly used for figures1 etc41 for which the reader may consult ,the ,manual of ,instructions in ,army ,signalling4 ,the same system is used for signalling by flags2 and by stopping off light of lamps this system is most valuable for the surveyor in new countries for information of forward ground and other matters4 #hjd4--,lights for ,observations by ,night4--,under many conditions an observation of a distant station may be much more conveniently and accurately taken at night by observation of a luminous object of limited area4 ,for this purpose the arc light1 lime light1 blue signal light and others have been employed4 ,for the civil engineer where regular stations are not erected1 as with geodetic work1 oil lights or the burning of magnesium ribbon are the most convenient4 #hje4--,oil ,lanterns4--,in the great trigonometrical survey of ,india large reverberatory lamps were used1 which were furnished with ,argand burners with circular wicks about #b inches in diameter4 ,the back arc of rays was reflected by a parabolic reflector #ab inches in diameter and #di inches in depth4 ,the lamp was enclosed in a strong box with a plate-glass face #ab inches in diameter1 with apertures to admit sufficient air and chimney to carry off fumes4 ,the box was constructed to form a packing case for conveyance of the apparatus4#eh #hjf4--,the oil lantern which will be found most convenient for the civil engineer will be one of the same form of construction as the bull's-eye lantern1 but much larger--#f inches square is a good size4 ,this may be made to go on the same tripod as the heliograph1 and will take its place for signalling by night1 or telegraphing by the ,morse signals by the hand or bat shown ,fig4 #chg1 ,d4 ,a #f-;inch bull's-eye lamp with treble wick may be seen well in clear weather #e miles to #aj miles off4 ,a railway signalman's hand lamp forms a very good signal1 or even an ordinary #d-;inch bull's-eye is very useful in working over new countries4 #hjg4--,magnesium4--,the intense light given by burning ribbon magnesium1 and the extreme lightness in weight of this material1 render it of especial value for night signalling4 ,magnesium ribbon is now sold at a very low price 7about two shillings per oz471 and #a oz4 will give a continuous intense light1 visible at #cj miles1 for over an hour1 whereas for a night signal arranged to be given at a stated time1 fifteen minutes is amply sufficient for a single observation4 ,great difficulty is often found in lighting magnesium ribbon when this is slightly oxidized from exposure to air4 ,the best method is to employ the flame of a portable spirit lamp1 made for the purpose4 ,under any condition the burning ribbon should be shaded from wind4 ,a common plan is to hang a straight slip of ribbon from the centre of a tripod which can be readily shaded by a pocket handkerchief4 ,where expense is not the object to be considered1 lamps may be had for burning the wire4 ,tin cases are made for soldering up and storing the ribbon in for use abroad4 ,,footnotes3 #ef ,manual of ,surveying for ,india1 p4 #dgh1 #ahge4 #eg ,patent ,no4 #ccij1 ,october #ahgd4 #eh ,for full description and plate1 see ,everest's ,measurement of the ,meridional ,arc of ,india1 ,introd4 p4 cxv4 ,,chapter ,,xviii4 ,,measurement ,,of ,,altitudes ,,by ,,differences ,,of ,,atmospheric ,,pressure-- ,,historical ,,note--,,mercurial ,,barometer--,,construction--,,operation --,,aneroid ,,barometer--,,construction--,,various ,,improvements--,,hypsometer4 #hjh4--;,historical ,note4--,the observation that the atmosphere decreases in density with increase of height is due to ,alhazen the ,saracen1 about a4d4 #ajjj4 ,by this he explains that a ray of light entering the atmosphere obliquely follows a curvilinear path1 bending towards the denser strata1 that is concave towards the earth4 ,he showed that a body will receive difference of pressure in a rare and a dense atmosphere1 and calculated that the height of the atmosphere to its final attenuation would be from his data nearly #eh miles4 ,the practical instruments that have been devised for measuring altitudes1 by the differences of pressure due to the weight of superincumbent atmosphere are the barometer1 the aneroid1 and the hypsometer4 ,the barometer was invented by ,torricelli about the year #afdj4 ,its principle was demonstrated and first applied to altitude measurement by ,pascal in #afdg4 ,the aneroid barometer was suggested by ,conti in #agih1 and said to be devised as a practical instrument by ,vidie in #ahjh4 ,the hypsometer or boiling-point thermometer1 which depends for its boiling temperature upon the pressure of the atmosphere above the liquid which surrounds it1 was suggested by ,fahrenheit in #agbd1 experimented with by de ,luc in #aggb1 and brought to its present practical form by ,regnault about #ahdj4 ,at the present time the aneroid is almost exclusively used by the civil engineer1 as this instrument when made with great care is sufficiently reliable1 more portable1 and not so delicate in use as the others4 ,so that it is only when very great precision is desired1 or when the one instrument is used as a check upon the other1 that the mercurial barometer1 or the hypsometer1 or both are now employed4 ,at the same time it must be understood that the aneroid barometer scale is in a certain degree arbitrary1 as the divisions at best are only made up from a certain number of points taken from observations of the mercurial barometer placed simultaneously with the aneroid under an air pump1 and therefore its errors comprise those of the particular mercurial barometer with which it is compared1 and those due to the difficulties of the comparison1 and of making subdivision afterwards in the same relative proportion1 by copying to the scale of the aneroid4 #hji4--,the ,mercurial ,barometer4--,the principle of the barometer is generally understood4 ,if a glass tube1 closed at one end1 #cc inches long1 say of inch or over in bore1 be filled brimful of mercury and the point of the forefinger be firmly pressed on the surface of the mercury1 the tube may be inverted without the admission of air4 ,if the covered end of the tube be now plunged into a basin of mercury and the finger slowly withdrawn from under the tube beneath the surface of the mercury1 the latter will sink in the tube to about #cj inches above the surface of that in the basin--that is1 if the experiment be performed at about the sea level4 ,the empty space in what now becomes the top of the tube is termed a ,torricellian vacuum4 #haj4--;,in removing the pressure of the atmosphere from its surface in the tube1 which in the above experiment produces the barometer1 the pressure of the atmosphere then falls only upon the exposed surface of the mercury in the basin1 or what is technically termed the cistern4 ,this pressure is equal per area1 according to hydrostatic laws1 to the upper surface area of any equal column of mercury that the barometer may contain4 ,therefore the weight of the column of mercury in the tube1 if cylindrical1 above the surface of that in the cistern1 is the same as that of a column of air of equal size reaching upwards to the full height of the atmosphere4 ,in fact the one exactly balances the other1 and it is by the difference of the weight or quantity of air above the barometer per area of bearing surface that it is possible to ascertain the altitude of its position by means of the height of mercury in the tube1 after proper allowance is made for sudden changes of conditions of the atmosphere itself from time to time1 capillary attraction of the tube1 temperature1 etc4 #haa4--,the mean height of the barometrical column in ,great ,britain1 at sea level at the temperature of #cb ,fahr41 is about #biie ins4 ,a cubic inch of mercury at this temperature weighs #jdhifg lbs4 ,therefore #biie #jdhifg #adff lbs4 gives the mean pressure of the atmosphere on each square inch of surface of the earth in this latitude4 ,nearer the tropics the pressure is greater1 near the poles less4 ,it can be shown that as the heights ascended by the barometer increase in arithmetical progression1 the pressure upon the mercury diminishes in geometrical progression4 #hab4--,mountain ,barometer4--,the barometer used for measuring altitudes1 to which the above term has been applied1 is now made only upon ,fortin's plan1 in which the bottom of the cistern wherein the glass tube is plunged is made of fine1 close-grained leather1 the best for the purpose being a stout kid4 ,the pores of the leather must be sufficiently fine not to admit of the escape of the mercury1 and yet at the same time sufficiently soft and pliable to transmit the exterior pressure of the air4 ,fortin's construction permits the cistern to be closed entirely secure from leakage of the mercury1 in whatever position the barometer may be placed4 ,the closing is effected by means of an adjusting screw1 ,fig4 #cij ,f1 which by its pressure decreases the capacity of the cistern and forces the mercury up the tube1 or adjusts it to a given height1 so that the scale of the barometer may be read correctly from a given point ,x placed within the cistern4 ,to prevent injury to the tube the adjusting screw is made of a length just sufficient to force the mercury to fill it1 so that when it is closed home there is no jar or percussion of the mercury in carrying the barometer4 ,the details of the mountain barometer may be best followed by the illustrations4 #hac4--,the ,glass ,tube is made of mild flint glass thoroughly annealed and sufficiently stout to resist all the strain and percussion that may occur with fair usage4 ,one end of the tube is slowly sealed by the blow-pipe1 so that the closed end may be as strong as the other parts4 #had4--,mercury--,filling the ,barometer ,tube4--,the mercury of commerce is generally impure1 and it contains occluded air4 ,for standard and mountain barometers the mercury should be distilled in an iron apparatus1 at just its boiling heat1 leaving about one-sixth of the mercury in the still4 ,the tube1 which should be perfectly clean1 is left about #ab inches too long for the barometer4 ,it is charged with clean mercury for about #cf inches in height4 ,it is then boiled in a special circular charcoal stove1 in the centre of which there is a vertical iron tube of #b inches diameter4 ,the barometer tube is introduced from the bottom of the stove1 to heat about #d inches of the top of the mercury only4 ,the tube remains in this position till the mercury boils4 ,it is then elevated for another #d inches and again brought to boiling point1 and so on until the end of the tube is reached4 ,under this process the air and some impurities rise to the surface of the mercury1 and the tube is considered to be properly boiled4 ,the end of the tube is then cut off to its proper length and inserted in the cistern1 in which there is left sufficient clean mercury to complete the barometer4 #hae4--,the lower part of the barometer tube1 after it is filled1 is attached to a thin boxwood socket of about an inch in depth by means of hot thin glue4 ,the socket piece is afterwards bound over with sewing silk1 which is again covered with glue1 and is finally varnished so as to form an elastic1 secure fitting upon the glass4 ,the socket-piece is secured to a wide boxwood collar1 ,fig4 #cij1 ,d4 ,upon the under side of the collar an ivory gauge peg ,x is inserted1 which forms the index point for reading the surface of the mercury in the cistern upon the ,fortin principle4 #haf4--,the ,cistern4--,the glass sighting tube1 ,fig4 #cij ,h1 of the cistern1 through which the mercury and gauge point ,x are visible1 is made about #a inches long and from #a inch to #a inches internal diameter1 the glass being #a_/h inch to #a_/e inch in thickness1 ground square at its ends4 ,the upper end of the glass fits upon the boxwood collar ,d1 with the interval of an indiarubber band to make the fitting air-tight4 ,the lower end of the glass tube fits upon the boxwood collar ,i1 with an interval of a turned leather collar4 ,the boxwood collar prolonged forms the lower part of the cistern4 ,this has a second boxwood collar screwed upon it1 to which the leather bag ,e is attached by silk and glue4 ,a stout leather capping plug is glued upon the lower end of the bag1 upon which the boxwood cap of the adjusting screw ,f presses for adjustment of the mercury1 or to close the tube4 ,illustration3 ,fig4 #chi4--,mountain barometer erected for use4 ,illustration3 ,fig4 #cij4--,section through the cistern4 ,illustration3 ,fig4 #cia4--,vernier reading1 showing gauge point ,s4 ,illustration3 ,fig4 #cib4--,sling case for carrying4 #hag4--,the ,cistern ,casing1 which is of brass1 consists of upper and lower collar pieces1 ,fig4 #cij ,,aa and ,,bb1 and their attachments4 ,the upper collar is fixed to the casing tube of the barometer4 ,in the inside of this collar a leather washer is placed1 which comes above the boxwood collar on the glass tube ,d and makes soft contact between these parts4 ,the lower collar has been partly described with the cistern4 ,this has a brass tube ,e screwed upon it1 covering the bag and lower part of the plug of the cistern4 ,the lower closed end of the covering tube is formed into a nut for the adjusting screw ,f placed in the axis of the tube4 ,there are four bolts or screws ,,gg which bring the two collars of the cistern casing towards each other1 support the lower part of this casing1 and produce a pressure between the boxwood collar on the barometer tube and the top of the glass sighting tube with the intervening rubber collar1 so that the mercury at this point is secured4 #hah4--,the ,stem1 or ,barometer ,casing ,tube1 is made of brass1 about inch diameter4 ,this has a slot1 of about inch in width1 down two concentrically opposite sides1 from near the top of the tube downwards for about #bj inches4 ,the tube is graduated along one open edge next the slot in inches and tenths1 these being again subdivided to twentieths1 and figured to read from #ac inches to #cb inches of mercury1 as shown in detail for the upper part in ,fig4 #cia4 ,the same space is divided into centimetres and millimetres if metrical measure be used4 ,within the outer tube an inner tube of about #ab inches in length fits telescopically to move with a soft smooth motion4 ,this inner tube carries one vernier at top and one at bottom1 ,fig4 #chi1 rr4 ,the top vernier1 shown ,fig4 #cia1 is placed above a slot in this tube which corresponds with the outer tube1 so that the level of the mercury can be seen below the top vernier-piece at ,s4 ,the verniers are divided into #ej1 so that1 reading into the #bj1 they give reading #ej #bj1 or #ajjj to the inch4 ,the inner tube carries a rack about #aa inches long1 which moves by a pinion fixed upon a cock-piece1 ,fig4 #chi m1 on the outer tube in the same manner as before described for telescope racking1 art4 #if4 ,two stay-pieces placed over the outer tube hold the slots firmly at an equal opening4 ,a ring is placed at the head of the barometer to suspend it in a room1 to be used1 if required1 as an ordinary meteorological barometer1 as shown at the top of ,fig4 #cia4 #hai4--,mounting of the ,barometer4--,the barometer is mounted upon a tripod formed of three light tubes with steel points1 as shown ,fig4 #chi4 ,these screw into a collar which is packed in the cap of the leather case4 ,the collar has two opposite screws that screw into a second collar1 which is also held by two opposite points at right angles to the first4 ,the points of the screws form axes in the manner of a ,hook's joint1 permitting the barometer to take a vertical position by the superior gravity of its cistern and lower parts4 #hbj4--,the ,thermometer1 shown at ,fig4 #chi t1 has its bulb brought as nearly as possible into contact with the glass tube enclosed in the casing tube4 ,it is commonly divided with both centigrade and ,fahrenheit scales4 ,correct observation of the thermometer is necessary to be made with every observation of the barometer1 as the specific gravity of the mercury1 and consequently the height of the column1 depend partly upon this for its correct determination4 #hba4--,the ,packing ,case1 ,fig4 #cib1 is made of solid leather lined with thick felt to fit the barometer4 ,the legs are placed in packings outside the case4 ,in packing for carriage the screw of the cistern is turned nearly home1 leaving only sufficient space for any probable expansion of the mercury from increase of temperature4 ,the barometer should always be carried in an inverted position1 as this precludes the possibility of air getting into it1 and even tends to exclude1 by the jarring motion of carrying1 any air that may have accidentally become occluded4 ,a strap is attached to the case for holding it over the shoulder4 #hbb4--,reading the ,barometer4--,it will be observed that the mercury against the sides of the tube presents an upward curved appearance1 due to the resistance of the glass to perfect contact1 and the cohesion of the mercury in what is termed capillary action4 ,this beading1 as it is termed1 varies according to whether the mercury is rising or falling4 ,it is always necessary before taking an observation to raise the mercury1 by turning the screw ,f1 until its surface just touches the peg ,x1 to make observations uniform4 ,the reading is taken by slowly lowering the index-piece by means of the milled screw until light is just excluded between the fore and back index surfaces1 as shown ,fig4 #cia at ,s1 at the highest point of the surface of the mercury4 ,the inches1 tenths1 and half-tenths 7#je7 are read on the scale1 and the thousandths on the vernier4 ,thus1 suppose the scale reads #bfde and the vernier #be #be thousandths1 the reading will be-- #bfde #jbe ------ #bfdge ,for altitude the upper and lower stations are taken1 and the difference subtracted for difference of barometrical scale4 #hbc4--;,difference in ,altitude in feet taken from ,barometrical ,inches4--,complete barometrical tables for this comparison will be found in ,molesworth's and other pocket-books in use by all engineers4 ,it is therefore unnecessary to occupy our space with them4 ,a very approximate rule may be given1 which was proposed by ,mr4 ,r4 ,strachan in the ,meteorological ,magazine1 as follows3-- ,read the barometer to the nearest hundredth of an inch2 subtract the upper reading from the lower1 leaving out the decimal point2 and then multiply the difference by #i1 which gives the elevation in feet4 ,thus3-- ,lower station #bibe inches ,upper #bhjb ------ #abc #i ------ ,elevation #aajg feet4 #hbd4--;,capillarity4--,for meteorological observations a quantity must be added to the reading equal to the resistance of the tube in capillary action to the rise of the mercury4 ,this is greater in an unboiled tube than in one in which the mercury is boiled4 ,for altitude measurements with a single barometer1 or by two barometers with equal tubes1 it may be neglected1 as it will be equal in all parts of the tube4 ,where two barometers of different bores are used1 the following table gives the correction3-- ,correction of ,capillarity to be ,added to the ,reading4 ,diameter of ,tube in ,inches #f #ee #e #de #d #ce #c #be #b ,unboiled ,tube1 ,inches #jjd #jje #jjg #ja #jad #jb #jbe #jd #jei ,boiled #jjb #jjc #jjd #jje #jjg #ja #jac #jb #jbi #hbe4--,temperature ,correction4--,as the mercury increases in temperature it becomes specifically lighter1 therefore rises higher in the tube under equal atmospheric pressure4 ,the temperature is indicated by the thermometer1 shown at ,fig4 #chi t4 ,the expansion of mercury for #a ,fahr4 is #jjjjaja2 but the brass tube also expands #jjjjjajd1 and it is the difference between the two expansions that we require1 the mercury expanding about #gae more than the brass4 ,if we subtract from the reading #jjjad of the observed altitude for every degree of ,fahrenheit above #cb1 the correction will be practically very near4 ,thus for a single reading--thermometer1 #eb ,fahr42 barometer1 #cj inches -7#eb - #cb7 #cj #jjjad #jhd1 making the true reading #cj - #jhd #biiaf inches at #cb ,fahr4 ,tables for correction without any calculation will be found in ,molesworth's and other pocket-books4 #hbf4--;,gravity ,correction4--,the force of gravity decreases as we ascend to a higher level in proportion to the square of the distance from the centre of the earth4 ,it follows that the force of gravity as we ascend at the equator diminishes at a less rapid rate than at the poles4 ,its amount is always small--on an average it may be taken at about #jjja inch of mercury per #djj feet of ascent4 ,time4--,humboldt discovered that the barometer varied within the tropics at different hours of the day4 ,this has also been found to be general to some extent in all countries1 depending upon many conditions4 ,it is only important for consideration of altitude measurements1 that it is advisable if possible to take the upper and lower stations simultaneously by a pair of barometers for exact determination of altitude4 #hbg4--;,aneroid ,barometer4--,the first introduction of this instrument into ,england was by ,pierre ,armand1 le ,comte de ,fontainmareau4#ei ,this instrument consisted of a vacuum chamber as its prime mover4 ,the chamber was made a flat cylindrical box1 with its upper surface of thin metal1 with corrugations covering its surface in concentric rings4 ,the chamber was filled with a number of spiral springs which resisted the pressure of air1 to prevent the collapsing of the corrugated surface when the chamber was exhausted1 and so placed the surface in equilibrium with the pressure it received from the atmosphere4 ,the movements under various pressures were multiplied by gear work and levers so as to make a small movement of the corrugated surface evident in the extent of motion of an index hand reading upon a dial4 ,illustration3 ,fig4 #cic4--,stanley's civil engineer's aneroid4 ,the aneroid practically in its present form was devised by ,lucien ,vidie from #ahdh to #ahfb4fj ,in this instrument the vacuum chamber1 which is a thin1 flat1 circular box1 is corrugated equally on both sides1 so as to obtain double area of active surface under atmospheric pressure to that of the older form4 ,the chamber has its surfaces drawn apart by an exterior spring1 the point of communication or tension being placed at the centre of its corrugated sides only4 ,illustration3 ,fig4 #cid4--,perspective view of the interior of an aneroid4 #hbh4--,the construction of this aneroid is shown in ,fig4 #cid1 which is of a #d-;inch instrument1 aneroids made for surveying being of two sizes1 #c inches and #d inches4 ,a is a solid plate of metal #a_/h inch in thickness1 termed the base plate2 ,b the vacuum chamber1 circularly corrugated on both sides1 made of thin1 hard-rolled ,german silver containing a large percentage of nickel4 #hbi4--;,an axis is projected from the lower side of the chamber1 of about #a_/e inch diameter4 ,this is tapped with a screw and screwed firmly down into the base plate with a counternut4 ,on the upper side of the vacuum chamber the axis is projected upwards to receive the tension of a strong1 very flexible spring ,d above it1 to be described4 ,a bridge-piece ,,ee of steel of strong section strides over the vacuum chamber4 ,this piece has a stout arm-piece projecting from it towards ,a1 which is secured to the base plate by a screw that is left open to a hole indicated near ,a through the outer case of the instrument1 by means of which the bridge-piece can be rocked so as to produce more or less tension of the spring ,d upon the vacuum chamber for final adjustment4 ,the bridge-piece has two points of rigid support in right line1 which form a primary--adjusted when the instrument is made--of the spring contra to the pull of the vacuum chamber4 ,the main spring ,d is made of fine thin steel1 carefully tempered1 as broad as the chamber4 ,this spring is constructed so that by its elasticity it may have sensitive movement under the pull of #aj lbs4 to #ae lbs4 per inch of active surface of the vacuum chamber4 ,it is upon the perfection of this spring as much as upon the construction of the vacuum chamber that the sensitiveness of the instrument depends4 ,the upper axis of the vacuum chamber is secured by a cross cotter pin ,c which gives an exact point of resistance and yet secures flexibility of the spring at the junction4 ,this cotter pin is placed in the centre of the three points of support of the bridge-piece ,,ee4 ,a lever arm ,g is fixed to the main spring ,d upon a stout plate of metal which is in direct connection with the point of tension of the vacuum chamber4 ,it is the small movement of this lever arm 7about #ja inch at the chamber7 that gives motion to the indicating apparatus4 ,the lever moves a cranked arm on the axis ,,hk1 which communicates through the axis to a second cranked arm placed at right angles to the first ,i4 ,this pulls a chain ,q attached to the arm ,j4 ,the chain is wound round a small drum fixed upon the axis which carries the hand near ,r4 ,the drum keeps the hand in one direction contra to the pull of the chain by a hair spring ,r which is just sufficient to overcome the friction of the axis of the hand ,f4 ,the hand and drum and their fixings are carried by the plate ,m1 which is a light piece of brass projected from a stiff standard fixed from the base plate ,k4 ,the compound lever apparatus described moves the point of the hand about five hundred times the amount of movement over the first fulcrum of the lever at the chamber4 #hcj4--;,compensation for ,temperature4--,this is a somewhat difficult matter1 which is generally brought about by several modifications of parts4 ,some ordinary aneroids will move upwards about #a_/aj inch of mercury by a rise of temperature of #h centigrade only4 ,this is caused principally by the increase of temperature softening the spring to render it less rigid1 and the softening of the vacuum chamber to render it more flexible or sensitive to atmospheric pressure4 ,some little difference is also caused by the unequal relative expansion of the lever1 arms1 spring1 and chain1 these parts being of steel and brass4 ,compensation can be made in the lever arm ,g by making this curved and of two unequally expansive metals1 as zinc and steel1 so that the curvature increases with increase of temperature and the lever shortens4 ,compensation can also be partially made by making the base plate in two metals--iron and brass--so as to press the standards fixed through the two metals nearer or further apart with temperature changes4 ,but the whole subject is too technical to be entered upon in our limited space1 as it depends so much upon the construction of the instrument1 which is modified in various ways by different makers in order to effect this correction4 #hca4--;,dial and ,hand4--,from the delicacy of the structure of the aneroid it becomes evident that no two instruments can be made to exactly the same rate of movement2 therefore each instrument has to be separately graduated when it is intended to measure altitudes with it exactly4 ,however close or open the scale may be1 it becomes closer as greater altitudes are ascended1 the density of the atmosphere as a gaseous fluid decreasing in geometrical progression as the altitude increases in arithmetical progression4 ,from this we can understand that a vernier to the index hand can only read approximately1 although it will act fairly well at a certain point of the scale4 ,the best and possibly only correct method of dividing the scale is to put at first a false scale to the instrument1 and to read this scale by the index hand with a microscope under an air-pump1 compared at every half-inch of height of the column of the mercury by the gauge attached to the pump4 ,when this is carefully done1 a zero point is taken of the position of the index hand at the atmospheric pressure at the time1 as indicated on the false scale4 ,the proper scale1 as it appears upon the dial1 is divided from the position of the readings of the false scale1 the two scales being superimposed upon a special dividing machine4 ,the dial is afterwards figured and finished4 #hcb4--,the ordinary method of reading the aneroid is to let the index point read over the divisions4 ,the author devised a plan1 which he has used for many years1 of fixing a small plate of aluminium upon the point of the hand1 level with the scale1 which is raised on a step to read it upon its inside edge1 to a fine line on the aluminium4 ,by this means error of parallax in reading is entirely avoided4 ,the author also places an adjustable magnifier to move over the index for reading4 ,this last improvement is now followed by other makers4 ,a pointer also revolves with the outer rim to show the last reading before ascent or descent4 ,instruments made with care in the points just indicated must necessarily become expensive4 ,where the aneroid is to be used as a weather glass1 or even as a travelling companion to judge of approximate heights in climbing mountains1 such care is not needed1 and the instrument may be produced very cheaply of useful quality4 ,on the other hand1 where precision is required1 a delicately made aneroid will indicate a movement of #c feet or less in raising or depressing1 when holding the instrument horizontally in the hand and giving a light tap on the glass with the finger-nail before reading1 so as to put all motive parts in equilibrium4 #hcc4--,the ,altitude ,scale is generally placed near the periphery of the dial2 it is the all-important part to the surveyor4 ,this scale is usually set out from a mean of atmospheric pressure at sea level1 taken from ,sir ,george ,b4 ,airy's tables1 which give the extreme pressure of #ca inches barometric pressure for zero at sea level4 ,with this pressure altitudes are taken at intervals according to the indices tested under the air-pump1 and the intermediate divisions are graduated to scale4 ,these index points are shown in the table below for a few points3-- ,table of ,altitude with ,barometrical ,scale4 ,height ,barometer in ,height ,barometer in in ,feet4 ,inches4 in ,feet4 ,inches4 #j #ca #fjjj #bdhge #bej #cjgag #gjjj #bcigi #ejj #cjdcf #hjjj #bcabe #gej #cjaei #ijjj #bbbhb #ajjj #bihhc #aj1jjj #badgi #aejj #bicdj #aa1jjj #bjgjf #bjjj #bhhjg #ab1jjj #aiiei #bejj #bhbhc #ac1jjj #aibcf #cjjj #bggfi #ad1jjj #ahece #djjj #bfgfi #ae1jjj #aghec #ejjj #behjd ,it may be generally observed that the more open the scale the less altitude can be obtained by a single revolution of the hand2 therefore the more points can be taken per #ajjj feet4 ,thus1 with an altitude barometer reading to #cjjj feet1 readings can be pointed in construction at every #bej feet2 with one of #fjjj feet1 at every #ejj feet2 and over this at every #ajjj feet4 #hcd4--,movable ,altitude ,scale4--,in this the altitude scale revolves so as to be able to set it at zero for ascending from any point4 ,as the barometrical scale diminishes1 it is necessarily inaccurate1 and cannot therefore be used upon a surveying aneroid2 but the plan is pleasant for approximate measurements for amusement in making ascents4 ,it is only mentioned here for the reason that the inaccuracy of the movable scale is not always recognised4 #hce4--;,adjustment of the ,aneroid4--,there is a screw at the back of every aneroid somewhere under the point ,a1 ,fig4 #cid1 by means of which an aneroid may be brought to the reading of a mercurial barometer at the position the mercury may be read4 ,where a good instrument has been set by the maker to a standard barometer1 it is not wise to alter it frequently if it keeps in good working order for altitude measurements without being again set by a standard4 ,on the other hand1 however well the aneroid may have been made it works gradually to a slight change1 caused by the smooth wearing of parts in action4 ,it is well to have an aneroid1 after one or two years' wear1 cleaned and adjusted by the maker4 ,it will then1 if a good instrument1 work well for many years4 #hcf4--;,directions for ,measuring ,altitudes4--,turn the outer rim of the instrument until the index carried thereby reads to the same point as the index hand4 ,raise the magnifier until the reading comes into sharp focus4 ,hold the instrument as nearly horizontal as possible1 and tap the case lightly with the thumb-nail two or three times1 so as to overcome any slight friction of its mechanism4 ,this places the action of the works in equilibrium4 ,write down the observation as it now reads in the pocket-book1 taking thousands from the right hand 7large figures71 hundreds from the right hand 7small figures71 tens from the lines to the left of this1 and units from observation of the position of the index line in the space between the last and the next line4 ,say this observation reads #bdfe4 ,whether we ascend or descend1 the instrument acts similarly4 ,we will now presume we ascend to the height we require to ascertain1 and take a second reading1 #aide2 the difference between these numbers1 #bdfe - #aide #ebj feet1 is the number of feet ascent4 ,it is necessary1 where exact measurement is required1 to take the reverse reading1 as the atmospheric pressure may have changed4 ,we now descend1 taking the last observation1 #aide1 and find the reading at the first position #bdfc instead of #bdfe1 that is #b difference1 which proves that the atmospheric pressure has decreased4 ,if we take half this difference #a and correct the first deduction1 #ebj - #a #eai will give us the correct measurement1 subject only in this instance to the irregular possible fall of atmospheric pressure1 which will not in many instances1 if the times of observation have been nearly equal1 be a quantity worthy of consideration4 ,it is not necessary to make any correction for the height of the observer in positions above ground1 as the instrument must be placed at a uniform distance from the eye to obtain the reading4 ,in mines it will frequently be necessary to measure the heights from the ground at which the observation is made4 #hcg4--,various ,improvements in the ,aneroid4--,it is uncertain whether any great internal improvements have been made in this instrument1 except by ,vidie1 at various times4 ,many attempts have been made to increase the length of scale to obtain more open reading4 ,these attempts have all been in the direction of increasing the difference of space between the fulcra of the levers or by additional gearwork1 producing thereby a greater multiplication of the small unit of displacement of the axis of the vacuum chamber beyond the normal #ejj1 which is already great4 ,the multiplication has been taken up to #bjjj or more4 ,this increases the difficulty of manufacture and certainty of permanent action4 ,many of these plans were tried by ,vidie and abandoned4 ,a plan of ,vidie's#fa of giving the hand three or four revolutions1 and to register this upon a spiral scale upon the dial1 also by counting on a second dial the number of revolutions1 has been repeated with slight variation by ,e4 ,t4 ,loseby in #ahfjfb and by ,major ,watkin later4 ,vidie's plan of drawing back the hand to read the spiral has been modified also by ,major ,watkin in a manner which may be a little less frictional4#fc ,illustration3 ,fig4 #cie4--,watkin's extended scale surveying aneroid4 #hch4--,watkin's ,extended ,scale ,aneroid4--,this instrument is shown at ,fig4 #cie1 and has a very extended reading1 consisting of three complete circles1 in place of the usual single scale1 with a hand or pointer sufficiently long to extend across them all4 ,in order to show clearly which circle of scales should be read there is an indicator attached to the movement of the instrument which causes a series of figures 7,i41 ,,ii41 ,,iii41 corresponding with the three circles7 to be exhibited through an aperture in the dial4 ,for instance1 when the instrument is in its normal state the hand will point to the first or outer circle1 and the figure ,i4 will appear and remain in the aperture until the barometer falls to #bgh1 where the break takes place in the circle1 as will be seen in the illustration4 ,the hand then takes up the reading on the second circle 7where the break appears at #bgh7 and figure ,,ii4 replaces figure ,i4 in the aperture1 remaining there until the barometer falls to #be1 when the reading is transferred to the third circle1 and figure ,,iii4 appears in the aperture4 ,illustration3 ,fig4 #cif4--;,face4 ,illustration3 ,fig4 #cig4--;,back4 #hci4--,watkin's ,new ,patent ,mountain ,aneroid ,barometer4--,this instrument1 of which both a front and back view is shown above at ,figs4 #cif and #cig1 is the invention of ,colonel ,h4 ,s4 ,watkin4 ,the special feature is that it can be put in or out of action as required1 and when out of action is impervious to the influence of variations in atmospheric pressure4 ,this relieves the strain on the mechanism of the aneroid1 as it is only put into action when a reading is required4 ,the lower portion of the vacuum-box instead of being a fixture 7as is the case with ordinary instruments7 is allowed to rise1 which is effected by attaching to the lower portion of the vacuum box a screw arrangement actuated by a fly nut on the outside of the case4 ,under ordinary conditions this screw is released1 and the vacuum-box put out of strain4 ,when a reading is required1 the fly nut is screwed up as far as it will go1 thus bringing the instrument into the normal condition in which it was graduated4 ,it has an aluminium case for lightness1 is made in two sizes 7#c inch and #d inch71 and has a sling leather case4 ,these plans are again on their trial4 ,it is the author's opinion on the subject1 knowing the delicacy and skill shown in ,vidie's work1 that little improvement is likely to be obtained by magnification of the small motion of the vacuum chamber by mechanical means1 which must necessarily be by a process both delicate and highly frictional4 ,attempts1 he thinks1 may otherwise be successfully made in the magnification of the small motion of the hand in a frictionless manner by optical means to obtain clearer definition4 #hdj4--;,an improvement was made in the aneroid in one direction by the late ,thomas ,cooke#fd by replacing the chain by a thin gold band upon1 and leading from1 the drum4 ,this obviated the small difference of rate of displacement due to separate jointed links as they leave the tangent of the drum4 ,it is said1 however1 to cause a little springiness at this point1 where it should be very dead1 which somewhat minimises the improvement2 so that it has not been very generally adopted4 #hda4--;,bourdon's ,aneroid1 invented by ,c4 ,bourdon in #ahdi4fe ,the motor of this instrument consists of a flat1 oval tube bent into a circular form4 ,this tube opens to greater and lesser curvature by difference of external pressure upon it4 ,the small motion given at one free end of the tube is multiplied up by gearwork4 ,this instrument is found to act most delicately as a steam gauge2 but experience has shown that it is not so sensitive or durable for indicating atmospheric pressure as the vacuum-chamber aneroid last described4 #hdb4--;,hypsometer1 or ,boiling-point ,thermometer4--,that water or any other liquid boils at a certain temperature1 according to the amount of atmospheric pressure surrounding it1 is easily observed by placing a cup of boiling hot water under the receiver of an air-pump4 ,at first the surface will remain still1 but as the pressure of the air is pumped off it may be made to boil time after time until it arrives at a low temperature4 ,the temperature at which the water boils as the air is rarified may be easily followed by observation of a thermometer immersed in the cup of water2 and at the same time1 if a barometer be placed in connection with the receiver it will indicate the pressure1 from which the scale of differences may be practically made4 ,for the civil engineer this instrument1 accompanied by the aneroid1 is in every way superior to the mountain barometer1 which must necessarily have a three-feet tube1 as the hypsometer is much lighter1 more portable1 and less liable to injury1 and perhaps1 from the uncertainty of keeping a pure vacuum in the barometer1 safer as a means of observation4 ,illustration3 ,fig4 #cih4--;,hypsometer1 or boiling point thermometer4 ,illustration3 ,fig4 #cii4--;,case for hypsometer4 #hdc4--,the modern form of instrument is shown in ,fig4 #cih4 ,the boiler shown immediately over the lamp is filled about half full of rain water by lifting off its covering tube ,c4 ,the covering tube has a smaller tube1 about #c inches long and inch diameter leading upwards from it1 through which the thermometer bulb is passed into the boiler4 ,this tube is covered by the jacket ,j1 formed of four telescopic tubes that are extended1 as shown in the figure1 for use1 but which close up quite compactly when the instrument is put in its case4 ,the upper drawer of the jacket tube is about inch diameter1 so that the tube enclosing it passes over the leading tube when the apparatus is closed4 ,the lamp1 which is filled with pure spirit1 draws out from the bottom of the outer casing ,o4 ,it carries a wick holder with screw cap1 and this again has a covering cap to secure the spirit perfectly when the instrument is carried about4 ,the inner casing ,a is perforated with holes to admit air at the level of the body of the lamp4 ,when the lamp is lighted and complete for use it is placed vertically in its outer case ,o1 which is jointed in two parts and perforated by large holes surrounding it top and bottom3 the bottom holes are covered with wire gauze4 ,by this arrangement the flame is not seriously disturbed by wind or rain4 #hdd4--,the ,thermometer1 upon which the action of the instrument depends1 has a stout stem about #f inches long and inch diameter1 with a very fine1 flat1 oval bore about #ja inch wide and not much over #jje inch in thickness4 ,the stem is divided very openly for about #be below #ajj centigrade1 each degree being subdivided into #aj1 below #bab if ,fahrenheit scale be used1 with each degree divided into #e4 ,the divisions are filled in with lamp-black1 and the stem is backed with white enamel to give clear reading4 ,the thermometer ,t when in use is surrounded by a vulcanized indiarubber collar ,i which slips over its stem to adjust it to position in the boiler tube as shown4 ,in placing the thermometer in its jacket1 it is important to hold it erect to be sure it passes into the leading tube from the boiler1 as there is generally just room for it to catch by the side of this tube1 where if it were pressed down it would break the bulb4 ,when the thermometer is out of use the rubber collar is removed1 and the thermometer is placed in a tubular metal case which is lined with indiarubber tubing1 so that no jar can injure it4 ,the whole apparatus when closed is carried in a solid leather case1 which contains divisions for the separate parts of the apparatus1 and a strap for passing over the shoulder for carrying it4 ,fig4 #cii shows the general form of case4 #hde4--,use of the ,hypsometer4--,saussure calculated1 from data of his ascents of ,swiss mountains1 that the temperature of boiling water decreased #a centigrade for every #ighe feet of ascent1 where the mean temperature of the atmosphere was estimated at #j centigrade1 or freezing point4 ,if the temperature of the surrounding atmosphere be taken as #ee centigrade1 the ascent per degree of that scale is #ajjj feet4 ,this becomes1 therefore1 the most convenient data to calculate from1 allowing #ci feet per #ajjj per degree centigrade for temperature above or below #ee centigrade at any two stations of observation1 of which the difference of level is required4 ,thus3--,if at the first station the temperature of air be #aef centigrade1 the boiling point #iee centigrade2 second station temperature of air #ada centigrade1 boiling point #idb centigrade1 the barometrical pressure of the lower station being taken as a constant1 or referred to the aneroid for correction2 then #aef - #ee 7#ia7 7#ci7 #bib dif4 #iee - #idb 7#ac7 7#ajjj7 #acbib - dif4 external temperature 7#aef - #ada7 7#ci7 #acbcd difference of level in feet4 ,sometimes the thermometer is divided to ,fahrenheit degrees1 subdivided into #e to read by interspace and line to #a ,f4 ,this may be changed to centigrade for use of the above formula by taking #cb ,f4 lower than the reading and multiplying by #e_/i4 ,thus-- #fj ,fahr4 #e_/i 7#fj - #cb7 #aeee centigrade4 ,the calculation proposed by ,lefroy is1 however1 simpler for ,fahrenheit scale4 ,to allow for diminution of boiling temperature1 with height from #bab1 with barometer at #cj inches1 take #eaa feet of altitude for the first degree and add #b feet for each succeeding degree4 ,thus1 taking height of first station h corrected for #bab ,fahr41 #cj inches barometer1 remembering decrease of barometrical pressure acts the same as increase of height4 ,then-- #baa boil point h #eaa feet4 #baj h #eaa #eac h #ajbd feet4 #bji h #eaa #eac #eae h #aeci feet4 ,,footnotes3 #ei ,british patent1 ,no4 #ajaeg1 ,april1 #ahdd4 #fj ,british patents--,no4 #acccb1 ,november1 #ahej2 and ,no4 #fhb1 ,march1 #ahfb4 #fa ,patent1 ,no4 #acccb1 ,may1 #ahej4 #fb ,patent ,no4 #cded1 ,december1 #ahfb4 #fc ,patent ,no4 #cdbe1 ,march1 #ahhf4 #fd ,patent ,no4 #bgad1 ,october1 #ahfe4 #fe ,patent ,no4 #abhhi1 ,december1 #ahdi4 ,,chapter ,,xix4 ,,miscellaneous ,,surveyors' ,,and ,,engineers' ,,instruments1 ,,appliances1 ,,and ,,accessories--,,cross ,,staff--,,mechanics' ,,levels ,,and ,,clinometers-- ,,boning ,,rods--,,footner',s ,,railway ,,gauge--,,girth ,,strap ,,for ,,timber ,,measurement--,,girth ,,tapes--,,timber ,,marker--,,slashing ,,knife--,,bill-,,hook-- ,,reconnoitring ,,glass--,,telescope--,,sun ,,spectacles--,,whistles--,,pioneer ,,tools--,,sketch ,,block ,,book--,,camera--,,geological ,,tools--,,wealemefna-- ,,opisometer--,,boucher',s ,,calculator--,,slide ,,rules--,,fuller',s ,,calculator-- ,,engineers' ,,pocket ,,books--,,chronometer--,,outfits4 #hdf4--;,cross ,staff4--,those of ,tycho ,brah and of ,gunter were very elaborate affairs1 consisting of a pair of notched cross-bars sliding on a divided rod which gave directions to form any angle in a quadrant from the eye by sliding the bars further from or nearer to it4 ,the surveying cross staff1 after better instruments were invented to take angles1 became a cross at right angles1 sawn upon a disc of wood and supported upon a staff which was pressed into the ground4 ,this was used by looking along the saw cuts to take offsets to the chain1 and for setting out buildings4 ,the fixed cross-head was much improved by making it a cross of metal with turned-up ends1 down the centre of which vertical saw cuts were made at right angles1 ,fig4 #djj4 ,this1 in the author's opinion1 is still the best form4 #hdg4--;,cylindrical heads superseded the open cross-head4 ,the modern instrument in use is the ,french form1 ,fig4 #dja1 which is made of octagon brass tube4 ,this is cut with alternate sight slit and opposite window1 with vertical hair on each of four rectangular sides of the octagon4 ,on the other four sides there are plain slits subtending #de to those first mentioned4 ,the octagon tube is mounted upon a socket-piece which fits upon a conical pointed staff4 ,the defect of this cross-head is the closeness of the slits1 due to the small diameter of the tube1 which renders the direction given for sighting uncertain4 ,illustration3 ,fig4 #djj4--,open cross-head4 ,illustration3 ,fig4 #dja4--;,french form4 ,illustration3 ,fig4 #djb4--;,adjustable cross staff head4 #hdh4--;,adjustable ,cross ,staff ,head4--,the cross staff head is sometimes made cylindrical1 in two parts1 ,fig4 #djb4 ,the upper part is centred upon the lower so that the upper series of sights move to any angle in relation to the lower4 ,in this construction a wheel is cut about the axis of the upper part1 which works into a pinion in the lower part1 so that the upper part may be revolved horizontally by it4 ,the meeting planes of the two cylinders are divided1 the lower into degrees and the upper with a vernier4 ,the vernier is almost an unnecessary refinement1 as the sighting distance from slit to hair is only about three inches1 and no very great exactness can be obtained in the sighting4 ,this instrument has commonly a magnetic compass upon the upper surface4 ,it is about as expensive as the semi-circumferenter1 shown ,fig4 #bcb1 p4 #cdg1 and very inferior to that instrument owing to the extreme closeness of the sights4 ,its use is obvious4 ,many of the following articles1 briefly described1 may be beyond the direct province of this work2 but the utility of these implements for completing the equipment of a surveyor or engineer for special work it is hoped will be sufficient apology for their introduction4 ,the subject can scarcely be treated except in a desultory manner4 #hdi4--,mechanics' ,levels4--,in crowded ,eastern cities1 in levelling through close passages1 in many cases the surveyor has to resort to mechanical levelling to carry his levels through4 ,mechanics' levels are too well known to need much description4 ,the ordinary good kinds are made from #f inches to #ah inches long1 generally of rosewood1 as this wood is very hard and stands well4 ,they have a brass plate at the top1 and tips of the same metal at the base4 ,the illustration1 ,fig4 #djc1 is of a #ab-;inch level4 ,the level tube1 which is of blown glass1 is fixed in plaster of ,paris1 and the upper plate screwed down over it4 ,illustration3 ,figs4 #djc1 #djd4--,mechanics' ,levels4 #hej4--,the ,author's ,hand ,level is shown ,fig4 #djd--ab inch4 ,this is made of a casting either of iron or brass4 ,the level tube is ground to curvature and is somewhat superior to the ordinary run of this class of work4 ,the level tube is fitted with ball socket at one end and stiff spring fitting at the other1 which is adjustable1 so that the tube may be easily replaced if broken4 ,these levels are commonly fixed upon a stout fir straight-edge of about #e feet to #aj feet in length by the lugs at the ends4 ,the level is taken by blockings upon the ground4 ,corrections of error1 both in level and straight-edge1 may be made for any considerable distance by reversing the forward and backward position of the level with its straight-edge alternately4 #hea4--,square ,level--,circular ,level4--,fig4 #dje represents a very useful class of level for setting up some instrument stands1 plane tables1 etc41 in which a pair of level tubes are placed at right angles to each other4 ,it is generally made very small--#a inches square only4 ,a circular level1 the upper surface of which is formed of a worked concave glass1 was lately very popular1 and is still used to a small extent4 ,as the spirit cannot be hermetically sealed in1 it evaporates1 and this level soon fails4 ,mr4 ,j4 ,j4 ,hicks has taken out a patent for a hermetically sealed circular level1 described p4 #if1 which appears to answer very well4 ,illustration3 ,fig4 #dje4--,square level4 ,illustration3 ,fig4 #djf4--,surface level and clinometer4 #heb4--;,incline ,level4--,for laying railway rails and drainage works the bubble is frequently made adjustable by the tube in which it is contained being hinged at one end and fitted in slides to rise with a screw at the other end1 as shown ,fig4 #djf4 ,a scale of percentage of inclination ,s is commonly divided upon the adjustable end4 ,the tube is raised or lowered by the key ,a1 which is removed after setting and cannot be tampered with4 ,illustration3 ,fig4 #djg4--,stanley's sight for mechanics' levels4 ,illustration3 ,fig4 #djh4--,section4 #hec4--,sighted ,levels4--,a mechanic's level is commonly made with a hole longitudinally through it of about inch diameter1 closed at one end1 except a small hole of #a_/cj inch or so1 and a cross upon a piece of glass at the other end4 ,this plan permits a sight to be taken through it which gives an approximate level4 ,occasionally the same form of sight as that described is hinged on the top surface at each end of the level4 ,the author has found a better plan of sighting to be given by a pair of sights placed on a centre upon the ends of the level to turn up when required for use1 as shown ,fig4 #djh1 ,p ,s one of the pair of points4 ,this1 when turned up1 shoulders on the stop-piece ,a ,b4 ,the stop-piece is made of sufficient thickness to admit the point in the hole near ,b for protection when it is folded away out of use4 ,the section of the level1 as shown by the end view ,d1 is the same as that of the level1 ,fig4 #djd4 ,very fair accuracy may be obtained by making these sights appear coincident upon a distant staff or rod4 ,illustration3 ,fig4 #dji4--;,boning-rod4 ,illustration3 ,fig4 #daj4--;,boning-rod with standard4 #hed4--;,boning-,rods1 ,fig4 #dji4 ,these are very commonly employed with mechanics' levels4 ,they are made somewhat like a stout ,t-square of #c feet to #d feet in length1 about #c inches in width1 and inch in thickness both of the stem and head4 ,they are at first placed at a distance apart1 #i or #aj feet1 and a straight-edge of this length is laid from one to the other1 upon which the mounted level is afterwards placed1 the boning-rod being tapped down in the ground till the bubble is in the centre of its run4 ,a third boning-rod is then placed at the same distance as the first pair1 and the straight-edge with the level upon it is reversed end for end4 ,this1 if the work be fairly down1 leaves the two outer boning-rods level1 however imperfect the straight-edge and level may be1 if the run of the bubble be taken correctly4 ,by removing the central boning-rod from the outer pair of rods1 levels may be continued by sighting over them1 or boning forward as it is termed4 ,on the ,continent boning-rods are commonly fixed by driving a separate standard into the ground1 which has a pair of brass slings by its side to hold the rod1 ,fig4 #daj4 ,this is a much neater plan than that in common use of blocking the rod up with stones4 ,boning-rods are also sometimes used conveniently with a proper surveying level1 from the tops of water-pipes1 etc4 ,illustration3 ,fig4 #daa4--;,footner's railway gauge and clinometer4 #hee4--,railway ,gauge1 combining level and clinometer4 ,this high-class gauge1 ,fig4 #daa1 is the invention of ,mr4 ,h4 ,footner1 ,c4,e41 late of the ,london and ,north-,western ,railway4 ,it is formed of a bar of ,spanish mahogany neatly shaped4 ,the end fittings are of steel4 ,the gauging part is formed of two turn-up steel flap-pieces with back stops4 ,a spirit level is sunk in the end fitting1 shown in the figure towards the left hand4 ,the clinometer is formed by a gun-metal pin of inch in diameter2 #i inches long4 ,this slides perpendicularly in a spring fitting sufficiently stiff to support the gauge1 and is made to fall on the centre of the rail4 ,the pin is divided into inches and eighths4 ,when it is out of use it slides up the end of the gauge and leaves the whole instrument smooth and portable to carry open or go into a leather case4 ,its use is implied4 #hef4--,timber ,girth ,strap4--,the direction for removal and estimate of the value of timber often falls into the hands of the surveyor4 ,the height of standing timber may be taken by a long rod1 or a pair united by a link1 art4 #gge1 or by the apomecometer1 art4 #fic4 ,the girth is most conveniently taken by a leather girth strap1 of which there are various patterns3 but that illustrated below1 ,fig4 #dab1 is perhaps the most popular form4 ,this strap is made of two straps of bullock's hide #a inch wide1 thinned down to about #a_/h inch in thickness2 the two pieces are stitched together to make it #ab feet to #ad feet long4 ,the strap is divided by lines into inches1 but figured in units at every #d inches single inches of quarter-girth4 ,the figures and lines are stamped4 ,a brass weight1 shown at one end of the strap1 is thrown by the strap with a swing round the standing tree1 and encompasses it in a second of time4 ,the weight is caught by the hand and the strap brought up to it to read the quarter-girth4 ,the quarter-girth gives roughly the equal sides of a square2 as1 for instance if a quarter-girth reads #aj1 the size of the tree is #aj #aj #ajj inches1 or #hd cubic foot-inches per foot run4 ,illustration3 ,fig4 #dab4--,leather girth strap with throwing reel4 ,some surveyors prefer a hook instead of a weight1 as being more convenient to measure close timber4 ,this is shown ,fig4 #dac4 ,the hook is stuck into the bark and the tree is girthed by walking round until the hook is met4 ,illustration3 ,fig4 #dac4--,leather girth strap with clutch hook4 #heg4--;,girth ,tapes1 similar to measuring tapes1 ,fig4 #cdi1 p4 #ejf1 are occasionally used1 but these are more convenient for felled timber4 ,tapes for the purpose are made from inch to #a inch wide1 and #f1 #ab1 and #bd feet long4 ,they have the ordinary feet and inches on one side and quarter-girths on the other4 ,it is customary to allow #a or #a inches1 and sometimes more for bark1 according to the species of tree and the custom of the country4 #heh4--,marking off ,timber4--,for this a special tool with a gouge point1 ,fig4 #dad1 and strong buck-horn handle1 termed a timber-marker1 is used for standing timber intended to be felled4 ,the contents of the tree are sometimes marked with the marker upon it if for sale1 good bark allowance being made in cases of difficulty of extraction from the forest1 etc4 ,a plain knife is usually put with the marker1 which is useful as a food knife4 ,illustration3 ,fig4 #dad4--,timber marker1 nearly full size4 #hei4--,the author makes a very small1 neat surveyor's knife1 with marker1 for the waistcoat pocket1 ,fig4 #dae1 which combines--,m tree marker 7small72 ,s screw-driver for small screws of instruments2 ,p tommy-pin for turning capstan heads2 ,f file for sharpening lead of pencil1 when this is used for the field-book2 and ,e ,r two penknife blades4 ,the knife is similar to the author's architect's knife1 which is well known4 ,the tree marker is not strong enough for constant work4 ,illustration3 ,fig4 #dae4--,surveyor's pocket knife4 #hfj4--,slashing ,knife--,bill-,hook--,axe4--,in new countries where sight way has to be obtained for the survey through forests and jungles1 one or more of the tools illustrated next is most valuable as a part of the surveyor's equipment4 ,the slashing knife1 ,fig4 #daf1 which is over a yard long1 wielded by a strong man will remove light brushwood very quickly4 ,where the wood is close and of larger growth the bill-hook1 ,fig4 #dag1 is better2 and with thickset timber the axe becomes necessary4 ,the well-known ,canadian axe is found to be the best4 ,illustration3 ,fig4 #daf4--,slashing knife4 ,illustration3 ,fig4 #dag4--;,bill-hook4 #hfa4--;,hedging ,gloves--,iron ,hooks for ,climbing ,trees4--,for clearing land to avoid spines hedging gloves are generally used2 these are made of soft horse-hide1 and although pliable resist thorns to a great extent4 ,clutch hooks are also very convenient to climb trees1 to look forward for the easiest direction for sight way4 #hfb4--,rods for ,measuring ,standing ,timber4--,these are generally made #be feet long1 jointed in #e feet lengths1 similar to a fishing rod1 but much stiffer4 ,the rod is set by the side of a tree to be measured and observed from a distance where the first breech cuts its length4 ,illustration3 ,fig4 #dah4--,reconnoitring glass1 ,india pattern4 #hfc4--,reconnoitring ,glass4--,at present it is customary to use a binocular field-glass in preference to a telescope4 ,the telescope gives greater penetration from its higher power2 the field-glass is preferred for its wider field of view4 ,the field-glass the author has supplied to the ,indian ,government has neutral-tint glasses centred on the eye-pieces to take off the glare when looking towards the sun1 ,fig4 #dah4 ,these have also hinge joints between the pair of bodies1 which permit adjustment of distance of centres to the distance of the eyes4 ,the object-glass should be #a inches1 not over this4 ,where a telescope is used1 the #cj-;inch--the original1 not the present--,india military telescope is to be recommended1 ,fig4 #dai4 ,this is portable1 has a sling case and a good #b-;inch object glass4 ,for lightness1 aluminium bodies are preferred by many for both field-glasses and telescopes2 at present the price of this metal is very low1 so that it is probable it may become in a short time general for the purpose4 ,illustration3 ,fig4 #dai4--;,army telescope4 #hfd4--,prism ,binoculars4--,these will be found a great improvement on the old form of field-glasses1 as owing to the optical arrangement a high power is obtained combined with a larger field of view and good illumination4 ,fig4 #dbj shows the most modern form with all refinements2 hinged body1 central focussing and separate focussing to suit each eye4 ,it has a very compact and strong body1 and the size magnifying #h diameters or about #fd times weighs only #ac ozs4 ,illustration3 ,fig4 #dbj4--,stanley's prism binocular4 #hfe4--;,dome ,spectacles--,bogles4--,spectacles of neutral tint are most comfortable for general wear in sunny or snowy countries4 ,the dome or globular form is generally preferred4 ,where there is hot dust gauze sides are to be preferred4 ,there is a very cheap form with gauze sides1 which holds on the head by an elastic band1 termed bogles4 ,these are rather hot to the face1 and the band after a time becomes sticky4 ,the spectacle form is much better4 ,the glasses are made in various shades to choice3 some very dark or even black1 the latter being made for viewing and tending arc lights4 #hff4--,whistles made very powerful are much used in exploring abroad to bring the party together1 and for signalling generally by sound1 using the ,morse signals1 art4 #hjc4 #hfg4--,pioneers' ,tools4--,a small set of these is often very useful to the surveyor in new forest countries4 ,the common set consists of a claw-hammer1 wood-chisel1 stone-chisel1 pincers1 screw-driver1 gimlet1 and brad-awl4 ,the leather case is #h by #d by #b inches2 it weighs #a lbs4 with strap4 ,this may be supplemented by a small ,american saw1 cutting both edges1 about #bj inches long1 and the axe previously described1 with a few pounds of wire nails4 ,the tools serve for marking trees or rocks1 erecting signals1 temporary covers1 etc4 #hfh4--,sketch ,block ,book--,pocket ,book4--,in reconnoitring no better information can be given of a track than forward sketches from commanding station to station4 ,sketch books about #g inches by #e inches are generally found sufficient4 ,the drawing-paper should be thin1 and the pocket large enough to contain all the separate sheets as they are taken off by the penknife after completion from the block4 ,the sketches may be made with pencil1 or a fine fountain pen2 or if the surveyor be a colourist a light box of moist colours and a water bottle will often leave pleasing sketches as reminiscences4 ,pocket-books with section lines to #a_/h inch or #a_/aj inch scale are sometimes used to give approximate plans to scale of buildings1 etc41 where required1 as well as the ordinary field-book record4 #hfi4--;,camera4--,recently the camera has been much used for reconnoitring4 ,these are now made very light and portable to take plate or #c #c inch films1 either on rollers or in separate films4 #hgj4--;,cement ,testers are made in various manners1 generally to test the cohesion of the cement as a homogeneous hard body4 ,mr4 ,mann's cement tester1 ,fig4 #dba1 goes on another principle--it tests the adhesion of the cement to stone1 which appears to the author to be its most important function2 it is always hard enough4 ,illustration3 ,fig4 #dba4--,mann's cement tester4 #hga4--,watson's ,improved ,vicat ,needle is a most refined and accurate instrument for determining the time taken by cement in setting4 ,the cement is placed in the circular container shown in the illustration1 and the weighted needle is lowered into it by means of the handle at the top4 ,the depth of penetration is shown in millimetres on the divided arc4 ,illustration3 ,fig4 #dbb4--,watson's vicat needle4 #hgb4--;,geological ,tools4--,acid-bottle--,blow-pipe--,touc h-stone4-- ,where countries are prospected for railways it often becomes important to examine the rocks1 both to detect the softer rocks for cutting and to find limestone suitable for mortar4 ,a geological hammer1 weight about #b lbs4 to #c lbs41 is the ordinary tool4 ,this1 with a chisel and sailcloth bag with strap1 is all the necessary appliance4 ,in searching for limestone a small bottle of sulphuric acid sewn up in a leather case is useful4 ,a dipper is blown on the stopper of the bottle1 and a single drop of acid will detect limestone by the bubble of froth it produces4 ,where minerals are to be examined1 a small blow-pipe apparatus is necessary4 ,this should be accompanied by a book of instructions4 ,where the surveyor has not been trained to use the blow-pipe1 one with constant blast should be employed4 ,for examination for precious metals a touch-stone and two-acid bottle--sulphuric and nitric--for silver and gold1 are useful4 ,the metal is merely rubbed on the stone and the acid applied4 ,if the metal is base the acid removes it from the surface of the stone4 ,if precious it removes other matter and leaves it visible4 #hgc4--,wealemefna--,opisometer4--,the wealemefna is a very neat form of space runner invented by ,mr4 ,e4 ,r4 ,morris1 which is found a very convenient instrument for measuring distances on maps in prospecting4 ,it is very small and light1 and may be1 if desired1 attached to the watch-chain4 ,it gives distances run over in inches and eighths1 to be afterwards calculated to the scale of the map1 ,fig4 #dbc4 ,the opisometer for the same purpose1 ,fig4 #dbd1 is formed of a spur wheel at the end of an ivory handle running upon a screw4 ,this instrument gives measurement by reversing its run upon the scale of the map4 ,illustration3 ,fig4 #dbc4--,wealemefna4 ,illustration3 ,fig4 #dbd4--,opisometer4 #hgd4--;,boucher ,calculator1 the invention of ,m4 ,alex4 ,e4 ,m4 ,boucher1 engineer1 of ,paris4#ff ,this is one of the most convenient pocket calculators that a civil engineer can desire1 being only of the size of an ordinary watch4 ,the instrument was formerly made in ,france for this country in a very slovenly manner4 ,it is now made in ,london by the author1 of sound work and accurate centring1 ,fig4 #dbe4 ,it has face back and front4 ,the front one1 which is shown in the illustration1 carries logarithmic scales of sines1 numbers and square roots1 and is made to revolve by turning the milled head placed under the handle1 as the winder of a keyless watch4 ,the back dial1 which is fixed and does not revolve1 has upon it a scale of equal parts giving the decimal parts of logarithms1 and a logarithmic scale of cube roots4 ,there are three index hands1 one fixed on the side of the case over the front dial1 as shown in ,fig4 #dbe1 and one on each end of the central axis made to revolve simultaneously over the back and front dials by means of the milled head at the side of the case4 ,any operation involving multiplication1 division1 proportion1 powers or roots can be performed approximately with great rapidity by the aid of this calculator1 and it is practically as simple to use as an ordinary slide rule1 as will be seen from the following explanation of its use3-- ,illustration3 ,fig4 #dbe4--;,boucher's calculator4 ,illustration3 ,fig4 #dbf4--,stanley-,boucher calculator4 ,multiplication1 using the second circle of divisions from the outside of the front dial3--,bring the first factor under the fixed index1 set the movable index to #a1 then bring the second factor under the movable index1 and the product will be found under the fixed index4 ,division is performed on the same scale as follows3--,bring the dividend under the fixed index1 set the movable index to the divisor1 then bring #a to the movable index1 and the quotient will be found under the fixed index4 ,for proportion the second circle is also used3--,set the first factor under the fixed index and set the movable index to the second one1 then the proportionate equivalent of any number brought under the former will be found at the movable index4 ,square roots1 using the same scale3--,bring the number under either of the indices1 and the square root will be found upon one of the two inner circles of the same dial4 ,cube root3--,in this case it is necessary to first bring the #a on the front dial under the fixed index1 then set the movable index to the number1 and the cube root will be found on one of the inner circles of the back or fixed dial4 ,to use the trigonometrical dial3--,bring the needle of this dial over the angle of which the sine or tangent is required1 and read upon the other dial 7indicated by the needle7 the natural trigonometrical line upon the inner circle1 or its logarithm upon the outer circle4 ,the book of instructions supplied with the instruments1 written by ,professor ,george ,fuller1 ,c4,e41 for the author1 gives all directions for working and also gauge points from which calculations are made as with the slide rule4 #hge4--;,in reduction of factors of a calculation collectively ,boucher's calculator may take more than one turn or less than unity4 ,the author has added a central index to record the number of turns4 ,this is said to be of great value for the perfection of the instrument1 ,fig4 #dbf4 #hgf4--,slide ,rules1 of which there are great varieties1 are of too complex a nature to discuss1 except very briefly1 in our limited space1 particularly as general descriptions have been often given4 ,the ordinary logarithmical scales of ,gunter 7#afai71 known as ,gunter's lines1 are placed upon most slide rules4 ,the arithmetical lines are lettered ,a1 ,b1 ,c1 ,d1 and ,e4 ,a and ,b are alike3 these are technically termed double radius log4 lines4 ,they are used for all processes of multiplication and division4 ,c and ,d are also alike and are termed single radius log4 lines4 ,they are used together for ordinary multiplication and division1 and in conjunction with ,a and ,b scales for squares and square roots4 ,the ,e line1 not originally a ,gunter's line1 but found early in the century on several rules1 is termed a triple radius log4 line4 ,the numbers of the divisions on this line are the cubes of the numbers of the corresponding divisions of the ,d line1 with which it generally works4 ,all these lines work reciprocally together1 performing the most complex calculations by simply setting them to numbers or gauge points of which given solutions are required1 as for instance1 the first four lines in combination give answers to such questions as3--,to divide by a number two numbers multiplied together1 one of which is squared2 to divide the product of two numbers by the square of a third number1 etc41 each of which calculations is performed at a single setting4 ,by inversion of the slide ,a to ,c the reciprocal of a given number is found1 also the mean proportional between two numbers1 the fourth term is inverse proportion1 etc4 ,trigonometrical calculations are performed by the lines of sines1 tangents1 etc4 ,instructions are to be found in the books supplied with the rules1 and as a part of many works4 ,among the most complete books may be mentioned ,the ,slide ,rule1 by ,r4 ,g4 ,blaine1 ,m4,e41 and ,the ,slide ,rule1 by ,chas4 ,n4 ,pickworth4 ,these both contain very full information on the subject4 #hgg4--,the ,slide ,rules in most general use are ,a4 ,nestler's and ,a4 ,w4 ,faber's4 ,both these well-known firms make a very complete series1 applicable to a great variety of technical calculations4 #hgh4--,the reviser has recently completed from the designs of the author an entirely automatic dividing engine for these rules1 which is the only one in existence4 ,a great number of slide rules are made for special purposes only3 some of these are very useful to the civil engineer4 #hgi4--;,hudson's ,slide ,rules give strength of shafts1 beams1 and girders2 pump duty2 and computation of horse-power in engines4 #hhj4--;,honeysett's ,hydraulic ,slide ,rule gives discharge of water from channels and pipes of different forms and inclinations4 #hha4--,tacheometrical ,slide ,rules with scale of sine#b and sine cos4 for calculating the horizontal equivalents and vertical heights from tacheometrical observations4 ,these are made either for use with instruments divided sexagesimally to #cfj or centesimally to #djj4 #hhb4--,sheppard's ,slide ,rule has duodecimal lines1 double reading1 for squaring and cubing timber4 #hhc4--,young's ,slide ,rule is designed for squaring and valuing timber simultaneously1 which operations it performs in a very expeditious manner4 #hhd4--;,essex's ,slide ,rule is the best for calculating the rates of velocity and discharge from sewers1 water mains1 channels1 and culverts of different forms1 as it works with all formul4 #hhe4--,the ,slide ,rule of ,prof4 ,geo4 ,fuller1 ,c4,e41 ,fig4 #dbg1 presents perhaps the highest present refinement of this class of rules1 capable of greatly facilitating the numerous arithmetical calculations of the civil engineer4 ,its range is greater than most calculating machines1 and besides the operations of multiplication and division1 squaring and cubing1 results requiring the reciprocals1 powers1 roots1 or logarithms of numbers can be quickly and easily worked out by its use4 ,illustration3 ,fig4 #dbg4--,professor ,fuller's calculating slide scale4 ,the rule consists of an outer cylinder that can be moved up or down1 and turned round upon the cylindrical axis which is held by the handle4 ,upon the outer cylinder a single spiral1 logarithmical scale is continued from end to end1 the total length of which makes the scale #ejj inches long4 ,this is graduated into #gbej divisions4 ,one index is fixed to the handle4 ,a second index is attached to the inner tube blocked out by a flange to read upon any part of the scale2 so that altogether there are three tubes which work together telescopically1 by means of which the indices may be set to any position on the graduated cylinder4 ,stops are placed so that the indices may be brought to zero4 ,by these means1 the indices being set to any of the gauge points1 the logarithmical scale1 moving by itself1 will maintain the same proportion for any numbers4 ,in this rule a single log4 radius is repeated by coincidence of indices1 so that its scale of divisions1 #da feet #h inches long1 if compared with an ordinary double radius slide rule1 becomes equal to a slide rule of #hc feet #d inches long4 ,the ordinary #ab-;inch slide rule has about #hj divisions to each radius1 so that it is easily seen how much more exact quantities may be brought out with a rule of #gbej divisions4 ,it is a most valuable rule for calculations for the tacheometer4 ,copious tables of gauge points for civil engineers are printed upon the central tube1 which is supplemented by a book of instructions4 ,the value of this rule has been much extended by scales to facilitate subtense calculations1 by ,mr4 ,w4 ,n4 ,bakewell1 ,c4,e41 in the ,fuller-,bakewell slide rule4 ,illustration3 ,fig4 #dbh4--;,improved ,fuller's slide rule4 ,an additional improvement1 as shown at ,fig4 #dbh1 has now been effected in these instruments by adapting the case to support the rule when in use1 thus overcoming the objection of being always obliged to hold it in the hand4 ,the use of ,professor ,fuller's rule is1 however1 confined to arithmetical computations4 ,the numerical solution of formul comprising trigonometrical functions can only be performed by extracting1 with considerable loss of time1 the values of these functions from a book of tables4 ,to do so requires a certain effort of mind with its consequent risk of mistakes4 ,this limitation has restricted its use in a considerable body of calculations1 such1 for example1 as in the computation of the co-ordinates of surveys from the lengths and bearings of their lines1 a method of plotting which is very largely used by land surveyors at present2 in astronomical computations2 in civil and mechanical engineering1 etc42 the use of logarithms being preferred on the score of speed1 although the degree of accuracy attained with ,professor ,fuller's rule is amply sufficient in the large majority of cases4 ,illustration3 ,fig4 #dbi4--;,barnard's co-ordinate spiral slide rule4 #hhf4--,the ,co-ordinate ,spiral ,slide ,rule has been designed to meet these requirements by ,mr4 ,h4 ,o4 ,barnard1 ,a4,c4,h41 ,f4,r4,a4,s41 etc41 ,superintendent of ,trigonometrical ,surveys1 ,ceylon1 ,fig4 #dbi4 ,like ,professor ,fuller's rule1 upon which it is an improvement1 it enables the user to perform with speed and accuracy arithmetical computations involving multiplication1 division1 proportion1 continuous fractions1 powers1 roots1 and logarithms2 but in addition1 the natural and logarithmic values of trigonometrical functions of any angle can be determined by inspection with the same accuracy as in numerical computation1 while the products1 quotients1 etc41 of these functions1 by lengths or numbers1 integral or fractional1 are obtained with equal ease1 rapidity and precision4 ,the scope of its operations will be gathered from the examples which are given to illustrate its use in the instructions supplied with the rule4 ,illustration3 ,fig4 #dcj4--,thacher's slide rule4 ,although the co-ordinate spiral rule1 as all varieties of slide rules1 is based primarily upon the theory of logarithms1 a knowledge of that theory is by no means essential to its practical use4 #hhg4--,thacher's ,slide ,rule4--,fig4 #dcj4 ,this contains a shorter scale than ,professor ,fuller's1 and the system is not quite so simple4 ,full printed instructions are given in the book supplied by the inventor1 ,mr4 ,edwin ,thacher1 of ,pittsburg1 ,u4,s4,a41 or of the author1 who is his agent for this country4 ,the original divisions of this rule were made by the author4 ,the scale is manufactured in the ,united ,states4 ,there appears to be found some difficulty in its construction to keep the scales to true length and get them to exact position4 #hhh4--,pocket ,sets of ,chain ,scales4--,these are made #c1 #d1 #e1 and #f inch4 ,three of #f inch form the ordinary set4 ,the chain scales1 if three only1 are #aj1 #bj1 #cj1 #dj1 #ej1 and #fj2 if six they generally contain the same scales with feet equal to the links4 ,an extra scale with the ordnance or other scale of the country is found also useful for measuring from maps or plans4 ,some civil engineers prefer the pocket scales made wide with quite square ends1 to be used as offsets or for sketching4 ,these scales are generally made in ivory and placed in a light morocco or ,russia leather case4 ,the numbers of divisions of the scales should be stamped on the ends to prevent the wrong scale being drawn from the case4 ,illustration3 ,fig4 #dca4--;,biram's anemometer4 ,illustration3 ,fig4 #dcb4--,lowne's anemometer4 #hhi4--;,anemometers are used by mining engineers for testing the ventilation of mines4 ,the original and best known form is that of ,biram1 ,fig4 #dca4 ,this instrument is held in any current of air1 and the velocity of the current is registered by the motion of oblique fans1 by means of ordinary decimal gearwork on five dials giving feet and multiples by #aj4 ,lowne's anemometer1 with the author's improvements1 ,fig4 #dcb1 is of similar principles of construction1 but it is arranged in portable form to go in a pocket case4 ,another well-known form of anemometer is built upon the same principle1 but of cubical form4 ,it is customary to take the velocity of the current for one minute by a watch1 there being a detent provided in most instruments to start and stop the motion of the hands upon the dials4 #hij4--;,books of ,tables and ,formul4--,few ,british ,surveyors are without ,molesworth's pocket-book4 ,this contains all the useful tables and notes of reference valuable to the civil engineer in his ordinary work--weight1 #e ozs4 ,many pocket-books have been written on the same plan4 ,hurst's pocket-book contains all matters of reference for the town surveyor among buildings4 ,trautwine's ,civil ,engineer's ,pocket-book 7,american7 is the most complete1 but it is of double the weight of the ,molesworth4 ,spon's ,engineers' ,tables for the ,waistcoat ,pocket--weight1 little over oz4--is a very useful little book4 ,of ,traverse ,tables both ,gurden's and ,boileau's are comprehensive and reliable4 ,there are several pocket-books of ,curve ,tables1 those of ,cutler ,edge1 ,beazeley1 and ,kennedy ,hackwood being perhaps in the most general use4 #hia4--,technical ,books--,ordnance ,maps are published on special districts and subjects which are often relative to the country or the special conditions of work abroad and at home for minerals1 etc4 ,it is very useful to possess such of these as may be required1 and the note is only made here as a reminder4 #hib4--,sling ,case for ,drawings4--,the most convenient method of carrying maps or drawings for public works in execution is to have a solid leather case similar to a telescope case4 ,this is best if made with the cap or lid of the same length as the body3 it can then be drawn out any distance according to the length of the rolled drawing4 ,if thought more convenient1 and the map or drawings are heavy1 a strap may be added to pass over the shoulder1 ,fig4 #dcc4 #hic4--;,chronometer4--,this may be any form of watch with compensated escapement4 ,at present the prices run high for this class of work2 but from the simplicity and moderate certainty of compensation it does not appear that this should be necessary for the production of a fair working instrument useful for the surveyor in new countries to check his longitude4 ,where a good chronometer is used it is better to keep it to ,greenwich time without alteration4 ,if there is a gaining or losing rate this will most probably remain constant in equal times1 so that corrections may be made pro rat for all observations until a check can be taken with certainty when arriving at a town which possesses an observatory4 ,the quality of a chronometer is fully ascertained by having a certificate from one of our observatories1 that of ,kew being the most popular4 ,illustration3 ,fig4 #dcc4--,sling case for drawings4 #hid4--;,chronograph4--,for the observation of stars in transit for the purpose of taking longitude1 a dead-stop watch or chronograph is most useful4 ,this can now be had in combination with an otherwise fair going watch at a very moderate price4 #hie4--,outfit of a ,surveyor for ,work in a ,new ,country4--,the ordinary items of strong1 dust-coloured woollen clothing1 good boots1 saddle1 firearms1 etc41 do not come within the province of this work4 ,the instruments he will require will depend partly upon the nature of the country and the kind of work to be done4 ,if for prospecting only1 light instruments are commonly selected--the sextant1 or box sextant with glass artificial horizon1 good pocket chronometer1 telescope1 aneroid barometer1 prismatic compass1 and clinometer4 ,if a general survey is to be made1 the first instrument of importance is the theodolite1 the #d or #e-;inch being the most usual4 ,with this1 pickets1 land chain and arrows1 a steel tape for testing1 and a linen tape4 ,if for survey in mineral districts1 a good mining-dial is required1 with all accessories of chains1 etc4 ,if for railway work1 a #e-;inch theodolite1 a good level1 staves1 pickets1 clinometer1 and prismatic compass4 ,in all cases1 field-books1 drawing instruments1 supply of paper1 drawing boards1 squares1 parallel rule1 pencils1 ,indian ink1 colours1 stencil plates1 and other articles for office use1 of which the established optician or trader will give full information from his experience1 or general reference may be taken from any complete catalogue of such instruments4 ,,footnote3 #ff ,patent1 ,no4 #dcaj1 ,november1 #ahgf4 ,,index ,abney's clinometer1 #daa ,achromatism explained1 #ce ,adjustable axis1 of plane table1 #dgi of theodolite1 #bcg ,adjustable tripod1 #cbi ,alidades for plane tables1 #dgc ,alloys used for surveying instruments1 #g ,altazimuth theodolite1 #bie ,altitudes1 measurements of1 #eej ,aluminium alloys1 #h ,anallatic telescope1 #cfd ,anemometers1 #eif ,aneroid barometers1 ,vidie's1 #eeh ,bourdon's1 #efh ,apomecometer1 #dfi ,arrows1 for chain1 #did ,artificial horizons1 #ddc ,atmospheric pressure1 measurements of1 #eej ,axes1 workmanship in1 #aa ,bakewell's tangential index1 #chd ,ball and socket adjustments3 ,hoffmann's1 ,pastorelli's1 #ccj ,bands1 steel1 for measuring land1 #ddi ,barker's clinometer1 #dae ,barometer1 aneroid1 #eeh mountain1 #eej mercurial1 #edi ,base line apparatus1 #eag ,beam compass measurements1 #eaj ,bellamy's road tracer1 #dbj ,bill-hook1 #ehb ,binoculars1 prism1 #ehd ,black1 optical1 #ad ,boiling-point thermometer1 hypsometer1 #efi ,boning rods1 #egh ,books1 levelling1 #agc ,boucher's calculator1 #ehg improved1 #eij ,box sextant1 #dea with continuous arc1 #dfa with supplementary arc1 #deh ,bronzing instruments1 #ad ,brunton mine transit1 #cec ,bubble trier1 #hh ,burel's reflecting level1 #add ,burnier's clinometer1 #daf ,caink's rule for correcting inclines1 #dih ,calculators3 ,barnard's1 #eid ,boucher's1 #ehg ,fuller's1 #eib ,thacher's1 #eie ,camera1 #bdc1 #ehe ,cases1 for carrying maps1 #eig leather1 for instruments1 #bc ,cavalry sketching case1 #dhh ,cement tester1 ,mann's1 #ehe ,centesimal division1 #ahe ,chain scales1 pocket sets1 #eif ,chain vice1 #dif ,chaining1 #dig ,chains1 land1 various1 #dij ,chains1 sounding1 #ebf ,chronometer and chronograph1 #eih ,circumferentor1 #cjg ,clamp and tangent motions1 various1 #bjb ,classification of instruments1 #e ,clinometer compasses1 #dah hanging1 #cdd ,clinometers1 various1 #daa ,coast survey lines1 #ebg ,coincidence rods1 #eaa ,collimation1 #ee ,collimator1 #aba ,compass1 surveying with1 #hj ,compasses3 magnetic1 bar1 #ei ,barker's1 #hd ,burnier's1 #hj hanging1 #cdd ,hutchinson's1 #gi luminous1 #hd mariners'1 #gc prismatic1 #ge pocket1 #hb ring1 #gb trough1 #gd1 #hc ,compensated rods1 #eab ,connecting link1 to extend hand rods1 #eca ,convex and concave lenses1 #cb ,cooke's level1 #ach ,co-ordinate slide rule1 #eid ,cross-staff heads1 #egc ,curvature1 correction for1 #agj ,cushing's level1 #acf ,de ,lisle's reflecting clinometer1 #dac ,declination of needles1 #fg ,deville's theodolite1 #bfc ,diagonal eye-piece1 #de ,dials1 mining1 #cji ,diaphragm of telescope1 #ej1 #aad1 #ace ,dip compass1 #ced ,dip of needles1 #ff ,dispersion of light1 #ce ,dividing engine1 #agf ,division of the circle1 #age ,double optical square1 #dfg ,drop arrow1 #did ,dumpy level1 #aaj improved1 #abc ,dynameter1 #dc ,edgeworth's stadiometer1 #dhb ,engineer's level1 #acc ,engraving1 note on1 #af ,everest's theodolite1 #bga tripod1 #bgc ,excise ink bottle1 #agd ,eye-pieces3 ,ramsden1 #da erecting1 #dd diagonal1 #de reflecting1 #df ,field-books1 #bhi1 #cgd1 #chj ,field-glasses1 #ehb ,finishing of surveying instruments1 #ad ,formation of images in a telescope1 #cc ,french forms of miners' dials1 #ccf ,fuller's rule1 #eib ,geological tools1 #ehg ,george's artificial horizon1 #ddf ,girth straps1 tapes1 etc41 #egi ,glass diaphragm1 #ec ,glass1 working1 #af refraction of1 #be ,gradient scale1 #bac ,gradienter ,screw1 #chf ,gradiometer1 #djd ,gradioplane1 #dji ,graduation1 #agi ,green1 ,william1 ,subtense instruments1 #cee ,hadley's quadrant1 #dbc ,hanging mining compass1 #cdd ,hedley's dial1 #cbb improved1 #cbf1 #cbi1 #ccc ,heliograph1 #edj ,heliostat and heliotrope1 #ecg ,henderson's miners' dial1 #cae ,hick's patent level1 #if ,historical sketch of surveying instruments1 #a ,hoffmann's ball and socket head1 #ccj ,horizontal scale of tangents1 #bac ,hypotenuse and base1 #bab ,hypsometer1 #efi ,illumination of axis of telescope1 #bcd ,inclinometer3 ,lister's1 #chi ,lacquering work1 #ae ,lamp1 magnesium1 #ede for levelling1 #afi mining1 #cdh theodolite1 #bce ,land chains1 #dij vice for adjusting1 #dif ,lanterns1 oil1 #ede ,lean's miners' dial1 #cae ,leather cases1 #bc ,lenses1 #cc achromatic1 #cf ,level3 for levelling staff1 #afc mechanics'1 #ege with inclines1 #egf ,levels3 surveyors'1 #ig ,cooke's1 #ach ,cushing's1 #acf dumpy1 #aaj same improved1 #abc engineers'1 #acc reflecting1 #add pocket1 #adb simple construction of1 #ada supplementary parts to1 #aci water1 #adf ,y-form1 #ih same improved1 #ajg ,level tubes1 #hf circular1 #if1 #egf curvature of1 #hg divisions upon1 #ij readers for1 #ie ,scott's1 #ic sensitiveness of1 #hi ,strange's1 #ib with air cell1 #ic ,level tube trier1 #hh ,levelling3 books1 #agb staves1 telescopic1 #adh semicircular1 #aej mining1 #aeh papering of1 #aei preservation of1 #afa various patterns of1 #aea holder for1 #afc pads for1 #afa pegs for1 #aga practice of1 #afc ,light for night observations1 #afi1 #ede ,light1 refraction of1 #bg ,line1 sounding1 #ebg ,lubrication of joints1 etc41 #bj ,luminous compass1 #hd ,magnesium lamp1 #edf ,magnetic compasses1 #ei correction of1 #fd declination of1 #fg inclination of1 #ff trough1 #gd variation of1 #fh various forms1 #hb ,magnetic needles1 #ei lifting1 #fe mounting1 #fd ,magnetic needles1 various1 #ei ,magnetism1 #ei preservation of1 #ga ,magnifying power of telescope1 #dc ,measuring rods1 #ecj ,mechanics' levels1 #ege ,mercurial barometer1 #edi ,metals employed in surveying instruments1 #g ,micrometer microscopes3 various1 #aib ,stanley's1 #aig ,micrometer theodolites1 #bei ,military sketching board1 #dhe cavalry1 #dhh ,miners' circumferentor1 #cjg ,miners' compasses3 ,french1 #ccf hanging1 #cdd ,stanley's prismatic1 #cdc ,miners' dials3 various1 #cji hanging1 #cdd ,hedley's1 #cbb ,henderson's1 #cae ,lean's1 #cae improvements in ,hedley's dial1 #cbf1 #cbi1 #ccc ,mining1 survey lamp1 #cdh targets1 #cdi theodolite1 #cdb ,morse signaling1 #edd ,mountain barometer1 #eej theodolite1 #beh ,nautical sextant1 #dbi ,needles1 magnetic1 #ei ,night signalling stations1 #ede ,octant or quadrant1 #dbb ,offset rods1 #ejg ,omnimeter1 #cgd ,opisometer1 #ehg ,optical black1 #ad ,optical principles of telescope1 #be ,optical square1 #dfe ,outfits for surveyors abroad1 #eih ,packing of instruments1 #ba ,parallax1 in eye-piece1 #ee ,parallel plates1 to level1 #ii to theodolite1 #bai ,passometer1 #ebe ,pastorelli's ball and socket head1 #ccj ,pedometer1 #ebd ,perambulator1 #eba ,permanent stations1 #ece ,pickets or ranging poles1 #ecc ,pine measuring rods1 #ejh ,pioneer tools1 #ehe ,photographic camera1 #bdc1 #ehe ,plain theodolite1 #bae1 #bfg ,plane tables1 #dgb ,platinum-iridium points1 #ec1 #abi1 #ace ,plummets1 #bcb ,pocket-books1 #ecd1 #eif ,pocket levels1 #if sighted1 #adb1 #ebe ,pocket magnetic compasses1 #hc ,point diaphragm1 #ec1 #abi1 #ace ,polishing work1 #ad ,preservation of instruments1 #bj ,prismatic clinometers1 #dad ,prismatic compasses1 #ge ,hutchinson's1 #gi stands1 #gh ,prismatic mining survey compass1 #cdc ,prisms as reflectors1 #bi ,protectors for the eyes1 #ehd ,protractors1 sketching1 #hb1 #cgd1 #dhe ,quadrant1 #dbb ,qualities of work1 #g of a telescope1 #ef ,quick-setting surveyor's level1 #acb ,quick-setting theodolites1 #beg ,quiver for arrows1 #did ,railway gauge1 #egi theodolite1 #beh ,ramsden eye-piece1 #da ,ranging poles1 #ecc ,ray shade1 #abi ,reader for level tube1 #ie ,reading microscopes1 #ahh ,reconnoitring glass and telescope1 #ehb ,reflecting cap to telescope1 #ccd ,reflecting circle1 #dbd ,reflecting clinometers1 #dac ,reflecting levels1 #add ,reflection of glass1 #be ,reflector in eye-piece1 #df ,refraction of light1 #be ,repairing sleeves for steel bands1 #eje ,revolving compass to dial1 #cah ,richmond's tension handle1 for steel band1 #ejc ,road tracer1 #dbj ,rods3 coincidence1 #eaa compensated1 #eab hand1 #ecj standard1 #ejh ,rule1 civil engineer's1 #ecb ,rule for correcting inclined measurement1 #dih ,rule form clinometer1 #dah ,semi-circumferentor1 #cdf ,sextants1 #dbe box1 #dea with supplementary arc1 #dfa continuous arc1 #deh sounding1 #ddi surveying 7open71 #dfd ,sight director to stadium1 #cfd ,sighted pocket level1 #adb ,silvering sextant glasses1 #dcg ,sketch books1 etc41 #ehe ,sketching board1 military1 #dhe ,slashing knife1 #ehb ,slide rules1 various1 #eij ,sliding stage to theodolite1 #bdi ,socket for station pole1 #ece ,solar attachment to theodolite1 #bci1 #bei ,soldering1 #ac ,sounding chain1 #ebf lines1 #ebg ,sounding sextant1 #ddi ,spectacles for protecting the eyes1 #ehd ,spherical aberration1 #cc ,spur shod picket1 #ece ,stadia points1 #aca webs1 #aad ,stadium for tacheometer1 #aee1 #cgc ,stadiometer1 #dhb ,standard rods1 #ejh ,stands of instruments1 #ai ,stations for observation1 #ecc ,staves1 levelling1 #adi ,steel bands and tapes1 #dii1 #ejg ,striding level1 #bcg ,style of work1 #af ,subtense1 instruments1 #cee diaphragm1 #aad1 #cfc ,supplementary arc to box sextant1 #dfa ,sun glass to telescope1 etc41 #dg ,tacheometers3 general description1 #cgj ,stanley's1 etc41 #cga ,tacheometers3 stadium for1 #aee1 #cgc field book1 #cgd ,tangent motions1 #bjb ,tapes1 linen1 etc41 #eje ,targets1 mining1 #cdi ,telemeters1 #ebh ,telescope3 general description of1 #bd ,kepler's1 ,galileo's1 #dj body of1 #dg ,telescope3 optical arrangements1 #dg optical principles1 #be qualities1 #ef reconnoitring1 #ehb ,telescopic pocket level1 #adc ,tension handles for steel bands1 #ejc ,theodolites1 #bad adjustment1 #bgf adjustable axis1 #bcg1 #bdh ,deville's1 #bfc ,everest's1 #bga micrometer1 #bei mountain1 #beh plain1 #bfe1 #bfg railway1 #beh simple construction1 #bge solar attachment to1 #bci ,souterrain #cdh ,stanley's1 #bdg transit1 #bae1 #bca1 #bdg #ad-;inch1 #bie #cf-;inch ,colonel ,strange's1 #bih ,universal1 #bfe ,thermometer for steel band1 #ejc boiling point1 #efi ,timber girth strap1 #egi marking knife1 #eha rods1 #ehb ,tools used in manufacture of instruments1 #aa ,triangle for levelling staff1 #afb ,tribrach adjustments1 #abf ,everest's1 #bgb with mechanical stage1 #bea ,tripods1 #aad1 #bag1 #cbb framed1 #bej miners'1 #cac ,tripods1 jointed1 for mining instruments1 #cac ,trough compass1 #gd1 #hc1 #bcf ,vernier scale readings1 #ahj ,vicat needle1 #ehf ,vice for adjusting land chain1 #dif ,water levels1 #adf ,waterproof covers1 #bc ,watkin's aneroid1 #efg ,watkin's clinometer1 #dag ,wealemefna1 #ehg ,webs1 collecting and mounting1 #ea ,whistles1 #ehe ,y-levels1 #ih improved construction1 #ajg ,illustration3 ,,wire ,,up ,,your ,,own ,,house ,have ,electric ,,light ,,heat ,,power ,this ,book ,,wiring ,,houses--,,schneider ,shows you in detail how to install electric wires4 ,read the contents4 ,contents of chapters3 #a1 ,introduction2 #b1 ,planning the wiring2 #c1 ,completing the installation2 #d1 ,installing the lights2 #e1 ,other methods of wiring2 #f1 ,materials and notes2 #g1 ,conduit and protected wiring1 armored cables1 pipe conduits1 latest condulet fittings and concentric wiring2 #h1 ,digest of #aiaf edition of the ,national ,code1 ,underwriters rules and notes4 #abh pages1 #de illustrations and #i plates1 #ab mo1 cloth4 ,price #ee cents--,postpaid ,,learn ,,to ,,do ,,things ,model ,library ,series ,,of ,,copyrighted ,,books #a4 ,the ,study of ,electricity for ,beginners4 #b4 ,dry ,batteries1 ,how to ,make them4 #c4 ,electrical ,circuits and ,diagrams1 ,part #a4 99 #d4 ,electric ,bells1 ,annunciators and ,alarms4 #e4 ,modern ,primary ,batteries4 #f4 ,experimenting with ,induction ,coils4 99 #g4 ,electric ,gas ,igniting ,apparatus4 99 #h4 ,small ,accumulators1 ,how to ,make and ,use4 #i4 ,model ,steam ,engine ,design4 99 #aj4 ,practical ,electrics4 #aa4 ,inventions1 ,how to ,protect and ,sell them4 #ab4 ,woodwork ,joints1 ,how to ,make and ,use4 99 #ac4 ,the ,fireman's ,guide to the ,care of ,boilers4 99 #ad4 ,the ,slide ,valve ,simply ,explained4 99 #ae4 ,the ,magneto ,telephone4 99 #af4 ,the ,corliss ,engine and ,its ,management4 99 #ag4 ,making ,wireless ,outfits4 #ah4 ,wireless ,telephone ,construction4 99 #ai4 ,the ,wimshurst ,machine1 ,how to ,make ,it4 #bj4 ,simple ,experiments in ,static ,electricity4 #ba4 ,small ,electrical ,measuring ,instruments4 #bb4 ,electrical ,circuits and ,diagrams1 ,part #b4 99 #bc4 ,induction ,coils1 ,how to ,make ,them4 #bd4 ,model ,vaudeville ,theatres4 99 #be4 ,alternating ,currents1 ,simply ,explained4 99 #bf4 ,how to ,build a #bj foot ,bi-plane ,glider4 99 #bg4 ,a ,b ,c of the ,steam ,engine4 99 #bh4 ,simple ,soldering1 ,hard and ,soft4 99 #bi4 ,telegraphy for ,beginners4 #cj4 ,low ,voltage ,lighting with ,storage ,batteries4 #cc4 ,house ,wiring for ,electric ,light4 99 #cd4 ,magnets and ,magnetism4 99 #cf4 ,small ,windmills and ,how to ,make ,them4 99 #ca4 ,gas ,engine ,management4 #cg4 ,collin's ,wireless ,plans1 ,part #a4 #ch4 ,collin's ,wireless ,plans1 ,part #b4 ,in paper covers ,price #be;c each ,postpaid4 99 ,these books can also be had in cloth binding at #ee;c each postpaid ,,spon ,,chamberlain ,,publishers ,,of ,,technical ,,books #abc-e ,,liberty ,,st41 ,,new ,,york