,,stargazing3 ,,past ,,and ,,present ,illustration ,illustration3 ,r4 ,s4 ,,newall',s ,,telescope4 ,,stargazing3 ,,past ,,and ,,present4 ,,by ,j4 ,,norman ,,lockyer1 ,f4,r4,s41 ,,correspondent ,,of ,,the ,,institute ,,of ,,france4 ,,expanded ,,from ,,shorthand ,,notes ,,of ,a ,,course ,,of ,,royal ,,institution ,,lectures1 ,,with ,,the ,,assistance ,,of ,g4 ,m4 ,,seabroke1 ,f4,r4,a4,s4 ,london3 ,,macmillan ,,and ,,co4 #ahgh4 ,the ,right of ,translation and ,reproduction is ,reserved4 ,,london3 ,r4 ,,clay1 ,,sons1 ,,and ,,taylor1 ,,bread ,,street ,,hill1 ,e4,c4 ,,preface4 ,in the year #ahgj ,i gave a course of eight ,lectures on ,instrumental ,astronomy at the ,royal ,institution4 ,the ,lectures were taken down by a shorthand writer1 my intention being to publish them immediately4 ,in this1 however1 ,i was prevented by other calls upon my time4 ,in #ahge my friend ,mr4 ,seabroke generously offered to take the burden of preparing the notes for the press off my shoulders2 ,i avail myself of this opportunity of expressing my very great obligations to him for his valuable services in this particular as well as for important help in the final revision of the proofs4 ,on looking over the so completed ,,mss41 however1 ,i saw that the eight hours at my disposal had not permitted me to touch upon many points of interest which could hardly be omitted from the book4 ,besides this1 the progress made in the various instrumental methods in the interval1 and the results obtained by them1 had been very remarkable4 ,i felt1 therefore1 that the object ,i had in view1 namely1 to further the cause of physical astronomy1 by creating and fostering1 so far as in me lay1 a general interest in it1 and by showing how all departments of physical inquiry were gradually being utilized by the astronomer1 would only be half attained unless the account were more complete4 ,i have1 therefore1 endeavoured to fill up the gaps1 and have referred briefly to the new instruments and methods4 ,the autotype of the twenty-five inch refractor is the gift of my friend ,mr4 ,newall1 and ,i take this opportunity of expressing my obligation to him1 as also to ,messrs4 ,cooke1 ,grubb and ,browning for several of the woodcuts with which the chapters on the ,equatorial are illustrated2 and to ,mr4 ,h4 ,dent-,gardner for some of those illustrating ,clock and ,chronometer ,escapements1 and for revising my account of them4 ,nor can ,i omit to thank ,mr4 ,cooper for the pains he has taken with the woodcuts1 especially those copied from ,tycho ,brahe's description of his ,observatory1 and ,messrs4 ,clay for the careful manner in which they have printed the book4 ,j4 ,,norman ,,lockyer4 ,november #afth1 #ahgg4 ,,contents4 ,,book ,i4 ,,the ,,pre-,,telescopic ,,age4 ,,chap4 ,,page ,i4-- ,,the ,,dawn ,,of ,,stargazing #a ,,ii4-- ,,the ,,first ,,instruments #af ,,iii4-- ,,hipparchus ,,and ,,ptolemy #be ,,iv4-- ,,tycho ,,brahe #cg ,,book ,,ii4 ,,the ,,telescope4 ,v4-- ,,the ,,refraction ,,of ,,light #ee ,,vi4-- ,,the ,,refractor #gc ,,vii4-- ,,the ,,reflection ,,of ,,light #ij ,,viii4-- ,,the ,,reflector #ajj ,,ix4-- ,,eyepieces #aji ,x4-- ,,production ,,of ,,lenses ,,and ,,specula #aag ,,xi4-- ,,the 8,,optick ,,tube0 #aci ,,xii4-- ,,the ,,modern ,,telescope #aeb ,,book ,,iii4 ,,time ,,and ,,space ,,measurers4 ,,xiii4-- ,,the ,,clock ,,and ,,chronometer #age ,,xiv4-- ,,circle ,,reading #baa ,,xv4-- ,,the ,,micrometer #bah ,,book ,,iv4 ,,modern ,,meridional ,,observations4 ,,xvi4-- ,,the ,,transit ,,circle #bcc ,,xvii4-- ,,the ,,transit ,,clock ,,and ,,chronograph #bec ,,xviii4-- 8,,greenwich ,,time10 ,,and ,,the ,,use ,,made ,,of ,,it #bga ,,xix4-- ,,other ,,instruments ,,used ,,in ,,astronomy ,,of ,,precision #bhd ,,book ,v4 ,,the ,,equatorial4 ,,xx4-- ,,various ,,methods ,,of ,,mounting ,,large ,,telescopes #bic ,,xxi4-- ,,the ,,adjustments ,,of ,,the ,,equatorial #cbh ,,xxii4-- ,,the ,,equatorial ,,observatory #ccg ,,xxiii4-- ,,the ,,siderostat #cdc ,,xxiv4-- ,,the ,,ordinary ,,work ,,of ,,the ,,equatorial #cdi ,,book ,,vi4 ,,astronomical ,,physics4 ,,xxv4-- ,,the ,,general ,,field ,,of ,,physical ,,inquiry #cga ,,xxvi4-- ,,determination ,,of ,,the ,,light ,,and ,,heat ,,of ,,the ,,stars #cgg ,,xxvii4-- ,,the ,,chemistry ,,of ,,the ,,stars3 ,,construction ,,of ,,the #chf ,,spectroscope ,,xxviii4-- ,,the ,,chemistry ,,of ,,the ,,stars 7,,continued73 ,,principles ,,of #dja ,,spectrum ,,analysis ,,xxix4-- ,,the ,,chemistry ,,of ,,the ,,stars 7,,continued73 ,,the #dbb ,,telespectroscope ,,xxx4-- ,,the ,,telepolariscope #dda ,,xxxi4-- ,,celestial ,,photography4--,,the ,,ways ,,and ,,means #ded ,,xxxii4-- ,,celestial ,,photography 7,,continued73 ,,some ,,results #dfc ,,xxxiii4-- ,,celestial ,,photography 7,,continued73 ,,recent ,,results #dfi ,,list ,,of ,,illustrations4 ,,fig4 ,,page #a4 ,the heavens according to ,ptolemy #c #b4 ,the zodiac of ,denderah #g #c4 ,illustration of ,euclid's statements #aj #d4 ,the plane of the ecliptic #ac #e4 ,the plane of the ecliptic1 showing the inclination of the #ad earth's axis #f4 ,the first meridian circle #bj #g4 ,the first instrument graduated into #cfj 7west side7 #ba #h4 ,astrolabe 7armill quatori of ,tycho ,brahe7 similar to the #bf one contrived by ,hipparchus #i4 ,ecliptic astrolabe 7the armill zodiacales of ,tycho ,brahe71 #bh similar to the one used by ,hipparchus #aj4 ,diagram illustrating the precession of the equinoxes #ca #aa4 ,revolution of the pole of the equator round the pole of the #cb ecliptic caused by the precession of the equinoxes #ab4 ,the vernal equinox among the constellations1 ,b4,c4 #bagj #cd #ac4 ,showing how the vernal equinox has now passed from ,taurus and #cd ,aries #ad4 ,instrument for measuring altitudes #ce #ae4 ,portrait of ,tycho ,brahe 7from original painting in the #ci possession of ,dr4 ,crompton1 of ,manchester7 #af4 ,tycho ,brahe's observatory on the island of ,huen #dc #ag4 ,tycho ,brahe's system #df #ah4 ,the quadrans maximus reproduced from ,tycho's plate #dh #ai4 ,tycho's sextant #ej #bj4 ,view and section of a prism #ef #ba4 ,deviation of light in passing at various incidences through #eg prisms of various angles #bb4 ,convergence of light by two prisms base to base #ei #bc4 ,formation of a lens from sections of prisms #fj #bd4 ,front view and section of a double convex lens #fa #be4 ,double concave1 plane concave1 and concavo-convex lenses #fa #bf4 ,double convex1 plane convex1 and concavo-convex lenses #fb #bg4 ,convergence of rays by convex lens to principal focus #fb #bh4 ,conjugate foci of convex lens #fc #bi4 ,conjugate images #fd #cj4 ,diagram explaining ,fig4 #bi #fd #ca4 ,dispersion of rays by a double concave lens #fe #cb4 ,horizontal section of the eyeball #ff #cc4 ,action of eye in formation of images #fh #cd4 ,action of a long-sighted eye #fi #ce4 ,diagram showing path of rays when viewing an object at an #gj easy distance #cf4 ,action of short-sighted eye #ga #cg4 ,galilean telescope #gc #ch4 ,telescope #ge #ci4 ,diagram explaining the magnifying power of object-glass #gf #dj4 ,scheiner's telescope #gh #da4 ,dispersion of light by prism #hj #db4 ,diagram showing the amount of colour produced by a lens #ha #dc4 ,decomposition and recomposition of light by two prisms #hc #dd4 ,diagram explaining the formation of an achromatic lens #hd #de4 ,combination of flint- and crown-glass lenses in an achromatic #hf lens #df4 ,diagram illustrating the irrationality of the spectrum #hg #dg4 ,diagram illustrating the action of a reflecting surface #ia #dh4 ,experimental proof that the angle of incidence angle of #ib reflection #di4 ,convergence of light by concave mirror #id #ej4 ,conjugate foci of convex mirror #id #ea4 ,formation of image of candle by reflection #ie #eb4 ,diagram explaining ,fig4 #ea #if #ec4 ,reflection of rays by convex mirror #ih #ed4 ,reflecting telescope 7,gregorian7 #aja #ee4 ,newton's telescope #ajb #ef4 ,reflecting telescope 7,cassegrain7 #ajc #eg4 ,front view telescope 7,herschel7 #ajc #eh4 ,diagram illustrating spherical aberration #aje #ei4 ,diagram showing the proper form of reflector to be an ellipse #ajf #fj4 ,huyghens' eyepiece #aaj #fa4 ,diagram explaining the achromaticity of the ,huyghenian #aaa eyepiece #fb4 ,ramsden's eyepiece #aab #fc4 ,erecting or day eyepiece #aac #fd4 ,images of planet produced by short and long focus lenses1 c4 #abc #fe4 ,showing in an exaggerated form how the edge of the speculum #abh is worn down by polishing #fe994 ,section of ,lord ,rosse's polishing machine #aca #ff4 ,mr4 ,lassell's polishing machine #acb #fg4 ,simple telescope tube1 showing arrangement of object-glass #adj and eyepiece #fh4 ,appearance of diffraction rings round a star when the #ada object-glass is properly adjusted #fi4 ,appearance of same object when object-glass is out of #ada adjustment #gj4 ,optical part of a ,newtonian reflector of ten inches aperture #adc #ga4 ,optical part of a ,melbourne reflector #adc #gb4 ,mr4 ,browning's method of supporting small specula #add #gc4 ,support of the mirror when vertical #adf #gd4 ,division of the speculum into equal areas #adg #ge4 ,primary1 secondary1 and tertiary systems of levers shown #adh separately #gf4 ,complete system consolidated into three screws #adh #gg4 ,support of diagonal plane mirror 7,front view7 #aej #gh4 ,support of diagonal plane mirror 7,side view7 #aej #gi4 ,a portion of the constellation ,gemini seen with the naked eye #aed #hj4 ,the same region1 as seen through a large telescope #aee #ha4 ,orion and the neighbouring constellations #aef #hb4 ,nebula of ,orion #aeg #hc4 ,saturn and his moons #afj #hd4 ,details of the ring of ,saturn #afa #he4 ,ancient clock escapement #agg #hf4 ,the crown wheel #agh #hg4 ,the clock train #ahj #hh4 ,winding arrangements #aha #hi4 ,the cycloidal pendulum #ahe #ij4 ,graham's1 ,harrison's1 and ,greenwich pendulums #ahh #ia4 ,greenwich clock3 arrangement for compensation for barometric #aid pressure #ib4 ,the anchor escapement #aig #ic4 ,graham's dead beat #aii #id4 ,gravity escapement 7,mudge7 #bjj #ie4 ,gravity escapement 7,bloxam7 #bjb #if4 ,greenwich clock escapement #bjd #ig4 ,compensating balance #bjg #ih4 ,detached lever escapement #bjh #ii4 ,chronometer escapement #bji #ajj4 ,the fusee #bji #aja4 ,diggs' diagonal scale #bac #ajb4 ,the vernier #bad #ajc4 ,system of wires in a transit eyepiece #bbj #ajd4 ,wire micrometer #bba #aje4 ,images of ,jupiter #bbd #ajf4 ,object-glass cut into two parts #bbe #ajg4 ,the parts separated1 and giving two images of any object #bbe #ajh4 ,double images seen through ,iceland spar #bbg #aji4 ,diagram showing the ordinary and extraordinary rays in a #bbg crystal of ,iceland spar #aaj4 ,crystals of ,iceland spar #bbh #aaa4 ,double image micrometer #bbi #aab4 ,tycho ,brahe's mural quadrant #bce #aac4 ,transit instrument 7,transit of ,venus ,expedition7 #bcf #aad4 ,transit instrument in a fixed observatory #bcg #aae4 ,diagram explaining third adjustment #bci #aaf4 ,the mural circle #bda #aag4 ,transit circle1 showing the addition of circles to the #bdb transit instrument #aah4 ,perspective view of ,greenwich transit circle #bdc #aai4 ,plan of the ,greenwich transit circle #bde #abj4 ,cambridge 7,u4,s47 meridian circle #bdh #aba4 ,diagram illustrating how the pole is found #bdi #abb4 ,diagram illustrating the different lengths of solar and #bee sidereal day #abc4 ,system of wires in transit eyepiece #beg #abd4 ,the ,greenwich chronograph4 7,general view7 #bfa #abe4 ,details of the travelling carriage which carries the magnets #bfb and prickers4 7,side view and view from above7 #abf4 ,showing how on the passage of a current round the soft iron #bfc the pricker is made to make a mark on the spiral line on the cylinder #abg4 ,side view of the carriage carrying the magnets and the #bfc pointer that draws the spiral #abh4 ,wheel of the sidereal clock1 and arrangement for making #bff contact at each second #abi4 ,arrangement for correcting mean solar time clock at ,greenwich #bfh #acj4 ,the chronopher #bgf #aca4 ,reflex zenith tube #bhf #acb4 ,theodolite #bhh #acc4 ,portable alt-azimuth #bhi #acd4 ,the #dj-;feet at ,slough #bid #ace4 ,lord ,rosse's #f-;feet #bie #acf4 ,refractor mounted on alt-azimuth tripod for ordinary #bif star-gazing #acg4 ,simple equatorial mounting #bih #ach4 ,cooke's form for refractors #cjj #aci4 ,mr4 ,grubb's form applied to a ,cassegrain reflector #cja #adj4 ,grubb's form for ,newtonians #cjc #ada4 ,browning's mounting for ,newtonians #cjd #adb4 ,the ,washington great equatorial #cji #adc4 ,general view of the ,melbourne reflector #cab #add4 ,the mounting of the ,melbourne telescope #cac #ade4 ,great silver-on-glass reflector at the ,paris observatory #caf #adf4 ,clock governor #cai #adg4 ,bond's spring governor #cbj #adh4 ,foucault's governor #cbc #adi4 ,illuminating lamp for equatorial #cbe #aej4 ,cooke's illuminating lamp #cbf #aea4 ,dome #cch #aeb4 ,drum #cch #aec4 ,new ,cincinnati observatory--7,font elevation7 #cch #aed4 ,cambridge 7,u4,s47 equatorial #cci #aee4 ,section of main building--,united ,states naval observatory #cda #aef4 ,foucault's siderostat #cdd #aeg4 ,the siderostat at ,lord ,lindsay's observatory #cdh #aeh4 ,position circle #cec #aei4 ,how the length of a shadow thrown by a lunar hill is measured #ced #afj4 ,the determination of the angle of position of the axis of #ceh ,saturn's ring #afa4 ,measurement of the angle of position of the axis of a figure #cei of a comet #afb4 ,double star measurement #cfj #afc4 ,ring micrometer #cfh #afd4 ,thermopile and galvanometer #cgd #afe4 ,rumford's photometer #cgh #aff4 ,bouguer's photometer #cgi #afg4 ,kepler's diagram #chg #afh4 ,newton's experiment1 showing the different refrangibilities #chh of colours #afi4 ,first observation of the lines in the solar spectrum #cia #agj4 ,solar spectrum #cib #aga4 ,student's spectroscope #cic #agb4 ,section of spectroscope #cid #agc4 ,spectroscope with four prisms #cif #agd4 ,automatic spectroscope 7,grubb's form7 #cig #age4 ,automatic spectroscope 7,browning's form7 #cig #agf4 ,last prism of train for returning the rays #cih #agg4 ,spectroscope with returning beam #cii #agh4 ,direct-vision prism #cii #agi4 ,electric lamp #djd #ahj4 ,electric lamp arranged for throwing a spectrum on a screen #dje #aha4 ,comparison of the line spectra of iron1 calcium1 and #djf aluminium1 with common impurities #ahb4 ,coloured flame of salts in the flame of a ,bunsen's burner #djh #ahc4 ,spectroscope arranged for showing absorption #dji #ahd4 ,geissler's tube #dac #ahe4 ,spectrum of sun-spot #dae #ahf4 ,diagram explaining long and short lines #daf #ahg4 ,comparison of the absorption spectrum of the sun with the #dah radiation spectra of iron and calcium1 with common impurities #ahh4 ,comparison prism #dbc #ahi4 ,comparison prism #dbc #aij4 ,foucault's heliostat #dbd #aia4 ,object-glass prism #dbf #aib4 ,the eyepiece end of the ,newall refractor #dbg #aic4 ,solar telespectroscope 7,browning's form7 #dbh #aid4 ,solar telespectroscope 7,grubb's form7 #dbh #aie4 ,side view of spectroscope #dbi #aif4 ,plan of spectroscope #dbi #aig4 ,cambridge star spectroscope elevation #dcj #aih4 ,cambridge spectroscope plan #dcj #aii4 ,direct-vision star spectroscope 7,secchi7 #dca #bjj4 ,types of stellar spectra #dcc #bja4 ,part of solar spectrum near ,f #dcf #bjb4 ,distortions of ,f line on sun #dch #bjc4 ,displacement of ,f line on edge of sun #dci #bjd4 ,diagram showing the path of the ordinary and extraordinary #dde ray in crystals of ,iceland spar #bje4 ,appearance of the spots of light on the screen shown in the #ddf preceding figure1 allowing the ordinary ray to pass and rotating the second crystal #bjf4 ,appearance of spots of light on screen on rotating the second #ddg crystal1 when the extraordinary ray is allowed to pass through the first screen #bjg4 ,instrument for showing polarization by reflection #ddh #bjh4 ,section of plate-holder #def #bji4 ,enlarging camera #deh #baj4 ,instantaneous shutter #dfj #baa4 ,photoheliograph as erected in a temporary observatory for #dfa photographing the transit of ,venus in #ahgd #bab4 ,copy of photograph taken during the eclipse of #ahfi #dgd #bac4 ,part of ,beer and ,mdler's map of the moon #dgf #bad4 ,the same region copied from a photograph by ,de ,la ,rue #dgg #bae4 ,comparison between ,kirchhoff's map and ,rutherfurd's #dhj photograph #baf4 ,arrangement for photographically determining the coincidence #dha of solar and metallic lines #bag4 ,telespectroscope with camera for obtaining photographs of the #dhb solar prominences ,,book ,i4 ,,the ,,pre-,,telescopic ,,age4 ,,stargazing3 ,,past ,,and ,,present ,,chapter ,i4 ,,the ,,dawn ,,of ,,stargazing4 ,some sciences are of yesterday2 others stretch far back into the youth of time4 ,among these there is one of the beginnings of which we have lost all trace1 so coeval was it with the commencement of man's history2 and that science is the one of which we have to trace the instrumental developments4 ,although our chief task is to enlarge upon the modern1 it will not be well1 indeed it is impossible1 to neglect the old1 because1 if for no other reason1 the welding of old and new has been so perfect1 the conquest of the unknown so gradual4 ,the best course therefore will be to distribute the different fields of thought and work into something like marked divisions1 and to commence by dividing the whole time during which man has been observing the heavens into two periods1 which we will call the ,pre-telescopic and the ,telescopic ,ages4 ,the work of the ,pre-telescopic age of course includes all the early observations made by the unaided eye1 while that of the ,telescopic age includes those of vastly different kinds1 which that instrument had rendered possible2 so that it divides itself naturally into some three or four sub-ages of extreme importance4 ,it is unnecessary to say one word here on the importance of the invention of the telescope2 it is well for the present purpose1 however1 to emphasize the further distinctions we obtain when we consider the various additions made from time to time to the telescope4 ,the ,telescope1 in fact1 was comparatively little used until astronomy annexed that important branch of physics to its aid which gave us a ,clock--a means of dividing time in the most accurate manner4 ,in quite recent times the addition of the ,camera to the ,telescope marks an important advance2 indeed the importance of photography is not yet recognised in the way it should be4 ,then1 again1 there is the addition of the ,spectroscope1 which1 though it is only now beginning to yield us rich fruit1 really dates from the beginning of the present century4 ,this is an ally to the telescope of such power that he would be a bold man who would venture to set bounds to the conquests their combined forces will make4 ,now not only is it essential for the proper understanding of the instruments used nowadays in every observatory1 by every stargazer1 to go back to the origin of the science of observation1 but in no other way can one fully see in what way the new instrumental methods have added themselves to the old ones4 ,further1 it is of importance to go back to the actual old field of work in which the geometric conceptions which grew up in the minds of the men of ancient time--conceptions which we are now utilizing and extending--were gradually elaborated4 ,to do this1 there is no better way than to dwell very briefly on the work actually done by the old astronomers4 99 99 99 99 99 ,this programme1 then1 being agreed to1 the first point is to trace the progress of astronomical instruments down to the time of ,copernicus and ,galileo4 ,during all this period the most generally received doctrine was1 that the earth was the centre of the visible heavens2 and although there were many variations of this1 still the arrangement of ,ptolemy1 ,fig4 #a1 is a good type of the ideas of the ancients4 ,illustration3 ,,fig4 #a4--,the ,heavens according to ,ptolemy4 ,we begin with man's first feeble efforts1 the work which man was enabled to do by his unaided eye2 and we end with the tremendous addition which he got to his observing powers by the invention of the telescope4 ,the first instrument used for astronomical observations was none of man's making4 ,in the old time the only instrument was the horizon2 and1 truth to tell1 in a land of extended plains and isolated hills1 it was not a bad one4 ,hence it was1 doubtless1 that observations in the first instance were limited to certain occurrences such as the risings and settings of the stars and the relative apparent distances of the heavenly bodies from each other4 ,so far as we are able to learn from ancient authors1 the observations next added were those of the conjunctions of the planets and of eclipses4 ,the ,egyptians are stated to have recorded #cgc solar1 and #hcb lunar eclipses2 and this statement is probably correct1 as the proportions are exact1 and there should be the above number of each in from #a1bjj to #a1cjj years4 ,the ,chinese also record an observation1 made between the years #bead and #bdcf ,b4,c41 of five planets being in conjunction4 ,the ,chaldeans appear to have observed the motions of the moon1 and an observation in #bbbg ,b4,c4 is recorded2 but these old dates are probably fictitious4 ,it is impossible to regard without surprise the general attention given to astronomical investigation in those early days compared with what we find now4 ,yet if we attempt to build up for ourselves any idea as to the problems of which the ancients attempted the solution1 it is difficult if not impossible to do it2 we cannot realize the blank which the heavens presented to them1 so many great men have lived between their time and our own1 by whose labours we1 even if unconsciously1 have profited4 ,the first idea seems to have been to observe which stars were rising or setting at seed or harvest time1 to divide the heavens into ,moon ,stations1 and then to mark astronomically their monthly and yearly festivals4 ,if one looks into the old records we find that all the labours of man which had to be performed in the country or elsewhere were determined1 by the rising or setting of the stars4 ,all the exertions of the navigator and the agriculturist were thus regulated4 ,of the planets in those early times we hear little1 except from the ,chinese annals which record conjunctions4 ,this was before man began to use the sun as a standpoint1 and hence it is that there are so many references in the ancient writers to the rising and setting of the most striking star cluster--the ,pleiades1 and the most striking constellation--,orion4 ,it is known that the year1 in later times at all events1 began in ,egypt when the brightest star in the heavens1 ,sirius1 the dog-star1 rose with the sun1 this day being called the #ast of the month ,thoth1#a which was the commencement of the ,sothiac period of #adfa years4 ,it would appear that observations of culminations1 that is1 of the highest points reached by the stars1 were not made till long after horizon observations were in full vigour2 and here it is a question whether pyramids and the like were not the first astronomical instruments constructed by man1 because for great nicety in such observations--a nicety1 let us say1 sufficient to determine astronomically by means of culminations the time for holding a festival--a fixed instrument of some kind was essential4 ,the rich mine recently opened up by ,mr4 ,haliburton and ,mr4 ,ernest de ,bunsen concerning the survival in all nations--in our own one takes the name the ,feast of ,all ,souls'--of ancient festivals governed by the midnight culmination of the ,pleiades will doubtless ere long call general attention to this earliest form of accurate astronomical observation1 and the determination by ,professor ,piazzi ,smyth of the fact that in #bagj ,b4,c41 when the ,pleiades culminated at midnight at the vernal equinox1 the passages in the north and south faces of the pyramid of ,gizeh were directed1 the southern one to this culmination1 and the northern one to the then pole star1 ,draconis1 at its transit1 about #d from the pole4 ,hence one may regard the pyramid as the next astronomical instrument to the horizon4 ,while then it is possible that such culmination observations soon replaced in some measure that class of observations which heretofore had been made on the horizon1 another teaching of horizon observations became apparent4 ,by and by travellers observed that as they travelled northwards the stars that were just visible on the southern horizon1 when culminating1 gradually disappeared below it4 ,these observations were at once seized on1 and ,anaximander accounted for them by supposing that the earth was a cylinder4#b ,the idea of a sphere did not come till later2 when it did come then came the circle as an astronomical instrument4 ,for let us consider that a person on the earth stands1 say1 at the equator2 then he will just be able to see along his north and south horizon the stars pointed to by the axis of the globe3 if now he is transported northwards1 his horizon will change with him2 he will no longer be able to see the southern stars1 but the northern ones will gradually rise above his horizon till he gets to the north pole1 when the north pole star1 instead of being on his horizon1 as was the case when he was at the equator1 will be over his head4 ,so by moving from the equator to the pole 7or a quarter of the distance round the earth7 the stars have moved from the horizon to the point overhead1 or the zenith1 that is also a quarter of a circle4 ,so it appears that if an observer moves to such a distance that the stars appear to move over a certain division of a circle with reference to the horizon1 he must have moved over an equal division on the earth's surface4 ,then1 as now1 the circle in the ,western world was divided into #cfj1 so that the observer in moving #a by the stars would have moved over #a_/cfj of the distance round the earth1 on the assumption that the earth is a globe2 and if the distance over which the observer has moved be multiplied by #cfj1 the result will be the distance round the earth4 ,illustration3 ,,fig4 #b4--,the ,zodiac of ,denderah4 ,now let us see how ,posidonius a long time afterwards 7he was born about #ace years ,b4,c47 applied this conception4 ,he observed that at ,rhodes the star ,canopus grazed the horizon at culmination1 while at ,alexandria it rose above it #g4 ,now #g is #a_/dh of the whole circle2 so he found that from the latitude of ,rhodes to that of ,alexandria was #a_/dh of the circumference of the earth4 ,he then estimated the distance1 getting #e1jjj stadia as the result2 and this multiplied by #dh gave him #bdj1jjj stadia1 his measure of the circumference of the earth4 ,when the sun's yearly course in the heavens had been determined1 it was found that it was restricted to that band of stars called the ,zodiac1 ,fig4 #b2 the sun's position in the zodiac at any one time of the year being found by the midnight culmination of the stars opposite the sun2 this and the apparent and heliacal risings and settings were alone the subjects of observation4 ,it is obvious1 then1 that when observations of this nature had gone on for some time1 men would be anxious to map the stars1 to make a chart of the field of heaven2 and such a work was produced by ,autolycus three and a half centuries before ,christ4 ,we also owe to ,autolycus and ,euclid1 who flourished about the same time 7#cjj ,b4,c471 the first geometrical conceptions connected with the apparent motions of the stars4 ,in the theorems of ,autolycus there is a particular reference to the twelve parts of the zodiac1 as denoted by constellations4 ,the following are the most important propositions which he lays down3-- #a4 8,the zodiacal sign occupied by the sun neither rises nor sets1 but is either concealed by the earth or lost in the sun's rays4 ,the opposite sign neither rises nor sets1 i4e41 visibly1 i4e41 after sundown1 but it is visible during the whole night4 #b4 8,of the twelve signs of the zodiac1 that which precedes the sign occupied by the sun rises visibly in the morning2 that which succeeds the same sign sets visibly in the evening4 #c4 8,eleven signs of the zodiac are seen every night4 ,six signs are visible1 and the five others1 not occupied by the sun1 afterwards rise4 #d4 8,every star has an interval of five months between its morning and its evening rising1 during which time it is visible4 ,it has an interval of at least thirty days--between its evening setting1 and its morning rising--during which time it is invisible40 7,that is1 the space passed over by the sun in its annual path is such that a star which you see on one side of the sun1 when the sun rises at one time1 would be seen a month afterwards on the other side of the sun47 ,autolycus makes no mention of the planets4 ,their irregular movements rendered them unsuited to the practical object which he had in view4 ,he is1 however1 stated by ,simplicius1 as quoted by ,sir ,g4 ,c4 ,lewis to have proposed some hypothesis for explaining their anomalous motions1 and to have failed in his attempt4 ,euclid carries the results arrived at in this early pre-telescopic age much further2 in a little-known treatise1 the ,phenomena1#c he thus sums up the knowledge then acquired3-- 8,the fixed stars rise at the same point1 and set at the same point2 the same stars always rise together1 and set together1 and in their course from the east to the west they always preserve the same distance from one another4 ,now1 as these appearances are only consistent with a circular movement1 when the eye of the observer is equally distant from the circumference of the circle in every direction 7as has been demonstrated in the treatise on ,optics71 it follows that the stars move in a circle and are attached to a single body1 and that the vision is equally distant from the circumference4 ,illustration3 ,,fig4 #c4--;,illustration of ,euclid's statements4 ,p the star between the ,bears4 ,d ,d the region of the always visible4 ,c ,b ,a the regions of the stars which rise and set4 8,a star is visible between the ,bears1 not changing its place1 but always revolving upon itself4 ,since this star appears to be equally distant from every part of the circumference of each circle described by the other stars1 it must be assumed that all the circles are parallel1 so that all the fixed stars move along parallel circles1 having this star as their common pole4 8,some of these neither rise nor set1 on account of their moving in elevated circles1 which are called the #8always visible4' ,they are the stars which extend from the visible pole to the ,arctic circle4 ,those which are nearest the pole describe the smallest circle1 and those upon the ,arctic circle the largest4 ,the latter appears to graze the horizon4 8,the stars to the south of this circle all rise and set1 on account of their circles being partly above and partly below the earth4 ,the segments above the earth are large and the segments below the earth are small in proportion as they approach the ,arctic circle1 because the motion of the stars nearest the circle above the earth is made in the longest time1 and of those below the earth in the shortest4 ,in proportion as the stars recede from this circle1 their motion above the earth is made in less time1 and that below the earth in greater4 ,those that are nearest the south are the least time above the earth1 and the longest below it4 ,the stars which are upon the middle circle make their times above and below the earth equal2 whence this circle is called the ,equinoctial4 ,those which are upon circles equally distant from the equinoctial make the alternate segments in equal times4 ,for example1 those above the earth to the north correspond with those below the earth to the south2 and those above the earth to the south correspond with those below the earth to the north4 ,the joint times of all the circles above and below the earth are equal4 ,the circle of the milky way and the zodiacal circle being oblique to the parallel circles1 and cutting each other1 always have a semicircle above the earth4 8,hence it follows that the heaven is spherical4 ,for if it were cylindrical or conical1 the stars upon the oblique circles1 which cut the equator1 would not in the revolution of the heaven always appear to be divided into semicircles2 but the visible segment would sometimes be greater and sometimes less than a semicircle4 ,for if a cone or a cylinder were cut by a plane not parallel to the base1 the section is that of an acute-angled cone1 which resembles a shield 7an ellipse74 ,it is1 therefore1 evident that if a figure of this description is cut in the middle both in length and breath1 its segments will be unequal4 ,but the appearances of the heaven agree with none of these results4 ,therefore the heaven must be supposed to be spherical1 and to revolve equally round an axis of which one pole above the earth is visible and the other below the earth is invisible4 8,the ,horizon is the plane reaching from our station to the heaven1 and bounding the hemisphere visible above the earth4 ,it is a circle2 for if a sphere be cut by a plane the section is a circle4 8,the ,meridian is a circle passing through the poles of the sphere1 and at right angles to the horizon4 8,the ,tropics are circles which touch the zodiacal circle1 and have the same poles as the sphere4 ,the zodiacal and the equinoctial are both great circles1 for they bisect one another4 ,for the beginning of ,aries and the beginning of the ,claws 7or ,scorpio7 are upon the same diameter2 and when they are both upon the equinoctial1 they rise and set in conjunction1 having between their beginnings six of the twelve signs and two semicircles of the equinoctial2 inasmuch as each beginning1 being upon the equinoctial1 performs its movement above and below the earth in equal times4 ,if a sphere revolves equally round its axis1 all the points on its surface pass through similar axes of the parallel circles in equal times4 ,therefore these signs pass through equal axes of the equinoctial1 one above and the other below the earth2 consequently the axes are equal1 and each is a semicircle2 for the circuit from east to east and from west to west is an entire circle4 ,consequently the zodiacal and equinoctial circles bisect one another2 each will be a great circle4 ,therefore the zodiacal and equinoctial are great circles4 ,the horizon is likewise a great circle2 for it bisects the zodiacal and equinoctial1 both great circles4 ,for it always has six of the twelve signs above the earth1 as well as a semicircle of the equator4 ,the stars above the horizon which rise and set together reappear in equal times1 some moving from east to west1 and some from west to east40 ,we have given this long extract in justice to the men of old1 containing as it does many of those geometrical principles which all our modern instruments must and actually do fulfil4 ,it is true that the present idea of the earth's place in the system is different4 ,euclid imagined the earth to be at the centre of the universe4 ,it is now known that the earth is one of various planets which revolve round the sun1 and further1 that the journey of the earth round the sun is so even and beautifully regulated that its motion is confined to a single plane4 ,year after year the earth goes on revolving round the sun1 never departing1 except to a very small extent1 from this plane1 which is one of the fundamental planes of the astronomer and called the ,plane of the ,ecliptic4 ,illustration3 ,,fig4 #d4--,the ,plane of the ,ecliptic4 ,suppose this plane to be a tangible thing1 like the surface of an infinite ocean1 the sun will occupy a certain position in this infinite ocean1 and the earth will travel round it every year4 ,if the axis of the earth were upright1 one would represent the position of things by holding a globe with its axis upright1 so that the equator of the earth is in every part of its revolution on a level with this ecliptic sea4 ,but it is known that the earth1 instead of floating1 as it were1 upright1 as in ,fig4 #d1 has its axis inclined to the plane of the ecliptic1 as in ,fig4 #e4 ,it is also known that by turning a globe round1 distant objects would appear to move round an observer on the globe in an opposite direction to his own motion1 and these distant objects would describe circles round a line joining the places pointed to by the poles of the earth1 i4e41 round the earth's axis4 ,illustration3 ,,fig4 #e4--,the ,plane of the ,ecliptic1 showing the ,inclination of the ,earth's ,axis4 ,it is now easy to explain the observations referred to by ,euclid by supposing the surface of the water in the tub to represent the plane of the ecliptic1 that is1 the plane of the path which the sun apparently takes in going round the earth2 and examining the relative positions of the sun and earth represented by two floating balls1 the latter having a wire through it inclined to the upright position2 it will be seen at once by turning the ball on the wire as an axis to represent the diurnal motion of our earth1 how ,euclid finds the ,bear which never sets1 being the place in the heavens pointed to by the earth's pole2 and how all the stars in different portions of the heavens appear to move in complete circles round the pole-star when they do not set1 and in parts of circles when they pass below the horizon4 ,by moving the ball representing the earth round the sun and so examining their relative positions1 during the course of a year it will be seen how the sun appears to travel through all the signs of the zodiac in succession in his yearly course1 remaining a longer or shorter time above the horizon at different times of the year4 ,for it will be seen that if the spectator on the globe1 when in the position that its inclined axis1 as shown in ,fig4 #e1 points towards the sun1 were looking at the sun from a place where one can imagine ,england to be at midday1 the sun would appear to be very high up above the horizon2 and if he looked at it from the earth in the opposite part of its orbit it would be very low and near the horizon4 ,when the earth1 therefore1 occupied the intermediate positions1 the sun would be half way between the extreme upper position and the extreme lower position as the earth moves round the sun1 and in this way the solstices1 equinoxes1 and the seasonal changes on the surface of our planet1 are easily explained4 ----- ,footnote #a3 ,corresponding to #bjth ,july1 #aci ,b4,c4 ,footnote #b3 ,anaximander flourished about #edg ,b4,c4 ,footnote #c3 ,quoted by ,sir ,g4 ,c4 ,lewis in his ,astronomy of the ,ancients1 p4 #ahg4 ,,chapter ,,ii4 ,,the ,,first ,,instruments4 ,the ancients called the places occupied by the sun when highest and lowest the ,solstices1 and the intermediate positions the ,equinoxes4 ,the first instrument made was for the determination of the sun's altitude in order to fix the solstices4 ,this instrument was called the ,gnomon4 ,it consisted of an upright rod1 sharp at the end and raised perpendicularly on a horizontal plane1 and its shadow could be measured in the plane of the meridian by a north and south line on the ground4 ,whenever the shadow was longest the sun was naturally lowest down at the winter solstice1 and vice vers for the summer solstice4 ,here then we leave observations on the horizon and come to those made on the meridian4 ,the ,gnomon is said to have been known to the ,chinese in the time of the ,emperor ,yao's reign 7#bcjj ,b4,c471 but it was not used by the ,greeks#d till the time of ,thales1 about #ehe ,b4,c41 who fixed the dates of the solstices and equinoxes1 and the length of the tropical year--that is1 the time taken by the sun to travel from the vernal equinoctial point round to the same point again4 ,the next problem was to discover the inclination of the ecliptic1 or1 what is the same thing1 the amount that the earth's equator is inclined to the ecliptic plane 7represented by the surface of the water in our tub74 ,now in order to ascertain this1 the angular distance between the positions occupied by the sun when at the solstices must be measured2 or1 since one solstice is just as much below the equinoctial line as the other is above it1 we might take half the angle between the solstices as being the obliquity required4 ,the first method of measuring the angle was to measure the length of the sun's shadow at each solstice1 and so1 by comparison of the length of the shadow with the height of the gnomon1 calculate the difference in altitude1 the half of which was the angle sought4 ,and this was probably the method of the ,chinese1 who obtained a result of #bc #ch #aa in the time of ,yao2 and also of ,anaximander in his early days1 who obtained a result of #bd4 ,but before trigonometrical tables1 the first of which seem to have been constructed by ,hipparchus and ,ptolemy1 were known1 in order to find this angle it was constructed geometrically1 and then what aliquot part of the circumference it was1 or how much of the circumference it contained was determined2 for the division of the circle into #cfj is subsequent to the first beginning of astronomy--and hence it was that ,eratosthenes said that the distance from the tropics was #aa_/hc of the circumference1 and not that it was #dg #df #bf4 ,the gnomon is1 without exception1 of all instruments the one with which the ancients were able to make the best observations of the sun's altitude4 ,but they did not give sufficient attention to it to enable it to be used with accuracy4 ,the shadow projected by a point when the sun is shining is not well defined1 so that they could not be quite certain of its extremity1 and it would seem that the ancient observations of the height of the sun made in this manner ought to be corrected by about half the apparent diameter of the sun2 for it is probable that the ancients took the strong shadow for the true shadow2 and so they had only the height of the upper part of the sun and not that of the centre4 ,there is no proof that they did not make this correction1 at least in the later observations4 ,in order to obviate this inconvenience1 they subsequently terminated the gnomon by a bowl or disc1 the centre of which answered to the summit2 so that1 taking the centre of the shadow of this bowl1 they had the height of the centre of the sun4 ,such was the form of the one that ,manlius the mathematician erected at ,rome under the auspices of ,augustus4 ,but in comparatively modern times astronomers have remedied this defect in a still more happy manner1 by using a vertical or horizontal plate pierced with a circular hole which allows the rays of the sun to enter into a dark place1 and in fact to form a true image of the sun on a floor or other convenient receptacle1 as we find is the case in many continental churches4 ,of course at this early period the reference of any particular phenomenon to true time was out of the question4 ,the ancients at the period we are considering used twelve hours to represent a day1 irrespective of the time of the year--the day always being reckoned as the time between sunrise and sunset4 ,so that in summer the hours were long and in winter they were short4 ,the idea of equal hours did not occur to them till later2 but no observations are closer than an hour1 and the smallest division of space of which they took notice was something like equal to a quarter or half of the moon's diameter4 ,when we come down1 however1 to three centuries before ,christ1 we find that a different state of things is coming about4 ,the magnificent museum at ,alexandria was beginning to be built1 and astronomical observations were among the most important things to be done in that vast establishment4 ,the first astronomical workers there seem to have been ,timocharis and ,aristillus1 who began about #bie ,b4,c41 and worked for twenty-six years4 ,we are told that they made a catalogue of stars1 giving their positions with reference to the sun's path or ecliptic4 ,it was soon after this that the gnomon gave way to the invention of the ,scarphie4 ,it is really a little gnomon on the summit of which is a spherical segment4 ,an arc of a circle passing out of the foot of the style was divided into parts1 and we thus had the angle which the solar ray formed with the vertical4 ,nevertheless the scarphie was subject to the same inconveniences1 and it required the same corrections1 as the gnomon2 in short1 it was less accurate than it4 ,that did not1 however1 hinder ,eratosthenes from making use of it to measure the size of the earth and the inclination of the ecliptic to the equator4 ,the method ,eratosthenes followed in ascertaining the size of the earth was to measure the arc between ,syene and ,alexandria by observing the altitude of the sun at each place4 ,he found it to be #a_/ej of the circumference and #e1jjj stadia1 so that if #a_/ej of the circumference of the earth is #e1jjj stadia1 the whole circumference must be #ej times #e1jjj1 or #bej1jjj stadia4#e ,illustration3 ,,fig4 #f4--,the ,first ,meridian ,circle4 ,and now still another instrument is introduced1 and we begin to find the horizon altogether disregarded in favour of observations made on the meridian4 ,the instrument in question was probably the invention of ,eratosthenes4 ,it consisted of two circles of nearly the same size crossing each other at right angles1 7,fig4 #f72 one circle represented the equator and the other the meridian1 and it was employed as follows3-- ,the circle ,a was fixed perfectly upright in the meridian1 so that the greatest altitude of the sun each day could be observed2 the circle ,b was then placed exactly in the plane of the earth's equator by adjusting the line joining ,c and ,d to the part of the heavens between the ,bears1 about which the stars appear to revolve4 ,this done1 the occurrence of the equinox was waited for1 at which time the shadow of the part of the circle ,e must fall upon the part marked ,f1 so as exactly to cover it4 ,illustration3 ,,fig4 #g4--,the ,first ,instrument ,graduated into #cfj 7,west ,side74 ,we now come to the time when the circle began to be divided into #cfj divisions or degrees--about the time of ,hipparchus 7#afj ,b4,c474 ,there are two instruments described by ,ptolemy for measuring the altitude of the sun in degrees instead of in fractions of a circle4 ,they1 like the gnomon1 were used for determining the altitude of the sun4 ,the first1 ,fig4 #g1 consisted of two circles of copper1 one1 ,c ,d1 larger than the other1 having the smaller one1 ,b1 so fitted inside it as to turn round while the larger remained fixed4 ,the larger was divided into #cfj1 and the smaller one carried two pointers4 ,this instrument was placed perfectly upright and in the plane of the meridian1 and with a fixed point1 ,c1 always at the top by means of a plumb-line hanging from ,c over a mark1 ,d4 ,on this small circle are two square knobs projecting on the side1 ,e and ,f4 ,when the sun was on the meridian the small circle was turned so as to bring the shadow of the knob ,e over the knob ,f1 and then the degree to which the pointer pointed was read off on the larger circle4 ,and of course1 as the position of the knobs had to be changed as the sun moved in altitude1 the angle through which the sun moved was measured1 and the circle being fixed1 the sun's altitude could always be obtained4 ,the other instrument consisted of a block of wood or stone1 one side of which was placed in the plane of the meridian2 and on the top corner of this side was fixed a stud2 and round it as a centre a quarter of a circle was described1 divided into #ij4 ,below this stud was another1 and by means of a plumb-line one stud could always be brought over the other2 so that the instrument could always be placed in a true position4 ,at midday then1 when the sun was shining1 the shadow of the upper stud would fall across the scale of degrees1 and at once give the altitude of the sun4 ,ptolemy1 who used this instrument1 found that the arc included between the tropics was #dg4 ,the result of all these accurate determinations of the solstices and equinoxes was the fixing of the length of the year4 ,we have so far dealt with the methods of observation which depend upon the use of the horizon and of the meridian2 we will now turn our attention to extra-meridional observations1 or those made in any part of the sky4 ,before we discuss them1 let us consider the principles on which we depend for fixing the position of a place on a globe4 ,on a terrestrial globe there are lines drawn from pole to pole1 called meridians of longitude2 and if a place is on any one meridian it is said to be in so many degrees of longitude1 east or west of a certain fixed meridian1 as there are degrees intercepted between this meridian and the one on which the place is situated4 ,there are also circles at right angles to the above and parallel to the equator2 these are circles of latitude1 and a place is said to have so many degrees ,n4 or ,s4 latitude as the circle which passes through it intercepts on a meridian between itself and the equator1 so that the latitude of a place is its angular distance from the equator1 and the longitude is its angular distance ,e4 or ,w4 of a fixed meridian--that of ,greenwich being the one used for ,english calculation2 and each large country takes the meridian of its central observatory for its starting-point4 ,the distance round the equator is sometimes expressed in hours instead of degrees2 for as the earth turns round in twenty-four hours1 so the equator can be divided into hours1 minutes1 and seconds4 ,so that if a star be just over the meridian of ,greenwich1 which is #j #j #j1 or #j;h #jm #js longitude at a certain time1 in an hour after it will be over a meridian #ae or one hour west of ,greenwich1 and so on1 till at the end of twenty-four hours it would be over ,greenwich again4 ,now let us turn to the celestial globe4 ,what we call latitude and longitude on a terrestrial globe is called declination and right ascension on the celestial globe1 because in the heavens there is a latitude and longitude which does not correspond to our latitude and longitude on the earth4 ,if we imagine the lines of latitude and longitude on the earth to be projected1 say as shadows thrown on the heavens by a light in the centre of the earth1 the lines of right ascension 7generally written ,r4,a47 and declination 7written ,dec4 or ,d47 will be perfectly depicted4 ,but there is another method of co-ordinating the stars1 in which we have the words latitude and longitude used also1 as we have said1 for the heavens2 meaning the distance of a star from the ecliptic instead of the equator1 and its distance east or west measured by meridians at right angles to the ecliptic4 ,this premised1 we are in a position to see the enormous advance rendered possible by the methods of observation introduced by ,hipparchus and ,ptolemy4 ----- ,footnote #d3 ,this instrument is also reported to have been used by the ,chaldeans in #hej ,b4,c42 the invention of it being attributed to ,anaximander4 ,this philosopher1 says ,diogenes ,laertes1 observed the revolution of the sun1 that is to say1 the solstices1 with a gnomon2 and probably he measured the obliquity of the ecliptic to the equator1 which his master had already discovered4 ,footnote #e3 #bh1bgi miles4 ,,chapter ,,iii4 ,,hipparchus ,,and ,,ptolemy4 ,among the astronomers of antiquity there are two figures who stand out in full relief--,hipparchus and ,ptolemy4 ,the former1 8the father of astronomy10 is especially the father of instrumental astronomy4 ,as he was the first to place observation on a sure basis1 and left behind him the germs of many of our modern instruments and methods1 it is desirable to refer somewhat at length to his work and that of his successor1 ,ptolemy4 ,hipparchus introduced extra-meridional observations4 ,he followed ,meton1 ,anaximander1 and others in observing on the meridian instead of on the horizon1 and then it struck him that it was not necessary to keep to the meridian1 and he conceived an instrument1 called an ,astrolabe1 fixed on an axis so that the axis would point to the pole-star1 like the one represented in ,fig4 #h4 ,this engraving is of one of ,tycho ,brahe's instruments1 which is similar to but more elaborate than that of ,hipparchus no drawing of which is extant4 ,c1 ,d1 is the axis of the instrument pointed to the pole of the heavens2 ,e1 ,b1 ,c1 the circle placed ,north and ,south representing the meridian2 ,r1 ,q1 ,n1 the circle placed at right angles to the polar axis1 representing the equator1 but in the instrument of ,hipparchus it was fixed to the circle ,e1 ,b1 ,c1 and not movable in its own plane as this one is4 ,m1 ,l1 ,k1 is a circle at right angles to the equator1 and moving round the poles1 being a sort of movable meridian4 ,thus1 then1 if the altitude of a star from the equator 7or its declination7 was required to be observed1 the circle was turned round on the axis1 and the sights1 ,q1 ,m1 moved on the circle till they1 together with the sight ,a1 pointed to the star2 the number of degrees between one of the sights and the equator1 was then read off1 giving the declination required4 ,the number of degrees1 or hours and minutes1 of ,right ,ascension1 from ,k to ,e could be then read off along the circle ,r1 ,q1 ,n1 giving the distance of the object from the meridian4 ,as the stars have an apparent motion1 the difference in right ascension between two stars only could be obtained by observing them directly after each other1 and allowing for the motion during the interval between the two observations4 ,illustration3 ,,fig4 #h4--;,astrolabe 7,armill quatori of ,tycho ,brahe7 similar to the one contrived by ,hipparchus4 ,in this manner1 then1 ,hipparchus could point to any part of the heavens and observe1 on either side of the meridian1 the sun1 moon1 planets or any of the stars1 and obtain their distance from the equatorial plane2 but another fixed plane was required2 and ,hipparchus1 no longer content with being limited to measuring distances from the equator1 thought it might be possible to get another starting-point for distances along the equator4 ,it was the determination of this plane1 or starting-point from which to reckon right ascension1 that was one of the difficulties ,hipparchus had to encounter4 ,this point he decided should be the place in the heavens where the sun crosses the equator at the spring equinox4 ,but the stars could not be seen when the sun was shining2 how1 then1 was he to fix that point so that he could measure from it at night8 ,illustration3 ,,fig4 #i4--;,ecliptic ,astrolabe 7the ,armill ,zodiacales of ,tycho ,brahe71 similar to the one used by ,hipparchus4 ,he found it at first a tremendous problem1 and at last hit upon this happy way of solving it4 ,he reasoned in this way3 8,as an eclipse of the moon is caused by the earth's shadow being thrown by the sun on the moon1 if this happen near the equinox1 the sun and moon must then be very near the equator1 and very near the ecliptic--in fact1 near the intersection of the two fundamental planes which are supposed to cross each other4 ,if ,i can observe the distance1 measured along the equator1 between the moon and a star1 ,i shall have obtained the star's actual place1 because1 of course1 if the moon is exactly opposite the sun1 the sun will be #ahj degrees of right ascension from the moon1 and the right ascension of the sun being known it will give me the position of the star40 ,this method of observation was an extremely good one for the time1 but it could only have been used during an eclipse of the moon1 and when the sun was so near the equator that its distance from the equinoctial point along the ecliptic1 as calculated by the time elapsed since the equinox1 differed little from the same distance measured along the equator1 or its right ascension1 so that the right ascension of the sun was very nearly correct4 ,hipparchus hit upon a very happy alteration of the same instrument to enable him to measure latitude and longitude instead of declination and right ascension--in fact1 to measure along the ecliptic instead of the equator4 ,instead of having the axis of the inner rings parallel to the axis of the earth1 as in ,fig4 #i1 he so arranged matters that the axis of this system was separated from the earth's axis to the extent of the obliquity of the ecliptic1 the circle ,r1 ,q1 ,n1 therefore instead of being in the plane of the equator1 was in that of the ecliptic4 ,then it was plain to ,hipparchus that he would1 instead of being limited to observe during eclipses of the moon1 be able to reckon from the sun at all times2 because the sun moves always along the ecliptic and the latitude of the sun is nothing4 ,we will now describe the details of the instrument4 ,there is first a large circle1 ,e1 ,b1 ,c1 ,fig4 #i 7which is taken from a drawing of this kind of instrument as constructed subsequently by ,tycho ,brahe71 fixed in the plane of the meridian1 having its poles1 ,d1 ,c1 pointing to the poles of the heavens2 inside this there is another circle1 ,f1 ,i1 ,h1 turning on the pivots ,d1 ,c1 and carrying fixed to it the circle1 ,o1 ,p1 arranged in a plane at right angles to the points ,i1 ,k1 which are placed at a distance from ,c and ,d equal to the obliquity of the ecliptic2 so that ,i and ,k represent the poles of the ecliptic1 and the circle1 ,o1 ,p1 the ecliptic itself4 ,there is then another circle1 ,r1 ,m1 turning on the pivots ,i and ,k1 representing a meridian of latitude1 and along which it is measured4 ,then1 as the sun is on that part of the ecliptic nearest the north pole1 in summer1 its position is represented by the point ,f on the ecliptic1 and by ,n at the winter solstice2 so1 knowing the time of the year1 the sight ,q can be placed the same number of degrees from ,f as the sun is from the solstice1 or in a similar position on the circle ,o ,p as the sun occupies on the ecliptic4 ,the circle can then be turned round the axis ,c1 ,d1 till the sight ,q1 and the sight opposite to it1 ,q1 are in line with the sun4 ,the circle1 ,o1 ,r1 will then be in the plane of the ecliptic1 or of the path of the earth round the sun4 ,the circle1 ,r1 ,m1 is then turned on its axis1 ,i1 ,k1 and the sights1 ,r1 ,r1 moved until they point to the moon4 ,the distance ,q1 ,l1 measured along ,o1 ,p1 will then be the difference in longitude of the moon and sun1 and its latitude1 ,l1 ,r1 measured along the circle ,r1 ,m4 ,but why should he use the moon8 ,his object was to determine the longitude of the stars1 but his only method was to refer to the motion of the sun1 which could be laid down in tables1 so that its longitude or distance from the vernal equinox was always known4 ,but we do not see the stars and the sun at the same time2 therefore in the day time1 while the moon was above the horizon1 he determined the difference of longitude between the sun and the moon1 the longitude of the sun or its distance from the vernal equinox being known by the time of the year2 and after the sun had set he determined the difference of longitude between the moon and any particular star2 and so he got a fair representation of the longitude of the stars1 and succeeded in tabulating the position of #a1jbb of them4 ,it is to the use of this instrument that we owe the discovery of the precession of the equinoxes4 ,illustration3 ,,fig4 #aj4--;,diagram ,illustrating the ,precession of the ,equinoxes4 ,after ,hipparchus had fixed the position of a number of stars1 he found that on comparing the place amongst them of the sun at the equinoxes in his day with its place in the time of ,aristillus that the positions differed--that the sun got to the equinox1 or point where it crossed the equator1 a short time before it got to the place amongst the stars where it crossed in the time of ,aristillus2 in fact1 he found that the equinoctial points retrograded along the equator1 and ,ptolemy 7,b4,c4 #ace7 appears to have established the fact that the whole heavens had a slow motion of one degree in a century which accounted for the motion of the equinoxes4 ,illustration3 ,,fig4 #aa4--,revolution of the ,pole of the ,equator round the ,pole of the ,ecliptic caused by the ,precession of the ,equinoxes4 ,let us see what we have learned from the observation of this motion1 for motion there is1 and the ancients must be looked on with reverence for their skill in determining it with their comparatively rude instruments4 ,in ,fig4 #aj1 ,a represents the earth at the vernal equinox1 and at this time the sun appears near a certain star1 ,s1 which was fixed by ,aristillus2 but in the time of ,hipparchus the equinox happened when the sun was near a star1 ,s1 and before it got to ,s4 ,now we know that the sun has no motion round the earth1 and that the equinox simply depends on the position of the earth's equator in reference to the ecliptic2 so that in order to produce the equinox when the earth is at ,e and before it get to ,a1 its usual place1 all we have to do is to turn the pole of the earth through a small arc of the dotted circle1 and so alter its position to that shown at ,f1 when its equator and poles will have the same position as regards the sun as they have at ,a1 so the equinox will happen when the earth is at ,e1 and before it reaches ,a4 ,this may be practically represented by taking an orange and putting a knitting-needle through it1 and drawing a line representing the equator round it1 and half immersing it in a tub of water1 the surface of which represents the ecliptic4 ,we are then able to examine these motions by moving the orange round the tub to represent the earth's annual motion1 and at the same time making the orange slowly whobble like a spinning-top just before it falls1 by moving the top of the knitting-needle through a small arc of a circle in the same direction as the hands of a clock at every revolution of the orange round the centre of the tub4 ,the points where the equator is cut by the surface of the water 7or ecliptic7 will then change1 as the orange whobbles1 and the line joining them1 will rotate1 and as the equinox happens when this line passes through the sun1 it will be seen that this will take place earlier at each revolution of the orange round the tub4 ,the equinox will therefore appear to happen earlier each year1 so that the tropical year1 or the time from equinox to equinox1 is a little shorter than the sidereal year1 or the time that the earth takes to travel from a certain place in its orbit to the same again2 for if the earth start from an equinoctial point1 the equinox will happen before it gets to the same place where the equinoctial point was at starting4 ,this is called the precession of the equinoxes4 ,illustration3 ,,fig4 #ab4--,the ,vernal ,equinox among the ,constellations1 ,b4,c4 #bagj4 ,illustration3 ,,fig4 #ac4--,showing how the ,vernal ,equinox has now passed from ,taurus and ,aries4 ,this discovery must be regarded as the greatest triumph obtained by the early stargazers1 and there is much evidence to show that when the zodiac was first marked out among the central zone of stars1 the ,bull and not the ,ram was the first of the train4 ,even the ,ram1 owing to precession1 is no longer the leader1 for the sign ,aries is now in the constellation ,pisces4 ,the two accompanying drawings by ,professor ,piazzi ,smyth of the position of the vernal equinox among the stars in the years #bagj ,b4,c4 and #ahhc ,a4,d4 will show how precession has brought about celestial changes which have not been unaccompanied by changes of religious ideas and observances in origin connected with the stars4 ,illustration3 ,,fig4 #ad4--;,instrument for ,measuring ,altitudes4 ,we now come to ,ptolemy4 ,there was another instrument used by ,ptolemy1 and described by him1 which we may mention here2 it was called the ,parallactic ,rules1 so named perhaps because that ancient astronomer used it first for the observation of the parallax of the moon4 ,it consists of three rods1 ,d ,e1 ,d ,f1 ,e ,f1 ,fig4 #ad1 two of which formed equal sides of an isosceles triangle2 and the third1 which had divisions on it1 made the one at the base1 or was the chord of the angle at the summit4 ,one of the equal sides1 ,d ,f1 was furnished with pointers1 over which a person observed the star1 whilst the other1 ,d ,e1 was placed vertically1 so that they read off the divisions on ,e ,f1 and then1 by means of a table of chords1 the angle was found2 this angle was the distance of the star from the zenith4 ,ptolemy1 wishing to observe with great accuracy the position of the moon1 made himself an instrument of this kind of a considerable size2 for the equal rulers were four cubits long1 so that its divisions might be more obvious4 ,he rectified its position by means of a plumb-line4 ,purbach1 ,regiomontanus1 and ,walther1 astronomers of the fifteenth century1 employed this manner of observing1 which1 considering the youth of astronomy1 was by no means to be despised4 ,this instrument1 constructed with great care1 would have sufficiently been useful as far as concerns certain measurements and would have furnished results sufficiently exact2 but the part of ancient astronomy that failed was the way of measuring time with any precision4 ,there were astronomers who proposed clepsydras for this purpose2 but ,ptolemy rejected them as very likely to introduce errors2 and indeed this method is subject to much inconvenience and to irregularities difficult to prevent4 ,however1 as the measurement of time is the soul of astronomy1 ,ptolemy had recourse to another expedient which was very ingenious4 ,it consisted in observing the height of the sun if it were day1 or of a fixed star if it were night1 at the instant of a phenomenon of which he wished to know the time of occurrence1 for the place of the sun or star being known to some minutes of declination and right ascension as also was the latitude of the place1 he was able to calculate the hour2 thus when they observed1 for example1 an eclipse of the moon1 it was only necessary to take care to get the height of some remarkable star at each phase of the eclipse1 say at the commencement and at the end1 in order to be able to conclude the true time at which it took place4 ,this was the method adopted by astronomers until the introduction of the pendulum4 ,,chapter ,,iv4 ,,tycho ,,brahe4 ,leaving behind us the results of the researches of ,ptolemy1 who succeeded ,hipparchus and whose methods have been described1 and passing over the astronomy of the ,arabs and ,persians as being little in advance of ,hipparchus and ,ptolemy1 we come down to the sixteenth century of our era4 ,here we find ourselves in presence of the improvements in instruments effected by a man whose name is conspicuous--,tycho ,brahe--a ,danish nobleman who1 in the year #aegf1 established a magnificent observatory at ,huen1 which may be looked upon as the next building of importance after that great edifice at ,alexandria which has already been referred to4 ,what ,hipparchus was to the astronomy of the ,ancients such was ,tycho to the astronomy of the ,middle ,ages4 ,as such his life merits a brief notice before we proceed to his work4 ,he was born at ,knudsthorp1 near ,helsingborg1 in ,sweden1 in #aedf1 and went to the ,university of ,copenhagen to prepare to study law2 while there he was so struck with the prediction of an eclipse of the sun by the astrological almanacks that he gave all his spare time to the study of astronomy4 ,in #aefe his uncle died and ,tycho ,brahe fell into possession of one of his uncle's estates2 and as astronomy1 or astrology as it was then called1 was thought degrading to a man in his position by his friends1 who took offence at his pursuits and made themselves very objectionable1 he left for a short stay at ,wittenberg1 then he went to ,rostock and afterwards to ,augsburg1 where he constructed his large quadrant4 ,he returned to his old country in #aega2 while there1 ,frederick ,,ii41 ,king of ,denmark1 requested him to deliver a course of lectures on astronomy and astrology and became his most liberal patron4 ,the ,king granted to ,tycho ,brahe for life the island of ,huen1 lying between ,denmark and ,sweden1 and built there a magnificent observatory and apartments for ,tycho1 his assistants and servants4 ,the main building was sixty feet square1 with observing towers on the north and south1 and a library and museum4 ,tycho called this ,uraniberg--the city of the heavens2 and he afterwards built a smaller observatory near called by him ,sternberg--city of the stars1 the former being insufficiently large to contain all his instruments4 ,the following is a list of these instruments as given in ,sir ,david ,brewster's excellent memoir of ,brahe1 in ,martyrs of ,science3-- ,in the ,south and greater ,observatory4 #a4 ,a semicircle of solid iron1 covered with brass1 four cubits radius4 #b4 ,a sextant of the same materials and size4 #c4 ,a quadrant of one and a half cubits radius1 and an azimuth circle of three cubits4 #d4 ,ptolemy's parallactic rules1 covered with brass1 four cubits in the side4 #e4 ,another sextant4 #f4 ,another quadrant1 like ,no4 #c4 ,illustration3 ,,fig4 #ae4--,portrait of ,tycho ,brahe 7from original painting in the possession of ,dr4 ,crompton1 of ,manchester74 #g4 ,zodiacal armillaries of melted brass1 and turned out of the solid1 of three cubits in diameter4 ,near this observatory there was a large clock with one wheel two cubits in diameter1 and two smaller ones which1 like it1 indicated hours1 minutes1 and seconds4 ,in the ,south and lesser ,observatory4 #h4 ,an armillary sphere of brass1 with a steel meridian1 whose diameter was about four cubits4 ,in the ,north ,observatory4 #i4 ,brass parallactic rules1 which revolved in azimuth above a brass horizon1 twelve feet in diameter4 #aj4 ,a half sextant1 of four cubits radius4 #aa4 ,a steel sextant4 #ab4 ,another half sextant with steel limb1 four cubits radius4 #ac4 ,the parallactic rules of ,copernicus4 #ad4 ,equatorial armillaries4 #ae4 ,a quadrant of a solid plate of brass1 five cubits in radius1 showing every ten seconds4 #af4 ,in the museum was the large globe made at ,augsburg4 ,in the ,sternberg ,observatory4 #ag4 ,in the central part1 a large semicircle1 with a brass limb1 and three clocks1 showing hours1 minutes1 and seconds4 #ah4 ,equatorial armillaries of seven cubits1 with semi-armillaries of nine cubits4 #ai4 ,a sextant of four cubits radius4 #bj4 ,a geometrical square of iron1 with an intercepted quadrant of five cubits1 and divided into fifteen seconds4 #ba4 ,a quadrant of four cubits radius1 showing ten seconds1 with an azimuth circle4 #bb4 ,zodiacal armillaries of brass1 with steel meridians1 three cubits in diameter4 #bc4 ,a sextant of brass1 kept together by screws1 and capable of being taken to pieces for travelling with4 ,its radius was four cubits4 #bd4 ,a movable armillary sphere1 three cubits in diameter4 #be4 ,a quadrant of solid brass1 one cubit radius1 and divided into minutes by ,nonian circles4 #bf4 ,an astronomical radius of solid brass1 three cubits long4 #bg4 ,an astronomical ring of brass1 a cubit in diameter4 #bh4 ,a small brass astrolabe4 ,tycho ,brahe carried on his work at ,uraniberg for twenty-one years1 and appears to have been visited by many of the princes of the period and by students anxious to learn from so great a man4 ,in ,frederick's treatment of ,tycho ,brahe we have an early and munificent and1 in its results1 most successful instance of the endowment of research4 ,on the death of ,frederick ,,ii41 in #aehh1 ,christian ,,iv4 came to the throne4 ,the successor cared little for astronomy1 and his courtiers1 who were jealous of ,tycho's position1 so acted upon him that the pension1 estate and canonry with which ,tycho had been endowed were taken away4 ,unable to put up with these insults and loss of his money1 he left for ,wandesburg in #aeig1 where he was entertained by ,count ,henry ,rantzau4 ,it was now that he wrote and published the ,astronomi instaurat ,mechanica1 a copy of which1 together with his catalogue of #ajjj stars1 was sent to the ,emperor ,rudolph ,,ii41 who invited him to go to ,prague4 ,this he accepted1 and he and his family went to the castle of ,benach in #aeii1 and a pension of #cjjj crowns was given to him4 ,ten years afterwards he removed with his instruments into ,prague to a house purchased and presented to him by the ,emperor2 here he died in the same year4 ,the wonderful assistance which ,tycho ,brahe was able to bring to astronomy shows that then1 as now1 any considerable advance in physical investigation was more or less a matter of money1 and whether that money be found by individuals or corporations1 now or then1 we cannot expect any considerable advance without such a necessary adjunct4 ,illustration3 ,,fig4 #af4--,tycho ,brahe's ,observatory on the ,island of ,huen4 ,the principal instruments used at first by ,tycho ,brahe resembled the ,greek ones1 except that they were much larger4 ,hipparchus was enabled to establish the position of a heavenly body within something less than one degree of space--some say within ten minutes2 but there was an immense improvement made in this direction in the instruments used by ,tycho4 ,one of the instruments which he used was in every way similar to the equatorial astrolabe designed1 by ,hipparchus1 and was called by ,tycho1 the #8armill equatori' 7,fig4 #h74 ,with that instrument in connection with others ,tycho was enabled to make an immense advance upon the work done by ,hipparchus4 ,tycho1 like ,hipparchus1 having no clock1 in the modern sense1 was not able to determine the difference of time between the transit of the sun or a particular star over the meridian1 so that he was compelled to refer everything to the sun at the instant of observation1 and he did that by means of the moon4 ,hipparchus1 as we have seen1 determined the difference of longitude1 or right ascension1 between the sun and the moon and between the moon and the stars1 in the manner already described1 and so used the moon as a means of determining differences between the longitude or right ascension of the sun and the stars4 ,now ,tycho1 using an instrument similar to that of ,hipparchus1 saw that he would make an improvement if instead of using the ,moon he used ,venus2 for the measure of the surface of the moon was considerable1 and could not be easily reckoned1 and its apparent position in the heavens was dependent on the position of a person on the earth1--because it is so near the earth that it has a sensible parallax1 that is1 a person at the equator of the earth might see the moon in the direction of a certain star2 but1 on going to the pole1 the moon would appear below the line of the star4 ,if one were looking at a kite in the air to the south and then walked towards the south1 the kite would gradually get over head1 and on proceeding further it would get north4 ,to persons at different stations the kite would appear in different positions1 and the nearer the kite was to the observer the less distance he would have to go to make it change its place4 ,so also with the moon2 it is so near to us that a change of place on the earth makes a considerable difference in the direction in which it is seen4 ,instead1 therefore1 of using the ,moon1 ,tycho used ,venus1 and so mapped #a1ejj stars after determining their absolute right ascensions1 in this manner without the use of clocks4 ,fig4 #h shows the instrument called the 8armill equatori10 which he constructed1 and which was based upon the principle of that which ,hipparchus had used4 ,here the axis of motion1 ,c1 ,d1 of these circles is so arranged that it is absolutely parallel to the axis of the earth2 but instead of the circle ,r1 ,q1 ,n1 representing the equator1 being fixed1 it revolved in its own plane while held by the circle ,g1 ,h1 ,i1 making its use probably more easy1 but leaving the principles unaltered4 ,tycho ,brahe also used another similar instrument of much larger size for the same purposes as the one we have just considered4 ,it consisted of a large circle1 which was seven cubits in diameter1 corresponding to the circle ,k1 ,l1 ,m1 ,fig4 #h2 and carrying the sights in the same manner1 it was placed in a circular pit in the ground1 with its diameter pointing towards the pole4 ,this was used for measuring declinations4 ,the circle ,r1 ,q1 ,n1 ,fig4 #i1 was represented by a fixed circle carried on pillars surrounding the pit1 and along which the right ascension of the star was measured4 ,this instrument1 therefore1 was more simple than the smaller one1 and probably much more accurate4 ,tycho was not one of those who was aware of the true system of the universe2 he thought the earth fixed1 as ,ptolemy and others did2 but whether we suppose the earth to be movable in the middle of the vault of stars or stationary1 in either case that position is absolutely immaterial in ascertaining the right ascension of stars4 ,if one takes the terrestrial globe1 and looks upon the meridians1 it is at once clear that the distance from meridian to meridian remains unaltered1 whether the globe is still or turning round3 so the stars maintain their relative positions to each other1 whether we consider the earth in motion or the sphere in which the stars are placed to revolve round it4 ,illustration3 ,,fig4 #ag4--,tycho ,brahe's ,system4 ,the introduction of clocks gave ,tycho the invention of the next instrument1 which was the transit circle4 ,at this time the pendulum had not been invented2 but it struck him and others that there was no necessity for having two or more circles rotating about an axis parallel to the earth's axis1 as in the astrolabes or armill1 but only to have one circle in the plane of the meridian of the place4 ,so that1 by the diurnal movement of the earth round its own axis1 all the stars in the heavens would gradually and seriatim be brought to be visible along the arc of the circle1 so he arranged matters in the following way4 ,the stars were observed through a hole in a wall and through an eyehole1 sliding on a fixed arc4 ,the number of degrees marked at the eyehole on the arc at once gave the altitude of the heavenly bodies as seen through that hole4 ,if a star was very high1 it would be necessary for an observer to place his eye low down to be able to see it4 ,if it were near the horizon1 he would have to travel up to the top of this circle to determine its altitude1 and having done that1 and knowing the latitude of the place of observation1 the observer will be able to determine the position of the star with reference to the celestial equator4 ,the actual moment at which the star was seen was noted by the clock1 and the time that the sun had passed the hole being also previously noted1 the length of time between the transits was known2 and as the stars appear to transit or pass the meridian every twenty-four hours1 it was at once known what part of the heavens was intercepted between the sun and the star in degrees1 or1 as is usually the case1 the right ascension of the star was left expressed in hours and minutes instead of degrees2 thus he had a means of determining the two co-ordinates of any celestial body4 ,the places of the comet of #afgg1 which ,tycho discovered1 and of many stars1 were determined with absolute certainty2 but astronomers began to be ambitious4 ,it was necessary in using this instrument to wait till a celestial body got to the meridian4 ,if it was missed1 then they had to wait till the next day2 and further1 they had no opportunity whatever of observing bodies which set in the evening4 ,illustration3 ,,fig4 #ah4--,the ,quadrans ,maximus reproduced from ,tycho's plate4 ,seeing1 therefore1 that clocks were improving1 it was suggested by one of ,tycho's compeers1 the ,landgrave of ,hesse-,cassel1 that by an instrument arranged something like ,fig4 #ah1 it would be possible to determine the exact position of any body in the heavens when examined out of the meridian1 and so they got again to extra-meridional observations4 ,the instrument used by ,tycho ,brahe for the purpose1 called the ,quadrans ,maximus1 is represented in ,fig4 #ah4 ,in this there is the quadrant ,b1 ,d1 one pointer being placed1 as shown at the bottom1 near ,h1 and the other at the top1 ,c4 ,these pointers or sights were directed at the star by moving the arm ,c1 ,h1 on the pivot ,a1 and turning the whole arm and divided arc round on the axis ,n1 ,r4 ,the altitude of the star is then read off on the quadrant ,b1 ,d1 and the azimuth1 or number of degrees east or west of the north and south line1 is then read off on the circle ,q1 ,r1 ,s4 ,the screws ,y1 ,y1 served to elevate the horizontal circle1 and level it exactly with the horizon1 and the plummets ,w and ,v1 hanging from ,g1 were to show when the circle was level or not2 for the part ,a1 ,g1 being at right angles to the circle should be upright when the circle is level1 so that if ,a1 ,g1 is upright in all positions when moved round the circle in azimuth1 the circle is horizontal4 ,here1 then1 is an instrument very different in principle from what we had before4 ,in this case the heavens are viewed from the most general standpoint we can obtain--the horizon2 but observations such as these refer to the position of the place of observation absolutely1 without any reference to the position of the body with respect to the equator or the ecliptic2 but knowing the latitude of the place of observation and the time1 it was possible for a mathematical astronomer to reduce the co-ordinates to right ascension and declination1 and so actually to look at the position of these bodies with reference to the celestial sphere4 ,tycho also had various other instruments of the same kind1 differing only in the position of the quadrant ,d1 ,b1 and of the circle on which the azimuth was measured4 ,these instruments are the same in principle as our modern alt-azimuth1 which will be described hereafter1 one form having a telescope and the other being without it4 ,illustration3 ,,fig4 #ai4--,tycho's ,sextant4 ,fig4 #ai is yet another very important instrument invented by ,tycho ,brahe2 it is the prototype of our modern much used sextant4 ,it was used by ,tycho ,brahe for determining the distance from one body to another in a direct line2 a star or the moon1 say1 was observed by the pointers ,c1 ,a1 while another was observed by the pointers ,n1 ,a1 by another observer4 ,the number of degrees then between ,n and ,c gave the angular distance of the two bodies observed4 ,this instrument was mounted at ,e1 so that it could be turned into any position4 ,not only then had this instrument its representative in our present sextant1 but it was used in the same way1 not requiring to be fixed in any one position4 ,we also find represented in ,tycho ,brahe's book another form of the same instrument1 the sight ,a being next the observer1 instead of away from him1 so that he could observe the two stars through the sights ,n and ,c without moving the eye4 ,in this form only one observer was required instead of two as in the last4 ,there was also another instrument1 ,fig4 #f1 used by this great astronomer1 very similar to ,ptolemy's parallactic rules1 used for measuring zenith distances1 or the distances of stars from the part exactly overhead4 ,the star or moon was observed by the sights ,h1 ,i1 and the angle from the upright standard ,d1 ,k1 given by divisions on the rod ,e1 ,f1 ,d1 ,e being placed exactly upright by a plummet1 and being also able to turn on hinges at ,b and ,c1 any part of the sky could be reached4 ,there is one more of his instruments that needs notice--he had so many of all kinds that space will not allow reference to more than a very few4 ,this one was for measuring the altitudes of the stars as they passed the meridian2 it is a more convenient form of the mural quadrant1 and instead of a hole in the wall1 there are sights on a movable arm1 working over a divided quadrant fixed in the plane of the meridian1 just like the quadrant outside the horizontal circle1 so the observer had no reason to move up or down according as the star was high or low4 ,here then ends the pre-telescopic age4 ,tycho was one of the very last of the distinguished astronomers who used instruments without the telescope4 ,we began with the horizon1 and we have now ended with the meridian4 ,we also end with a power of determining the position of a heavenly body to ten seconds of space1 the instrument of the ,greeks reading to #aj and those of ,tycho to #aj4 ,we began with the immovable earth fixed in the midst of the vault of the sky1 and on this assumption ,tycho ,brahe made all his observations1 which ended in enabling ,kepler to give us the true system of the world1 which was the requisite basis for the crowning triumph of ,newton4 ,,book ,,ii4 ,,the ,,telescope4 ,,chapter ,v4 ,,the ,,refraction ,,of ,,light4 ,it is difficult to give the credit of the invention of the telescope to any one particular person1 for1 as in the case of most instruments1 its history has been a history of improvements2 and whether we should give the laurel to ,jansen1 ,baptista ,porta1 ,galileo or to others whose names are unknown1 is an invidious task to decide2 we will therefore not enter in any way into the question1 interesting though it be1 as to who was the inventor of the 8optick tube10 as the telescope was called by its first users4 ,the telescope is not a thing in the ordinary sense--it is a combination of things1 the things being certain kinds of lenses1 concave and convex1 known and used as spectacles long before they were combined to form the telescope4 ,the first telescopes depended on the refraction of light2 others1 to which attention will be called in a future chapter1 depended on reflection4 ,illustration3 ,,fig4 #bj4--,view and ,section of a ,prism4 ,in order to understand the action of a lens1 it is necessary to understand the action of a prism4 ,by the aid of ,fig4 #bj the action of the lenses of which telescopes are constructed will be understood4 ,a prism is a piece of glass1 or other transparent substance1 the sides of which are so inclined to each other that its section is a triangle1 and its action on light passing through it is to change the direction of the course of the beam4 ,if we examine ,fig4 #ba we shall understand the action clearly4 ,it is a known law1 that when a beam of light falls obliquely on the surface of a medium more dense than that through which it has been passing1 its direction is changed to a new one1 nearer the line drawn at right angles to that surface1 railed the normal4 ,for instance1 the ray ,s1 ,i1 falling on the prism at ,i1 is bent into the course ,i1 ,e1 which is in a direction nearer to that of ,n1 ,i1 produced inside the prism4 ,on emerging1 the reverse takes place1 and the ray is bent away from the normal ,e1 ,n1 and takes the course ,e1 ,r4 ,in the second diagram1 ,fig4 #ba1 the ray ,s1 ,i1 called the incident ray1 coincides with the normal to the surface1 so it is not refracted until it reaches the second surface1 when it has its path changed to ,e1 ,r1 instead of taking its direct course shown by the dotted line4 ,this bending of the ray is very plainly shown with an electric lamp and screen4 ,if a trough with parallel sides be placed so as to intercept part of the light coming from the electric lamp1 so that part shall pass through it and part above1 we have the image of the hole in the diaphragm of the lantern on the screen unchanged4 ,now1 if the trough be filled with water1 no difference whatever is made in the position of the light on the screen1 because the water1 which is denser than the air1 is contained in a trough with parallel sides2 but by opening the sides like opening a book1 or by interposing another trough with inclined sides1 shaped like a ,v1 that parallelism is destroyed1 and then the light passing through it will be deflected upwards from its original course1 and will fall higher on the screen2 by opening the sides more and more1 one is able to alter the direction of the light passing through the prism1 which has been constructed by destroying the parallelism of the two sides4 ,illustration3 ,,fig4 #ba4--;,deviation of ,light in ,passing at ,various ,incidences through ,prisms of ,various ,angles4 ,the refraction of light then depends upon the density of the substance through which it passes1 on the angle of incidence of the ray1 on the angle of the prism1 and also on the colour of the light1 about which we shall have something to say presently4 ,let us now pass from the prism to the lens2 for having once grasped the idea of refraction there will be no difficulty in seeing what a lens really is4 ,with the prism just considered1 placed so that a vertical section is represented by a ,v1 a ray is thrown upwards2 if another similar prism be placed with its base in contact with the base of the other1 and its apex upwards1 so that its section will be represented by a ,v reversed1 1 it is clear this will turn the rays downwards1 so that the rays1 on emerging from both prisms will tend to meet each other1 as shown1 in ,fig4 #bb1 where one ray is turned down to the same extent that the other is turned up2 so that by the combination of two prisms the two rays are brought to a point1 which is called a focus4 ,now1 if instead of putting the prisms base to base1 they are put apex to apex1 a contrary action takes place1 and by this means one is able to cause two rays of light to diverge instead of converging1 so that the prisms1 placed apex to apex1 cause the rays to diverge1 and when placed base to base they cause the light to converge4 ,illustration3 ,,fig4 #bb4--;,convergence of ,light by ,two ,prisms ,base to ,base4 ,if instead of having two prisms merely1 there be taken a system having different angles at their apices1 and from each prism there be cut a section1 beginning by cutting off the apex of the most powerful prism1 a slice from below the apex of the next1 and a slice below the corresponding part of the next1 and so on2 and then if these slices be laid on each other so as to form a compound prism1 and another similar prism be placed with its base to this one1 we get what is represented in ,fig4 #bc4 ,these different slices of prisms become more and more prismatic1 that is1 they form parts of prisms of greater angle1 as they approach the ends4 ,we can imagine a section of such a system as thin as we please4 ,suppose we had such a section and put it in a lathe1 rotating it on the axis ,a ,b1 we should describe a solid figure1 and if we suppose all the angles rounded off1 so that it is made thinner and thinner as we recede from the centre1 the prism system is turned into a lens having the form represented in ,fig4 #bd4 ,in a similar manner1 lenses thinner in the middle than at the edges1 called concave lenses1 can he constructed1 some forms of which are represented in section in ,fig4 #be4 ,it is also obvious that convex lenses of all curves and combinations of curves can be made1 some of which appear in ,fig4 #bf4 ,illustration3 ,,fig4 #bc4--;,formation of a ,lens from ,sections of ,prisms4 ,illustration3 ,,fig4 #bd4--;,front ,view and ,section of a ,double ,convex ,lens4 ,illustration3 ,,fig4 #be4--;,double ,concave1 ,plane ,concave1 and ,concavo-,convex ,lenses4 ,the action of such lenses upon the light proceeding from any source may now be considered4 ,if there is a parallel beam proceeding from a lamp1 or from the sun1 and it falls on the form of lens1 called a convex lens1 which bulges out in the middle1 we learn from ,fig4 #bg1 that the upper part acts like the upper prism just considered and turns the light down1 and the lower acts in the reverse manner and turns the light up1 and the sides act in a similar manner2 and as the inclination of the surfaces of the lens increases as we approach the edge1 the rays falling on the parts near the edge are turned out of their course more than those falling near the centre1 so that we have the rays converged to a point ,f1 called the focus of the lens2 and as the rays from an electric lamp are generally rendered parallel by means of the lenses in the lantern1 called the condensers1 the rays from such a lamp falling on a convex lens will come to a focus at just the same distance from the lens1 called its principal focal length as they would do if they came from the sun or stars4 ,illustration3 ,,fig4 #bf4--;,double ,convex1 ,plane ,convex1 and ,concavo-,convex ,lenses4 ,illustration3 ,,fig4 #bg4--;,convergence of ,rays by ,convex ,lens to ,principal ,focus4 ,so far we have brought rays to a focus1 and on holding a piece of paper at the focus of the convex lens1 as just mentioned1 there appears on it a spot of light2 and every one knows that if this experiment be performed with the sun1 one brings all the rays falling on the lens almost to a point1 and the longer waves of light will set fire to the paper2 and on this principle burning-glasses are constructed4 ,if1 however1 the rays are not parallel when falling on the lens1 but diverging1 they are not brought to a focus so near the lens1 and the nearer the luminous source or object is1 the further off will the light be brought to a focus on the other side4 ,if matters are reversed1 and the luminous source be placed in the focus1 the rays of light1 when they leave the lens1 will converge to the position of the original source2 so that there are two points1 one on either side of the lens1 which are the foci of each other ,s1 ,s1 ,fig4 #bh1 called conjugate foci2 as one approaches the lens the other recedes1 and vice vers1 and it is obvious that when the one approaches the lens so as to coincide with the principal focus1 the other recedes to an infinite distance1 and the emergent rays are parallel4 ,illustration3 ,,fig4 #bh4--;,conjugate ,foci or ,convex ,lens4 ,illustration3 ,,fig4 #bi4--;,conjugate ,images4 ,illustration3 ,,fig4 #cj4--;,diagram explaining ,fig4 #bi4 ,now let us consider how images are formed4 ,if we take a candle1 ,fig4 #bi1 and hold the lens a little distance away from it1 then1 on placing a screen of paper just on the other side of the lens1 there will be a small flame depicted on it1 an exact representation of the real flame3 and it is formed in this way3 ,consider the rays proceeding from the top of the flame1 which are represented separately in ,fig4 #cj1 where ,a represents the top4 ,one of these rays1 ,a a1 passing through the centre of the lens o1 will he unaffected because the surfaces through which it passes are parallel to each other2 and we know from the property of the lens that all the other rays from ,a will1 on passing through it1 be brought to a focus somewhere on ,a a1 depending on the curvature of the lens1 and in the case of our lens it is at a4 ,illustration3 ,,fig4 #ca4--;,dispersion of ,rays by a ,double ,concave ,lens4 ,in like manner also all the rays from ,b are brought to a focus at b1 and so on with all other parts of ,a1 ,b1 which in this case represents the flame1 each will have its corresponding focus2 there being cones of rays from every point of the object and to every point of the image1 having for their bases the convex lens1 and we get an image or exact representation of our candle flame4 ,it will further be noticed that the image a b is smaller than ,a ,b1 in proportion as the distance a b is less than ,a ,b2 so that if we increase the focal length of the lens till a b is twice the distance away from the lens1 it will become double its present size4 ,if now the flame be brought nearer the lens1 its image a b becomes indistinct2 and we must move the screen further away in order to render the image again clear2 hence the place of the focus depends on the distance of the object1 and the candle and its image must correspond to two conjugate foci4 ,illustration3 ,,fig4 #cb4--;,horizontal ,section of the ,eyeball4 ,scl1 the sclerotic coat2 ,cn1 the cornea2 ,r1 the attachments of the tendons of the recti muscles2 ,ch1 the choroid2 ,cp1 the ciliary processes2 ,cm1 the ciliary muscle2 ,ir1 the iris2 ,aq1 the aqueous humour2 ,cry1 the crystalline lens2 ,vi1 the vitreous humour2 ,rt1 the retina2 ,op1 the optic nerve2 ,ml1 the yellow spot4 ,if now rays be passed from the lantern or sun through a concave lens1 ,fig4 #ca1 they are not brought to a focus1 but are dispersed and travel onwards1 as if they came from a point1 ,f1 which is called its virtual focus2 and if rays are first converged by a convex lens1 and then1 before they reach the focus are allowed to fall on a concave one1 we can1 by placing the lenses a certain distance apart1 render the converging rays again parallel2 or we can make them slightly divergent1 as if they came1 not from an infinite distance1 but from a point a foot or two off4 ,the application of this arrangement will appear hereafter4 ,what has now been said on the action of the convex lens will enable us to consider the optical action of the eye1 without which we do little in astronomy4 ,as to the way that the brain receives impressions from the eye we need say nothing1 for that belongs to the domain of physiology1 except indeed this1 that an image is formed on the retina by a chemical decomposition1 brought about by the dissociating action of certain rays of light in exactly the same way as on a photographic plate4 ,optically considered1 the eye consists of nothing more than a convex lens1 ,cry1 ,fig4 #cb1 and a surface1 ,rt1 extending over the back of the eyeball1 called the retina1 on which the objects are focussed1 but the rays of light falling on the cornea ,cn1 are refracted somewhat1 so that it is not quite true to say that the crystalline lens does all the work1 but for our present purpose it is sufficiently correct1 and we shall consider their combined action as that of a single lens4 ,the outer coat of the eyeball1 shown in section in ,fig4 #cb1 is called the sclerotic1 with the exception of that more convex part in front of the eye1 called the cornea2 behind this comes the aqueous humour and then the iris1 that membrane of which the colour varies in different people and races4 ,in the centre of this is a circular aperture called the pupil1 which contracts or expands according to the brightness of the objects looked at1 so that the amount of light passing into the eye is kept as far as possible constant4 ,close behind the iris comes the crystalline lens1 the thickness of which can be altered slightly by the ciliary muscle4 ,in the space between the lens and the back of the eye is a transparent jelly-like substance called the vitreous humour4 ,finally comes the retina1 a most delicate surface chiefly composed of nerve fibres4 ,it is on this surface1 that the image is formed by the curved surfaces of the anterior membranes1 and through the back of the eyeball is inserted the mass of filaments of the optic nerve making communication with the brain2 these filaments on reaching the inside of the eye spread out to receive the impressions of light4 ,here then1 we have a complete photographic camera2 the crystalline lens and cornea1 separated by the aqueous humour1 representing the compound-glass camera lens1 and the retina standing in the place of the sensitive plate4 ,illustration3 ,,fig4 #cc4--;,action of ,eye in ,formation of ,images4 ,the path of the light forming an image on the retina is shown in ,fig4 #cc1 where ,a ,b is the object1 and a b its image1 formed in exactly the same way as the image of the candle-flame which we have just considered2 in fact1 the eye is exactly represented by a photographic camera1 the iris acting in the same manner as the stops in the lens1 limiting its available area1 and by contracting1 decreasing the amount of light from bright objects1 and at the same time increasing the sharpness of definition1 for in the case of the eye1 the luminous rays obey the known laws of propagation of light in media of variable form and density1 and we have only simple refraction to deal with4 ,the next matter to be considered is that the nearer the object ,a ,b is to the eye1 the larger is the angle ,a1 o1 ,b1 and also a1 o1 b1 and therefore the image on the retina is larger2 but there is a limit to the nearness to which the object can be brought1 for1 as we found with the candle1 the distance between the lens and the image must be increased as the object approaches1 or the curvature of the lens itself must be altered1 for if not the ray forming the rays from each point of the object will be too divergent for the lens to be able to bring them to a focus4 ,now in the eye there is an adjustment of this sort1 but it is limited so that objects begin to get indistinct when brought nearer the eye than perhaps six inches1 because the rays become too divergent for the lens to bring them to a focus on the retina1 and they tend to come to a focus behind the retina1 as in ,fig4 #cd2 but we may assist the eye lens by using a glass convex lens in front of it1 between it and the object4 ,it is for this reason that spectacle glasses are used to enable long-sighted persons to see clearly4 ,illustration3 ,,fig4 #cd4--;,action of a ,long-sighted ,eye4 ,we may also use a much stronger lens1 and so get the object very near the lens and eye1 as in ,fig4 #ce1 where a b is the object so near the eye that1 if it were not for the lens ,l1 its image would not come to a focus on the retina at all4 ,the effect of the lens is to make the rays proceeding in a cone from a and b less divergent1 so that after passing through it1 they proceed to the eye-lens as if they were coming from the points ,a and ,b1 a foot or so away from the eye1 and so the object a b appears to be a much larger object at a greater distance from the eye4 ,illustration3 ,,fig4 #ce4--a4 ,diagram showing path of rays when viewing an object at an easy distance4 #b4 ,object brought close to eye when the lens ,l is required to assist the eye-lens to observe the image when it is magnified4 ,a convex lens then has the power of magnifying objects when brought near the eye1 and its action is clearly seen in ,fig4 #ce1 where the upper figure shows the arrow at as short a distance from the eye as it can be seen distinctly with an ordinary eye1 and the lower figure shows the same arrow brought close to the eye1 and rendered distinctly visible by the lens when a magnified image is thrown on the retina1 as if there was a real larger arrow somewhere between the dotted lines at the ordinary distance of distinct vision4 ,it is also obvious that the nearer the object can be brought to the eye-lens the more magnified it is1 just as an object appears larger the nearer it is brought to the unaided eye4 ,we have been hitherto dealing with the effect of a convex lens on the rays passing to the eye4 ,we will now deal with a concave one4 ,we found that the power of adjustment of the normal eye was sufficient to bring parallel rays1 or those proceeding from a very distant object1 and also slightly diverging rays1 to a focus on the retina4 ,parallel or slightly divergent rays are most easily dealt with1 and slightly convergent rays can also be focussed on the retina2 but if the eye-lens is too convex1 as is the case with short-sighted people1 ,fig4 #cf1 a concave lens of slight curvature is used to correct the eye-lens and bring the image to a focus on the retina instead of in front of it4 ,illustration3 ,,fig4 #cf4--;,action of ,short-sighted ,eye4 ,if the rays are very convergent1 as those proceeding from a convex lens and coming to a focus1 the lens of a normal eye will bring them to a focus far in front of the retina1 as if the person were very short-sighted4 ,but by interposing a sufficiently powerful concave lens the rays are made less convergent or parallel1 and the eye-lens brings them to a focus on the retina1 as if they came from a near object1 so the use of convex and concave lenses placed close to the eye is to render divergent or convergent rays nearly parallel1 so that the eye-lens can easily focus them1 and therefore one of the conditions of the telescope is that the rays which come into our eye shall be parallel or nearly so4 ,,chapter ,,vi4 ,,the ,,refractor4 ,in the telescope as first constructed by ,galileo there are two lenses1 so arranged that the first1 a convex one1 ,a ,b ,fig4 #cg1 converges the rays1 while the second1 ,c ,d1 a concave one1 diverges them1 and renders them parallel1 ready for the eye2 the rays then1 after passing through ,c ,d1 go to the eye as if they were proceeding along the dotted lines from an object ,m ,m1 closer to the eye instead of from a distant object1 and so1 by means of the telescope1 the object appears large and close4 ,illustration3 ,,fig4 #cg4--;,galilean ,telescope4 ,a ,b1 convex lens converging rays2 ,c ,d1 concave lens sending them parallel again and fit for reception by the eye4 ,it is this that constitutes the telescope4 ,but nowadays we have other forms1 as we are not content with the convex combined with the concave lens1 and modern astronomy requires the eyepiece to be of more elaborate construction than those adopted by ,galileo and the first users of telescopes1 although this form is still used for opera-glasses and in cases where small power only is required4 ,having the power of converging the light and forming an image by the first convex lens or object glass1 as we saw with the candle flame 7,fig4 #bi71 and an opportunity of enlarging this image by means of a magnifying or convex eyepiece1 we can bring an image of the moon1 or any other object1 close to the eye1 and examine it by means of a convex lens1 or a combination of such lenses4 ,so we get the most simple form of refracting telescopes represented in ,fig4 #ch1 in which the rays from all points of the object--let us take for instance an arrow--are brought to a focus by the object-glass ,a1 forming there an exact representation of the real arrow4 ,in the figure two cones of rays only are delineated1 namely1 those forming the point and feather of the arrow1 but every other point in the arrow is built up by an infinite number of cones in the same way1 each cone having the object-glass for its base4 ,by means of the lens ,c we are able to examine the image of the arrow ,b1 since the rays from it are thus rendered parallel1 or nearly so1 and to the eye they appear to come from a much larger arrow at a short distance away4 ,we can draw their apparent direction1 and the apparent arrow 7as is done in ,fig4 #cg by the dotted lines71 and so the object appears as magnified1 or1 what comes to the same thing1 as if it were nearer4 ,the difference between this form and that contrived by ,galileo is this3 in the latter the rays are received by the eyepiece while converging1 and rendered parallel by a concave lens1 while in the former case the rays are received by the eyepiece on the other side of the focus1 where they have crossed each other and are diverging1 and are rendered parallel by a convex lens4 ,we may now sum up the use of the eye-lens4 ,the image is brought to a focus on the retina1 because the object is some distance off1 and the rays from every point1 7as from ,a and ,b1 ,fig4 #ce71 on reaching the eye1 are nearly parallel2 but it is not necessary that they should be absolutely parallel1 as the eye is capable of a small adjustment1 but if one wishes to see an object much nearer 7as in the lower figure71 it is impossible to do it unless some optical aid is obtained1 for the rays are too divergent1 and cannot be brought to a focus on the retina4 ,what does that optical aid effect8 ,it enables us to place the object in the focus of another lens which shall make the rays parallel1 and fit for the lens of the eye to focus on the retina1 and since the object can by this means be brought close to the lens and eye1 it forms a larger image on the retina4 ,dependent on this is the power of the telescope4 ,illustration3 ,,fig4 #ch4--,telescope4 ,a1 object-glass1 giving an image at ,b2 ,c1 lens for magnifying image ,b4 ,we shall refer later on to the mechanical construction of the telescope4 ,here it may be merely stated that the smaller ones consist of a brass tube1 the object-glass held in a brass ring screwed in at one end of the tube and a smaller tube carrying the eyepiece sliding in and out of the large tube and sometimes moved by a rack and pinion motion1 at the other4 ,the larger ones as mounted for special uses will also be fully described farther on4 ,illustration3 ,,fig4 #ci4--;,diagram ,explaining the ,magnifying ,power of ,object-glass4 ,the power of the telescope depends on the object-glass as well as on the eyepiece2 if we wish to magnify the moon1 for instance1 we must have a large image of the moon to look at1 and a powerful lens to see that image4 ,by studying ,fig4 #ci the fundamental condition of producing a large image by a lens will be seen4 ,suppose we wish to look at an object in the heavens1 the diameter of which is one degree2 if the lens throws an image of that body on to the circumference of a circle of #cfj inches1 then1 as there are #cfj degrees in a circle1 that image will cover one inch2 let the circle be #cfj yards1 and the image of a body of one degree will cover one yard2 and to take an extreme case and suppose the circumference of the circle to be #cfj miles1 then the image will be one mile in diameter4 ,this is one of the principal conditions of the action of the object-glass in enabling us to obtain images which can be magnified by a lens1 and by such magnification made to appear nearer to us than they are4 ,galileo used telescopes which magnified four or five times1 and it was only with great trouble and expense that he produced one which magnified twenty-three times4 ,now1 after what has been said of focal length1 one will not be surprised to hear of those long telescopes produced in the very early days1 a few of which are still extant2 these show as well as anything the enormous difficulty which the early employers of telescopes had to deal with in the material they employed4 ,one can scarcely tell one end of the telescope from the other2 all the work was done in some cases by an object-glass not more than half an inch in effective diameter4 ,it might be supposed that those who studied the changes of places and the positions of the heavenly bodies would have been the first to gain by the invention of the telescope1 and that telescopes would have been added to the instruments already described1 replacing the pointers4 ,for such a use as this a telescope of half an inch aperture would have been a great assistance4 ,but things did not happen so1 because the invention of the telescope gave such an impetus to physical astronomy that the whole heavens appeared novel to mankind4 ,groups of stars appeared which had never been seen before2 ,jupiter and ,saturn were found to be attended by satellites2 the sun1 the immaculate sun1 was determined after all to have spots1 and the moon was at once set upon and observed with diligence and care2 so that there was a very good reason why people should not limit the powers of the telescope to employing it to determine positions only4 ,the number of telescopes was small1 and they could not be better employed than in taking a survey of all the marvellous things which they revealed4 ,it was at this time that the modern equatorial was foreshadowed4 ,galileo1 and his contemporaries ,scheiner and others1 were observing sun-spots1 and the telescope1 ,fig4 #dj1 which ,scheiner arranged1 a very rough instrument1 with its axis parallel to the earth's axis1 and allowed to turn so that ,scheiner might follow the sun for many hours a day1 was one of the first4 ,this instrument is here reproduced1 because it was one of the most important telescopes of the time1 and gathered in to the harvest many of the earliest obtained facts4 ,illustration3 ,,fig4 #dj4--,scheiner's ,telescope4 ,since by means of little instruments like these1 so much of beauty and of marvel could be discovered in the skies1 it is no wonder that every one who had anything to do with telescopes strained his nerves to make them of greater power1 by which more marvels could be revealed4 ,it was not long before those little instruments of ,scheiner expanded into the long telescopes to which reference has been made4 ,but there was a difficulty introduced by the length of the instrument4 ,the length of the focus necessary for magnification spread the light over a large area1 and therefore it was necessary to get an equivalent of light by increasing the aperture of the object-glasses in order that the object might be sufficiently bright to bear considerable magnification by the eyepiece1--and now arose a tremendous difficulty4 ,one part of refraction1 namely1 deviation1 enables us to obtain1 but the other half1 dispersion1 prevents our obtaining1 except under certain conditions1 an image we can make use of4 ,by dispersion is meant the property of splitting up ordinary light into its component colours1 of which we shall say more in dealing with spectrum analysis4 ,if we wish to get more light by increasing the aperture of the telescope1 the deviation of the light passing through the edge of the object-glass is increased1 and with it the dispersion1 the result of this increase of deviation4 ,if the light of the sun be allowed to fall through a hole into a darkened chamber1 and then through a prism1 ,fig4 #da1 it is refracted1 and instead of having an exact reproduction of the bright circle we have a coloured band or spectrum4 ,the white light when refracted is not only driven out of its original course--deviated--but it is also broken up--dispersed--into many colours4 ,we have a considerable amount of colour2 and this the early observers found when they increased the size of their telescopes1 for it must be remembered that a lens is only a very complex prism4 ,illustration3 ,,fig4 #da4--;,dispersion of ,light by ,prism4 ,first1 they increased the size by enlarging the object-glasses1 and not the focal length2 but when they had done that they had that extremely objectionable colour which prevented them seeing anything well4 ,the colour and indistinctness came from an overlapping of a number of images1 as each colour had its own focus1 owing to varying refrangibilities4 ,they found1 therefore1 that the only effective way of increasing the power of the telescope was by increasing its focal length so as to reduce the dispersing action as much as possible1 and so enlarging the size of the actual image to be viewed1 without at the same time increasing the angular deviation of the rays transmitted through the edges of the lens4 ,the size of the image corresponding to a given angular diameter of the object is in the direct proportion of the focal length1 while the flexure of the rays which converge to form any point of it is in the same proportion inversely4 ,illustration3 ,,fig4 #db4--;,diagram ,showing the ,amount of ,colour ,produced by a ,lens4 ,to take an example4 ,in the case of an object-glass of crown-glass1 the space over which the rays are dispersed is one-fiftieth of the distance through which they are deviated1 and it will be seen by reference to ,fig4 #db1 that if the red rays are at ,r1 and the blue at ,b1 the distance ,a ,b is fifty times ,r ,b1 and as these distances depend on the diameter of the lens only1 we can increase the focal length1 and so increase the size of the image without altering the dispersion ,r ,b1 and so throw the work of magnifying on the object-glass instead of on the eyepiece1 which would magnify ,r ,b equally with the image itself4 ,so that in that time1 and in the time of ,huyghens1 telescopes of #ajj1 #bjj1 and #cjj feet focal length were not only suggested but made1 and one enthusiastic stargazer finished an object-glass1 the focal length of which was #fjj feet4 ,telescopes of #ajj and #aej feet focal length were more commonly used4 ,the eyepiece was at the end of a string1 and the object-glass was placed free to move on a tall pole1 so that an observer on the ground1 by pulling the string1 might get the two glasses in a line with the object which he wished to observe4 ,so it went on till the time of ,sir ,isaac ,newton1 who considered the problem very carefully--but not in an absolutely complete way4 ,he came to the conclusion1 as he states in his ,optics1 that the improvement of the refracting telescope was 8desperate20 and he gave his attention to reflecting telescopes1 which are next to be noticed4 ,let us examine the basis of ,sir ,isaac ,newton's statement1 that the improvement of the refracting telescope was desperate4 ,he came to the conclusion that in refraction through different substances there is always an unchanged relation between the amount of dispersion and the amount of deviation1 so that if we attempt to correct the action of one prism by another acting in an opposite direction in order to get white light1 we shall destroy all deviation4 ,but ,sir ,isaac ,newton happened to be wrong1 since there are substances which1 for equivalent deviations1 disperse the light more or less4 ,so by means of a lens of a certain substance of low dispersive power we can form an image slightly coloured1 and we can add another lens of a substance having a high dispersive power and less curvature and just reverse the dispersion of the first lens without reversing all its deviating power4 ,the following experiments will show clearly the application of this principle4 ,we first take two similar prisms arranged as in ,fig4 #dc4 ,the last through which the light passes corrects the deviation and dispersion of the first4 ,we then take two prisms1 one of crown glass and the other of flint glass1 and since the dispersion of the flint is greater than that of the crown1 we imagine with justice that the flint-glass prism may be of a less angle than the other and still have the same dispersive power1 and at the same time1 seeing that the angles of the prisms are different1 we may expect to find that we shall get a larger amount of deviation from the crown-glass prism than from the other4 ,illustration3 ,,fig4 #dc4--;,decomposition and ,recomposition of ,light by ,two ,prisms4 ,if then a ray of light be passed through the crown-glass prism1 we get the dispersion and deviation due to the prism ,a ,fig4 #dd1 giving a spectrum at ,d4 ,and now we take away the crown glass and place in its stead a prism of flint glass inverted2 the ray in this instance is deviated less1 but there is an equal amount of colouring at ,d4 ,if now we use both prisms1 acting in opposite directions1 we shall be able to get rid of the colours1 but not entirely compensate the deviation4 ,we now place the original crown-glass prism in front of the lantern and then interpose the flint-glass prism1 so that the light shall pass through both4 ,the addition of this prism of flint1 of greater dispersive power1 combines1 or as it were shuts off1 the colour1 leaving the deviation uncompensated1 so that we get an uncoloured image of the hole in front of the lantern at ,d4 ,this is the foundation of the modern achromatic telescope4 ,illustration3 ,,fig4 #dd4--;,diagram ,explaining the ,formation of an ,achromatic ,lens4 ,a1 crown-glass prism2 ,b1 flint-glass prism of less angle1 but giving the same amount of colour2 ,c1 the two prisms combined1 giving a colourless yet deviated band of light at ,d4 ,another method of showing the same thing is to bring a ,v-shaped water-trough into the path of the rays from the lantern2 then1 while no water is in it1 the beam of light passing through it is absolutely uncoloured and undeviated4 ,in this case we have no water inclosed by these surfaces1 and it is not acting as a prism at all4 ,if1 however1 a prism of flint glass1 a substance of high dispersive power1 is introduced into it1 with its refracting edge upwards1 it destroys the condition we had before1 and we have a coloured band on the screen1 because the glass that the prism is made of has the faculty of strong dispersion in addition to its deviation4 ,we can get rid of that dispersion by throwing dispersion in a contrary direction by filling up the trough with water1 and so making1 as it were1 a water prism on either side of the glass one1 water being a substance of low dispersive power4 ,we have a colourless beam thrown on the screen1 which is deviated from the original level1 because the water prisms are together of a greater angle than the glass one4 ,the experiments of ,hall and ,dolland have resulted in our being able to combine lenses in the same way that we have here combined prisms1 bearing in mind what has been said in reference to the action of lenses being like that of so many prisms2 and we may consider two lenses1 one of crown and the other of flint glass1 ,fig #de4 ,the crown glass being of a certain curvature will give a certain dispersion2 the flint glass1 in consequence of its great dispersive power1 will require less curvature to correct the crown glass4 ,what will happen will be this3 assuming the second lens to be away1 the rays will emerge from the first 7convex7 lens and form a coloured image at ,a4 ,but if the second flint-glass concave lens be interposed it will1 by means of its action in a contrary direction1 undo all the dispersion due to this first lens and a certain amount of deviation1 so that we shall get the combination giving an almost colourless image at ,b4 ,illustration3 ,,fig4 #de4--;,combination of ,flint- and ,crown-glass ,lenses in an ,achromatic ,lens4 ,it will not be absolutely colourless1 for the reasons which will be now explained4 ,if light be passed through different substances placed in hollow prisms1 or through prisms of flint and crown glass1 and the spectra thus produced be observed1 we find there are important differences4 ,when we expand the spectra considerably1 we see that the action of these different substances is not absolutely uniform1 some colours extending over the spectrum further than others4 ,in the case of one kind of glass the red end of the spectrum is crushed up1 while in the other we have the red end expanded4 ,this is called the irrationality of the spectrum produced by prisms of different substances4 ,the crown and the flint-glass lenses--and for telescopes we must use such glass--give irrational spectra1 so that the achromatic telescope is not absolutely achromatic1 in consequence of this peculiarity2 for if ,r1 ,g1 ,b1 ,fig4 #df1 are the centres of the red1 green1 and violet in the spectrum given by a prism composed of the glass of which one lens is made1 and ,r1 ,g1 ,b1 are those of the other1 if the lenses are placed so as to counteract each other1 and are of such curves that the reds and violets are combined1 the greens will remain slightly outstanding4 ,suppose1 as in the drawing1 the second prism disperses the violet as much as the first one does1 then1 when these are reversed they will exactly compensate red and violet4 ,but the second one acts more strongly on the green than the first1 which will be over-compensated2 and if we weaken the second prism so that the green and red are correct1 then the violet will be slightly outstanding1 which in practice is not much noticed1 except with a very bright object when there is always outstanding colour4 ,illustration3 ,,fig4 #df4--;,diagram ,illustrating the ,irrationality of the ,spectrum4 ,this is1 however1 not a matter of any very great importance for ordinary work1 since the visual rays all lie in the neighbourhood of the yellow1 so that opticians take care to correct their lenses for the rays in this part of the spectrum1 and at the same time1 as a matter of necessity1 over-correct for the violet rays1 that is1 reverse the dispersion of the exterior lens1 so that the violet rays have a longer instead of a shorter focus than the red1 and1 therefore1 in looking at a bright object1 such as a first magnitude star1 it appears surrounded by a violet halo2 with fainter objects the blue light is not of sufficient intensity to be visible4 ,it is1 therefore1 always preferable to correct for the most visible rays and leave the outstanding violet to take care of itself2 but nevertheless various proposals have been made to get rid of it4 ,object-glasses containing fluids of different kinds have been tried1 but they have never become of any practical value1 and it does not seem probable that they ever will4 ,in order to get rid of the outstanding violet colour when the remainder of the spectrum was corrected1 ,dr4 ,blair constructed object-glasses the space between the lenses of which were filled with certain liquids1 generally a solution of a salt of mercury or antimony1 with the addition of hydrochloric acid2 for in the spectrum given by the metallic solution the green is proportionally nearer the red than is the case with the spectrum produced by hydrochloric acid1 so that by the adjustment of the different solutions he exactly destroyed the outstanding colour of the ordinary combination4 ,in this way ,sir ,john ,herschel tells us he was able to construct lenses of three inches aperture and only nine inches focal length1 free from chromatic and spherical aberration4 ,it was proposed by ,mr4 ,barlow to correct a convex crown-glass lens for chromatic aberration by a hollow concave lens containing bisulphide of carbon1 a highly dispersive fluid1 having double the power of flint glass4 ,this lens was placed in the cone of rays between the object-glass and the eyepiece4 ,its surfaces were concavo-convex1 calculated to destroy spherical aberration1 and its distance from the object-glass was varied until exact achromatism was obtained4 ,a telescope of this principle of eight inches aperture was made by ,mr4 ,barlow1 which proved highly satisfactory4 ,in the early part of the last century it was proposed by ,wolfius to interpose between the object-glass and eyepiece a concave lens in order to give greater magnification of the image1 with a slight increase of focal length2 if an ordinary lens be used the achromatism of the images given by the object-glass will be destroyed4 ,messrs4 ,dolland and ,barlow1 however1 proposed to make the concave lens achromatic1 so that the image is as much without colour when the lens is used as without it4 ,mr4 ,dawes found such a lens to work extremely well4 ,these lenses1 usually called 8,barlow lenses10 are generally made about one inch in diameter1 and by varying their distance from the eyepiece the image is altered in size at pleasure4 ,in the reflecting telescope1 with which we will now proceed to deal1 there is an absence of colour2 but the reflector is not without its drawbacks1 for there are imperfections in it as great as those we have been considering in the case of the refractor4 ,,chapter ,,vii4 ,,the ,,reflection ,,of ,,light4 ,we have now dealt with the refraction of light in general1 including deviation and dispersion1 in order to see how it can assist us in the formation of the telescope2 and we have shown how the chromatic effect of a single lens can be got rid of by employing a compound system composed of different materials1 and so we have got a general idea of the refracting telescope4 ,we have now to deal with another property of light1 called reflection2 and our object is to see how reflection can help us in telescopes4 ,in the case of reflection we get the original direction of the ray changed as in the case of refraction1 but the deviation is due to a different cause4 ,take a bright light1 a candle will do1 and a mirror fixed so that the light falls on its surface and is thrown back to the eye1 ,fig4 #dg1 we see the image of the candle apparently behind the mirror2 the rays of light falling on the mirror are reflected from it at exactly the same angle at which they reach it4 ,this brings us in the presence of the first and most important law of reflection2 and it is this1 at whatever angle the light falls on a mirror1 at that angle will it be reflected4 ,as it is usually expressed1 the angle of incidence1 which is the angle made by the incident ray with an imaginary line drawn at right angles to the mirror1 called the normal1 is equal to the angle of reflection1 that is1 the angle contained by the reflected ray1 and the normal to the surface4 ,in order1 therefore1 to find in what direction a ray of light will travel after striking a flat polished surface1 we must draw a line at right angles to the surface at the point where the ray impinges on it1 then the reflected ray will make an angle with the normal equal to that which the incident ray makes1 or the angles of incidence and reflection will be equal4 ,illustration3 ,,fig4 #dg4--;,diagram ,illustrating the ,action of a ,reflecting ,surface4 ,very simple experiments1 which every one can make will show us the laws which govern the phenomena of reflection4 ,let us employ a bath of mercury for a reflecting surface1 and for a luminous object a star1 the rays of which1 coming from a distance which is practically infinite1 to the surface of the earth1 may be considered exactly parallel4 ,the direction of the beams of light coming from the star1 and falling on the mirror formed by the mercury1 is easily determined by means of a theodolite1 ,fig4 #dh4 ,if we look directly at the star1 the line ,i ,s of the telescope indicates the direction of the incident luminous rays1 and the angle ,s ,i ,n1 equal to the angle ,s1 ,i1 ,n1 is the angle of incidence1 that is to say1 that formed by the luminous ray with the normal to the surface at the point of incidence4 ,illustration3 ,,fig4 #dh4--;,experimental ,proof that the ,angle of ,incidence ,angle of ,reflection4 ,in order to find the direction of the reflected luminous rays1 we must turn the telescope on its axis1 until the rays reflected by the surface of the mercury bath enter it and produce an image of the star4 ,when the image is brought to the centre of the telescope1 it is found that the angle ,r ,i ,n is equal to the angle of reflection ,n1 ,i1 ,r4 ,thus1 in reading the measure on the graduated circle of the theodolite the angle of reflection can be compared with the angle of incidence4 ,now1 whatever may be the star observed1 and whatever its height above the horizon1 it is always found that there is perfect equality between these angles4 ,moreover1 the position of the circle of the theodolite which enables the star and its image to be seen evidently proves that the ray which arrives directly from the luminous point and that which is reflected at the surface of the mercury are both in the same vertical plane4 ,now this demonstrates one of the most important laws of reflection4 ,the laws of refraction do not deal directly with the angles themselves1 but with the sines of the angles2 in reflection the angles are equal2 in refraction the sines have a constant relation to each other4 ,so far we have dealt with plane surfaces1 but in the case of telescopes we do not use plane surfaces1 but curved ones1 so we will proceed at once to discuss these4 ,illustration3 ,,fig4 #di4--;,convergence of ,light by ,concave ,mirror4 ,illustration3 ,,fig4 #ej4--;,conjugate ,foci of ,convex ,mirror4 ,in ,fig4 #di1 ,a represents a curved surface1 such as that of a concave mirror1 the centre of curvature being ,c4 ,now we can consider that this curved surface is made up of an infinite number of small plane surfaces1 and since all lines drawn from the centre1 ,c1 to the mirror1 will be at right angles to the surface at the points where they meet it1 we find1 from our experiment with the plane mirror1 that rays falling on the mirror at these points will be reflected so that the angles on either side of each of these lines shall be equal2 so1 for instance1 in ,fig4 #di1 we wish to find to what point the upper ray will be reflected1 and we draw a line from the centre1 ,c1 to the point where it falls on the mirror1 and then draw another line from that point making the angle of reflection equal to that made by the incident ray1 and we can consider the small surface concerned in reflection flat1 so that the ray will in this case be reflected to ,f4 ,if now we take any other ray1 and perform the same operation we shall find that it is also reflected nearly to ,f1 and so on with all other parallel rays falling on the mirror2 and this point1 ,f1 is therefore said to be the focus of the mirror4 ,if now the rays1 instead of falling parallel on the mirror1 as if they came from the sun or a very distant object1 are divergent1 as if they came from a point ,s1 ,fig4 #ej1 near the mirror1 the rays approach nearer to the lines drawn from the centre to the mirror1 one of which is represented by the dotted line2 or1 in other words1 the angles of incidence become reduced1 and so the angles of reflection will also be reduced1 and the focus of the rays from ,s will approach the centre of the mirror1 and be at s2 just so it will be seen that if an illuminated point be at s1 its focus will be at ,s1 and these two points are therefore called conjugate foci4 ,illustration3 ,,fig4 #ea4--;,formation of ,image of ,candle by ,reflection4 ,illustration3 ,,fig4 #eb4--;,diagram explaining ,fig4 #ea4 ,if a candle is held at a short distance in front of a concave mirror1 as represented in ,fig4 #ea1 its image appears on the paper between the candle and the mirror1 so that the rays from every point of the flame are brought to a focus1 and produce an image just as the image is produced by a convex lens4 ,if we study ,fig4 #eb the formation of this image will be clearly understood4 ,first we must note that the rays ,a1 ,c1 a1 and ,b1 ,c1 b1 which pass through the centre of curvature of the mirror ,c1 will fall perpendicularly on the surface1 and be reflected back on themselves1 so that the focus of the part a of the arrow will be somewhere on ,a a1 and that of ,b on ,b b1 and by drawing another ray we shall find it reflected to a1 which will be the focus of the point ,a1 and so also by drawing another line from ,b1 we shall find it is reflected to b1 which is the focus of the part ,b2 and we might repeat this process for every part of the arrow1 and for every ray from those parts4 ,we now see that since the rays ,a a and ,b b cross each other at ,c1 the distance from a to b bears the same proportion to the distance from ,a to ,b as their respective distances from the point ,c2 or1 in other words1 the image is smaller than the object in the same proportion as the distance from the image to ,c is smaller than the distance from the object to ,c4 ,now1 in dealing with the stars1 which are at a practically infinite distance1 the rays are parallel1 and will be brought to a focus half-way between the mirror and its centre of curvature4 ,in this case1 therefore1 the distance from the image to the mirror is equal to that from the image to the centre1 so that we can express the size of the image by saying that it is smaller than the object1 in proportion as its distance from the mirror is smaller than the distance of the object from ,c2 and as it makes little difference whether we measure the distance of the stars from ,c or from the mirror1 and as ,c is not always known1 we can take the relation of the distances of the object and image from the mirror as representing the proportionate sizes of the two4 ,we will now consider the case of rays falling on a mirror curved the other way1 that is1 a convex mirror4 ,let us consider the ray impinging at ,d1 ,fig4 #ec1 which would go on to ,c1 the centre of the mirror4 ,now1 as ,c ,d is drawn from the centre1 it is at right angles to the mirror at ,d1 and the ray ,l ,d1 being in the same straight line on the opposite side1 will also be at right angles1 and will be reflected back on itself4 ,now take the ray ,i ,a1 draw ,c ,e through ,a1 then ,e ,a will be perpendicular to the surface at ,a1 and ,i ,a ,e will be the angle of incidence1 and ,e ,a ,g the angle of reflection1 so that this ray ,a ,g will be reflected away from ,l ,d1 and so will all the other rays falling on the mirror as ,k ,b3 and if we continue the lines ,g ,a and ,h ,b backwards1 they will meet at ,m1 and therefore the rays diverge from the mirror as if they came from a point at ,m1 and this point is called the virtual focus4 ,illustration3 ,,fig4 #ec4--,reflection of ,rays by ,convex ,mirror4 ,so much for parallel rays4 ,next let us consider another case which happens in the telescope1 namely1 where converging rays fall on a convex mirror1 as in ,fig4 #ec1 where we consider the light proceeding to the mirror from a converging lens along the lines ,h ,b and ,g ,a1 these will be made parallel1 at ,b ,k and ,a ,f1 after reflection1 and it is manifest that by making the mirror sufficiently convex1 these rays1 tending to come to a focus at ,m1 could be rendered divergent2 and if the curvature is decreased by making the centre of curvature at a certain distance beyond ,c1 it will be seen at once by the diagram that these rays will after reflection1 converge towards ,l and will come to a focus in front of the mirror at a point further in front than ,c is behind it1 so that they have been rendered less convergent only by the mirror in this supposed case4 ,it will be seen from what has been stated here and in ,chapter ,v41 that we get nearly the same results from reflection as we did from refraction when we were considering the functions of glasses instead of mirrors2 that a concave mirror acts exactly as a convex lens1 and vice vers1 so that they can be substituted the one for the other4 ,if we take a mirror1 and allow the light to fall on it from a lamp1 no one will have any difficulty in seeing that the mirror grasps the beam1 and forms an image which is seen distinctly in front of the mirror1 just as one gets an image from a convex lens behind it4 ,,chapter ,,viii4 ,,the ,,reflector4 ,the point we have next to determine is how we can utilise the properties of reflection for the purposes of astronomical observation4 ,many admirable plans have been suggested4 ,the first that was put on paper was made by ,gregory1 who pointed out that if we had a concave mirror1 we should get from this mirror an image of the object viewed at the focus in front of it1 as in ,fig4 #ea4 ,of course we cannot at once utilise this focal image by using an eyepiece in the same way as we do in a refractor1 because the observer's head would stop the light1 and the mirror would be useless1 and all the suggestions which have been made1 have reference to obtaining the image in such a position that we are able to view it conveniently4 ,gregory1 the ,scottish astronomer above referred to1 in #affc suggested a method1 and it has turned out to be a good one1 of utilizing reflection by placing a small mirror ,d ,c1 ,fig4 #ed1 on the other side of the focus ,a of the large one1 at such a distance that the image at ,a is again focussed at ,b by reflection from the small mirror2 and at ,b we get of course an enlarged image of ,a4 ,the rays of light proceeding to ,b would1 however1 be intercepted by the large mirror1 unless an aperture were made in the large mirror of the size of the small one through which the rays could pass and be rendered parallel by means of an eyepiece placed just behind the large mirror4 ,so that towards the object is the small mirror ,c1 and there is an eyepiece ,e1 which enables the image of the object to be viewed after two reflections1 first from the large mirror and then from the small one4 ,mr4 ,short 7who made the best telescopes of this construction1 and did much for the optical science of the last century7 altered the position of the small mirror with reference to the focus of the large one1 by sliding it along the tube by a screw arrangement1 ,f1 and so was enabled to focus both near and distant objects without altering the eyepiece4 ,illustration3 ,,fig4 #ed4--,reflecting ,telescope 7,gregorian74 ,but before this was put into practice1 ,sir ,isaac ,newton 7in #afff7 made telescopes on a totally different plan4 ,the eyepiece of the ,newtonian telescope is at the side of the tube1 and not at the end1 as in ,gregory's4 ,we have next to inquire how this arrangement is carried out1 and1 like most things1 it is perfectly simple when one knows how it is done4 ,there is a large mirror at the bottom of the tube as in the ,gregorian1 but not perforated1 and the focus of the mirror would be somewhere just in front of the end of the tube4 ,now in this case we do not allow the beam to get to the focus at all in the tube or in front of it2 but before it comes to the focus it is received on a small diagonal plane surface m1 and thus it is at once thrown outwards at right angles through the side of the tube1 and comes to a focus in front of an eyepiece1 placed at the side1 ready to be viewed the same as an image from a refractor 7,fig4 #ee74 ,illustration3 ,,fig4 #ee4--,newton's ,telescope4 ,the next arrangement is one which ,mr4 ,grubb has recently rescued from obscurity1 and it is called the ,cassegrainian form4 ,it will be seen on referring to that1 ,fig4 #ef1 if the small mirror1 ,c1 were removed1 the rays from the mirror ,a ,b would come to a focus at ,f4 ,in the ,gregorian construction a concave reflector was used outside that focus 7at ,c1 ,fig4 #ed71 but ,cassegrain suggested that if1 instead of using a concave reflector outside the focus1 a reflector with a convex surface were placed inside it1 we should arrive at very nearly the same result1 provided we retain the hole in the large mirror4 ,the converging rays from ,a ,b will fall on the convex surface of the mirror ,c1 which is of such a curvature and at such a distance from ,f1 the focus of the large mirror1 that the rays are rendered less converging1 and do not come to a focus until they reach ,d1 where an image is formed ready to be viewed by the eyepiece ,e4 ,it appears from this1 that the convex mirror is in this case acting somewhat in the same manner as the concave lens does in the ,galilean telescope4 ,illustration3 ,,fig4 #ef4--,reflecting ,telescope 7,cassegrain74 ,illustration3 ,,fig4 #eg4--;,front ,view ,telescope 7,herschel74 ,then1 lastly1 we have the suggestion which ,sir ,william ,herschel soon turned into more than a suggestion4 ,the mirror ,m in this arrangement is placed at the bottom of the tube as in the other forms1 but1 instead of being placed flat on the bottom it is slightly tipped1 so that if the eyepiece is placed at the edge of the extremity of the tube all parallel rays falling on the mirror are reflected to the side of the tube at the top where the eyepiece is1 instead of being reflected to a convex or other mirror in the middle4 ,this is called the front view telescope1 and it enabled ,sir ,william ,herschel to make his discoveries with the forty-feet reflector4 ,with small telescopes this form could not be adopted1 as the observer's head would cover some part of the tube and obstruct the light1 but with large telescopes the amount of light stopped by the head is small in proportion to what would be lost by using a small mirror4 ,these are in the main the four methods of arranging reflecting telescopes--the ,gregorian1 the ,cassegrainian1 the ,newtonian1 and the ,herschelian4 ,in order to make large reflectors perfect--large telescopes of short focus1 because that is one of the requirements of the modern astronomer--we have to battle against spherical aberration4 ,we have already seen that the power of substances to refract light differs for different colours1 and we have seen the varied refraction of different parts of the spectrum1 and the necessity of making lenses achromatic4 ,now there is one enormous advantage in favour of the reflector4 ,we do not take our light to bits and put it together again as with an achromatic lens4 ,but curiously enough1 there is a something else which quite lowers the position of the reflector with regard to the refractor4 ,although1 in the main all the light falling in parallel lines on a concave surface is reflected to a focus1 this is only true in a general sense1 because1 if we consider it1 we find an error which increases very rapidly as the diameter of the mirror increases or as the focal length diminishes4 ,for instance1 ,d ,i1 ,fig4 #eh1 is the segment of a circle1 or the section of a sphere--if we deal with a solid figure4 ,d ,c1 ,e ,g and ,h ,i1 are three lines representing parallel rays falling on different parts of it4 ,according to that law which we have considered1 we can find where the ray ,e ,g will fall4 ,we draw a line ,l1 ,g1 from the centre to the point of reflection1 and make the angle ,f ,g ,l1 equal to the angle of incidence ,e ,g ,l2 then ,f will be the focus1 so far as this part of the mirror is concerned4 ,now let us repeat the process for the ray ,h ,i1 and we shall find that it will be reflected to ,k1 a point nearer the mirror than ,f1 and it will be seen that the further the rays are from the axis ,d ,c1 the further from the point ,f is the light reflected2 so that if we consider rays falling from all parts of the reflecting surface1 a not very large but a distinctly visible surface is covered with light1 so that a spherical surface will not bring all the rays exactly to a point1 and with a spherical mirror we shall get a blurred image4 ,we can compare this imperfection of the reflector1 called spherical aberration1 with the chromatic aberration of the object-glass4 ,illustration3 ,,fig4 #eh4--;,diagram ,illustrating ,spherical ,aberration4 ,illustration3 ,,fig4 #ei4--;,diagram ,showing the ,proper ,form of ,reflector to be an ,ellipse4 ,newton early calculated the ratio of imperfection depending upon these properties of light1 first of dispersion and then of spherical aberration1 and he found that in the refracting telescope the chromatic aberration was more difficult to correct and get rid of than the spherical aberration of the reflector1 so that in ,newton's time1 before achromatic lenses were constructed1 the reflector with its aberration had the advantage4 ,it must now be explained how this difficulty is got over4 ,what is required to produce a mirror capable of being used for astronomical purposes1 is to throw back the edges of the mirror to the dotted line ,a ,c ,i1 ,fig4 #eh1 which will make the margin of the mirror a part of a less concave mirror1 and so its focus will be thrown further from itself--to ,f1 instead of to ,k4 ,now let us consider what curve this is1 that will throw all the rays to one point4 ,it is an ellipse1 as will be seen by reference to ,fig4 #ei1 in which1 instead of having a spherical surface the section of which is a circle1 we deal with a surface whose section is an ellipse4 ,it will be seen in a moment1 that by the construction of an ellipse any light coming in any direction from the point ,a1 which represents one of the foci of the curve1 must necessarily be reflected back to the other focus1 ,b1 of the curve1 for it is a well-known property of this curve that the angles made with a tangent ,c ,d1 by lines from the foci are equal2 and the same holds good for the angles made at all other tangents2 and it will be seen at once that this is better than a circular curve1 because by making the distance between the foci almost infinite we shall have the star or object viewed at one focus and its image at the other2 if we use any portion of the reflecting surface we shall still get the rays reflected to one point only4 ,it must also be noticed1 that unless we have an ellipse so large that one focus shall represent the sun or a particular star we want to look at1 this curve will not help us in bringing the light to one point1 but if we use the curve called the parabola1 which is practically an ellipse with one focus at an infinite distance1 we do get the means of bringing all the rays from a distant object to a point4 ,hence the reflector1 especially when of large diameter1 is of no use for astronomical purposes without the parabolic curve4 ,that it is extremely difficult to give this figure may be gathered from ,sir ,john ,herschel's statement1 that in the case of a reflecting telescope1 the mirror of which is forty-eight inches in diameter and the focal distance of which is forty feet1 the distance between the parabolic and the spherical surface1 at the edges of the mirror1 will be represented by something less than a twenty-one thousandth part of an inch1 or1 more accurately1 #a_/baccc inch4 ,in ,fig4 #eh the point ,a represents the extreme edge of the curve of the parabolic mirror1 and ,d that of the circular surface before altered into a parabola4 ,at the time of ,sir ,william ,herschel the practical difficulties in constructing large achromatic lenses led to the adoption by him of reflectors beginning with small apertures of six inches to a foot1 and increasing till he obtained one of four feet in diameter and forty-six feet focal length4 ,this has been surpassed by ,lord ,rosse1 whose well-known telescope is six feet diameter1 and fifty-three feet focal length4 ,mr4 ,lassell1 ,mr4 ,de ,la ,rue1 ,m4 ,foucault and ,mr4 ,grubb1 have also more recently succeeded in bringing reflectors to great perfection4 ,how the work has been done will be fully stated in the sequel4 ,,chapter ,,ix4 ,,eyepieces4 ,we have considered the telescope as a combination of an object-glass and eyepiece in the one case1 and of a speculum and eyepiece in the other2 that is to say1 we have discussed the optical principles which are applied in the construction of refracting and reflecting telescopes1 the telescope being taken as consisting of an object-glass or speculum and an eyepiece of the most simple form1 viz41 a simple double convex lens4 ,we must now go into detail somewhat on the subject of eyepieces1 and explain the different kinds4 ,it will be recollected that when we spoke of the object-glass1 its aberration1 both chromatic and spherical1 was mentioned4 ,now every ordinary lens has these errors1 and eyepieces must be corrected for them1 but this is not done in exactly the same way as with object-glasses4 ,in the case of eyepieces the error is corrected by using two lenses of such focal lengths or at such a distance apart that each counteracts the defects of the other2 not by using two kinds of glass as in the case of the object-glass1 but by so arranging the lenses that the coloured rays produced by the first lens shall fall at different angles of incidence on the second and become recombined4 ,illustration3 ,,fig4 #fj4--;,huyghens' ,eyepiece4 ,let us take the case of a well-known eyepiece1 called the ,huyghenian eyepiece1 after its inventor4 ,it consists of two plano-convex lenses1 ,a and ,b ,fig4 #fj1 with their convexities turned towards the object-glass1 and having their focal lengths in the proportion of three to one4 ,the strongest lens1 ,a1 being next the eye1 the lens ,b is placed inside the focus of the object-glass1 so that it assists in bringing the image1 say of a double star1 to a focus at ,f1 half way between the lenses1 and nearer to the object-glass than it would have been without the lens4 ,this image is then viewed by the eye-lens1 ,a1 and a magnified image of it seen apparently at ,f1 as has been before explained4 ,now let us see how the fieldlens renders this combination achromatic4 ,let us consider the path of a ray falling on the lens near ,b1 shown in section in ,fig4 #fa3 it is there refracted1 but1 the blue rays being refracted more than the red1 there will be two rays produced1 r and v1 giving of course a coloured edge to the image2 but when this image is viewed by the eye-glass1 ,a1 it no longer appears coloured1 for the ray v1 falling nearer the axis of ,a1 is less bent than r1 and they are rendered nearly parallel and appear to proceed from the point ,f where the whole image appears without colour4 ,in order to get the best result with this form of eyepiece the focal length of the fieldlens should be three times that of the eye-lens and they should be placed at a distance of half their joint focal lengths apart4 ,illustration3 ,,fig4 #fa4--;,diagram ,explaining the ,achromaticity of the ,huyghenian ,eyepiece4 ,the next eyepiece which comes under consideration is that called ,ramsden's1 ,fig4 #fb4 ,it consists of two plano-convex lenses of the same focus1 ,a and ,b1 placed at a distance of two-thirds of the focal length of either apart2 they are both on the eye side of the focus of the telescope1 and act together1 to render the rays parallel and give a magnified virtual image of ,f,f4 ,this eyepiece is not strictly achromatic1 but it suffers least of all lenses from spherical aberration2 it also has the advantage of being placed behind the focus of the object-glass1 which makes it superior to others in instruments of precision1 as we shall presently see4 ,illustration3 ,,fig4 #fb4--,ramsden's ,eyepiece4 ,it must be remembered that these eyepieces give an inverted image--or rather the object glass gives an inverted image1 and the eyepiece does not right it again2 but there are eyepieces that will erect the image1 and ,rheita's is one of this kind4 ,it is1 as will be seen from ,fig4 #fc1 merely a second application of the same means that first inverts the object1 namely1 a second small telescope4 ,a is the object-glass1 a b the image inverted in the usual way2 ,b is an ordinary convex lens sending the rays from a and b parallel4 ,now1 instead of placing the eye at ,c1 as in the ordinary manner1 another small lens1 acting as an object-glass1 is placed in the path of the rays1 bringing them to a focus at a1 b1 and forming there an erect image which is viewed by the eye-lens ,d4 ,this is the erecting eyepiece or 8day eyepiece10 of the common 8terrestrial telescope40 ,dollond substituted an ,huyghenian eyepiece for the eye-lens ,d1 and so made what is called his four-glass eyepiece4 ,dr4 ,kitchener devised and ,mr4 ,g4 ,dollond made an alteration in this eyepiece in order to vary its power at pleasure4 ,it is done in this way3 ,the size of the image a b depends upon the relation of the distances a ,b and ,e a1 which can be varied by altering the distance of the combination of the lenses ,b and ,e1 from the image a b1 and so making a b larger and at a focus further from ,e2 the tube carrying d slides in and out1 so that it can be focussed on a b at whatever distance from ,e it may be4 ,this arrangement is called ,dollond's ,pancratic eyepiece4 ,illustration3 ,,fig4 #fc4--;,erecting or day eyepiece4 ,on the sliding tube carrying the lens ,d1 or rather the ,huyghenian eyepiece in place of the single lens1 are marked divisions1 showing the power of the eyepiece when drawn out to certain lengths1 so that if we want the eyepiece to magnify say #ajj times1 the tube carrying the eye-lens is drawn out to the point marked #ajj1 and the whole eyepiece moved in or out of the telescope tube by the focussing screw1 until the image of the object viewed is focussed in the field of the eyepiece ,d4 ,to increase the power1 we have only to draw out the eyepiece ,d1 and move the whole combination nearer to the object-glass so as to throw the image a b further from the lens ,e4 ,this eyepiece1 though so convenient for changing powers1 is little used1 owing perhaps chiefly to four lenses being required instead of two1 hence a loss of light1 so a stock of eyepieces of various powers is generally found in observatories4 ,when very high powers are required1 a single plano-convex lens is sometimes used1 but although there is less loss of light in this case1 the field of view is so contracted in comparison with that given with other eyepieces that the single lens is seldom used4 ,this form is1 however1 adopted in ,dawes' solar eyepiece1 to be hereafter mentioned1 and a number of lenses are in this case fixed in holes near the circumference of a disc of metal which turns on its centre1 so that by rotating the disc the lenses come in succession in front of the focus of the object-glass1 and the power can be changed almost instantaneously4 ,in order that objects near the zenith may be observed with ease1 a diagonal reflector is sometimes used1 so that the eye looks sidewise into the telescope tube instead of directly upwards4 ,this reflector may take the form of two short pieces of tube joined together at right angles1 and having a piece of silvered glass or a right-angled prism at the angle1 so that when one tube is screwed into the telescope1 the rays of light falling on the reflector are sent up the other1 in which the ordinary eyepiece is placed4 ,the eyepieces just described are suitable1 without further addition1 for observing all ordinary objects1 but when the sun has to be examined a difficulty presents itself4 ,the heat rays are brought to a focus along with those of light1 and with an object-glass of more than one or two inches aperture there is great danger of the heat cracking the lenses1 but with such telescopes the interposition--and neglect of this may cost an eye--of smoked or strongly-coloured glass in front of the eye is generally sufficient to protect it from the intense glare4 ,with larger telescopes1 however1 dark glasses are apt to split suddenly and allow the full blaze of sunlight to enter the eye and do infinite mischief1 and some other method of reducing the heat and light is required4 ,perhaps the most simple method of effecting this object is to allow the light to fall on a diagonal plane glass reflector at an angle of #de1 which lets the greater part of the light and heat pass through1 reflecting only a small portion onwards to the eyepiece and thence to the eye2 a coloured glass is1 however1 required as well1 and the glass reflector must form part of a prism of small angle1 otherwise there will be two images1 one produced by each surface4 ,another arrangement is to reflect the rays from the surfaces of two plates of glass inclined to them at the polarizing angle1 so that by turning the second plate1 or a ,nicols' prism1 in its place round the ray as an axis1 the amount of light allowed to pass to the eye can be varied at pleasure4 ,the late ,mr4 ,dawes constructed a very convenient solar eyepiece1 depending on the principle of viewing a very small portion of the sun's image at one time1 and thereby diminishing the total quantity of heat passing through the eye-lens4 ,the details of the eyepiece are as follows3 very minute holes of varying diameters are made in a brass disc near its circumference1 and as this is turned each successive hole is brought into the centre of the field of view and the common focus of the eye-lens and object-glass4 ,small areas on the sun of different sizes can thus be examined at pleasure4 ,a number of eye-lenses of different powers arranged in a disc of metal can be successively brought to bear1 giving a means of quickly varying the power1 while coloured glasses of different shades can be passed in front of the eye in the same manner4 ,the surface of the disc of brass containing the holes is covered on one side--that on which the sun's image falls--with plaster of ,paris1 which1 being a bad conductor1 prevents the heat from affecting the whole apparatus4 99 99 99 99 99 ,the true magnifying power of the eyepiece is found by dividing the focal length of the object-glass by that of the eyepiece2 in practice it is found approximately by comparing the diameter of the object-glass with that of its image formed by the eyepiece when the telescope is in its usual adjustment2 the former divided by the latter giving the power required4 ,the diameter of the image can be measured by a small compound microscope carrying a transparent scale in its focus1 when the image of the object-glass is brought to a focus and enlarged on the scale and then viewed1 together with the divisions1 by the microscope2 or the image can be measured with tolerable accuracy by ,mr4 ,berthon's dynameter1 consisting of a plate of metal traversed longitudinally by a wedge-shaped opening4 ,this is placed close to the eye-lens in the case of the ,huyghenian eyepiece1 or at the point where the image of the object-glass is focussed with other forms of eyepieces1 and the plate moved until the sides of the wedge-shaped opening are exactly tangential to the image2 the point of the opening at which this occurs is read off on a scale1 which gives the width of opening at this point and therefore the diameter of the image4 ,,chapter ,x4 ,,production ,,of ,,lenses ,,and ,,specula4 ,before we go on to the use and various mountings of telescopes1 the optical principles of which have been now considered1 a few words may be said about the materials used and the method of obtaining the necessary and proper curves4 ,object-glasses1 of course1 have always been made of glass1 and till a few years ago specula were always made of metal2 but so soon as ,liebig discovered a method of coating glass with a thin film of metallic silver1 ,steinheil1 and after him the illustrious ,foucault1 so well known for his delicate experiments on the velocity of light and his invention of the gyroscope1 suggested the construction of glass mirrors coated by ,liebig's process with an exceedingly thin film of silver1 chemically deposited4 ,this arrangement much reduced the price of reflectors and rendered their polishing extremely easy1 and at the present time discs of glass up to four feet in diameter are being thus produced and formed into mirrors1 though in the opinion of competent judges this size is likely to be the limit for some time4 ,but there is this important difference1 that although glass is now used both for reflectors and refractors1 almost any glass1 even common glass1 will do1 if we wish to use it for a speculum2 but if we wish to grind it into lenses it is impossible to overrate the difficulty of manufacture and the skill and labour required in order to prepare it for use1 first in the simple material1 and then in the finished form in which it is used by the astronomer4 ,in a former chapter we considered some chefs-d'uvre of the early opticians1 some specimens of a quarter or half-an-inch in diameter1 with extremely long focus2 and as we went on we found object-glasses gradually increasing in diameter1 but they were limited to the same material1 namely1 crown glass4 ,dollond1 whose name we have already mentioned in connection with that of ,hall1 gave us the foundation of the manufacture of the precious flint glass1 the connection of which with crown glass he had insisted upon as of critical importance4 ,the existence of a piece of flint glass two inches in diameter was then a thing to be devoutly desired1 that is to say1 flint glass of sufficient purity for the purpose2 it could not be made of a size larger than that1 and not only was the material wanted1 but the material in its pure state4 ,in the year #ahbj we hear of a piece of flint glass six inches in diameter1 and in #ahei ,mr4 ,simms reported that a piece of flint glass of seven and three-quarter inches was produced1 six inches of which were good for astronomical purposes4 ,but even at this time they did these things better in ,germany and ,switzerland1 where ,m4 ,guinand made large discs at the beginning of the present century4 ,he was engaged by ,fraunhofer and ,utzschneider at their establishment in ,bavaria in #ahje1 and by his process achromatics of from six to nine inches in diameter were constructed4 ,afterwards ,merz1 the successor of ,fraunhofer1 succeeded in obtaining flint glass of the then unprecedented diameter of fifteen inches4 ,now we have in part turned the tables1 and ,mr4 ,chance1 of ,birmingham1 owing to the introduction of foreign talent1 has since constructed discs of glass of a workable diameter of twenty-five inches for ,mr4 ,newall's telescope1 and for the ,american ,government he has completed the large discs used in constructing the refractor of #bf inches' diameter for the observatory at ,washington 7the ,americans are never content till they go an inch beyond their rivals71 while ,m4 ,feil of ,paris1 a descendant of the celebrated ,guinand1 has also made one of nearly #bh inches' diameter for the ,austrian ,government4 ,messrs4 ,chance and ,feil1 however1 have the monopoly of this manufacture1 and the production of these discs is a secret process4 ,what we know is that the glass is prepared in pots in large quantities1 it is then allowed to cool1 and is broken up in order that it may be determined which portions of the glass are worth using for optical purposes4 ,these are gathered together and fused at a red heat into a disc1 and it is this disc which1 after being annealed with the utmost care1 forms the basis of the optician's work4 ,for the glass used for reflectors1 purity is of little moment1 as we only require a surface to take a polish1 since we look on to it1 and not through it2 but in the case of the glass that has to be shaped into a lens the purity is of the utmost importance4 ,the practical and scientific optician1 on his commencement to make an object-glass1 will grind the two surfaces of both flint and crown as nearly parallel as possible1 and polish them4 ,in this state he can the better examine them as to veins1 stri1 and other defects1 which would be fatal to anything made out of it4 ,he has next to see that the annealing is perfectly done by examining the discs with polarized light1 to see by the absence of the 8black cross0 that there is no unequal tension4 ,it is so difficult to run the gauntlet through all these difficulties when the aperture is considerable that refractors of forty inches' aperture may be perhaps despaired of for years to come1 though the glassmaker is willing to try his part4 ,next1 as to metallic specula4 ,as we are dealing with the instruments that are now used1 we will be content with considering the compounds that have been made successfully1 and omit the variations which have never been brought into practice4 ,to put it roughly1 the metal used for ,lord ,rosse's reflector consisted of two parts of copper and one part of tin2 but here we have an idea of the ,scylla and the ,charybdis which are always present in these inquiries4 ,if we use too much tin1 which tends to give a surface of brilliancy to the speculum1 a few drops of hot water poured on it will be enough to shiver it to atoms4 ,this brittleness is objectionable1 and what we have to do is to reduce the quantity of tin4 ,but then comes the ,charybdis4 ,if we do this1 the colour is no longer white1 but it is yellow1 and in addition we have introduced a surface that quickly tarnishes instead of a surface which remains bright4 ,the proportions which seem to answer best are copper sixty-four parts and tin twenty-nine4 ,lord ,rosse1 we believe1 uses #cagi per cent1 of tin2 or very nearly the above proportions4 ,mr4 ,grubb in the ,melbourne mirrors used copper and tin in the proportion of #cb to #adgg4 ,having the metal1 we have roughly to cast it in the shape of a speculum1 but if an ordinary casting is made in a sand mould the speculum metal is so spongy that we can do nothing with it4 ,if it is put in a close mould it will probably be cast very well1 but it will shiver to atoms with a very slight change of temperature4 ,the difficulty was got over by ,lord ,rosse1 using an open mould called a 8bed of hoops20 the bottom of the mould being composed of strips of iron set edgeways1 held together by an iron ring and turned to the proper convexity2 sand is then placed round the iron to form the edges1 the metal is then poured in1 and the bubbles and vapours run down through the small apertures at the bottom of the mould1 so that the speculum is fairly cast4 ,mr4 ,lassell proposed a different method1 which was introduced by ,mr4 ,grubb in his arrangements for the ,melbourne telescope4 ,instead of having the bottom of the bed of hoops perfectly horizontal it is slightly inclined2 the crucible1 which contains the metal of which the speculum is to be cast1 is then brought up to it--the amount of metal being something under two tons in the case of the ,melbourne telescope--and the bed of the mould is kept tipped up as the metal is poured into it1 and so arranged as to keep the melted metal in contact with one side2 and as it gets full it is brought into a perfectly horizontal position4 ,having cast the speculum1 the next thing is to put it in an annealing oven1 raised to a temperature of #a1jjj1 where it is allowed to cool slowly for weeks till it has acquired nearly the ordinary temperature4 ,on being removed from the oven the speculum is placed on several thicknesses of cloth and rough ground on front1 back1 and edge4 ,having got the material roughly into form we now pass on to see what is done next4 ,in the case of the reflector1 whether of metal or glass1 the optician next attempts to get a perfectly spherical surface of the proper curvature for the required focus4 ,in the case of the refractor matters are somewhat more complicated2 we have there four spherical surfaces to deal with1 and the optician has work to do of quite a different kind before he even commences to grind4 ,presuming the refractive and dispersive properties of the glass not known1 it will be necessary to have a small bit of glass of the same kind to experiment with4 ,that the optician may make no mistake in this important matter1 some glass manufacturers make the discs with projecting pieces to be cut off2 these the object-glass maker works into prisms to determine the exact refraction and dispersion1 including the position in the spectrum of the ,fraunhofer lines ,c and ,g1 for both the crown and flint glass4 ,with these numbers and the desired focal length he has all the necessary data for the mathematical operation of calculating the powers to be given to the two lenses--flint and crown1 and the radii of curvature of the four surfaces in order that the object-glass may be aplanatic or free from aberration both spherical and chromatic4 ,the problem is what mathematicians call an indeterminate one1 as an infinite number of different curvatures is possible4 ,assume1 however1 the radius of curvature of one surface1 and all the rest are limited4 ,in assuming the radius of curvature on one of the crown-glass surfaces1 it is well to avoid deep ones4 ,it is better to divide the refraction of the four surfaces as equally as the nature of the problem will admit1 as any little deviation from a true spherical figure in the polishing will produce less effect in injuring the performance of the object-glass from surfaces so arranged than if the curves were deep4 ,but whatever curves he chooses he goes to work so that the spherical aberration of the compound lens shall be eliminated as far as possible1 and the chromatism in one lens shall be corrected by the other1 or in other words1 that what is called the secondary spectrum shall be as small as possible2 and it is to be feared that this will never be abolished4#f ,illustration3 ,,fig4 #fd4--;,images of planet produced by short and long focus lenses of the same aperture giving images of different size1 but with the same amount of colour round the edges4 ,this matter requires a somewhat detailed treatment in order that it may be seen how the four surfaces to which reference has been made are determined4 ,the chromatic dispersion1 in the case of the object-glass1 may be roughly stated to be measured by about one fiftieth of the aperture4 ,suppose for instance the discs1 ,fig4 #fd1 to represent the image of any object1 say the planet ,jupiter4 ,then round that planet we should have a coloured fringe1 and the dimensions of that coloured fringe1 that is1 the joint thickness of colour at ,a and ,d1 will be found by dividing the diameter of the object-glass used by fifty4 ,now this is absolutely independent of the focal length of the telescope2 therefore one way of getting rid of it is to increase the focal length of telescopes2 and as the size of the image depends on focal length1 and has nothing whatever to do with aperture1 we may imagine that with the same sized object-glass1 instead of having a little ,jupiter as on the left of ,fig4 #fd1 we may have a very large ,jupiter1 due to the increased focal length of the telescope4 ,then1 it may be asked1 how about the chromatic aberration8 ,it will not be disturbed4 ,the aperture of the object-glass remains unaltered1 and there is no more chromatic aberration here than in the first case2 so that the relation between the visible planet ,jupiter and the colour round it is changed by altering the focal length4 ,but as we have seen1 we are able by means of a combination of flint and crown glass to counteract this dispersion to a very great extent4 ,how then about spherical aberration8 ,up to the present we have assumed that all rays falling on a convex lens are brought to a point or focus1 but this is not strictly true1 for the edges of a lens turn the rays rather too much out of their course1 so that they will not come to a point2 just as the rays reflected from a spherical mirror do not form a single focus4 ,the marginal rays will be spread over a certain circular surface1 just as the colour due to chromatic aberration covered a surface surrounding the focus4 ,it was explained that for the same diameter of lens the circle of colour remained the same1 irrespective of focal length1 but in the case of spherical aberration this is not so2 it diminishes as the square of the focal length increases2 that is to say1 if we double the focal length we shall not only halve1 but half-halve1 or quarter the aberration4 ,newton calculated the size of the circle of aberration in comparison with that due to colour1 and he found that in the case of a lens of four inches diameter and ten feet focus1 the spherical aberration was eighty-one and a half times less than that of colour4 ,it is found that by altering the relative curvatures of the surfaces of the lens1 this aberration can be corrected without altering the focal length2 for any number of lenses can be made of different curvatures on each side but of the same thickness in the middle1 so that they have all the same focal length1 but the one1 having one surface about three times more convex than the other1 will have least aberration1 so that it is the adaptation of the surfaces of lenses to each other that exercises the art of the optician4 ,so far we have got rid of this aberration in a single lens2 it can also be done in the case of achromatic lenses4 ,the foci of the two lenses in an achromatic combination must bear a certain relation to each other1 and the curvatures of the surfaces must also have a certain relation for spherical aberration4 ,in the achromatic lens there are four surfaces1 two of which can be altered for one aberration and two for the other4 ,for instance1 in the case of the lens1 ,fig4 #de1 where the interior surfaces of the lenses are cemented together1 although shown separate for clearness1 we find that if the exterior surface of the crown double convex lens be of a curvature struck by a radius #fgb units in length1 and the exterior surface of the flint glass lens to a curvature due to a radius of #a1dbj units1 the lens will be corrected for spherical aberration1 and these conditions leave the interior surfaces to be altered so that the relation between the powers of the lenses is such as to give achromatism4 ,the flint is as useful in correcting the spherical aberration as the chromatic aberration2 for although the relative thicknesses of the flint and crown are fixed in order to get achromatism1 still we have by altering both the curvatures of each lens equally1 and keeping the same foci1 the power of altering the extent of spherical aberration2 and it is in the applications of these two conditions that much of the higher art of our opticians is exercised4 ,we have now therefore practically got rid of both aberrations in the modern object-glass1 and hence it is that lenses of the large diameter of twenty-five and twenty-six inches are possible4 ,the nearest approach to achromatism is known to be made when looking at a star of the first or second magnitude1 the eyepiece being pushed out of focus towards the object-glass1 the expanded disc has its margin of a claret colour4 ,when the eyepiece is pushed beyond the focus outwards the margin of the expanded disc is of a light green colour4 ,if the object-glass is well corrected for spherical aberration1 the expanded discs both within and without the focus will be constituted of a series of rings equally dense with regard to light throughout1 with the exception of the marginal ring1 which will be a little stronger than the rest4 99 99 99 99 99 ,having determined the radius of curvature of surface1 both he who grinds the speculum1 whether of speculum metal or glass1 and he who grinds the object-glass1 starts fair2 only one has four times the work to do that the other has4 ,the grinding is managed in a simple way1 and the process of grinding or polishing an object-glass or speculum1 either of glass or of metal1 is the same4 ,supposing we wish to make a reflecting telescope of six feet focus1 or a surface of an object-glass of twelve feet radius1 all we have to do is to get a long rod1 a little more than twelve feet long1 and pin it to a wall at its upper end so that it can swing1 pendulum fashion2 then at a distance of twelve feet below the point of suspension a pin is stuck through the rod and its point made to scratch a line on a sheet of metal laid against the wall2 then this line will be part of a circle struck with a radius of twelve feet4 ,if then the plate be cut along this line we get a convex and a concave surface of the desired radius1 and then we can take a block of iron or brass and turn its surface1 convex or concave1 to fit the sheet of metal or template4 ,for a reflector we should make a convex tool1 and for a refractor a concave one4 ,generally this grinding tool is divided into squares or furrows all over it1 in order that the emery which is used in rough grinding may flow freely about with the water4 ,a disc of glass is then laid on the tool1 or the tool on the glass1 the two being pressed together by a weight or spring2 emery powder1 with water1 is strewn between them1 and one is rubbed over the other by a machine similar to those used for polishing1 which we shall explain presently4 ,this operation is continued until the glass is ground all over1 and in this process of rough grinding the rough emery is used between the tool and the glass1 so that whatever irregularities the glass or tool may have they are got rid of1 and it is easy to obtain a spherical surface1 and indeed1 it is the only surface that can be obtained4 ,then finer and finer emery is used1 till it ceases to be a sufficiently fine substance to use1 and a surface of iron or lead is also too hard a surface4 ,now the polishing begins1 and the optician and amateur avail themselves of a suggestion due to ,sir ,isaac ,newton1 who always saw much further through things than other people4 ,illustration3 ,,fig4 #fe4--,showing in an exaggerated form how the edge of the speculum is worn down by polishing4 ,even when he first began to make the first reflector1 he used pitch1 a substance not too hard1 nor yet too soft1 and one that can be regulated by temperature2 therefore for polishing1 instead of having a tool made of metal1 pitch laid on glass or wood and supplied with rouge and water is used4 ,this polisher of pitch is divided into squares by channels to allow free flow of rouge and water1 and is laid on the mirror or object-glass1 or vice vers1 and moved about over it4 ,when the maximum of polish is attained the work is done1 and the object-glass finished1 as here we have to do with a spherical surface4 ,in the grinding of the two discs for ,mr4 ,newall's telescope #a1efj hours were consumed1 the thickness of the crown disc having been reduced one inch in the process4 ,in the case of specula1 however1 there is more to be done2 and it is in this polishing of specula that the curve is altered from a circle to a parabola by using a certain length of stroke1 size of polisher1 consistency of pitch1 and numbers of other smaller matters1 the proper proportionment of which constitutes the practical skill of the optician1 and it is in accomplishing this that the finest niceties of manipulation come into play1 and the utmost patience is required4 #a1agj hours were occupied in the grinding and polishing of the four-feet ,melbourne speculum4 ,this was equivalent to #b1jej1jjj strokes of the machine at #cc per minute for rough and #bd for fine grinding4 ,dr4 ,robinson1 in his description of the grinding operations1 states that at the edge of one of the four-feet specula the distance of its parabola from the circle was only #jjjjajf4 ,in the early times of specula the polishing was invariably done by hand1 a handle being cemented by pitch to the back of the speculum to work it with4 ,mudge tells us that at first1 when the mirror was rough from the emery grinding1 it was worked round and round on the pitch1 which was supplied with rouge and water and cut by channels into small squares1 carrying the edge but little over the polisher1 an occasional cross stroke being made4 ,the effect of this was to press the pitch towards the centre where the polish always commenced1 and gradually spread to the circumference4 ,as soon as the polishing was complete the speculum was worked by short straight strokes across the centre1 tending to bring it back to a sphere2 then the circular strokes were recommenced to restore the paraboloid form3 these were continued for a short time only1 otherwise it would pass the proper curve and require reworking with straight strokes again4 ,by this method some small mirrors of first-class definition were constructed4 ,when ,sir ,w4 ,herschel began his labours he constructed a machine for working the speculum over the polisher2 the polisher was a little larger than the mirror1 the proportion given by him from a number of trials being #ajf to #a4 ,the speculum was held in a circular frame1 which was free to turn round in another ring or frame2 this frame was moved backwards and forwards by a vibrating lever to which it was attached by rods1 carrying the speculum over the polisher4 ,this motion he designates the stroke4 ,besides this there was the side motion produced by a rod attached to the side of the frame opposite to that to which the rods giving it the stroke were attached and at right angles to the direction of stroke3 this rod was in connection1 by means of intermediate levers1 with a pin on a rachet wheel1 which was turned a tooth at a time by a rod in connection with the lever giving the stroke motion1 so that the rod giving the side motion was pushed and pulled back by the pin on the rachet wheel every time it turned round1 which it did every twenty or thirty strokes4 ,there were also teeth on the ring fastened round the edge at the back of the speculum1 into which claws worked which were attached by rods to a point on the lever a little distance from the attachment of the rod giving the stroke1 so that the claws had a less motion than the speculum and its ring1 and consequently pulled the ring1 and with it the speculum1 round a tooth or more at each stroke4 ,the polisher was also turned round in the same manner in a contrary direction to the motion of the speculum4 ,the speculum had therefore three motions1 a revolving one on its centre1 a stroke1 and a side motion1 making its centre describe a number of parallel lines over the polisher on each side of its centre4 ,sir ,w4 ,herschel gives as a good working length of stroke1 #jbi1 and #jai side motion measured from side to side1 the diameter of the speculum being #a4 ,to produce a seven-inch mirror with this instrument he would work continuously for sixteen hours1 his sister 8putting the victuals by bits into his mouth40 ,illustration3 ,,fig4 #fe994--,section of ,lord ,rosse's polishing machine4 ,lord ,rosse adopted a similar arrangement2 the polisher1 ,k ,l1 ,fig4 #fe1 was worked over the speculum in straight strokes with side motion1 the requisite straight motion being given by a crank-pin and rod and the side motion by the continuation of this latter rod on the other side of the polisher working in a guide on another crank-pin1 which threw it from side to side as the wheel carrying the pin revolved4 ,the trough ,e ,f carrying the speculum also revolved slowly1 and the requisite motions were given by pulleys and straps of various sizes under the table on which the machine rested2 the weight of the polisher was in a great measure counterpoised by strings from its upper surface to a weighted lever ,m above4 ,the polisher was free to turn in its ring1 which it did once in about twenty strokes1 and for the six feet speculum the velocity of working was about eight strokes a minute1 the length of stroke being one-third of the diameter of the speculum1 and that of the side motion one-fifth4 ,the speculum was polished on the same system of levers that were afterwards to support it1 in order that no change of form might be produced in moving it to a different mounting4 ,the consistency of the pitch is a matter of importance1 ,mr4 ,lassell's test of the requisite hardness being the number of impressions left by a sovereign standing on edge on it2 this should leave three complete impressions of the milled edge in one minute at the ordinary temperature of the atmosphere4 ,illustration3 ,,fig4 #ff4--,mr4 ,lassell's polishing machine4 ,fig4 #ff represents the machine contrived by ,mr4 ,lassell for his method of polishing1 and shows what a complicated arrangement is essential in order to arrive at any good result in these matters4 ,the speculum is placed on a bed1 and above it is a train of wheels terminating in a crank-pin that gives motion to the polisher1 which is made to take a very devious path by the motion of the wheels above4 ,the pin giving motion to the polisher ,g at its centre can be set at a variable distance from the axis of the lowest pinion ,f to which it is attached1 by moving it in its slide1 so that when the pinion is turned1 the pin and centre of the polisher describe a circle4 ,the pinion in question is carried on a slide ,c above it1 attached to the main vertical driving shaft ,a1 so that as the shaft revolves the centre of the pinion describes a circle of a diameter variable at pleasure by moving it in the slide ,c1 the result of the two motions being that the centre of the polisher describes circles about a moving centre1 and consequently in constantly varying positions on the speculum4 ,motion is given to the vertical shaft by the cog-wheel and endless screw above1 worked by some prime mover1 and as the cogwheels on the shaft ,e parallel to the main shaft are carried round the latter by the arm ,d holding them1 they are caused to revolve by gearing into the fixed wheel ,b1 through the centre of which the main shaft passes1 and they in their turn impart motion to the pinion carrying the pin giving motion to the polisher4 ,the speculum is also maintained in slow rotation by the wheel and endless screw below it4 ,the speculum and its supports are surrounded by water contained in a circular trough not shown in the engraving1 so that the consistency of the pitch shall be constant4 ,this arrangement1 pure and simple1 was found to bring on the polish in rings over the speculum1 and as an improvement1 the speculum1 or rather the system of levers supporting it1 was carried on a plate which had the power of sliding backwards and forwards on the wheel turning it round2 the edges of this plate pressed against a fixed roller1 and it was made of such a shape that as it revolved it was forced to take a side motion as its edges passed by the fixed roller1 so that the speculum had a side motion in addition to the rotatory one4 ,mr4 ,de ,la ,rue improved on this by giving the speculum a rotatory motion irrespective of that of the sliding plate1 so that the side motion should not always be along the same diameter of the speculum4 ,this was done by allowing the speculum to turn freely on a pivot on the sliding plate1 and giving it a rotatory motion by means of a cord going round the plate carrying the speculum supports4 ,as a further improvement ,mr4 ,de ,la ,rue controls the motion of the polisher on the central pin1 giving it motion by a crank carrying a system of wheels in place of the lowest crank1 so that the pin gets a rotatory motion in addition to these4 ,mr4 ,grubb's arrangement for polishing is different4 ,the speculum is made to rotate1 the polisher is made to execute curves variable at pleasure by altering the throw of the cranks which move rods attached to the centre of the polisher1 giving it a motion similar to that of ,mr4 ,lassell's machine4 ,the polisher moves a little off the edge1 so that the edge is worn down more than the centre1 thus giving the parabolic form4 ,m4 ,foucault1 of whom we have already spoken1 proceeds in a different manner in parabolising his glass mirrors4 ,he first obtains a spherical surface1 fairly reflective1 by grinding4 ,he then alters the surface to a paraboloid form by handwork1 only testing the surface from time to time to ascertain the parts requiring reduction by the polishing pad4 ,the method of testing is as beautiful as it is simple4 ,the approximate estimate of the curvature of the speculum is made by placing a small and well-defined object1 such as the point of a pin1 close to the centre of curvature and examining its image formed close by its side with a lens4 ,as a nicer test1 he places an object having parallel sides1 say a flat ruler1 near the centre of curvature1 and views its image with the naked eye at the distance of distinct vision1 then each point of the edge is seen by rays converging only from a small portion of the surface of the mirror1 the remainder of the diverging cone from each point of the edge passes on beside the eye1 and by moving the eye about1 any point of the edge can be seen formed by rays proceeding from any particular part of the mirror1 viz41 that part in line with the eye and point of the edge examined2 if the curvature be not uniform the edge will appear distorted1 and points on it will appear in different positions1 as rays from different parts of the mirror are received by the eye as it is moved1 making the edge appear to move in waves4 ,finally1 he allows light from a very small hole in a metal plate near the centre of curvature to fall on the mirror1 and places the eye just on the side opposite to the point where the image is formed1 so as to receive the rays as they diverge after having come to a focus4 ,the whole of the light thus passes into the eye1 and the mirror is seen illuminated in every part4 ,a sharp edge of metal is then gradually brought into the focus1 when the illumination of the mirror decreases1 and just before the light disappears the irregularities will plainly appear1 showing themselves by patches of light1 which prove that those parts still bright are so inclined as to reflect the rays by the side of the true focus4 ,by moving the metallic edge so as to advance upon the focus from all sides1 a very good idea of the irregularities may be obtained4 ,if1 however1 the surface be truly spherical1 the light will disappear regularly over the whole surface4 ,m4 ,foucault commences by making the surface truly spherical1 and then by polishing off in concentric circles1 increasing the polishing from the centre1 an elliptic and at last a parabolic curve is attained4 ,the ellipse is tested from time to time by removing the perforated plate further and further away from the mirror until the ellipse becomes practically a parabola4 ,the great advantage of this method is1 that the effect of the polishing can be examined as it proceeds1 and the work can always be applied wherever necessary1 and the test is entirely independent of hot-air currents which are seen to fluctuate over the mirror as waves of light1 leaving the irregularities of form permanently marked4 ,it further appears that the method may be varied to form a first-rate test of a finished mirror already mounted2 for one has nothing to do but bring a star into the field of view1 and remove the eyepiece1 and bring the eye into such a position as to receive the diverging rays from the focus of the star4 ,a knife is then gradually moved across in front of the eye1 say from the right2 then if the mirror commences to get darkened on the right side distinctly before the left the knife is on the mirror side of the focus2 if1 however1 the left side of the mirror becomes darkened first it is on the eye side of the focus4 ,after a few trials it can be got to cut across the focus and darken the mirror at all points at once1 and show up all irregularities4 ,we have now1 then1 by one system or another1 got our mirror1 either of speculum metal or of glass1 and if of the latter substance we have to silver it2 processes have been published by ,mr4 ,browning1 and ,m4 ,martin1#g by which1 on the plan proposed in the first instance by ,liebig1 an extremely thin coating of silver is deposited on the glass4 ,this film is susceptible of taking a high polish1 which1 in the case of small mirrors1 can be renewed as often as is wished without repolishing the mirror2 the resilvering of one of large aperture however is a most formidable affair4 ,to those who wish to silver their own mirrors1 let us say that it should be done in summer1 or in a room kept by a stove at an equable summer heat1 and the silvering solution should be kept for a day or more to settle1 and for probably some chemical change to take place before the reducing solution is added4 ,it will be found easy enough to silver the small planes for ,newtonian reflectors1 but large mirrors require much greater care and trouble4 ----- ,footnote #f3 ,professor ,stokes and ,mr4 ,vernon ,harcourt some time ago made experiments with phosphatic glass1 and some of this material was worked into a lens by ,mr4 ,grubb1 who states that 8the result was successful so far as the obtaining of specimens of phosphatic glass with rational spectra2 but phosphatic glass is almost unworkable1 and when the experiment was tried on a siliceous glass it failed4 ,some alleviation of this secondary spectrum can be got by using a triple objective1 but with1 of course1 a corresponding loss of light40 ,footnote #g3 ,mr4 ,browning's method of silvering glass specula is as follows3-- ,prepare three standard solutions3 ,solution ,a ,crystals of nitrate of silver #ij grains ,dissolve4 ,distilled water #d ounces ,solution ,b ,potassa1 pure by alcohol #a ounce ,dissolve4 ,distilled water #be ounces ,solution ,c ,milk-sugar 7in powder7 ounce ,dissolve4 ,distilled water #e ounces ,solutions ,a and ,b will keep1 in stoppered bottles1 for any length of time2 ,solution ,c must be fresh4 ,to prepare sufficient for silvering an #h in4 speculum1 pour two ounces of ,solution ,a into a glass vessel capable of holding thirty-five fluid ounces4 ,add1 drop by drop1 stirring all the time 7with a glass rod71 as much liquid ammonia as is just necessary to obtain a clear solution of the grey precipitate first thrown down4 ,add four ounces of ,solution ,b4 ,the brown-black precipitate formed must be just re-dissolved by the addition of more ammonia1 as before4 ,add distilled water until the bulk reaches fifteen ounces1 and add1 drop by drop1 some of ,solution ,a1 until a grey precipitate1 which does not re-dissolve after stirring for three minutes1 is obtained2 then add fifteen ounces more of distilled water4 ,set this solution aside to settle2 do not filter4 ,when all is ready for immersing the mirror1 add to the silvering solution two ounces of ,solution ,c1 and stir gently and thoroughly4 ,solution ,c may be filtered4 ,the mirror should be suspended face downwards about -inch deep in the liquid1 by strings attached to pieces of wood fastened to the back of the mirror with pitch1 and before being immersed should be cleaned with nitric acid and washed with distilled water4 ,the silvering is completed in about an hour1 and when finished the surface should be washed in distilled water and dried1 and then polished with soft leather1 finishing with a little rouge4 ,the following method is used by ,m4 ,martin3-- ,make solutions3 #a4 ,nitrate of silver #d per cent4 #b4 ,nitrate of ammonia #f per cent4 perfectly free #c4 ,caustic potash #aj per cent4 from carbonates4 #d4 ,dissolve twenty-five grammes of sugar in #bej grammes of water2 add three grammes of tartaric acid2 heat it to ebullition during ten minutes to complete the conversion of sugar2 cool down1 and add fifty cubic centimetres of alcohol in summer to prevent fermentation1 add water to make the volume to litre in winter and more in summer4 ,clean well the surface of the glass4 ,take equal quantities of the four solutions3 mix #a and #b together1 and #c and #d also together3 mix the two1 pouring it at once into the vessel where the silvering is to be done4 ,the mirror is suspended face downwards in the liquid1 and the deposit begins after about three minutes1 and is finished after twenty minutes4 ,take out the mirror1 clean well with water1 dry it in the air1 and rub it then gently with a very fine leather4 ,,chapter ,,xi4 ,,the 8,,optick ,,tube40 ,having now obtained the lenses and specula we come1 in order to complete our consideration of the purely optical portion of the subject1 to the question of mounting these lenses and specula in tubes and thus connecting them with the eyepieces so as to become of practical utility4 ,we will first consider the adjustment of lenses in a tube1 the combination forming a simple telescope that can be supported1 in any manner desirable1 by mountings we shall presently consider1 according to the purpose for which it is required4 ,the adjustment of specula will be considered as we advance further4 ,the smaller telescopes consist of a brass tube1 the object-glass1 held in a brass ring1 being screwed in at one end of the tube3 a smaller tube sliding in and out of the other end of the large tube1 generally moved by a rack and pinion motion1 carries the eyepiece4 ,in larger telescopes the mounting is similar1 only somewhat more elaborate1 the object-glass being carried in a brass cell1 or a steel one if the dimensions are very large4 ,this screws into the ring at the end of the tube1 and this ring can be slightly tipped on either side by set screws1 so that the object-glass can be brought exactly at right angles to the axis of the tube4 ,illustration3 ,,fig4 #fg4--,simple telescope tube1 showing arrangement of object-glass and eyepiece4 ,it is important1 in order that an object-glass shall perform its best1 that the lenses forming it shall be properly centred3 this is generally done by the maker once and for ever4 ,wollaston pointed out an ingenious method of centring them2 it is as follows3--,the eyepiece is removed1 and a lighted candle put in its place3 the object-glass is then examined from the opposite side1 when1 if all the lenses are correctly placed1 the images of the candle produced by the successive reflections of the candle from the surfaces of the lenses will be concentric1 and in a straight line from the candle through the centre of the system of lenses1 a fact easily judged of1 by moving the eye slightly from side to side1 and if they are not1 they are easily corrected by tipping the lens in fault slightly in the cell4 ,in case the lenses are cemented together1 this method of course is applicable in setting the object-glass at right angles to the axis of the tube4 ,the adjustment of an object-glass can also be judged of by examining a star as it is thrown in and out of focus by the focusing screw2 the disc of the star should be perfectly round in and out of focus1 and the rings produced by interference should also be circular when in focus1 and the disc of light1 when out of focus1 must be circular4 ,any elongation of the disc or rings1 or a 8flare0 appearing1 shows a want of a slight alteration of the setting screw1 on the same side of the object-glass as the 8flare0 or elongation appears4 ,in some object-glasses the curves of the two interior surfaces are such that three pieces of tin foil are placed at equal distances round the edge to prevent the central portions from coming in contact4 ,illustration3 ,,fig4 #fh4--;,appearance of diffraction rings round a star when the object-glass is properly adjusted4 ,illustration3 ,,fig4 #fi4--;,appearance of same object when object-glass is out of adjustment4 ,the flexure of small object-glasses by their own weight is of little importance1 because every surface is affected alike2 but when the aperture is large special precautions have to be taken4 ,the late ,mr4 ,cooke when he had completed the #be-;inch object-glass for ,mr4 ,newall's telescope1 introduced a system of counterpoise levers just within the edge which helped to support the object-glass in all positions4 ,mr4 ,grubb states that with an aperture of #ae inches1 supported on three points1 there is decided evidence of flexure1 and he proposes1 in the #bg-;inch ,vienna refractor1 not only to introduce six intermediate supports1 thereby following in the footsteps of ,mr4 ,cooke1 but with larger apertures to introduce boldly a central support1 or to hermetically seal the tube and fill it with compressed air4 ,he has calculated that in the case of an object-glass #dj inches aperture1 weighing #fjj lbs41 two-thirds of its weight could be supported by an air pressure of one-third of a pound to the square inch4 ,the tube of the telescope when of large size is usually made of iron or wood1 and a tube of the latter substance may be made very light and yet sufficiently strong1 by wrapping layers of veneer round a central core and fastening the layers firmly with glue4 ,there are generally two or more tubes sliding inside each other at the eye end of the telescope1 to carry the eyepiece so as to give plenty of power of adjustment of the length of the tube to suit the different eyepieces1 or other instruments used in their place4 ,the tube then is ready to be adapted to any of the mountings to be hereafter considered4 99 99 99 99 99 ,we now come to the mounting of specula1 and when we recollect the enormous weights of some of the specimens to which we have referred1 it will be obvious that some additional precautions1 which are not at all necessary in the case of a refractor1 must be taken to insure success4 ,in reflecting telescopes1 the speculum is carried at the bottom of a tube in a sort of tray or cell1 which can be adjusted by screws at the back1 so as to set the mirror at right angles to the tube1 and the conditions of support should be such that the mirror should be as free from strain as if it were floating in mercury4 ,a system of lateral supports in all positions is also necessary4 ,the action of the telescope depends greatly on the backing of the speculum1 and numerous methods of carrying specula on soft backing and systems of levers have been suggested1 all aiming at carrying them so that they are free from all possible strain and flexure occasioned by their own weight4 ,for smaller mirrors a soft back of flannel or cloth can be used1 and a leather strap placed round the mirror and its back1 so as to form the side of a sort of circular tray1 will give it sufficient support when inclined to the horizontal4 ,mr4 ,browning adopts the plan of making the back of the mirror and its support perfectly flat1 so as not to require levers or soft backing2 this arrangement would probably fail for mirrors larger than one foot in diameter1 although answering admirably for those of less size4 ,illustration3 ,,fig4 #gj4--,optical part of a ,newtonian reflector of ten inches aperture1 showing eyepiece1 adjusting screws for large speculum1 finder1 door for uncovering speculum1 and counterpoise4 ,illustration3 ,,fig4 #ga4--,optical part of ,melbourne reflector1 showing the lattice arrangement for supporting the convex mirror ,y1 ,t more solid part of tube fixed to declination axis1 ,w finder4 ,illustration3 ,,fig4 #gb4 ,mr4 ,browning's method of supporting small specula4 ,the bottom of the speculum ,a is a carefully prepared plane surface1 and the outer rim of the inner iron cell ,b1 on which it rests1 is also a plane4 ,the speculum is kept in this cell by the ring ,g ,g1 and it may be removed from1 and replaced in1 the telescope1 without altering its adjustment4 ,we will now consider the methods of mounting specula of larger size1 and will take as an instance the mounting of some of the largest specula in existence which must act so as to prevent flexure in any position of the speculum4 ,the speculum is1 in the case of the ,melbourne telescope1 of the weight of something like two tons4 ,when it is inclined at any considerable angle to the horizon1 it is apt to bend over at the top1 and thus destroy its proper curvature2 and when horizontal1 if not equally supported1 it will also bend1 and unless some measures are taken to prevent this flexure it will so entirely alter its figure by its own weight as to render minute observations of any delicate stars absolutely impossible4 ,mr4 ,lassell was the first to suggest an arrangement for preventing this flexure4 ,through the back of the speculum case--the case which holds and supports the speculum1 which we shall have to speak about presently--he inserts a large number of very small levers1 the centres of which are fixed to the exterior part of this case1 the forward part of each resting against a small aperture made in the back of the speculum4 ,the ends of the levers furthest from the speculum are crowned with small weights1 the weights varying on different parts of the speculum4 ,now so long as the speculum is perfectly horizontal1 i4e4 so long as the zenith is being observed1 these levers will have no action whatever2 but the moment the reflector is brought into any other position1 as1 for instance1 when we wish to observe a star near the horizon1 the more the mirror is inclined to the horizon the greater will be the power of these small levers1 and at length their total effect comes into action when a star close to the horizon is being observed4 ,then the whole weight of the mirror is carried by these levers acting at points all over its back4 ,in the ,melbourne reflector1 which has recently been finished1 ,mr4 ,grubb manages this somewhat differently1 as will be seen by ,figs4 #gc-gf4 ,in ,fig4 #gc the speculum is in a vertical position4 ,it is supported in a frame1 ,b ,b1 all round it1 which consists of a slightly flexible hoop of metal a little larger than the speculum4 ,this in its turn is supported by a large fixed hoop1 ,a ,a1 having a hook-shaped section4 ,this hoop is attached to the tube of the telescope ,c ,c4 ,the hoop1 ,b ,b1 is rather larger than the part of ,a on which it hangs1 so that it can adjust itself to the form of the mirror2 and not only is the mirror supported in the hoop ,b ,b1 like as in a strap in the position shown1 but in every other position of the tube the speculum still hangs evenly supported4 ,illustration3 ,,fig4 #gc4--,support of the mirror when vertical4 ,as we have already seen1 there is another point to consider4 ,not only must we be able to support the mirror when inclined to the horizon1 but we must support it bodily at the end of the tube when it is horizontal4 ,we will next examine an arrangement adopted by ,mr4 ,grubb1 similar to that adopted by others1 for supporting the ,melbourne speculum1 and we cannot do better than quote ,mr4 ,grubb's own explanation of it4 ,he says3-- 8,to understand it1 suppose the speculum to be divided into forty-eight portions1 as in ,fig4 #gd1 each of them being exactly equal in area1 and consequently in weight4 ,now1 if the centre of gravity of each of these pieces rested on points which would bear up with a force the weight of each segmental piece1 it is evident that there would be no strain in the mass from segment to segment4 ,illustration3 ,,fig4 #gd4--;,division of the speculum into equal areas4 8,this is exactly what is accomplished by this system2 in fact1 if when the speculum is resting on these supports it could be divided up into segments corresponding to those lines1 they would have no inclination to leave their places1 showing a perfect absence of strain across those lines4 ,suppose now the points representing the centres of gravity of these segments were supported on levers and triangles1 so as to couple them together1 as at ,a1 ,fig4 #ge1 and each of these couplings to be supported from a point a1 representing the centre of gravity of the sum of the segments supported by that particular couple1 and it is evident that there can be no strain between the components of these couples4 ,again1 let these points1 a1 be coupled together by the system shown at ,b1 ,fig4 #ge1 and their centres of gravity1 b1 coupled as at ,c1 and it is evident that the whole weight of the speculum ultimately condensed by this system into these points is supported on forty-eight points of equal support being the centres of gravity of the forty-eight segments at ,fig4 #ge4 ,in ,fig4 #gf is seen the whole system complete4 ,it consists of three screws passing through the back of the speculum box 7which serve for levelling the mirror71 the points of which carry levers 7primary system7 supporting triangles on their extremities 7secondary system71 from the vertices of which are hung two triangles and one lever 7tertiary system74 ,all the joints of this apparatus are capable of a small rocking motion1 to enable them to take their positions when the speculum is laid upon them4 ,illustration3 ,,fig4 #ge4--,primary1 secondary1 and tertiary systems of levers shown separately4 ,illustration3 ,,fig4 #gf4--;,complete system consolidated into three screws4 8,in the system of levers made by ,lord ,rosse for his six-feet speculum1 the primary1 secondary1 and tertiary systems were piled up one over the other1 so that the distance from the support of the primary to the back of the speculum was about fifteen inches4 ,this1 as will be readily seen on consideration1 introduced a new strain when the telescope was turned off the zenith1 and had to be counterpoised by another very complicated system of levers4 ,but in the ,melbourne telescope1 by the substitution of cast-steel for cast-iron1 and by hanging the tertiary system from the secondary1 and allowing it 7the tertiary7 to act in some places through the secondary1 the whole system is reduced to three and a half inches in height1 and the distance from the support of the primary lever to the back of the speculum is only one and three-quarter inch1 by which means this cumbersome apparatus is entirely done away with4 8,the ultimate points of the tertiary system are gunmetal cups1 which hold truly ground cast-iron balls with a little play1 and when the speculum is laid on these it can be moved about a little by a person's finger with such ease as to seem to be floating in some liquid40 ,it may perhaps be thought that it would be better to support these great specula on a flat surface1 and it might be1 if we could do so without extreme difficulty2 but ,lord ,rosse has stated that if we attempt to support a large speculum on a surface extremely flat1 a thread placed across that surface1 or even a piece of dust1 is quite enough to bend the mirror and render it absolutely useless4 ,that will show the extreme importance of the support of the speculum4 ,let us then assume that we have the speculum and the tube perfectly adjusted4 ,the next thing1 in all constructions except the ,herschelian1 is to apply the second small reflector1 concave in the case of the ,gregorian1 convex in the case of the ,cassegrainian1 and plane in the case of the ,newtonian4 ,this small mirror is generally supported by a thin strip of metal firmly fastened to the side of the tube1 with power of movement parallel to the axis of the telescope1 in the case of the ,gregorian and ,cassegrainian1 for the purpose of focussing4 ,in the ,newtonian1 the reflecting diagonal prism or plane mirror1 inclined at an angle of #de to the axis1 is preferably supported in the manner suggested by ,mr4 ,browning4 ,see ,figs4 #gg and #gh4 ,in these ,b ,b ,b represent strips of strong chronometer spring steel1 placed edgewise towards the speculum2 by these the prism or small mirror ,d is suspended4 ,the mirror thus mounted1 does not produce such coarse rays on bright stars as when it is fixed to a single stout arm2 it is also less liable to vibration1 which is very injurious to distinct vision1 or to flexure1 which interferes with the accuracy of the adjustments4 ,illustration3 ,,fig4 #gg4--,support of diagonal plane mirror 7,front view74 ,illustration3 ,,fig4 #gh4--,support of diagonal plane mirror 7,side view74 ,the most usual form of reflector is the ,newtonian1 large numbers of which kind are now made2 and just as the object-glasses of refractors require adjusting1 so do not only the large mirror1 but also the 8flat0 or diagonal mirror of this form4 ,in the ,newtonian the flat must be adjusted first2 to do this1 first place the large mirror in its cell in the tube1 and secure it by turning it in the bayonet joint1 with the cover on the mirror4 ,then remove the glasses from one of the eyepieces1 insert it into the eyetube1 and fix the diagonal mirror loosely in its position4 ,then1 looking through the eyetube1 move the diagonal mirror1 by means of the motions which are provided1 until the reflected image of the cover of the speculum is seen in the centre of it4 ,this is accomplished by first loosening the milled-headed screw behind the mirror1 and turning the mirror until the image of the speculum cover appears central in one direction4 ,the screw at the back of the mirror enables the reflected image to be brought central in the other direction4 ,next comes the turn of the large mirror4 ,take off the cover by screwing off the side opening and place the eye at the eyetube after having removed the eyepiece2 the reflection of the diagonal mirror will be seen in the reflected image of the speculum4 ,the adjusting screws1 at the back of the speculum1 must then be moved until the diagonal mirror is seen in the centre of the speculum4 ,the adjustment should then be complete4 ,this may be judged of by bringing a star to the centre of the field1 and sliding the focussing-tube in or out1 when the circle of light should expand equally1 and its centre should remain central in the field4 ,as another test a bright star should be viewed with a high power1 and the image examined2 if it is round and the circles of light round it are concentric without rays in any one direction1 then all is correct2 but if a flare is seen1 it is evidence that the part of the diagonal mirror towards which the flare extends must be moved from the eye by the setting-screws at the back4 ,,chapter ,,xii4 ,,the ,,modern ,,telescope4 ,the gain to astronomy from the discovery of the telescope has been twofold4 ,we have first1 the gain to physical astronomy from the magnification of objects1 and secondly1 the gain to astronomy of position from the magnification1 so to speak1 of space1 which enables minute portions of it to be most accurately quantified4 ,looking back1 nothing is more curious in the history of astronomy than the rooted objection which ,hevel and others showed to apply the telescope to the pointers and pinnules of the instruments used in their day2 but doubtless we must look for the explanation of this not only in the accuracy to which observers had attained by the old method1 but in the rude nature of the telescope itself in the early times1 before the introduction of the micrometer4 ,we shall show in a future chapter how the modern accuracy has step by step been arrived at2 in the present one we have to see what the telescope does for us in the domain of that grand physical astronomy which deals with the number and appearances of the various bodies which people space4 ,let us1 to begin with1 try to see how the telescope helps us in the matter of observations of the sun4 ,the sun is about ninety millions of miles away2 suppose1 therefore1 by means of a telescope reflecting or refracting1 whichever we like1 we use an eyepiece which will magnify say #ijj times1 we obviously bring the sun within #ajj1jjj miles of us2 that is to say1 by means of this telescope we can observe the sun with the naked eye as if it were within #ajj1jjj miles of us4 ,one may say1 this is something1 but not much2 it is only about half as far as the moon is from us4 ,but when we recollect the enormous size of the sun1 and that if the centre of the sun occupied the centre of our earth the circumference of the sun would extend considerably beyond the orbit of the moon1 then one must acknowledge we have done something to bring the sun within half the distance of the moon4 ,suppose for looking at the moon we use on a telescope a power of #a1jjj1 that is a power which magnifies a thousand times1 we shall bring the moon within #bdj miles of us1 and we shall be able to see the moon with a telescope of that magnifying power pretty much as if the moon were situated somewhere in ,lancashire--,lancaster being about #bdj miles from ,london4 ,it might appear at first sight possible in the case of all bodies to magnify the image formed by the object-glass to an unlimited extent by using a sufficiently powerful eyepiece4 ,this1 however1 is not the case1 for as an object is magnified it is spread over a larger portion of the retina than before2 the brightness1 therefore1 becomes diminished as the area increases1 and this takes place at a rate equal to the square of the increase in diameter4 ,if1 therefore1 we require an object to be largely magnified we must produce an image sufficiently bright to bear such magnification2 this means that we must use an object-glass or speculum of large diameter4 ,again1 in observing a very faint object1 such as a nebula or comet1 we cannot1 by decreasing the power of the eyepiece1 increase the brightness to an unlimited extent1 for as the power decreases1 the focal length of the eyepiece also increases1 and the eyepiece has to be larger1 the emergent pencil is then larger than the pupil of the eye1 and consequently a portion of the rays of the cone from each point of the object is wasted4 ,illustration3 ,,fig4 #gi4--;,a portion of the constellation ,gemini seen with the naked eye4 ,we get an immense gain to physical astronomy by the revelations of the fainter objects which1 without the telescope1 would have remained invisible to us2 but1 as we know1 as each large telescope has exceeded preceding ones in illuminating power1 the former bounds of the visible creation have been gradually extended1 though even now we cannot be said to have got beyond certain small limits1 for there are others beyond the region which the most powerful telescope reveals to us2 though we have got only into the surface we have increased the #c1jjj or #f1jjj stars visible to the naked eye to something like twenty millions4 ,this space-penetrating power of the telescope1 as it is called1 depends on the principle that whenever the image formed on the retina is less than sufficient to appear of an appreciable size the light is apparently spread out by a purely physiological action until the image1 say of a star1 appears of an appreciable diameter1 and the effect on the retina of such small points of light is simply proportionate to the amount of light received1 whether the eye be assisted by the telescope or not2 the stars always1 except when sufficiently bright to form diffraction rings1 appearing of the same size4 ,it1 therefore1 happens that as the apertures of telescopes increase1 and with them the amount of light1 7the eyepieces being sufficiently powerful to cause all the light to enter the eye17 smaller and smaller stars become visible1 while the larger stars appear to get brighter and brighter without increasing in size1 the image of the brightest star with the highest power1 if we neglect rays and diffraction rings1 being really much smaller than the apparent size due to physiological effects1 and of this latter size every star must appear4 ,illustration3 ,,fig4 #hj4--,the same region1 as seen through a large telescope4 ,the accompanying woodcuts of a region in the constellation of ,gemini as seen with the naked eye and with a powerful telescope will give a better idea than mere language can do of the effect of this so-called space-penetrating power4 ,illustration3 ,,fig4 #ha4--,orion and the neighbouring constellations4 ,with nebul and comets matters are different1 for these1 even with small telescopes and low powers1 often occupy an appreciable space on the retina4 ,on increasing the aperture we must also increase the power of the eyepiece1 in order that the more divergent cones of light from each point of the image shall enter the pupil1 and therefore increase the area on the retina1 over which the increased amount of light1 due to greater aperture1 is spread2 the brightness therefore is not increased1 unless indeed we were at the first using an unnecessary high power4 ,on the other hand1 if we lengthen the focus of the object-glass1 and increase its aperture1 the divergence of the cones of light is not increased and the eyepiece need not be altered1 but the image at the focus of the object-glass is increased in size by the increase of focal length1 and the image on the retina also increases as in the last case4 ,we may1 therefore conclude that no comet or nebula of appreciable diameter1 as seen through a telescope having an eyepiece of just such a focal length as to admit all the rays to the eye1 can be made brighter by any increase of power1 although it may easily be made to appear larger4 ,illustration3 ,,fig4 #hb4--,nebula of ,orion4 ,very beautiful drawings of the nebula of ,orion and of other nebul1 as seen by ,lord ,rosse in his six-foot reflector1 and by the ,american astronomers with their twenty-six inch refractor1 have been given to the world4 ,the magnificent nebula of ,orion is scarcely visible to the naked eye2 one can just see it glimmering on a fine night2 but when a powerful telescope is used1 it is by far the most glorious object of its class in the ,northern hemisphere1 and surpassed only by that surrounding the variable star ,args in the ,southern4 ,and although1 of course1 the beauty and vastness of this stupendous and remote object increase with the increased power of the instrument brought to bear upon it1 a large aperture is not needed to render it a most impressive and awe-inspiring object to the beholder4 ,in an ordinary #e-;foot achromatic1 many of its details are to be seen under favourable atmospheric conditions4 ,those who are desirous of studying its appearance1 as seen in the most powerful telescopes1 are referred to the plate in ,sir ,john ,herschel's 8,results of ,astronomical ,observations at the ,cape of ,good ,hope10 in which all its features are admirably delineated1 and the positions of #aej stars which surround in the area occupied by the ,nebula1 laid down4 ,in ,fig4 #hb it is represented in great detail1 as seen with the included small stars1 all of which have been mapped with reference to their positions and brightness4 ,this then comes from that power of the telescope which simply makes it a sort of large eye4 ,we may measure the illuminating power of the telescope by a reference to the size of our own eye4 ,if one takes the pupil of an ordinary eye to be something like the fifth of an inch in diameter1 which in some cases is an extreme estimate1 we shall find that its area would be roughly about one-thirtieth part of an inch4 ,if we take ,lord ,rosse's speculum of six feet in diameter the area will be something like #d1jjj inches3 and if we multiply the two together we shall find1 if we lose no light1 we should get #abj1jjj times more light from ,lord ,rosse's telescope than we do from our unaided eye1 everything supposed perfect4 ,let us consider for a moment what this means2 let us take a case in point4 ,suppose that owing to imperfections in reflection and other matters two-thirds of the light is lost so that the eye receives #dj1jjj times the amount given by the unaided vision1 then a sixth magnitude star--a star just visible to the naked eye--would have #dj1jjj times more light1 and it might be removed to a distance #bjj times as great as it at present is and still be visible in the field of the telescope1 just as it at present is to the unaided eye4 ,can we judge how far off the stars are that are only just visible with ,lord ,rosse's instrument8 ,light travels at the rate of #ahe1jjj miles a second1 and from the nearest star it takes some #c years for light to reach us1 and we shall be within bounds when we say that it will take light #cjj years to reach us from many a sixth magnitude star4 ,but we may remove this star #bjj times further away and yet see it with the telescope1 so that we can probably see stars so far off that light takes #fj1jjj years to reach us1 and when we gaze at the heavens at night we are viewing the stars not as they are at that moment1 but as they were years or even hundreds of years ago1 and when we call to our assistance the telescope the years become thousands and tens of thousands--expressed in miles these distances become too great for the imagination to grasp2 yet we actually look into this vast abyss of space and see the laws of gravitation holding good there1 and calculate the orbit of one star about another4 ,whether the telescope be of the first or last order of excellence1 its light-grasping powers will be practically the same2 there is therefore a great distinction to be drawn between the illuminating and defining power4 ,the former1 as we have seen1 depends upon size 7and subsidiarily upon polish71 the latter depends upon the accuracy of the curvature of the surface4 ,illustration3 ,,fig4 #hc4--,saturn and his moons 7general view with a #c-;inch object-glass47 ,if the defining power be not good1 even if the air be perfect1 each increase of the magnifying power so brings out the defects of the image1 that at last no details at all are visible1 all outlines are blurred1 or stellar character is lost4 ,the testing of a glass therefore refers to two different qualities which it should possess4 ,its quality as to material and the fineness of its polish should be such that the maximum of light shall be transmitted4 ,its quality1 as to the curves1 should be such that the rays passing through every part of its area shall converge absolutely to the same point1 with a chromatic aberration not absolutely nil1 but sufficient to surround objects with a faint violet light4 ,illustration3 ,,fig4 #hd4--;,details of the ring of ,saturn observed by ,trouvelot with the #bf-;inch ,washington ,refractor4 ,in close double stars therefore1 or in the more minute markings of the sun1 moon1 or planets1 we have tests of its defining power2 and if this is equally good in the instruments examined1 the revelations of telescopes as they increase in power are of the most amazing kind4 ,a #c-;inch suffices to show ,saturn with all the detail shown in ,fig4 #hc1 while ,fig4 #hd shows us the further minute structure of the rings which comes out when the planet is observed with an aperture of #bf inches4 ,in the matter of double stars1 a telescope of #b inches aperture1 with powers varying from #fj to #ajj1 should show the following stars double3-- ,polaris4 ,piscium4 ,draconis4 ,arietis4 ,herculis4 ,urs ,majoris4 ,geminorum4 ,leonis4 ,cassiope4 ,a #d-;inch aperture1 powers #hj-abj1 reveals the duplicity of-- ,orionis4 ,hydr4 ,botis4 ,leonis4 ,lyr4 ,urs ,majoris4 ,ceti4 ,geminorum4 ,cassiope4 ,draconis4 ,a #f-;inch1 powers #bdj-cjj-- ,arietis4 #cb ,orionis4 ,ophiuchi4 #bj ,draconis4 ,geminorum4 ,equulei4 ,herculis4 ,botis4 ,an #h-;inch-- ,cygni4 #b ,andromed4 ,sirius4 #ai ,draconis4 #b ,herculis4 #b ,botis4 ,the 8spurious disk10 which a fixed star presents1 as seen in the telescope1 is an effect which results from the passage of the light through the object-glass2 and it is this appearance which necessitates the use of the largest apertures in the observation of close double stars1 as the size of the star's disk varies1 roughly speaking1 in the inverse ratio of the aperture of the object-glass4 ,in our climate1 which is not so bad as some would make it1 a #f- to an #h-;inch glass is doubtless the size which will be found the most constantly useful2 a larger aperture being frequently not only useless1 but hurtful4 ,still1 #d or #c inches are apertures by all means to be encouraged2 and by object-glasses of these sizes1 made of course by the best makers1 views of the sun1 moon1 planets1 and double stars may be obtained1 sufficiently striking to set many seriously to work as amateur observers1 and with a prospect of securing good1 useful results4 ,observations should always be commenced with the lowest power1 gradually increasing it until the limit of the aperture1 or of the atmospheric condition at the time1 is reached4 ,the former may be taken as equal to the number of hundredths of inches which the diameter of the object-glass contains4 ,thus1 a #c-;inch object-glass1 if really good1 should bear a power of #cge on double stars where light is no object2 the planets1 the ,moon1 c41 will be best observed with a much lower power4 7,see chapter on eyepieces47 ,care should be taken that the object-glass is properly adjusted4 ,and we may here repeat that this may be done by observing the image of a large star out of focus4 ,if the light be not equally distributed over the image1 or the diffraction rings are not circular1 the screws of the cell should be carefully loosened1 and that part of the cell towards which the rings are thrown very gently tapped with wood1 to force it towards the eyepiece1 or the same purpose may be effected by means of the setscrews always present on large telescopes1 until perfectly equal illumination is arrived at4 ,this1 however1 should only be done in extreme cases2 it is here especially desirable that we should let well alone4 ,the convenient altitude at which ,orion culminates in these latitudes renders it particularly eligible for observation2 and during the first months of the year our readers who would test their telescopes will do well not to lose the opportunity of trying the progressively difficult tests1 both of illuminating and separating power1 afforded by its various double and multiple systems1 which are collected together in such a circumscribed region of the heavens that no extensive movement of their instruments--an important point in extreme cases--will be necessary4 ,beginning with 1 the upper of the three stars which form the belt1 the two components will be visible in almost any instrument which may be used for seeing them1 being of the second and seventh magnitudes1 and well separated4 ,the companion to 1 though of the same magnitude as that to 1 is much more difficult to observe1 in consequence of its proximity to its bright primary1 a first-magnitude star4 ,quaint old ,kitchener1 in his work on telescopes1 mentions that the companion to ,rigel has been seen with an object-glass of #b-;inch aperture2 it should be seen1 at all events1 with a #c-;inch4 1 the bottom star in the belt1 is a capital test both of the dividing and space-penetrating power1 as the two bright stars of the second and sixth magnitudes1 of which the close double is composed1 are exactly #b apart1 while there is a companion to one of these components of the twelfth magnitude about distant4 ,the small star below1 which the late ,admiral ,smyth1 in his charming book1 8,the ,celestial ,cycle10 mentions as a test for his object-glass of #ei inches in diameter1 is now plainly to be seen in a #c4 ,the colours of this pair have been variously stated2 ,struve dubbing the sixth magnitude--which1 by the way1 was missed altogether by ,sir ,john ,herschel--8olivaceasubrubicunda40 ,that either our modern opticians contrive to admit more light by means of a superior polish imparted to the surfaces of the object-glass1 or that the stars themselves are becoming brighter1 is again evidenced by the point of light preceding one of the brightest stars in the system composing 4 ,this little twinkler is now always to be seen in a #c-;inch1 while the same authority we have before quoted--,admiral ,smyth--speaks of it as being of very difficult vision in his instrument of much larger dimensions4 ,in this very beautiful compound system there are no less than seven principal stars2 and there are several other faint ones in the field4 ,the upper very faint companion of is a delicate test for a #c-;inch1 which aperture1 however1 will readily divide the closer double of the principal stars which are about #e apart4 ,these objects1 with the exception of 1 have been given more to test the space-penetrating than the dividing power2 the telescope's action on #eb ,orionis will at once decide this latter quality4 ,this star1 just visible to the naked eye on a fine night1 to the right of a line joining and 1 is a very close double4 ,the components1 of the sixth magnitude1 are separated by less than two seconds of arc1 and the glass which shows a good wide black division between them1 free from all stray light1 the spurious disk being perfectly round1 and not too large1 is by no means to be despised4 ,then1 again1 we have a capital test object in the great nebula to which reference has already been made4 ,the star1 to which we wish to call especial attention1 is situate 7see ,fig4 #hb7 opposite the bottom of the 8fauces10 the name given to the indentation which gives rise to the appearance of the 8fish's mouth40 ,this object1 which has been designated the 8trapezium10 from the figure formed by its principal components1 consists1 in fact1 of six stars1 the fifth and sixth 7 and 7 being excessively faint4 ,our previous remark1 relative to the increased brightness of the stars1 applies here with great force2 for the fifth escaped the gaze of the elder ,herschel1 armed with his powerful instruments1 and was not discovered till #ahbf1 by ,struve1 who1 in his turn1 missed the sixth star1 which1 as well as the fifth1 has been seen in modern achromatics of such small size as to make all comparison with the giant telescopes used by these astronomers ridiculous4 ,sir ,john ,herschel has rated and of the twelfth and fourteenth magnitudes--the latter requires a high power to observe it1 by reason of its proximity to 4 ,both these stars have been seen in an ordinary #e-;foot achromatic1 by ,cooke1 of #c-;inches aperture1 a fact speaking volumes for the perfection of surface and polish attained by our modern opticians4 ,let us now try to form some idea of the perfection of the modern object-glass4 ,we will take a telescope of eight inches aperture1 and ten feet focal length4 ,suppose we observe a close double star1 such as ,urs1 then the images of these two stars will be brought to a focus side by side1 as we have previously explained1 and the distance by which they will be separated will be dependent on the focal length of the object-glass4 ,if we refer once again to ,fig4 #ci we shall see that this distance depends on the focal length and on the angle subtended by the images of the stars at the object-glass1 which is of course the same as the angle made by the real stars at the object-glass1 which is called their angular distance1 or simply their distance1 and is expressed in seconds of arc4 ,if we take a telescope ten feet long and look at two stars #a apart1 the angle will be #a2 and at ten feet off the distance between the two images will be something like #b inches1 and therefore1 if the angle be a second1 the lines will be the #a_/cfjjth part of that1 or about #a_/agjjth part of an inch apart1 so that in order to be able to see the double star ,urs1 which is a #a star1 by means of an eight-inch object-glass1 all the surfaces1 the #ej square inches of surface1 of both sides of the crown1 and both sides of the flint glass1 must be so absolutely true and accurate1 that after the light is seized by the object-glass1 we must have those two stars absolutely perfectly distinct at the distance of the seventeen hundredth part of an inch1 and in order to see stars apart1 their images must be distinct at one-half of this distance or at #a_/cdjjth part of an inch from each other4 ,we know that both with object-glasses and reflectors a certain amount of light is lost by imperfect reflection in the one case1 and by reflection from the surfaces and absorption in the other2 and in reflectors we have generally two reflections instead of one4 ,this loss is to the distinct disadvantage of the reflector1 and it has been stated by authorities on the subject1 that1 light for light1 if we use a reflector1 we must make the aperture twice as large as that of a refractor in order to make up for the loss of light due to reflection4 ,but ,dr4 ,robinson thinks that this is an extreme estimate2 and with reference to the four-foot reflector which has recently been constructed1 and of which mention has already been made1 he considers that a refractor of #ccgc inches aperture would be probably something like its equivalent if the glass were perfectly transparent1 which is not the case1 and when the thickness of such a lens came to be considered1 it was calculated that instead of its being equal to the four-foot reflector1 it would only be equal to one of #cg of similar construction1 and that even a refractor of #dh inches aperture1 if such could be made1 would not come up to the same sized reflector just referred to in illuminating power4 ,on the assumption1 therefore1 that no light is lost in transmission through the object-glass1 ,dr4 ,robinson estimates that the apertures of a refractor and a reflector of the ,newtonian construction must bear the relation to each other of #a to #adb4 ,in small refractors the light absorbed by the glass is small1 and therefore this ratio holds approximately good1 but we see from the example just quoted how more nearly equal the ratio becomes on an increase of aperture1 until at a certain limit the refractor1 aperture for aperture1 is surpassed by its rival1 supposing ,dr4 ,robertson's estimate to be correct4 ,but with specula of silvered glass the reflective power is much higher than that of speculum metal2 the silvered glass1 being estimated to reflect about #ij per cent4#h of the incident light1 while speculum metal is estimated to reflect about #fc per cent42 but be these figures correct or not1 the silvered surface has undoubtedly the greater reflective power2 and1 according to ,sir ,j4 ,herschel1 a reflector of the ,newtonian construction utilizes about seven-eighths of the light that a refractor would do4 ,speaking generally1 refractors of sizes usually obtainable are preferable to reflectors of equal and even greater aperture for ordinary work2 as in addition to the want of illuminating power of reflectors1 the absence of rigidity of the mounting of the speculum militates against its comfort of manipulation4 ,in treating of the question of the future of the telescope1 we are liable to encroach on the domain of opinion and go beyond the facts vouched for by evidence1 but there are certain guiding principles which are well worthy of discussion4 ,there are the two classes of telescopes1 the refractors and reflectors1 each possessing advantages over the other4 ,we may set out with observing that the light-grasping power of the reflector varies as the square of the aperture multiplied by a certain fraction representing the proportion of the amount of reflected light to that of the total incident rays4 ,on the other hand1 the power of the refractor varies as the square of the aperture multiplied by a certain fraction representing the proportion of transmitted light to that of the total incident rays4 ,now in the case of the reflector the reflecting power of each unit of surface is constant whatever be the size of the mirror1 but in that of the refractor the transmitting power decreases with the thickness of the glass1 rendered requisite by increased size1 although for small apertures the transmitting power of the refractor is greater than the reflecting power of the reflector2 still it is obvious that on increasing the size a stage must be at last reached when the two rivals become equal to each other4 ,this limit has been estimated by ,dr4 ,robinson to be #cedce inches1 a size not yet reached by our opticians by some #aj inches1 but object-glasses are increasing inch by inch1 and it would be rash to say that this size cannot be reached within perhaps the lifetime of our present workers1 but up to the present limit of size produced1 refractors have the advantage in light-grasping power4 ,the next point worthy of attention is the question of permanence of optical qualities4 ,here the refractor undoubtedly has the advantage4 ,it is true that the flint glass of some objectives gets attacked by a sort of tarnish1 still1 that is not the case generally1 while1 on the other hand1 metallic mirrors often become considerably tarnished after a few years of use1 and although repolishing is not a matter of any great difficulty in the hands of the maker1 still it is a serious drawback to be obliged to return mirrors every few years to be repolished4 ,there are1 however1 some exceptions to this1 for there are many small mirrors in existence whose polish is good after many years of continuous use1 just as on the other hand there are many object-glasses whose polish has suffered in a few years1 but these are exceptions to the rule4 ,the same remarks apply to the silvered glass reflectors1 for although the silvering of small mirrors is not a difficult process1 the matter becomes exceedingly difficult with large surfaces1 and indeed at present large discs of glass1 say of four or six feet diameter1 cannot be produced4 ,if1 however1 a process should be discovered of manufacturing these discs satisfactorily and of silvering them1 there are objections to them on the grounds of the bad conductivity of glass1 whereby changes of temperature alter the curvature to a fatal extent1 and there is also a great tendency for dew to be deposited on the surface4 ,the next point to be considered is the general suitability for observatory work1 and this depends upon the quality of the work required1 whether for measuring positions1 as in the case of the transit instrument1 where permanency of mounting is of great importance1 or for physical astronomy1 when a steady image for a time is only required4 ,for the first purpose the refractor has decidedly the advantage1 as the object-glass can be fixed very nearly immovably in its cell1 whereas its rival must of necessity1 at least with present appliances1 have a small1 yet in comparison considerable1 motion4 ,again1 the refractor has the advantage over the other in not being of so large aperture when of equal power1 so that the disturbing effects of air currents is considerably less1 but the method of making the tubes of open lattice-work materially reduces this objection4 ,we have mentioned the difficulty of mounting mirrors1 especially of large size1 but this has now been got over very perfectly4 ,this difficulty does not occur in the mounting of object-glasses of sizes at present in use1 but when we come to deal with lenses of some #cj inches diameter1 the present simple method will in all probability be found insufficient4 ,on the other hand the cost of mirrors is of course much less than that of object-glasses1 a matter of considerable importance4 ,the late ,m4 ,merz1 on being asked as to price of a #cj-;inch object-glass1 estimated that1 if it were possible to make it1 its cost would be between #h1ejj and #i1jjj4 ,there is one great point of advantage in the use of the reflector in physical work1--the absence of secondary spectrum2 but it is by no means certain that stellar photography will not be more easy with refractors4 ----- ,footnote #h3 ,sir ,john ,herschel1 in his work on the telescope1 gives the following table of reflective powers3-- ,after transmission through one surface of glass not in contact #jieg with any other surface ,after transmission through one common surface of two glasses #ajjj cemented together ,after reflection on polished speculum metal at a perpendicular #jfcb incidence ,after reflection on polished speculum metal at #de obliquity #jfij ,after reflection on pure polished silver at a perpendicular #jije incidence ,after reflection on pure polished silver at #de obliquity #jiaj ,after reflection on glass 7external7 at a perpendicular #jjdc incidence ,the effective light in reflectors 7irrespective of the eyepieces7 is as follows3-- ,herschelian 7,lord ,rosse's speculum metal7 ,a4 #jfcb ,newtonian 7both mirrors ditto7 ,b4 #jdcf ,newtonian 7small mirror or glass prism7 ,c4 #jfcb ,gregorian or ,cassegrainian ,d4 #jcii ,a4 #jije ,the same telescopes1 all the metallic ,b4 #jhbd reflections being from pure silver ,c4 #jije ,d4 #jhai ,,book ,,iii4 ,,time ,,and ,,space ,,measurers4 ,,chapter ,,xiii4 ,,the ,,clock ,,and ,,chronometer4 ,i4 ,,the ,,rise ,,and ,,progress ,,of ,,time-,,keeping4 ,when we dealt with the astronomical instruments of ,hipparchus1 we saw that although the astrolabe which that great observer used was the germ of our modern instruments1 the time recorded by ,hipparchus and those who lived after him down to the later times of the ,roman ,empire was1 as they measured it1 a time which would be entirely useless for us4 ,the ancients contented themselves with dividing the interval between sunrise and sunset1 regardless whether this was in summer or winter1 into twelve equal hours4 ,now1 as in summer the sun is longer above the horizon than in winter in these northern latitudes1 we have more time during which the sun is above the horizon in summer than in winter1 and if that period of time is to be divided into twelve hours1 the hours would be much longer in summer than in other seasons4 ,as we are informed by ,herodotus1 tables were made by which these varying lengths of hours might be indicated by the shadows of a pole1 which they called a gnomon or style4 ,this was placed in a given locality1 and the hour of the day was determined by the position of the shadow of the gnomon2 and we need scarcely say that as ,hipparchus observed he was compelled to find the position of the sun in order to determine the absolute longitude of a star at night4 ,the ancients were limited to such ideas of time as could be got from slaves1 who watched the risings and settings of the constellations1 and who tried to bring to their own minds and those of their masters some idea of the lapse of time2 and this even a few centuries ago was ordinarily depended upon in several countries4 ,then1 a little later1 we come to the time being measured by monks repeating psalms--a certain number perhaps in the hour2 and there were the water and sand clocks dating from ,aristophanes1 which were the predecessors of our sand-glasses4 ,candles were also at one time used with divisions on them to show how long they had been burning4 ,but when we come to clocks proper1 the history of which is very imperfectly known1 we find an enormous improvement upon this state of things2 because the clock1 being dependent upon a constant mechanical action produced by the fall of a weight1 could not be got to imitate these varying hours4 ,still the clock had to fight its own battle for all that2 and the first clocks were altered from week to week1 or from month to month1 so that the time-keeper1 which did its best to be constant1 was made inconstant to represent the ever-varying hours4 ,doubtless the history of the first clocks--by which we do not mean the sand clocks or water clocks of the ancients1 but such as those used by ,archimedes when he attached wheels together--is lost in obscurity2 and whether clocks1 as we have them1 were suggested in the sixth 7,boethius1 ,a4,d4 #ebe7 or ninth century matters little for our inquiry2 but beyond all doubt the first clock of considerable importance that was put up in ,england was the one erected in ,old ,palace ,yard in the year #abhh1 as the result of a fine imposed upon the ,lord ,chief ,justice of that time4 ,illustration3 ,,fig4 #he4--;,ancient ,clock ,escapement4 ,if we have a falling weight as a time-measurer we must also have some opposing force--a regulator in fact1 so that the weight becomes the source of power1 and the regulator the time-measurer2 therefore1 in addition to the fall of the weight1 we find in the earliest clocks a regulating power to prevent the weight falling too fast4 ,so we have the two contending powers1 first the weight causing the motion and then the regulator4 ,the first thing which was introduced as a regulator was a fly-wheel4 ,there was a fly-wheel of a certain weight1 and the force which was applied to the clock had to turn the wheel against the resistance of the air2 but that did not answer well1 and the first tolerable arrangement was suggested by ,henry de ,wyck1 who constructed a bell and a clock in #acfd1 in which the fall of the weight was prevented by an oscillating balance1 similar to that shown in ,fig4 #he4 ,illustration3 ,,fig4 #hf4--,the ,crown ,wheel4 ,here we see what is called the crown wheel 7,s ,s1 shown in plan1 ,fig4 #hf71 on which the escapement depends1 and into the teeth of which work two pallets1 ,p#a ,p#b1 which are placed on a vertical axis pivoted above and below4 ,now if we suppose a weight attached to the cord passing over a drum1 so as to propel the intermediate wheels and pull them round1 the crown wheel tends to rotate1 but is prevented from moving until the pallets give way4 ,let us see how the clock goes4 ,when the bottom tooth1 presses against the pallet ,p#a1 in order to make it get out of the way and enable the wheel to go on1 it twists the rod and moves the horizontal bar ,m ,m1 on which are several saw-like teeth1 on the intervals of which1 as in the modern steelyard1 weights are placed1 so that the wheel pushes away the pallet and makes the horizontal beam describe a part of a circle4 ,and what happens is this3--the upper pallet is turned out of its position and driven into the upper teeth of the wheel1 and driven out by the further revolution of the wheel1 so that the fall of the weight depends on the oscillations of the horizontal beam which carries the weights4 ,the clock was regulated by the distance of the weights from the pivots on which the balance swung4 ,such was the form of clock used by ,tycho ,brahe1 but with little success1 for it was extremely irregular in its action1 and ,tycho still had to compare the position of one star with another instead of trusting to his clock4 ,there is no necessity to say much regarding the train of wheels between the weight or spring and the escapement4 ,their office is simply to create a great difference in velocity of rotation between the wheel turned by the weight or spring and the escape wheel1 so that a slow motion with great force may be transformed into a quick motion with small force4 ,the train of wheels is so arranged1 by the consideration of the number of teeth in the wheels1 that one wheel shall go round once an hour1 and another once a minute1 so that the first may carry the minute-hand and the other the second-hand4 ,the hour-hand wheel is also geared to the minute-wheel1 so that it shall turn once in twelve hours or twenty-four hours1 according to the purposes for which the clock is required4 ,weights are usually used when space is no object1 being more regular in their action than springs2 but the latter are used for chronometers and watches1 and other portable time-keepers4 ,the general arrangement of the clock train is shown in ,fig4 #hg1 where ,w is the weight1 hung by a cord passing over the barrel ,b1 on the axis of wheel ,g4 ,the teeth of the wheel ,g gear into the pinion ,p#a1 which again is carried on the axis of the wheel ,c1 and so on up the last wheel--the escape-wheel1 which generally is cut to thirty teeth1 so that it goes round once a minute and carries a second-hand4 ,the pinion ,p#a is so arranged by the number of teeth between it and the escape-wheel that it goes round once an hour or to sixty turns of the escape-wheel4 ,illustration3 ,,fig4 #hg4--,the ,clock ,train4 ,illustration3 ,,fig4 #hh4--,winding ,arrangements4 ,to wind up the clock the barrel ,b1 ,fig4 #hh1 is turned round by the key on the square2 the pawl ,l fastened to the wheel ,g allows the barrel to be turned in one direction without turning the wheel4 ,it is obvious1 however that directly we begin to wind up1 the pressure on the pawl tending to turn the wheel ,g is removed1 and the clock stops--a very objectionable thing in astronomical and other clocks supposed to keep good time4 ,the following is one of the devices for keeping the clock going during winding1--in this case everything is the same as before1 with the exception of an additional rachet-wheel ,r#b1 ,fig4 #hh1 carrying the pawl ,l2 this wheel is loose on the axis but attached to the wheel ,g through the spring ,s4 ,the weight therefore acts on the pawl ,l1 and tends to drive the wheel ,r#b1 which again presses round the wheel ,g by means of the spring ,s1 and1 as the whole moves round1 the teeth of the wheel ,r#b pass the pawl ,k ,k fixed to some part of the clock-frame4 ,when now we commence to wind1 the pressure on the pawl ,l and wheel ,r#b is removed1 and the spring ,s ,s1 which is always kept bent by the action of the weight1 endeavours to open2 and since the wheel ,r#b is prevented from going backwards by the pawl ,k1 the wheel ,g is continually urged onwards by the spring1 and the clock kept going for the short period of winding4 ,,ii4 ,,the ,,pendulum4 ,the clock1 as left by ,henry de ,wyck1 was only an exceedingly irregular time-keeper1 and some mechanical contrivance that should beat or mark correct intervals of time was urgently required4 ,the contrivance for beating correct intervals of time--the pendulum--was thought of by ,galileo1 who showed that its oscillations were isochronous1 although their lengths might vary within small limits4 ,the pendulum then was just the very thing required1 and ,huyghens1 in #afeh1 applied it to clocks4 ,in the next form of clock1 therefore1 we find the pendulum introduced as a regulator4 ,there was a crown wheel like the one in the balance clock1 only instead of being vertical it was horizontal4 ,this wheel was allowed to go round and the weight was allowed to fall by means of alternating pallets2 it was in fact like that shown in ,fig4 #hf1 with the balance weights and the rod carrying them removed1 and instead thereof there was a rod1 attached at right angles to the end of that carrying the pallets1 and hanging downwards1 which1 by means of a fork at its lower end1 swung a pendulum to an extent equal to the go of the balance first used4 ,thus the pendulum was adapted by ,huyghens4 ,we have here something extremely different from the rough arrangement in which the weight was controlled by the horizontal oscillating bar carrying the weights1 for the balance would go faster or slower as the crown wheel pressed harder or softer against the pallets1 and so1 if the weight acted at all irregularly the clock would go badly4 ,but with the pendulum the control of the weight over it is small1 for the bob can be made of considerable weight1 because it swings from its suspending spring without friction1 and such a heavy weight at the end of a long rod is scarcely altered in its rate by variations of pressure on the pallets4 ,galileo and ,huyghens who followed him found that the oscillations of a simple pendulum are isochronous at all places where the force of gravity is equal1 and that the time of oscillation depends on the length of the pendulum--the shorter the pendulum the shorter time of oscillation1 and vice vers4 ,the time of oscillation varying as the square root of the length4 ,in #afeh1 then1 the pendulum was applied to clocks1 as the balance had been before that time4 ,but ,huyghens was not slow to perceive that the circular arc of a rigid pendulum would not be sufficiently accurate for an astronomical time-keeper1 when used with a clock like that employed by ,tycho ,brahe and the ,landgrave of ,hesse for their astronomical observations4 ,huyghens next showed that with a clock of that kind1 requiring a large swing of pendulum1 the oscillations were not quite isochronous1 but varied in time according as the arc increased or diminished4 ,it was clear therefore that this simple form of pendulum would not do well for the large and varying arc required to be described1 but that the theoretical requirements would be satisfied if the pendulum1 instead of being suspended from a rigid rod1 were suspended by a cord or spring or some elastic substance which would mould itself against two curved pieces of metal1 ,c ,c1 ,fig4 #hi1 attached one on either side of the suspending spring4 ,in swinging1 the spring would wrap1 as it were1 gradually round either curved surface1 and so virtually alter the point of suspension1 and with it1 of course1 the virtual length of the pendulum2 so that the extreme point of the pendulum ,u1 instead of describing a circular arc ,k ,b as before1 would1 by means of the portions of metal at the top1 have a cycloidal motion ,d ,l1 the pendulum becoming virtually shorter as the spring wrapped round the pieces of metal1 so that it becomes isochronous for any length of swing4 ,but it was very soon found that the theoretically perfect clock did not after all go as well as the clock it was to replace4 ,and it would now be difficult to say what would have happened if a few years afterwards clocks had not been made much more simple and perfect by the introduction of an entirely new escapement which permitted a very small swing4 ,illustration3 ,,fig4 #hi4--,the ,cycloidal ,pendulum4 ,if we wish a clock to go perfectly well1 we have only to consider a very few things--,first1 the weight should be as small as possible2 secondly1 within reason1 the pendulum should be as solidly suspended and as heavy as possible2 and1 thirdly1 the less connection there is between the pendulum which controls the clock1 and the weight which drives the clock1 the better4 ,the latter point is provided for in the dead beat arrangement of ,graham1 and in the 8gravity0 and other forms of escapement1 about which more presently4 ,at present we have been dealing with pendulums as if they were simple pendulums1 which are almost mathematical abstractions4 ,everything that we have said assumes that there is a mass depending from such a fine line that the mass of the line shall not be considered2 but if we examine the pendulum of some clocks we see that the rod is of steel1 and that its weight or bob is elongated1 and consists of a long cylinder of glass filled with mercury1 and carried in a sort of stirrup of steel2 this is very different from our simple pendulum--it is a compound pendulum4 ,in a compound pendulum we have first of all the axis of suspension1 which is the axis where the pendulum is supported on the top1 and below that1 near the centre of gravity of the pendulum1 we have what is called the centre of oscillation4 ,it will at once be perceived that as the rate of the pendulum depends upon its length1 the particles in the upper part of the pendulum will be trying to go more rapidly than they can go1 seeing that they are connected in one series of particles1 and that the particles at the lowest portion are carried with greater velocity than they would be if they were left to themselves1 because they are connected rigidly with the upper ones4 ,therefore we have to find a point1 which oscillates at the same rate as it would if all the other particles were absent4 ,this is called the centre of oscillation1 and it is on the distance of this from the point of suspension that the rate depends4 ,what is the use of the mercury8 ,it is to compensate for the expansion of the rod by temperature4 ,we shall at once see the reason of this from the fact that the pendulum gets longer by being heated1 and the rate of the pendulum depends on the square root of its length2 that is1 if we multiply the length by four1 the square root of which is two1 we shall only multiply the rate by two1 or double the time of oscillation4 ,therefore1 since temperature causes all metals to vary in length1 and metals are the most useful things we can employ for the support of the weights1 we find that we have to consider further the alteration of the length of the pendulum due to the variation of the length of the metal we employ4 ,hence1 in addition to the necessity of an arrangement which gives the shortest possible swing1 we require also a method for compensating for changes of temperature4 ,illustration3 ,,fig4 #ij4--;,graham's1 ,harrison's1 and ,greenwich ,pendulums4 ,we have not space to go through the history of compensating pendulums1 but we may direct attention to some of the best results which have been obtained in this matter4 ,we will first examine the mercurial pendulum1 ,fig4 #ij1 which we have referred to4 ,in this case the compensation is accomplished as follows3 ,mercury is inclosed in a glass cylinder ,m ,m2 shown in the left hand side of the figure2 and as the mercury expands more than the glass1 it will rise to a higher level on being heated2 and the lengthening of the steel rod ,r ,r will be counteracted by a similar lengthening due to the expansion of mercury1 so that the centre of oscillation is carried down by the steel rod1 and up by the mercury1 and it is therefore not displaced if the proper ratio is maintained between the length of the steel rod and the column of mercury in the glass vessel4 ,the mercury in the glass will lengthen fifteen times as much as the steel rod1 if we have equal lengths of each1 so that in order that they may expand equally the rod must be fifteen times as long as the mercury column4 ,this would keep the top of the mercury at the same distance from the point of suspension1 but we want to keep the centre of oscillation1 which is about half way down the column1 at the same distance1 so we double the height of the mercury1 making it two-fifteenths of the length of the steel rod1 so that the surface is over-compensated1 but the centre of oscillation is exactly corrected4 ,an astronomer can alter the amount of mercury as he pleases1 making it now more1 now less1 till the stars tell him he has done the right thing1 and the pendulum is compensated1 and the clock keeps correct time at all temperatures4 ,the little sliding cup ,c is to carry small weights for final delicate adjustment1 the addition of a weight thus obviously tending to increase the rate of the pendulum4 ,this is ,graham's mercurial pendulum1 invented by him in #agae4 ,there is another compensating pendulum1 called ,harrison's gridiron pendulum1 from the bars of metal sustaining the pendulum being arranged gridiron fashion1 ,fig4 #ij4 ,at the top is a knife edge or spring for the centre of suspension1 and the pendulum bob is suspended by a system of rods1 the five black ones being made of a less expansible metal than the other four2 consequently1 as the five black ones expand and tend to lower the bob1 the intermediate ones expand also and tend to raise it2 the length of the black rods exceeding that of the others1 these latter must be made of a more expansible metal to make up for their smaller length4 ,thus the acting length of the shaded rods is two-thirds of the acting length of the black ones 7each pair is considered as one rod because they act as such71 so that a metal is used for the former which expands more than that used for the latter in the proportion of about three to two1 and brass is found to answer for the most expansible metal1 and steel for the less4 ,these rods are packed side by side1 and look very ornamental4 ,if l be the length of the brass rods1 and l that of the steel rods1 and e the coefficient of expansion of the brass1 and e that of the steel1 then l3 l33 e3 e4 ,the pendulum is then compensated1 and the bob remains at the same distance from the centre of suspension at all temperatures4 ,for the pendulum of the clock at the ,royal ,observatory a modification of the gridiron form has been adopted2 for it was found on trial with a mercurial pendulum that the steel rod gained in temperature more rapidly than the mercury1 and lost heat quicker1 so that the pendulum did not compensate immediately on a change of temperature4 ,the form adopted is as follows 7,fig4 #ij73--;,a steel rod is suspended as usual1 and is encircled by a zinc tube resting on the nut for rating the pendulum2 the zinc tube is again encircled by a steel tube resting on the top of the zinc tube and carrying at its lower end a cylindrical leaden bob attached at its centre to the steel tube2 slots and holes are cut in the tubes to expose the inner parts to the air1 so that each will experience the change of temperature at the same time4 ,it is of course possible that the tubes forming the pendulum rod are not of exactly the right length to perfectly compensate2 a final delicate adjustment is therefore added4 ,on the crutch axis1 and held by a collar to it1 are two compound bars of brass and steel1 h and i1 ,fig4 #if4 ,the collar fits loosely on the axis1 so that the rods1 which carry small weights at their extremities1 can be easily shifted to make any angle with the horizontal2 then1 since brass expands more than steel for the same degree of heat1 the bars will bend on being heated or cooled1 and if the brass be uppermost the weights at the ends of the rods will be lowered with an increase of temperature1 and will tend to increase the rate of the pendulum1 and vice vers4 ,so long as the rods are horizontal and in the same straight line their centre of gravity is in the crutch axis1 and they are therefore balanced in every position2 they therefore only retard the pendulum by their inertia2 but when the ends are bent down the centre of gravity is lowered1 and they have a tendency to come to a horizontal position and to balance each other like a scale beam1 and so swing with the pendulum and overcome its retardation4 ,it is obvious that they would1 if alone1 swing in a shorter time than the pendulum and so1 being connected1 they increase its rate4 ,when the rods are vertical they have no compensating action1 for the centre of gravity is simply thrown sidewise1 and acts as a continuous force tending to make the pendulum oscillate further on one side than on the other2 and in the intermediate positions of the rods their action varies1 and a consideration of the position of their centre of gravity will give the intensity of the compensating action4 ,in order to make a small change in the rate of the clock without stopping it to turn the screw at the bottom of the pendulum1 the following contrivance is adopted4 ,a weight k slides freely on the crutch rod1 but is tapped to receive the screw cut on the lower portion of the spindle l1 the upper end of which terminates in a nut m at the crutch axis4 ,by turning this nut the position of the small weight on the crutch rod is altered1 and the clock rate correspondingly changed4 ,to make the clock lose1 the weight must be raised4 ,there is also another method of compensation1 depending on differential expansion4 ,attached to an ordinary pendulum just above the bob1 and at right angles to it1 is a composite rod1 made of copper and iron1 the lower half being copper2 then1 as the pendulum rod lengthens and lets down the bob1 the copper expands more than the iron1 and causes the rod to bend1 like a piece of wood wetted on one side1 and by this bending or warping the weights at either end are raised as the bob is lowered1 so the centre of oscillation keeps at the same height at all temperatures4 ,we have dealt with clocks and pendulums somewhat in the order of their invention4 ,we may add that the great majority of clocks of modern manufacture of any pretention to time-keepers are constructed with the dead beat escapement of ,graham or a modification of it1 combined with a mercurial or gridiron pendulum4 ,for the best ,observatory clocks of the more expensive kind other more elaborate forms of escapement are sometimes used1 as1 for example1 that in the clock at the ,royal ,observatory1 ,greenwich1 which we shall refer to in detail further on1 on account of other new points in its construction4 ,now1 having a clock good enough to use with the transit instrument1 it is necessary to take the utmost precautions with reference to it4 ,the ,russian astronomers have inclosed their clock in a stone case1 and placed it many yards below the ground1 endeavouring thus to get rid of the action of temperature1 which changes the length of the steel pendulum rod4 ,but that is not all2 after we have corrected our clock as well as we can from the point of view of temperature1 it is still found that there may be a variation1 amounting to something considerable1 due to another cause4 ,if the barometer changes an inch or an inch and a half by change of pressure of the air1 the rate of the pendulum will alter1 and the cause of the variation it is impossible to prevent without putting the clock in a vacuum1 so that changes of the barometer must be allowed for4 ,there are1 however1 methods of compensating the pendulum for changes of pressure if desirable3 one way of doing this is to pass the suspending spring of the pendulum through a slit in a metal plate1 which then becomes virtually the point of suspension2 this plate is then raised or lowered by an aneroid barometer1 or by a float in an ordinary cistern barometer so that the length of the pendulum is virtually altered with the pressure of the atmosphere4 ,at ,greenwich the ,astronomer-,royal has adopted the following expedient3 ,a magnet at the lower end of the pendulum passes at each swing near a magnet which is raised or lowered by means of a float in the cistern of a barometer4 ,the magnet then has a greater or less influence on the pendulum magnet according as the pressure of the air varies1 and so adds a variable amount to the effect of gravity and therefore to the rate of oscillation4 ,illustration3 ,,fig4 #ia4--;,greenwich ,clock3 arrangement for ,compensation for ,barometric ,pressure4 ,this principle is carried out as follows3--,two bar magnets1 each about six inches long1 are fixed vertically to the bob of the clock pendulum2 one in front1 a1 ,fig4 #ia1 the other at the back4 ,the lower pole of the front magnet is a north pole2 the lower pole of the back magnet is a south pole4 ,below these a horse-shoe magnet1 b1 having its poles precisely under those of the pendulum magnets1 is carried transversely at the end of the lever c1 the extremity of the opposite arm of the lever being attached by the rod d1 to the float e in the lower leg of a syphon barometer4 ,the lever turns on knife edges4 ,a plan of the lever 7on a smaller scale7 is given1 as well as a section through the point ,a4 ,weights can be added at f to counterpoise the horse-shoe magnet4 ,the rise or fall of the mercurial barometer correspondingly raises or depresses the horse shoe magnet1 and1 increasing or decreasing the magnetic action between its poles and those of the pendulum magnets1 compensates1 by the change of rate produced1 for that arising from variation in the pressure of the atmosphere4 ,the shorter leg of the barometer in which the float rests has an area of four times that of the barometer tube at the upper surface of the mercury1 so that for a large change of barometric height the magnet is only moved a small distance1 a change of one inch of the barometer lowering the surface in the short leg #b_/aj inch2 the distance between the pendulum magnets and the horse-shoe magnets is #c inches4 ,,iii4 ,,escapements4 ,the invention of the pendulum1 its application1 and the improvements thereon having been described1 it remains to treat of the equally important improvements on the escapement4 ,the first change for the better appears to have been due to ,hooke1 who in #afff brought before the ,royal ,society the crutch1 or anchor escapement1 whereby the arc through which the pendulum vibrated was so much reduced that ,huyghens's cycloidal curves became unnecessary1 and the power required to drive the clock was materially reduced4 ,this escapement1 common in ordinary eight-day clocks1 is different from that previously described in the way in which the crown wheel or escape wheel is regulated4 ,we have come back to a vertical escape wheel as it was in the clock used by ,tycho2 but instead of using two pallets on a rod which regulated the wheel1 we have here an anchor escapement 7,fig4 #ib7 in connection with the pendulum2 and what happens is this--when the pendulum is made to oscillate1 these pallets ,p ,p gradually move in and out of the teeth of the wheel1 and let a tooth pass at every swing2 and it is obvious that when the wheel and anchor are nicely adjusted1 an extremely small motion of the anchor1 and consequently a small oscillation of the pendulum1 allows the escape wheel to turn round1 and the clock to go4 ,the greater regularity of this form of escapement is due to a smaller oscillation of the pendulum being required than with the form first described2 for it is found that the motion of a pendulum when vibrating through not more than six degrees is practically cycloidal1 and it is only with larger arcs that the circle materially differs from the theoretical curve required4 ,the pendulum is kept in vibration by the escape wheel1 or rather by its teeth pressing against the inclined surfaces of the pallets1 and forcing them outwards1 and so giving the pendulum an impulse prior to each tick4 ,illustration3 ,,fig4 #ib4--,the ,anchor ,escapement4 ,this anchor escapement1 which was invented by 8,clement1 of ,london1 clockmaker10 forms1 as it were1 the basis of our modern clocks1 and1 with the exception of the dead beat1 which was due to ,graham some years afterwards1 is in almost exclusive use at the present date4 ,we see that as soon as a tooth has escaped on one side1 a tooth on the other begins immediately to retard the action of the pendulum by pressing against the inclined surface of the other pallet1 and as the pendulum swings on1 the tooth gives way1 and the motion of the wheel is reversed2 then when the pendulum begins to return1 it is assisted again by the tooth1 so that the pendulum is always under the influence of the escape wheel1 some times accelerated1 and sometimes retarded4 ,the principle of ,graham's dead beat is to get rid of the retarding action of the escape wheel1 so that there should be no necessity for so much accelerating power1 and the pendulum should be out of the influence of the escape wheel during a large portion of its vibration4 ,this he accomplished by doing away with a large portion of the inclined surface of the pallet 7,fig4 #ic71 so that the teeth have no accelerating action on the pendulum until just as they leave the ends of the pallets where they are inclined2 the greater portion of both the pallets on which the escape wheel works being at right angles to its direction of motion1 the teeth have no tendency to force the pallet outwards4 ,in ,fig4 #ic the tooth ,v has fallen on the pallet ,d1 the tooth ,t having just been released1 and as the pendulum still swings on in the direction of the arrow1 the pallet ,d will be pushed further under the tooth ,c but without pressing the wheel backwards1 and without retardation other than that of friction4 ,when the pendulum returns and the pallet just gets past the position shown1 it gets an impulse1 and this is given as nearly as possible as much before the pendulum reaches its vertical position as after it passes it1 its action is therefore neither to increase nor diminish the rate4 ,in this escapement not only is the arc of oscillation considerably lessened and the motion of the pendulum brought near to the cycloidal form1 but in addition to this there is this important point1 that the weight is acting upon the pendulum for the least possible time4 ,illustration3 ,,fig4 #ic4--;,graham's ,dead ,beat4 ,illustration3 ,,fig4 #id4--;,gravity ,escapement 7,mudge74 ,we will now describe the more elaborate forms of escapement1 and we will take first the gravity escapement1 as it is called4 ,the principle of its action consists in there being a small impulse given to the pendulum at each oscillation1 by means of two small rods hanging1 one on each side of it1 and tending by their own weight to force the pendulum into a vertical position2 these rods are alternately pushed outwards by the escapement before the pendulum in its swing arrives at them1 and then they are allowed to press against it on its return towards the vertical1 so that the pendulum has a constant force acting on it at each oscillation1 unconnected with the clock movement4 ,this is carried out in the escapement invented by ,mudge1 as shown in ,fig4 #id4 ,the pendulum rod is supposed to be hanging just in front of the rods hanging from the pivots ,y#a ,y#b1 and on swinging it presses against the pins at the lower ends of the rods and so lifts the pallets ,s#a ,s#b out of the teeth of the escape wheel4 ,in the position shown the pendulum is moving to the right1 having been gently urged from the left by the weight of the pallet rod ,y#b ,s#b1 and the pallet ,s#a has been lifted outwards by the tooth acting on its inclined surface4 ,on the pendulum rod reaching the pin the rod is moved outwards and the end of the pallet ,s#a pushed out of the tooth when the wheel moves on1 at the same time pushing outwards the pallet ,s#b4 ,as the pendulum returns towards the left again the rod ,y#a follows it1 giving it a gentle impulse by its own weight until it returns nearly to the vertical or to the corresponding position in which ,y#b ,s#b is shown4 ,on the pendulum swinging on and releasing ,t#b the pallet ,s#a is again pushed outwards by the inclined plane to the position shown in the diagram4 ,in this escapement there was danger of the pallets being thrown too violently outwards so that the teeth were not caught by the flat surfaces at the ends1 and ,mr4 ,bloxam improved on it by letting the pallets be thrown outwards by a small wheel on the axis of the escape wheel so that the action was less rapid2 he accomplished this in the following manner4 ,on the end of the axis of the last wheel are a number of arms ,a ,a1 ,fig4 #ie1 say nine1 about #a inches long1 which are prevented from revolving by studs ,l#a ,l#b on the inside of each hanging rod ,p#a ,p#b2 then1 as each rod is pushed outwards by the pendulum1 an arm escapes from a stud and the clock goes on one second4 ,each rod is pushed outwards by the clock almost sufficiently far for the arm to escape1 but not quite1 so that the pendulum just releases the arm at the end of its swing in the same manner as in ,mudge's escapement1 ,fig4 #id2 but instead of the teeth of the escape wheel pushing the rods outwards there is the small wheel ,t#a ,t#b1 having the same number of teeth as there are arms on the axis and close to them1 and the projecting pieces ,h#a ,h#b at right angles to each swinging rod rest against the teeth of this wheel1 one resting against the teeth at the top and the other at the bottom1 so that they catch against the teeth after the manner of a ratchet1 and the rods are pushed outwards by this wheel as it revolves4 ,the arms and ratchet wheel are so set that1 during the motion of an arm ,a1 to a stud1 a tooth of the ratchet wheel is pushing outwards the rod carrying that stud4 ,the action is as follows3--,the pendulum having just swung up to a rod and released the arm pressing against its stud1 the arms and ratchet wheel revolve1 and the tooth of the ratchet wheel1 which had been pressing outwards the swinging rod1 passes on free of the projecting piece1 which can now move backwards to the next tooth2 so the rod1 being no longer supported1 presses against the pendulum rod on its return oscillation4 ,the arms and ratchet wheel revolve until an arm on the opposite side comes in contact with the stud on the other rod1 and in revolving the ratchet wheel throws outwards this rod just so far that the arm is not released4 ,the pendulum is assisted by the weight of the first rod to the vertical position1 when the projecting piece of the rod comes in contact with the next tooth of the ratchet wheel where it rests until the oscillation is completed1 and the second arm is released4 ,it is then forced outwards1 and the next arm on that side presses against the stud1 when a repetition of the foregoing takes place4 ,in this way the clock is kept going without any direct action of the clock train on the pendulum4 ,illustration3 ,,fig4 #ie4--;,gravity ,escapement 7,bloxam74 ,another very beautiful escapement is that devised by the ,astronomer-,royal and carried out in the clock erected in #ahga at ,greenwich4#i ,in this case the pendulum is free except during a portion of every alternate second1 when it releases the escapement and receives an impulse1 so that there is a tick only at every other second4 ,illustration3 ,,fig4 #if4--;,greenwich ,clock ,escapement4 ,the details of the escapement may be seen in ,fig4 #if1 which gives a general view of a portion of the back plate of the clock movement1 supposing the pendulum removed2 a and b are the front and back plates respectively of the clock train2 c is a cock supporting one end of the crutch axis2 d is the crutch rod carrying the pallets1 and e an arm carried by the crutch axis and fixed at f to the left-hand pallet arm2 g is a cock supporting a detent projecting towards the left and curved at its extreme end2 at a point near the top of the escape wheel this detent carries a pin 7jewel7 for locking the wheel1 and at its extreme end there is a very light 8passing spring40 ,the action of the escapement is as follows3--,suppose the pendulum to be swinging from the right hand4 ,it swings quite freely until a pin at the end of the arm e lifts the detent2 the wheel escapes from the jewel before mentioned1 and the tooth next above the left-hand pallet drops on the face of the pallet 7the state shown in the figure71 and gives impulse to the pendulum2 the wheel is immediately locked again by the jewel1 and the pendulum1 now detached1 passes on to the left2 in returning to the right1 the light passing spring1 before spoken of1 allows the pendulum to pass without disturbing the detent2 on going again to the left1 the pendulum again receives impulse as already described4 ,the right-hand pallet forms no essential part of the escapement1 but is simply a safety pallet1 designed to catch the wheel in case of accident to the locking-stone during the time that the left-hand pallet is beyond the range of the wheel4 ,the escape wheel carrying the seconds hand thus moves once only in each complete or double vibration of the pendulum1 or every two seconds4 ,,iv4 ,,the ,,chronometer4 ,we have now given a description of the astronomical clock--the modern astronomical instrument which it was our duty to consider4 ,there is another time-keeper--the chronometer--which we have to dwell upon4 ,in the chronometer1 instead of using the pendulum1 we have a balance1 the vibration of which is governed by a spiral spring1 instead of by gravity1 as the pendulum is4 ,by such means we keep almost as accurate time as we do by employing a pendulum1 the balance being corrected for temperature on principles1 one of which we shall describe4 ,we must premise by saying that fully four-fifths of the compensation required by a chronometer or watch-balance is owing to the change in elasticity of the governing spiral spring1 the remainder1 comparatively insignificant1 being due to the balance's own expansion or contraction4 ,the segments ,r#a1 ,r#b of the balance 7see ,fig4 #ig7 are composed of two metals1 say copper and steel1 the copper being exterior2 then as the governing spiral spring loses its elasticity by heat1 the segments ,r#a1 ,r#b curve round and take up positions nearer the axis of motion1 the curvature being produced by the greater expansion of copper over steel2 and thus the loss of time due to the loss of elasticity of the spiral spring is compensated for4 ,this balance may be adjustable by placing on the arms small weights1 ,w ,w1 which may be moved along the arms1 and so increase or diminish the effect of temperature at pleasure4 ,illustration3 ,,fig4 #ig4--;,compensating ,balance4 ,of the number of watch and chronometer escapements we may mention the detached lever--the one most generally used for the best watches1 the form is shown in ,fig4 #ih4 ,p ,p are the pallets working on a pin at ,s as in the dead-beat clock escapement2 the pallets carry a lever ,l which can vibrate between two pins ,b ,b4 ,r is a disc carried on the same axis with the balance1 and it carries a pin ,i1 which as the disc goes round in the direction of the arrow1 falls into the fork of the lever1 and moves it on and withdraws the pallet from the tooth ,d1 which at once moves onwards and gives the lever an impulse as it passes the face of the pallet4 ,this impulse is communicated to the balance through the pin ,i1 the balance is kept vibrating in contrary directions under the influence of the hair-spring1 gaining an impulse at each swing4 ,on the same axis as ,r is a second disc ,o with a notch cut in it into which a tongue on the lever enters2 this acts as a safety lock1 as the lever can only move while the pin ,i is in the fork of the lever4 ,illustration3 ,,fig4 #ih4--;,detached ,lever ,escapement4 ,the escapement we next describe is that most generally used in chronometers4 ,s ,s1 ,fig4 #ii1 is the escape wheel which is kept from revolving by the detent ,d4 ,on the axis of the balance are two discs1 ,r#a1 ,r#b1 placed one under the other4 ,as the balance revolves in the direction of the arrow1 the pin ,p#b will come round and catch against the point of the detent1 lifting it and releasing the escape-wheel1 which will revolve1 and the tooth ,t will hit against the stud ,p#a1 giving the balance an impulse4 ,the balance then swings on to the end of its course and returns1 and the stud ,p#b passes the detent as follows3 a light spring ,y ,y is fastened to the detent1 projecting a little beyond it1 and it is this spring1 and not the detent itself1 that the pin ,p#b touches3 on the return of ,p#b it simply lifts the spring away from the detent and passes it1 whereas in advancing the spring was supported by the point of the detent1 and both were lifted together4 ,illustration3 ,,fig4 #ii4--;,chronometer ,escapement4 ,illustration3 ,,fig4 #ajj4--,the ,fusee4 ,in watches and chronometers and in small clocks a coiled spring is used instead of a weight1 but its action is irregular1 since when it is fully wound up it exercises greater force than when nearly down4 ,in order to compensate for this the cord or chain which is wound round the barrel containing the spring passes round a conical barrel called a fusee 7,fig4 #ajj73 ,b is the barrel containing the spring and ,a ,a the fusee4 ,one end of the spring is fixed to the axis of the barrel1 which is prevented from turning round1 and the other end to the barrel1 so that on winding up the clock by turning the fusee the cord becomes coiled on the latter1 and the more the spring is wound the nearer the cord approaches the small end of the fusee1 and has therefore less power over it2 while as the clock goes and the spring becomes unwound1 its power over the axis becomes greater4 ,the power1 therefore1 acting to turn the fusee remains pretty constant4 ----- ,footnote #i3 ,by ,messrs4 ,e4 ,dent and ,co4 of the ,strand4 ,,chapter ,,xiv4 ,,circle ,,reading4 ,one of the great advantages which astronomy has received from the invention of the telescope is the improved method of measuring space and determining positions by the use of the telescope in the place of pointers on the old instruments4 ,the addition of modern appliances to the telescope to enable it to be used as an accurate pointer1 has played a conspicuous part in the accurate measurement of space1 and the results are of such importance1 and they have increased so absolutely pari passu with the telescope1 that we must now say something of the means by which they have been brought about4 ,for astronomy of position1 in other words for the measurement of space1 we want to point the telescope accurately at an object4 ,that is to say1 in the first instance we want circles1 and then we want the power of not only making perfect circles1 but of reading them with perfect accuracy2 and where the arc is so small that the circle1 however finely divided1 would help us but little1 we want some means of measuring small arcs in the eyepiece of the telescope itself1 where the object appears to us1 as it is called1 in the field of view2 we want to measure and inspect that object in the field of view of the telescope1 independently of circles or anything extraneous to the field4 ,we shall then have circles and micrometers to deal with divisions of space1 and clocks and chronographs to deal with divisions of time4 ,we require to have in the telescope something1 say two wires crossed1 placed in the field of view--in the round disc of light we see in a telescope owing to the construction of the diaphragm--so as to be seen together with any object4 ,in the chapter on eyepieces it was shown that we get at the focus the image of the object2 and as that is also the focus of the eyepiece1 it is obvious that not only the image in the air1 as it were1 but anything material we like to put in that focus1 is equally visible4 ,by the simple contrivance of inserting in this common focus two or more wires crossed and carried on a small circular frame1 we can mark any part of the field1 and are enabled to direct the telescope to any object4 ,in the ,huyghenian eyepiece1 ,fig4 #fj1 the cross should be between the two convex lenses1 for if we have an eyepiece of this kind the focus will be at ,f1 and so here we must have our cross wires2 but1 if instead of this eyepiece we have one of the kind called ,ramsden's eyepiece1 ,fig4 #fb1 with the two convex surfaces placed inwards1 then the focus will be outside1 at ,f1 and nearer to the object-glass3 therefore we shall be able to change these eyepieces without interfering with the system of wires in the focus of the telescope4 ,we hence see at once that the introduction of this contrivance1 which is due to ,mr4 ,gascoigne1 at once enormously increases the possibility of making accurate observations by means of the telescope4 ,illustration3 ,,fig4 #aja4--;,diggs' ,diagonal ,scale4 ,hipparchus was content to ascertain the position of the celestial bodies to within a third of a degree1 and we are informed that ,tycho ,brahe1 by a diagonal scale1 was able to bring it down to something like ten seconds4 ,fig4 #aja will show what is meant by this4 ,suppose this to be part of the arc of ,tycho's circle1 having on it the different divisions and degrees4 ,now it is clear that when the bar which carried the pointer swept over this arc1 divided simply into degrees1 it would require a considerable amount of skill in estimating to get very close to the truth1 unless some other method were introduced2 and the method suggested by ,diggs1 and adopted by ,tycho1 was to have a series of diagonal lines for the divisions of degrees2 and it is clear that the height of the diagonal line measured from the edge of the circle could give1 as it were1 a longer base than the direct distance between each division for determining the subdivisions of the degree1 and a slight motion of the pointer would make a great difference in the point where it cuts the diagonal line4 ,for instance1 it would not be easy to say exactly the fraction of division on the inner circle at which the pointer in ,fig4 #aja rests1 but it is evident that the leading edge of the pointer cuts the diagonal line at three-fourths of its length1 as shown by the third circle2 so the reading in this case is seven and three-quarters2 but that is1 after all1 a very rough method1 although it was all the astronomer had to depend upon in some important observations4 ,illustration3 ,,fig4 #ajb4--,the ,vernier4 ,the next arrangement we get is one which has held its own to the present day1 and which is beautifully simple4 ,it is due to a ,frenchman named ,vernier1 and was invented about #afca4 ,we may illustrate the principle in this way4 ,suppose for instance we want to subdivide the divisions marked on the arc of a circle1 ,fig4 #ajb a b1 and say we wish to divide them into tenths1 what we have to do is this--,first1 take a length equal to nine of these divisions on a piece of metal1 c1 called the vernier1 carried on an arm from the centre of the circle1 and then1 on a separate scale altogether1 divide that distance not into nine1 as it is divided on the circle1 but into ten portions4 ,now mark what happens as the vernier sweeps along the circle1 instead of having ,tycho's pointer sweeping across the diagonal scale4 ,let us suppose that the vernier moves with the telescope and the circle is fixed2 then when division #j of the vernier is opposite division #f on the circle we know that the telescope is pointing at #f from zero measured by the degrees on this scale2 but suppose1 for instance1 it moves along a little more1 we find that line #a of the vernier is in contact with and opposite to another on the circle1 then the reading is #f and 2 it moves a little further1 and we find that the next line #b1 is opposite to another1 reading #f and #b_/aj1 a little further still1 and we find the next opposite4 ,it is clear that in this way we have a readier means of dividing all those spaces into tenths1 because if the length of the vernier is nine circle divisions the length of each division on the vernier must be as nine is to ten1 so that each division is one-tenth less than that on the circle4 ,we must therefore move the vernier one-tenth of a circle division1 in order to make the next line correspond4 ,that is to say1 when the division of the vernier marked #j is opposite to any line1 as in the diagram1 the reading is an exact number of degrees2 and when the division #a is opposite1 we have then the number of degrees given by the division #j plus one-tenth2 when #b is in contact1 plus two-tenths2 when #c is in contact1 plus three-tenths2 when #d is in contact1 plus four-tenths1 and so on1 till we get a perfect contact all through by the #j of the vernier coming to the next division on the circle1 and then we get the next degree4 ,it is obvious that we may take any other fraction than to for the vernier to read to1 say #a_/fj1 then we take a length of #ei circle divisions on the vernier and divide it into #fj1 so that each vernier division is less than a circle division by #a_/fj4 ,this is a method which holds its own on most instruments1 and is a most useful arrangement4 ,but most of us know that the division of the vernier has been objected to as coarse and imperfect2 and ,sharp1 ,graham1 ,bird1 ,ramsden1 ,troughton1 and others found that it is easy to graduate a circle of four or five feet in diameter1 or more1 so accurately and minutely that five minutes of arc shall be absolutely represented on every part of the circle4 ,we can take a small microscope and place in its field of view two cross wires1 something like those we have already mentioned1 so as to be seen together with the divisions on the circle1 and then1 by means of a screw with a divided head1 we can move the cross wires from division to division1 and so1 by noting the number of turns of the screw required to bring the cross wires from a certain fixed position1 corresponding to the pointer in the older instruments1 to the nearest division1 we can measure the distance of that division from the fixed point or pointer1 as it were1 just as well as if the circle itself were much more closely divided4 ,we can have matters so arranged that we may have to make1 if we like1 ten turns of the screw in order to move the cross wires from one graduation to the next1 and we may have the milled head of the screw itself divided into #ajj divisions1 so that we shall be able to divide each of the ten turns into #ajj1 or the whole division into #a1jjj parts4 ,it is then simply a question of dividing a portion of arc equal to five minutes into a thousand1 or1 if one likes1 ten thousand parts by a delicate screw motion4 ,we are now speaking of instruments of precision1 in which large telescopes are not so necessary as large circles4 ,with reference to instruments for physical and other observations1 large circles are not so necessary as large telescopes1 as absolute positions can be determined by instruments of precision1 and small arcs can1 as we shall see in the next chapter1 be determined by a micrometer in the eyepiece of the telescope4 ,,chapter ,,xv4 ,,the ,,micrometer4 ,it will have been gathered from the previous chapter that the perfect circles nowadays turned out by our best opticians1 and armed in different parts by powerful reading microscopes1 in conjunction with a cross wire in the field of view of the telescope to determine the exact axis of collimation1 enable large arcs to be measured with an accuracy comparable to that with which an astronomical clock enables us to measure an interval of time4 ,we have next to see by what method small arcs are measured in the field of view of the telescope itself4 ,this is accomplished by what are termed micrometers1 which are of various forms4 ,thus we have the wire micrometer1 the heliometer1 the double-image micrometer1 and so on4 ,these we shall now consider in succession1 entering into further details of their use1 and the arrangements they necessitate when we come to consider the instrument in conjunction with which they are generally employed4 ,the history of the micrometer is a very curious one4 ,we have already spoken of a pair of cross wires replacing the pinnules of the old astronomers in the field of view of the telescope1 so that it might be pointed to any celestial object very much more accurately than it could be without such cross wires4 ,this kind of micrometer was first applied to a telescope by ,gascoigne in #afci4 ,in a letter to ,crabtree he writes3#aj 8,if here 7in the focus of the telescope7 you place the scale that measures 444 or if here a hair be set that it appear perfectly through the glass 444 you may use it in a quadrant for the finding of the altitude of the least star visible by the perspective wherein it is4 ,if the night be so dark that the hair or the pointers of the scale be not to be seen1 ,i place a candle in a lanthorn1 so as to cast light sufficient into the glass1 which ,i find very helpful when the moon appeareth not1 or it is not otherwise light enough40 ,this then was the first 8telescopic sight10 as these arrangements at the common focus of the object-glass and eyepiece were at first called4 ,it is certain that we may date the micrometer from the middle of the seventeenth century2 but it is rather difficult to say who it was who invented it4 ,it is frequently attributed to a ,frenchman named ,auzout1 who is stated to have invented it in #afff2 but we have reason to know that ,gascoigne had invented an instrument for measuring small distances several years before4 ,though first employed by ,gascoigne1 however1 they were certainly independently introduced on the ,continent1 and took various forms1 one of them being a reticule1 or network of small silver threads1 suggested by the ,marquis ,malvasia1 the arc interval of which was determined by the aid of a clock4 ,huyghens had before this proposed1 as specially applicable to the measures of the diameters of planets and the like1 the introduction of a tapering slip of metal4 ,the part of the slip which exactly eclipsed the planet was noted2 it was next measured by a pair of compasses1 and having the focal length of the telescope1 the apparent diameter was ascertained4 ,illustration3 ,,fig4 #ajc4--,system of ,wires in a ,transit ,eyepiece4 ,malvasia's suggestion was soon seized upon for determinations of position4 ,rmer introduced into the first transit instrument a horizontal and a number of vertical wires4 ,the interval between the three he generally used was thirty-four seconds in the equator1 and the time was noted to half seconds4 ,the field was illuminated by means of a polished ring placed outside of the object-glass4 ,the simple system of cross wires1 then1 though it has done its work1 is not to be found in the telescope now1 either to mark the axis of collimation1 or roughly to measure small distances4 ,for the first purpose a much more elaborate system than that introduced by ,rmer is used4 ,we have a large number of vertical wires1 the principal object of which is1 in such telescopes as the transit1 to determine the absolute time of the passage of either a star or planet1 or the sun or moon1 over the meridian2 and one or more horizontal ones4 ,these constitute the modern transit eyepiece1 a very simple form of which is shown in the above woodcut4 ,,the ,,wire ,,micrometer4 ,the wire micrometer is due to suggestions made independently by ,hooke and ,auzout1 who pointed out how valuable the reticule of ,malvasia would be if one of the wires were movable4 ,illustration3 ,,fig4 #ajd4--,wire ,micrometer4 x and y are thicker wires for measuring positions on a separate plate to be laid over the fine wires4 ,the first micrometer in which motion was provided consisted of two plates of tin placed in the eyepiece1 being so arranged and connected by screws that the distances between the two edges of the tin plates could be determined with considerable accuracy4 ,a planet could then be1 as it were1 grasped between the two plates1 and its diameter measured2 it is very obvious that what would do as well as these plates of tin would be two wires or hairs representing the edges of these tin plates2 and this soon after was carried out by ,hooke1 who left his mark in a very decided way on very many astronomical arrangements of that time4 ,he suggested that all that was necessary to determine the diameter of ,saturn's rings was to have a fixed wire in the eyepiece1 and a second wire travelling in the field of view1 so that the planet or the ring could be grasped between those two wires4 ,the wire-micrometer4 ,fig4 #ajd1 differs little from the one ,hooke and ,auzout suggested1 ,a ,a is the frame1 which carries two slides1 ,c and ,d1 across the ends of each of which fine wires1 ,e and ,b1 are stretched2 then1 by means of screws1 ,f and ,g1 threaded through these movable slides and passing through the frame ,a ,a1 the wires can be moved near to1 or away from1 each other4 ,care must be taken that the threads of the screw are accurate from one end to the other1 so that one turn of the screw when in one position would move the wire the same distance as a turn when in another position4 ,in this micrometer both wires are movable1 so as to get a wide separation if needful1 but in practice only one is so1 the other remaining a fixture in the middle of the field of view4 ,there is a large head to the screw1 which is called the micrometer screw1 marked into divisions1 so that the motion of the wire due to each turn of the screw may be divided1 say into #ajj parts1 by actual division against a fixed pointer1 and further into #a1jjj parts by estimation of the parts of each division4 ,hooke suggested that1 if we had a screw with #ajj turns to an inch1 and could divide these into #a1jjj parts1 we should obviously get the means of dividing an inch into #ajj1jjj parts2 and so1 if we had a screw which would give #ajj turns from one side of the field of view of the telescope to the other1 we should have an opportunity of dividing the field of view of any telescope into something like #ajj1jjj parts in any direction we chose4 ,the thick wires1 x1 y1 are fixed to the plate in front of1 but almost touching1 the fine wires1 and in measuring1 for instance1 the distance of two stars the whole instrument is turned round until these wires are parallel to the direction of the imaginary line joining them4 ,this was the way in which ,huyghens made many important measures of the diameters of different objects and the distances of different stars4 ,thus far we are enabled to find the number of divisions on the micrometer screw that corresponds to the distance from one star to another1 or across a planet1 but we want to know the number of seconds of arc in the distance measured4 ,in order to do this accurately we must determine how many divisions of the screw correspond to the distance of the wires when on two stars1 say1 one second apart4 ,here we must take advantage of the rate at which a star travels across the field when the telescope is fixed1 and we separate the wires by a number of turns of the screw1 say twenty1 and find what angle this corresponds to1 by letting a star on or near the equator#aa traverse the field1 and noticing the time it requires to pass from one wire to the next4 ,suppose it takes #bf seconds1 then1 as fifteen seconds of arc pass over in one second of time1 we must multiply #bf by #ae1 which gives #djj1 so that the distance from wire to wire is #djj seconds of arc2 but this is due to twenty revolutions of the screw1 so that each revolution corresponds to #djj_/bj1 or twenty seconds1 and as each revolution is divided into #ajj parts1 and #bj_/ajj therefore each division corresponds to of arc4 ,we shall return to the use of this most important instrument when we have described the equatorial1 of which it is the constant companion4 ,,the ,,heliometer4 ,illustration3 ,,fig4 #aje4--;,a ,b ,c4 ,images of ,jupiter supposed to be touching2 ,b being produced by duplication1 ,c duplicate image on the other side of ,a4 ,a ,b1 ,double ,star2 ,a1 ,a ,b1 ,b1 the appearance when duplicate image is moved to the right2 ,a1 ,a ,b1 ,b1 the same when moved to the left4 ,illustration3 ,,fig4 #ajf4--,object-glass cut into two parts4 ,illustration3 ,,fig4 #ajg4--,the parts separated1 and giving two images of any object4 ,there are other kinds of micrometers which we must also briefly consider4 ,in the heliometer#ab we get the power of measuring distances by doubling the images of the objects we see1 by means of dividing the object-glass4 ,the two circles1 ,a and ,b1 ,fig4 #aje1 represent the two images of ,jupiter formed1 as we shall show presently1 and touching each other2 now1 if by any means we can make ,b travel over ,a till it has the position ,c1 also just touching ,a1 it will manifestly have travelled over a distance equal to the diameters of ,a and ,b1 so that if we can measure the distance traversed and divide it by #b1 we shall get the diameter of the circle ,a1 or the planet4 ,the same principle applies to double stars1 for if we double the stars ,a and ,b1 ,fig4 #aje1 so that the secondary images become ,a and ,b1 we can move ,a over ,b1 and then only three stars will be visible2 we can then move the secondary images back over ,a and ,b till ,b comes over ,a1 and the second image of ,a comes to ,a4 ,it is thus manifest that the images ,a and ,b on being moved to ,a and ,b in the second position have passed over double their distance apart4 ,now all double-image micrometers depend on this principle1 and first we will explain how this duplication of images is made in the heliometer4 ,it is clear that we shall not alter the power of an object-glass to bring objects to focus if we cut the object-glass in two1 for if we put any dark line across the object-glass1 which optically cuts it in two1 we shall get an image1 say of ,jupiter1 unaltered4 ,but suppose instead of having the parts of the object-glass in their original position after we have cut the object-glass in two1 we make one half of the object-glass travel over the other in the manner represented in ,fig4 #ajg4 ,each of these halves of the object-glass will be competent to give us a different image1 and the light forming each image will be half the light we got from the two halves of the object-glass combined2 but when one half is moved we shall get two images in two different places in the field of view4 ,we can so alter the position of the images of objects by sliding one half of the object-glass over the other1 that we shall1 as in the case of the planet ,jupiter1 get the two images exactly to touch each other1 as is represented in ,fig4 #aje2 and further still1 we can cause one image to travel over to the other side4 ,if we are viewing a double star1 then the two halves will give four stars1 and we can slide one half1 until the central image formed by the object-glasses will consist of two images of two different stars1 and on either side there will be an image of each star1 so that there would appear to be three stars in the field of view instead of two4 ,we have thus the means of determining absolutely the distance of any two celestial objects from each other1 in terms of the separation of the centres of the two halves of the object-glass4 ,but as in the case of the wire micrometer we must know the value of the screw1 so in the case of the heliometer we must know how much arc is moved over by a certain motion of one half of the object-glass4 ,illustration3 ,,fig4 #ajh4--;,double images seen through ,iceland spar4 ,illustration3 ,,fig4 #aji4--;,diagram showing the path of the ordinary and extraordinary rays in a crystal of ,iceland spar1 producing two images apparently at ,e and ,o4 ,,the ,,double-,,image ,,micrometer4 ,now there is another kind of double-image micrometer which merits attention4 ,in this case the double image is derived from a different physical fact altogether1 namely1 double refraction4 ,those who have looked through a crystal of ,iceland spar1 ,fig4 #ajh1 have seen two images of everything looked at when the crystal is held in certain positions1 but the surfaces of the crystal can be cut in a certain plane such that when looked through1 the images are single4 ,for the micrometer therefore we have doubly refracting prisms1 cut in such a way as to vary the distance of the images4 ,generally speaking1 whenever a ray of light falls on a crystal of ,iceland spar or other double refracting substance1 it is divided up into two portions1 one of which is refracted more than the other4 ,if we trace the rays proceeding from a point ,s1 ,fig4 #aji1 we find one portion of the light reaching the eye is more refracted at the surfaces than the other1 and consequently one appears to come from ,e and the other from ,o1 so that if we insert such a crystal in the path of rays from any object1 that object appears doubled4 ,there is1 however1 a certain direction in the crystal1 along which1 if the light travel1 it is not divided into two rays1 and this direction is that of the optic axis of the crystal1 ,a ,a1 ,fig4 #aaj2 if therefore two prisms of this spar are made so that in one the light shall travel parallel to the axis1 and in the other at right angles to it1 and if these be fastened together so that their outer sides are parallel1 as shown in ,fig4 #aaa1 light will pass through the first one without being split up1 since it passes parallel to the axis1 but on reaching the second one it is divided into two rays1 one of which proceeds on in the original course1 since the two prisms counteract each other for this ray1 while the other ray diverges from the first one1 and gives a second image of the object in front of the telescope1 as shown in ,fig4 b4 ,the separation of the image depends on the distance of the prisms from the eyepiece1 so that we can pass the rays from a star or planet through one of these compound crystals and measure the position of the crystal and so the separation of the stars1 and then we shall have the means of doing the same that we did by dividing our object-glass1 and in a less expensive way1 for to take a large object-glass of eight or ten inches in diameter and cut it in two is a brutal operation1 and has generally been repented of when it has been done4 ,illustration3 ,,fig4 #aaj4--;,crystals of ,iceland ,spar showing1 ,a ,a1 the optic axis4 ,it is obvious that a ,barlow lens1 cut in the same manner as the object-glass of the heliometer1 will answer the same purpose2 the two halves are of course moved in just the same manner as the halves of the divided object-glass4 ,mr4 ,browning has constructed micrometers on this principle4 ,illustration3 ,,fig4 #aaa4--;,double ,image ,micrometer4 ,,fig4 a1 p q1 single image formed by object-glass4 ,,fig4 b1 p#a q#a1 p#b q#b1 images separated by the double refracting prism4 ,,fig4 c1 same1 separated less1 by the motion of the prism4 ,there is yet another double-image micrometer depending on the power of a prism to alter the direction of rays of light4 ,it is constructed by making two very weak prisms1 i4e41 having their sides very nearly parallel1 and cutting them to a circular shape2 these are mounted in a frame one over the other with power to turn one round1 so that in one position they both act in the same direction1 and in the opposite one they neutralise each other2 these are carried by radial arms1 and are placed either in front of the object-glass or at such a distance from it inside the telescope that they intercept one half of the light1 and the remaining portion goes to form the usual image1 while the other is altered in its course by the prism and forms another image1 and this alteration depends on the position of the movable prism4 ----- ,footnote #aj3 ,grant's ,history of ,physical ,astronomy1 p4 #ded4 ,footnote #aa3 ,more accurately the time of transit is to be multiplied by the cosine of the star's declination4 ,footnote #ab3 ,so called because the contrivance was first used to measure the diameter of the sun4 ,,book ,,iv4 ,,modern ,,meridional ,,observations4 ,,chapter ,,xvi4 ,,the ,,transit ,,circle4 ,we are now1 then1 in full possession of the stock-in-trade of the modern astronomer--the telescope1 the clock1 and the circle1--and we have first to deal with what is termed astronomy of position1 that branch of the subject which enables us to determine the exact position of the heavenly bodies in the celestial sphere at any instant of time4 ,before1 however1 we proceed with modern methods1 it will be well1 on the principle of reculer pour mieux sauter1 to refer back to the old ones in order that we can the better see how the modern instruments are arranged for doing the work which ,tycho1 for instance1 had to do1 and which he accomplished by means of the instruments of which we have already spoken4 ,first of all let us refer to the ,mural ,quadrant1 in which we have the germ of a great deal of modern work1 its direct descendant being the ,transit ,circle of the present time4 ,we begin then by referring to the hole in the wall at which ,tycho is pointing 7see ,fig4 #aab71 and the circle1 of which the hole was the centre1 opposite to it1 on which the position of the body was observed1 and its declination and right ascension determined4 ,this then was ,tycho's arrangement for determining the two co-ordinates1 right ascension and declination1 measured from the meridian and equator4 ,it is to be hoped that the meaning of right ascension and declination is already clear to our readers1 because these terms refer to the fundamental planes1 and distances as measured from them are the very ,a ,b ,c of anything that one has to say about astronomical instruments4 ,we know that ,tycho had two things to do4 ,in the first place he had to note when a star was seen through the slit in the wall1 which was ,tycho's arrangement for determining the southing of a star1 the sun1 or the moon2 and then to give the instant when the object crossed the sight to the other observer1 who noted the time by the clocks4 ,secondly1 he had to note at which particular portion of the arc the sight had to be placed1 and so the altitude or the zenith distance of the star was determined2 and then1 knowing the latitude of the place1 he got the two co-ordinates1 the right ascension and declination4 ,how does the modern astronomer do this8 ,here is an instrument which1 without the circle to tell the altitude at the same time1 will give some idea of the way in which the modern astronomer has to go to work4 ,in this we have what is called the ,transit ,instrument1 ,fig4 #aac2 it is simply used for determining the transit of stars over the meridian4 ,it consists essentially of a telescope mounted on trunnions1 like a cannon1 having in the eyepiece1 not simple cross wires1 but a system of wires1 to which reference has already been made1 so that the mean of as many observations as there are wires can be taken2 and in this way ,tycho's hole in the wall is completely superseded4 ,the quadrant is represented by a circle on the instrument called the transit circle1 of which for the present we defer consideration4 ,illustration3 ,,fig4 #aab4--,tycho ,brahe's ,mural ,quadrant4 ,illustration3 ,,fig4 #aac4--,transit ,instrument 7,transit of ,venus ,expedition74 ,illustration3 ,,fig4 #aad4--,transit ,instalment in a fixed ,observatory4 ,now there are three things to be done in order to adjust this instrument for observation4 ,in the first place we must see that the line of sight is exactly at right angles to the axis on which the telescope turns1 and when we have satisfied ourselves of that1 we must1 in the second place1 take care1 not only that the pivots on which the telescope rests are perfectly equal in size1 but that the entire axis resting on these pivots is perfectly horizontal4 ,having made these two adjustments1 we shall at all events be able1 by swinging the telescope1 to sweep through the zenith4 ,then1 thirdly1 if we take care that one end of this axis points to the east1 and the other to the west1 we shall know1 not only that our transit instrument sweeps through the zenith1 but sweeps through the pole which happens to be above the horizon--in ,england the north pole1 in ,australia the south pole4 ,that is to say1 by the first adjustment we shall be able to describe a great circle2 by the second1 this circle will pass through the zenith2 and by the third1 from the south of the horizon to the north1 through the pole4 ,of course1 if the pole star were at the pole1 all we should have to do would be to adjust the instrument 7having determined the instrument to be otherwise correct7 so as simply to point to the pole star1 and then we should assure ourselves of the east and west positions of the axis4 ,some details may here be of interest4 ,the first adjustment to be made is that the line of sight or collimation shall be at right angles to the axis on which the instrument moves3 to find the error and correct it1 bring the telescope into a horizontal position and place a small object at a distance away1 in such a position that its image is bisected by the central wire of the transit1 then lift the instrument from its bearings or ,ys1 as they are called1 and reverse the pivots east for west1 and again observe the object4 ,if it is still bisected1 the adjustment is correct1 but if not1 then half the angle between the new direction in which the telescope points and the first one as marked by the object is the collimation error1 which may be ascertained by measuring the distance from the object to the central wire1 by a micrometer in the field of view1 and converting the distance into arc4 ,to correct it1 bring the central wire half way up to the object by motion of the wire1 and complete the other half by moving the object itself1 or by moving the ,ys of the instrument4 ,this of course must be again repeated until the adjustment is sensibly correct4 ,the second adjustment is to make the pivots horizontal4 ,place a striding level on the pivots and bring the bubble to zero by the set screws of the level1 or note the position of it2 then reverse the level east for west1 and then if the bubble remains at the same place the axis of motion is horizontal1 but1 if not1 raise or lower the movable ,y sufficiently to bring the bubble half way to its original position1 and complete the motion of the bubble1 if necessary1 by the level screw until there is no alteration in the position of the bubble on reversing the level4 ,illustration3 ,,fig4 #aae4--;,diagram explaining third adjustment1 ,h1 ,r1 plane of the horizon2 ,h1 ,z1 ,a1 ,p1 ,b1 ,r1 meridian2 ,a and ,b places of circumpolar star at transit above and below pole ,p4 ,the third adjustment is to place the pivots east and west4 ,note by the clock the time of transit of a circumpolar star1 when above the pole1 over the central wire1 and then half a day later when below it1 and again when above it2 if the times from upper to lower transit1 and from lower to upper are equal1 then the line of collimation swings so as to bisect the circle of the star round the pole1 and therefore it passes through the pole1 and further it describes a meridian which passes through the zenith by reason of the second adjustment4 ,this is therefore the meridian of the place1 and therefore the pivots are east and west4 ,if the periods between the transits are not equal1 the movable pivot must be shifted horizontally1 until on repeating the process the periods are equal4 ,in practice these adjustments can never be made quite perfect1 and there are always small errors outstanding1 which when known are allowed for1 and they are estimated by a long series of observations made in different manners and positions4 ,the error of the first adjustment is called the collimation error1 that of the second the level error1 and that of the third the deviation error4 ,when the errors of an instrument are known the observations can be easily corrected to what they would have been had the instrument been in perfect adjustment4 99 99 99 99 99 ,now what does the modern astronomer do with this instrument when he has got it8 ,it is absolutely without circles1 but the faithful companion of the ,transit ,instrument is the ,astronomical ,clock--and the two together serve the purpose of a circle of the most perfect accuracy1 so that by means of these two instruments we shall be able to determine the right ascensions of all the stars merely by noting the time at which the earth's rotation brings them into the field of view4 ,the clock having been regulated to sidereal time1 a term fully explained in the sequel1 it will show #j;h4 #jm4 #js4 when the first point of ,aries passes the meridian1 and instead of dividing the day into two periods of twelve hours each1 the clock goes up to twenty-four hours4 ,if now a star is observed to pass the centre of the field of view 7that is the meridian7 at #a;h4 by the clock1 or one hour after the first point of ,aries1 it will be known to be in #a;h4 of right ascension2 or if it passes at #ab;h4 it will be #ab;h4 right ascension1 or opposite to the first point of ,aries1 and so on up to the twenty-four hours1 the clock keeping exact time with the earth4 ,the transit instrument thus gives us the right ascension of a star1 or one co-ordinate3 and now we want the other--the declination4 ,,the ,,transit ,,circle4 ,this is given by the ,transit ,circle1 which is a transit instrument with a circle attached1 to ascertain the angle between the object and the pole or equator4 ,illustration3 ,,fig4 #aaf4--,the ,mural ,circle4 ,the combination of the circle with the transit1 forming the transit- or meridian-circle1 is of comparatively recent date1 and the earlier method was to use a circle with a telescope attached1 fixed to a pivot moving on bearings in a wall1 and called therefore the ,mural ,circle1 ,fig4 #aaf4 ,since it is supported only on one side it cannot move so truly in the meridian as the transit1 but1 having a large circle1 it gives accurate readings4 ,illustration3 ,,fig4 #aag4--,transit ,circle1 showing the addition of circles to the transit instrument4 ,illustration3 ,,fig4 #aah4--,perspective view of ,greenwich ,transit ,circle4 ,fig4 #aag shows in what respect the ,transit ,circle is an advance upon the transit instrument and the mural circle1 for in addition to the transit instrument we have the circle4 ,this is a perspective view of the transit1 and the telescope is represented sweeping in the vertical plane or meridian4 ,in addition to the instrument resting with its pivots on the massive piers1 we have the circle attached to the side of the telescope4 ,we see at once that by means of this circle we are able to introduce the other co-ordinate of declination4 ,if the clock goes true with the earth--if they both beat in unison and keep time with each other--and further if the clock shows #j;h4 #jm4 #js4 when the first point of ,aries passes the centre of the field1 that is through the meridian plane1 then1 if we observe a star at the moment it passes over the meridian1 the clock will give its right ascension and the circle its declination1 when the latitude of the place is known4 ,the construction of the transit circle will repay a more detailed examination4 ,a system of weights suspended over pulleys 7,fig4 #aah7 reduces the weight of the instrument on the pivots1 in order that their form shall not be altered by too much friction1 and on the right-hand side of one of the piers the eyepieces of the microscopes for reading the circle are shown4 ,this is shown better in section in ,fig4 #aai4 ,one of the solid stone piers is pierced through diagonally1 as shown at 7m7 7m71 so that light proceeding from a gas-lamp 7q7 placed opposite the pivot of the telescope is allowed to fall through the openings1 and is condensed by means of the lens 7n7 on the graduations of the circle of five minutes each1 already referred to4 ,by the side of each illuminating hole is another hole 7o7 7o7 through which the reading microscopes1 six in number1 two of which are shown at 7q7 7p71 having their eye-ends arranged in a circle at the end of the pier1 are focussed on to the graduations of the circle4 ,there is also another reading microscope1 besides the six just mentioned1 of less power for reading the degrees1 or larger divisions of the circle4 ,hence from the side of the pier close to the lamp the observer can read the circle with accuracy1 and measure the angle1 to which we have alluded1 made by the telescope when pointed to any particular star4 ,we have now seen how the circle is illuminated1 and now we will inquire further as to the arrangements that are necessary in order to bring this instrument into use4 ,illustration3 ,,fig4 #aai4--,plan of the ,greenwich ,transit ,circle4 ,we must defer giving more explanation of the practical working of the instrument until we have considered the clock used in connection with it1 and we shall then show how the observations are made4 ,one important point to which attention should be given is the method of illuminating the wires in the eyepiece4 ,this is the arrangement4 ,there is a lamp at the end of one of the pivots which is hollow1 the light falls on a mirror1 placed in the centre of the telescope1 of such a shape and in such a position that it will not intercept the light from the object-glass falling through the diaphragms on to the eyepiece4 ,the mirror is ring-shaped1 something like the brim of a hat1 and is carried on two pivots1 so that it can be placed diagonally in the tube1 or at right angles to it2 it is arranged just outside the cone of rays from the object-glass1 so that when the mirror is diagonally placed the light will be grasped directly from the lamp at the end of the axis and reflected down and mixed up with the light coming from the star into the eyepiece4 ,in this way of course the wires can be rendered visible at night1 and without such a method they would be invisible4 ,this arrangement gives a bright field and dark wires2 but there is also a method of reversing matters2 for near the edge of the ring-shaped reflector are fixed prisms for reflecting the light1 and when the reflector is placed square with the axis of the telescope the small prisms on the reflector send the light down through apertures in the diaphragms1 so that the mirror in this position no longer sends the light down with the rays from the star1 but through holes in the diaphragms themselves1 to two small reflecting prisms1 one on each side of the wires in the eyepiece4 ,what has that light to do8 ,it has simply to do this1 it has to fall sideways on the wires themselves in such a manner that it does not fall on the eye except by reflection from the wires4 ,in this way we have the means of getting a bright system of wires on a dark field1 in which the wires and objects to be measured are the only things to be seen4 ,as with the pivots of the transit circle1 and in fact of any astronomical instrument1 so with the circles1 certain fundamental points have to be borne in mind2 and1 although it is absolutely impossible to ensure perfection1 still1 to go as near to it as possible1 the astronomer has to observe a great many times over in all sorts of positions in order to bring the error down to its minimum4 ,first1 the circle must be placed exactly at right angles to the axis of the telescope1 so that it is in the plane of the meridian4 ,secondly1 the error of centering must be found4 ,for instance1 if the ,greenwich circle were to be read by only one microscope1 an error in the pivot or any part of the axis round which the circle turns would vitiate the readings2 but we could get rid of that error1 due to a fault of the axis1 or to a want of centering1 by means of two readings1 at the extremities of a diameter2 but even then we should not get rid of the possible error due to graduation1 for even if the divisions on the circle were accurate at first1 they would not long remain so1 for the metal of which these circles are made is liable1 like other metals1 to certain changes due to temperature2 and if a circle is very large the weight of the circle itself1 supposing its form perfect when horizontal1 will1 when vertical1 sag it down and deflect it out of shape1 so that at ,greenwich the method adopted is to use six reading microscopes4 ,fig4 #abj1 which shows the ,cambridge ,transit ,circle1 indicates the arrangement of the five microscopes in use there1 set round the circumference of the circle1 much in the same manner as in the case of the ,greenwich instrument1 where there are holes through the pier in which the microscopes are placed with the eye-ends arranged in a circle at the side of it4 ,illustration3 ,,fig4 #abj4--;,cambridge 7,u4,s47 meridian circle4 ,when1 therefore1 the transit is pointed to any particular star1 not only is the time noted in order to determine the right ascension of the star1 in a careful and elaborate way1 but the readings of the circle are made by every one of these microscopes--reading from the next five minutes division of the circle which happens to be visible1--and there is an additional microscope giving the rough reading of the larger divisions of the circle from a certain zero4 ,and what1 then1 is this zero8 ,there is no doubt about the reading of the zero of right ascension1 it is the intersection of the two fundamental planes at the first point of ,aries2 but what zero shall be used in the case of the vertical circle8 ,illustration3 ,,fig4 #aba4--;,diagram illustrating how the pole is found4 ,let the circle1 ,h1 ,z1 ,r1 ,fig4 #aba1 represent a great circle of the heavens1 the meridian in fact1 and let the centre of this circle represent the centre of the transit instrument4 ,now what we want is1 not only to be able to measure degrees of arc along this circle1 but to determine some starting-point for those degrees4 ,one arrangement is to observe the reflection of the wires in the eyepiece of the transit circle1 from the surface of mercury in a vessel which is placed below the telescope1 turned with its object-glass downwards2 the vessel containing the mercury is out of sight1 between the two piers1 but in ,fig4 #aah are seen the two parallel bars1 with weights at the ends1 carrying it1 by which it may be brought into any position for the purpose referred to1 so that the light from the wires in the eyepiece may pass through the tube and be reflected back by the mercury 7the surface of which is of course perfectly horizontal71 up through the tube again to the eyepiece4 ,when the telescope is absolutely in the vertical position the images of the cross wires will be superposed over the cross wires themselves2 and then an observation will give the actual reading of the circle when the instrument is pointing at #ahj from the zenith2 deduct #ahj from this reading1 and we get the reading when the instrument is pointing at the zenith--the zero required4 ,this should be #j1 and the quantity by which it differs from #j must be applied to the observed position of stars1 so that the distance of a star from the zenith can be at once determined4 ,but this is not all4 ,if we assume for the moment that the observer is at the north pole1 the pole star will be exactly over head1 and therefore1 supposing the pole star to absolutely represent the pole of the heavens1 all the observer has to do is simply to take a reading of the pole star on the arc of his circle--call it #j ,o #j--;and then use it as another zero to reckon polar distance from1 seeing that every particular star or body we observe has so many degrees1 minutes1 seconds1 or tenths of seconds1 from the pole star4 ,but we are not at the north pole4 ,still we are in a position where the pole is well above the horizon1 and from that fact we can determine the polar distance1 although the absolute place of the pole is not pointed out by the pole star4 ,thus1 if we suppose any star1 ,a1 ,fig4 #aba1 to be a certain distance from the pole1 and the earth carrying the instrument to be in the centre of the circle ,h1 ,z1 ,r1 we can observe the zenith distance of that star1 ,z1 ,a1 when it transits our meridian above the pole1 ,p2 and we can then observe its distance1 ,z1 ,b1 when it transits below the pole2 and it is clear that the difference between those two measures will give the distance ,a1 ,b1 or double the polar distance of that star1 and the mean of the readings will give the distance1 ,z1 ,p1 the zenith distance of the pole1 so that it is perfectly easy to determine the distance between the pole and the zenith1 which1 subtracted from ninety degrees1 gives us the latitude of the place4 ,it is therefore perfectly easy by means of this instrument to determine either the zenith or polar distance1 and1 knowing the polar distance1 we get the declination1 or distance from the equator1 by subtracting it from ninety degrees4 ,in our case it is the north polar distance or declination of any object in the heavens that we record2 and if we take the precaution to do so with this instrument at the time given by the clock1 when the object passes the meridian1 we have the actual apparent place of that body in the sky2 and in this way all the positions of the stars and other bodies1 and their various changes1 and the courses of the planets1 have been determined4 ,the transit circle is the most important instrument of astronomy1 and such is the perfection of the ,greenwich instrument that nothing could be more unfortunate for astronomy than that that instrument should be in any way damaged4 ,and though many of us are admirers of physical astronomy1 we have yet to find the instrument that is as important to physical astronomy as the transit circle at ,greenwich is to astronomy of position4 ,the room in which these transit circles are worked--the transit room--is required to be of special construction4 ,a clear space from the southern horizon through the zenith to the north must at any time be available2 this entails the cutting of a narrow slit in the roof and both walls1 without the intervention of any beams across the room4 ,this slit is closed by shutters or windows which are made to open in sections1 so that any part of the meridian can be observed at pleasure4 ,,chapter ,,xvii4 ,,the ,,transit ,,clock ,,and ,,chronograph4 ,we have now to consider the way in which the transit instrument is used and the functions which both it and the transit circle fulfil4 ,the connection between the transit instrument and the transit clock is so intimate that either is useless without the other4 ,in the one case we should note the passage of a star across the meridian without knowing at what time it took place2 while1 on the other hand1 we should not learn whether the clock showed true time or not1 unless we could check its indications in the manner rendered possible by transit observations4 ,in what has been already said of time we referred to it as measured by our ordinary clocks1 i4e4 reckoning it from noon to midnight and midnight to noon1 and regulated entirely by the length of the solar day4 ,it would at first sight seem that it should be twelve o'clock by a clock so regulated when the sun passes the meridian2 but the earth's orbit is not circular1 and the sun's course is inclined to the equator1 so that1 as determined by such a clock1 sometimes he would get to the meridian a little too late1 and sometimes too early1 so that we should be continually altering our clocks if we attempted to keep time with the sun4 ,one of the greatest boons conferred by astronomy upon our daily life is an imaginary sun that keeps exact time1 called the ,mean ,sun1 so that the mean sun is on the meridian at twelve o'clock each day by our clocks1 regulated by the methods we have now to discuss4 ,such clocks regulated1 as it is called1 to mean time are sometimes a few minutes before1 and at others a few minutes behind the true sun1 by an amount called the ,equation of ,time1 which is given in the almanacs4 ,it would therefore be difficult to regulate our standard clock by the sun1 so we do it through the medium of the stars1 which go past our meridian with the greatest regularity1 since their apparent motion depends almost wholly upon the equable rotation of the earth on its axis1 while the apparent motion of the sun is complicated by the earth's revolution round it4 ,this method at first sight is complex1 and in fact we cannot obtain mean time directly by such transits of stars4 ,it is accomplished indirectly by means of a clock set to star- or sidereal-time1 and such a clock is the astronomer's companion1 to which he always refers his observations1 and the indications of which alone are always in his mind4 ,this he calls the ,sidereal ,clock4 ,illustration3 ,,fig4 #abb4--;,diagram illustrating the different lengths of solar and sidereal day4 ,we have1 then1 next to consider the difference between the clock used for the transit1 or the sidereal clock1 and an ordinary solar clock1 or between a solar and a sidereal day4 ,let ,s1 ,fig4 #abb1 represent the sun1 and the arc a part of the orbit of the earth1 the earth going in the direction of the arrow4 ,let #b represent the position of the earth one day1 and let #a represent the position of the earth on the day before4 ,a line drawn from the sun through the earth's centre will give us the places a1 b1 on the earth at which it is midday on the side turned towards the sun1 and midnight on the side turned from the sun4 ,now when a revolution of the earth with reference to the stars has been accomplished the earth comes to the second position1 #b2 and c is the point of midday2 and there is a certain angle here between a and c1 through which the earth must turn before it is noon at a1 due to the change of position of the earth1 or to the apparent motion of the sun among the stars1 by which the sun comes to the meridian rather later than the stars each day4 ,now let us suppose that1 while one observer in ,england is observing the sun at midday1 another is observing the stars at the antipodes at midnight1 the star is seen in the direction 4 ,we are aware that the stars are so far away1 that from any point of the earth's orbit they seem to be in absolutely the same place--they do not change their positions in the same way as the sun appears to do amongst them--an observer at b therefore sees on his meridian the star while the observer at a sees the sun on his meridian2 supposing b to represent the same observer1 on the second day1 he will see the star due south before the other observer at a sees the sun due south4 ,the result of that is1 that the sidereal day is shorter than the solar day1 and the sun appears to lose on the stars4 ,if we wish to have a clock to show #ab o'clock when the sun is southing1 we shall want it to go slower by nearly four minutes a day than one which is regulated by the stars and is at #ab o'clock when our starting-point of right ascension--which is the intersection of those two fundamental planes1 the equator and the ecliptic--passes over the meridian4 ,one of the uses of the clock showing sidereal time in connection with the convenient fiction of the 8,mean ,sun10 is to give to the outside world a constant flow of mean time regulated to the average southing of the sun in the middle of the period for which the sun is above the horizon each day in the year4 ,the stellar day1 that is the time from one transit of a star to the next1 is shorter than a solar day by #cm4 #efs41 so what is called sidereal time1 regulated by the transits of well-known stars1 in the manner we shall presently explain1 by no means runs parallel with mean time so far as the clock indications go4 ,indeed when we look at a sidereal clock1 we see something different to the clock we are generally accustomed to see4 ,in the first place1 we have twenty-four hours instead of twelve1 and then generally there is one dial for hours1 another for minutes1 and another for seconds4 ,that of course might happen in the case of the mean-time clock2 but the mean-time clock is not often divided into twenty-four hours1 although it formerly used to be1 as the dials in ,venice still testify4 ,we now see the importance of an absolutely correct determination of the right ascension of stars2 for this right ascension1 expressed in hours1 minutes1 and seconds1 is nothing more nor less than the time indicated by the sidereal clock1 by the side of the transit instrument1 when a star passes over1 or transits1 the central wire of that instrument4 ,hence it is the sidereal clock which keeps time with the stars1 and which we keep correct by means of the transit instrument4 ,illustration3 ,,fig4 #abc4--,system of wires in transit eyepiece4 ,let us show how this was always done some twenty or thirty years ago1 and how it is sometimes done now4 ,the transit room is kept so quiet that one can hear nothing but the ticking of the sidereal clock2 the star to be observed is then carefully watched as it traverses the field of view over the wires1 and the time of transit over each wire is estimated to the tenth of the time between each beat by the observer4 ,we reproduce in ,fig4 #abc a rough representation of what is seen in the field of view of a transit instrument4 ,now if we could be perfectly sure of making an accurate observation by means of the central wire1 it is not to be supposed that astronomers would ever have cared to use this complicated system of wires in their eyepieces2 but so great is the difficulty of determining accurately the time at which a star passes a wire1 that we have in eyepieces introduced a system of several wires1 so that we may take the transit of the star first at one wire1 then at another1 until every wire has been passed over4 ,we want one wire exactly in the middle to represent the real physical middle of the eyepiece so far as skill can do it1 and then there is a similar number of wires on either side at exactly equal distances2 so that the average of all the observations made at each of the wires will be much more likely to be accurate than a single observation at one wire4 ,in this way the astronomer gives himself a good many chances against one to be right4 ,if he lost his chance from any reason when using only one wire1 he would have to wait twenty-four more sidereal hours before he could make his measure again1 but by having five1 or seven1 or twenty-five or more wires in the eyepiece of the telescope1 he increases his chances of correctness3 and the way in which he works is this3 ,while the heavens themselves are taking the stars across the wires he listens to the beating of the clock4 ,if a star crosses one of the wires exactly as the clock is beating1 he knows that it has passed the wire at some second1 and he takes care to know what second that is2 but if1 instead of being absolutely coincident with one of the beats of the clock1 it is half-way between one beat and another1 or nearer to one beat than another1 he estimates the fraction of a second1 and by practice he has no difficulty at all in estimating divisions of time equal to tenths of a second1 and at each particular wire in the eyepiece the transit of the star is thus minutely observed4 ,then if the observations are complete and the mean of them is taken1 it should1 after the necessary corrections for instrumental errors have been applied1 give the actual observation made at the central wire2 if the astronomer cannot make observations at every wire1 he introduces a correction in his mean to make up for the lost observations4 ,this is what is called the 8eye and ear0 method1 because the observer is placed with his eye to the telescope1 and he depends upon his ear to give him the exact interval at which each beat of the clock takes place1 and he requires an exact power of mentally dividing the distance between each beat into ten equal parts1 which are tenths of seconds4 ,in this method of observation every observer differs slightly in his judgment of the instant that the star crosses the wire1 and his estimation differs from the truth by a certain constant quantity which he must always allow for2 this error is called his personal equation4 ,in this way then the transit instrument enables us1 having true time1 to determine the right ascension of a heavenly body as it transits the meridian1 and1 knowing the right ascension of a heavenly body1 we have only to watch its transit in order to know the true time2 so if the observer knows at what time a known star ought to transit1 he has an opportunity of correcting his clock4 ,so much for the eye and ear method of transit observation4 ,there is another which has now to a very large extent superseded it4 ,this is called the 8chronographic method02 we owe it to ,sir ,charles ,wheatstone1 who made it possible about #ahdj4 ,figs4 #abd-g are from drawings of the chronograph in use at ,greenwich1 and by their means we hope to make the principle of the instrument clear4 ,in this chronograph1 g is a long conical pendulum which regulates the driving clock in the case below it1 through the gearing of wheel-work1 as it turns the cylinder1 ,e1 gently and regularly round4 ,on the cylinder is placed paper to receive the mark registering the observations2 along the side of the cylinder or roller run two long screws1 ,k and ,n1 ,fig4 #abe1 which are also turned by the clock1 and on them are carried electro-magnets1 ,a1 ,b1 ,fig4 #abe1 and prickers1 #ce1 ,fig4 #abf2 as the screws turn1 the magnets and prickers are moved along the roller1 and1 as the roller turns1 the pointer1 #cf1 ,fig4 #abg1 traces a fine line on the paper like the worm of a screw on the surface2 and it is close to this line1 which serves as a guide to the eye1 that the prickers make a mark each time a current is sent through the electro-magnets2 this turns each of them into a magnet1 and they then attract a piece of iron which1 in moving upwards1 presses down its pricker by means of a lever1 and registers the instant the current is sent4 ,the different wires are brought1 first from the transit circle to work one pricker1 and then from the clock to work the other1 the clock sending a current and producing a prick on the roller every second4 ,illustration3 ,,fig4 #abd4--,the ,greenwich chronograph4 ,general view4 ,the observer1 instead of depending upon the eye and ear as he had to do before1 has then the means of impressing a mark at any instant upon the same cylinder1 in exactly the same way that the pendulum of the clock impresses the mark of any second1 so that as each wire in the eyepiece of the transit instrument is passed by the star1 he is able1 by the same method as the clock1 to record on this same revolving surface each observation1 which can afterwards be compared with the marks representing the seconds1 and so the exact time of each observation is read off more accurately and with less trouble than by the old method4 ,let us suppose we are making a transit observation3 the clock will be diligently pricking sidereal seconds1 while we1 by a contact-maker held in the hand1 are as diligently recording the moments at which the star passes each wire4 ,illustration3 ,,fig4 #abe4--;,details of the travelling carriage which carries the magnets and prickers4 ,side view and view from above4 ,illustration3 ,,fig4 #abf4--,showing how on the passage of a current round the soft iron the pricker is made to make a mark on the spiral line on the cylinder4 ,illustration3 ,,fig4 #abg4--,side view of the carriage carrying the magnets and the pointer that draws the spiral4 ,this is done by pressing a stud1 and sending a current at each transit2 so that we shall have a dot in every other space between the clock dots1 supposing the wires to be two seconds in time apart2 supposing them to be three seconds apart1 our dots will be in every third space2 supposing them to be four seconds apart1 our dots will be in every fourth space1 and so on2 and tenths and hundredths of seconds are estimated1 by the position of each transit dot between those which record the seconds4 ,in this way one sees that we have on the barrel an absolute record1 by one of the pointers1 of the seconds recorded by the clock1 and1 by the other1 of the exact times at which a star has been seen at each wire of the transit instrument4 ,now of course what is essential in this method is that there shall be a power of determining not only the precise second or tenth of a second of time1 but also the minute at which contact takes place1 otherwise there would be a number of seconds dots without knowing to what minute they corresponded2 it would be like having a clock with only a second-hand and no minute-hand4 ,the brass vertical sliding piece shown at the lower left-hand side in ,fig4 #if1 carries at its upper end two brass bars1 each of which has1 at its right-hand extremity1 between the jaws1 a slender steel spring for galvanic contact2 the lower spring carries a semicircular piece projecting downwards1 which a pin on the crutch rod lifts in passing1 bringing the springs in contact at each vibration3 the contact takes place when the pendulum is vertical1 and the acting surfaces of the springs are1 one platinum1 the other gold2 an arrangement that has been supposed to be preferable to making both surfaces of platinum4 ,by means of the screws n and o1 which both act on sliders1 the contact springs can be adjusted in the vertical and horizontal directions respectively4 ,other contact springs in connection with the brass bars p and q1 on the other side of the back plate1 are ordinarily in contact1 but the contact is broken at one second in each minute by an arm on the escape-wheel spindle4 ,the combination of these contacts permits the clock to complete a galvanic circuit at fifty-nine of the seconds in each minute1 and omit the sixtieth4#ac ,in this way we may suppress the sixtieth second1 thus leaving a blank that marks the minute2 and all that the observer has to do after he has made a record of the transit1 is to go quietly to the barrel1 and mark the hour and minute in the vacant space4 ,a barrel of this size will contain the observations which would be made in some hours2 so that at the end of that time it may be taken off1 and it will give1 with the least possible chance of error1 a permanent record of the work of the astronomer4 ,it is at once apparent that by the introduction of this application of electricity1 astronomy has been an enormous gainer2 but so far we have simply given a description of one instrument which has been suggested for that purpose4 ,a few words may be said on other forms4 ,in the instrument used in the ,royal ,observatory at ,greenwich the rotation of the roller is kept uniform1 as we have seen1 by a conical pendulum2 but there are other methods of attaining this end--there is the fly-wheel and fan1 similar to the arrangement for regulating the striking part of a clock2 there is the governor used for the steam-engine1 and others which give a fairly regular motion--for the motion need not be absolutely uniform1 because the dots1 which form the points from which to measure1 are made by the standard clock4 ,the particular instant at which each minute occurs may be recorded in another way4 ,the two steel springs above described may be pressed together1 not by a pin in the crutch1 but by cogs on a wheel attached to the spindle of the escape-wheel of the clock 7see ,fig4 #abh72 and then all we have to do to stop the transmission of a current at the sixtieth second is to remove one of the cogs4 ,illustration3 ,,fig4 #abh4--,wheel of the sidereal clock1 and arrangement for making contact at each second4 ,another simple method for transmitting seconds' currents has also been occasionally tried4 ,a wire runs down the whole length of the pendulum1 and ends in a projection of such a length that it swings through a small globule of mercury in a cup below it1 the pendulum being connected with one wire from the chronograph and the mercury with the other2 thus there will be a making and breaking of contact each time the point of the pendulum swings through the mercury4 ,it is uncertain which method is the better2 one would prefer that which1 under any circumstances1 could disturb the pendulum least3 but as to which this is opinions differ4 ,we have now described the modus operandi of making time observations with the transit instrument1 the final result of which is that the time shown by the sidereal clock corresponds with the right ascension of the 8clock stars0 as they transit the central wire4 ,the great use1 as we have already stated1 made of the sidereal clock thus kept right by the stars is to correct the mean-time clock with a view of supplying mean solar time to the outside world4 ,as the sidereal clock is regulated by the stars1 it can be corrected by them at any time by the clock stars given in the 8,nautical ,almanac10 whose time of passing the meridian is calculated beforehand much more accurately than a mean-time clock could be corrected by the sun2 we therefore correct our mean clock by the sidereal1 the two agreeing at the vernal equinox1 when the sun is in the first point of ,aries1 and the sidereal clock gaining about #cm4 #efs4 each day until it has gained a whole day1 and agrees again at the next vernal equinox4 ,illustration3 ,,fig4 #abi4--;,arrangement for correcting mean solar time clock at ,greenwich4 ,at ,greenwich there is1 as we have already seen1 a standard1 sidereal clock1 that is1 a clock keeping sidereal time2 and regulated from this is the standard solar time clock1 giving the time by which all our clocks and watches are governed4 ,in practice at ,greenwich the solar clock is regulated as follows3 in the computing room are two chronometers1 c and b1 ,fig4 #abi1 the one1 c1 regulated electrically by the mean-time clock1 and the other1 b1 regulated by the sidereal clock--the error of the latter being known by transit observations of stars on the ,nautical ,almanac list1 the difference between the observed time of transit and the right ascension of the star being the error required4 ,the proper difference between the two clocks is then calculated and the error allowed for1 which shows whether the solar clock is fast or slow2 to correct it the following method is adopted3 ,carried on the pendulum of the solar clock is a slender bar magnet1 about five inches long1 and below it1 fastened to the clock-case1 is a galvanic coil2 the magnet passes at each swing over the upper end of the coil2 if now a current is sent through this coil in one direction repulsion takes place between the magnet and coil1 and the clock is slowed2 if1 on the other hand1 the current is reversed1 the clock is made to gain4 ,now between the two chronometers is a commutator1 d1 which1 by moving the handle to one side or the other1 sends the current through the coil in such a manner that the clock is accelerated or retarded sufficiently to set it right2 when the handle of the commutator is in the position shown in the drawing no action takes place4 ,as an instance of another method of regulating one clock from another1 we will quote what ,professor ,piazzi ,smyth says of the clock arrangements at ,edinburgh4 ,correction of ,mean-time ,clock4--8,first get its error on the observing1 i4e4 sidereal clock4 ,this is always done by coincidence of beats1 safe and certain to within one-tenth of a second1 and with great ease and comfort by means of the loud-beating hammer which strikes the seconds of the sidereal clock on the outside of the case2 one can then watch the neck-and-neck race which takes place every six minutes between the second of a sidereal clock and the second of a mean-time clock1 the former always winning while you look at the motion of the mean-time seconds hand1 and hear the seconds of the sidereal time4 ,having got the error1 say three 7#jc7-tenths of a second slow1 this is the arrangement for correcting it4 ,the pendulum is suspended by a spring extra long1 and a long arm goes across the clock pier1 and the pendulum spring passes through a fine slit in the middle of it1 and the left end 7of said arm7 turns on a pivot1 while the right end rests on a cam1 which can be turned by a handle outside the clock-case4 ,turning the handle one way raises the arm1 and with that lengthens the acting length of the pendulum spring1 and turning the other way1 lowers it and shortens the pendulum1 but so slightly that it takes fifteen minutes of the quickened rate of the pendulum1 when shortened1 to add the required #jc seconds to the indications of the clock40#ad ,the sidereal clock is used in many ways besides the purpose of giving a basis from which we can at any time get solar time1 the distribution of which forms the subject of our next chapter4 ----- ,footnote #ac3 ,nature1 ,april #a1 #ahge4 ,footnote #ad3 ,this plan was devised and executed by ,mr4 ,sang1 ,c4,e41 ,edinburgh4 ,,chapter ,,xviii4 8,,greenwich ,,time0 ,,and ,,the ,,use ,,made ,,of ,,it4 ,we have now described the method of obtaining and keeping true ,greenwich time by means of transit observations1 and the next thing is to distribute it either by controlling or driving other clocks electrically1 or by sending electric signals at known times for persons to set their clocks right4 ,nearly all1 if not quite the whole1 of the mean-time clocks in the ,observatory are driven by a current controlled by the standard clock1 as also is a seconds relay1 a ,fig4 #abi4 ,the clock controls1 by currents sent every second by the relay1 one or two clocks in ,london1 by special wires4 ,so long ago as the year #ahdj ,sir ,charles ,wheatstone read a paper before the ,royal ,society in which he described an apparatus for controlling any number of clocks by one standard clock at a distance away4 ,the principle was1 that at each beat of the standard clock an electric current was sent from it through a wire to the clocks to be worked by it or governed2 and this current made an electro-magnet attract a piece of iron each time it was sent2 and this piece of iron moved backwards and forwards two pallets1 something like those of an ordinary clock1 which turned a wheel1 and so worked the clock4 ,instead of a spring or weight being used to work it regulated by the pallets1 the pallets moved the clock themselves1 and of course keep time with the standard clock4 ,sir ,charles ,wheatstone in this most valuable pioneer paper1 indicates several modifications of this plan4 ,he proposed to the ,astronomer-,royal to test his method by using the then new telegraph line to ,slough1 but the idea was not carried out4 ,this method of driving clocks by electricity naturally required considerable battery power1 and in the more modern systems the clocks are simply controlled1 and not driven1 by electric currents4 ,a very pretty method of regulating clocks by a standard clock is that in use at ,edinburgh4 ,on the pendulum rod of the clock to be regulated1 and low down on the same1 is a coil of fine covered wire wound round a short tube4 ,two permanent magnets are placed in line with each other1 with their ,n or ,s ends close together and the other ends attached to the clock-case1 in such a manner that the coil1 on swinging with the pendulum1 can slide over the magnets without touching4 ,the terminal wires of the coil are led up to near the point of suspension of the pendulum1 so as not to affect its swing1 and the regulating current is sent through a wire like a telegraph wire from the standard clock1 and from this wire round the coil and then to the earth1 or back by another wire4 ,currents are sent through the wires in contrary directions during each successive second1 so that the current in the coil flows in one direction during its swing from1 say1 right to left1 and in the contrary direction when swinging from left to right2 the effect of the current flowing in one direction is to cause one magnet to repel the coil off it1 and the other to attract it over it1 so that there is a tendency to throw the coil from one side of its swing to the other1 and back again when the current is reversed4 ,a little consideration will make it clear that if the pendulum tries to go too fast the coil will tend to commence its return swing before the current assisting the previous swing has stopped1 and it will therefore meet with resistance1 and be brought back to correct time4 ,the alternate currents during each second may be sent by having a wheel of thirty long teeth on the axis of the seconds hand4 ,above the wheel1 and insulated from each other1 are fixed two light springs which descend side by side on either side of the teeth of the wheel1 and at right angles to each spring there projects sideways a little bar of agate with sloping sides1 which is lifted up by the teeth as they pass2 one agate is fastened a little lower down its spring than the other1 so that they are held one above the other1 and half the distance between two teeth apart3 the wheel is so arranged that while at rest one of the teeth presses against one of the agates and pushes the spring outwards1 while the other agate drops between two teeth4 ,at the next tick of the clock the wheel will move one-half a tooth's distance and the other agate will be raised and the first dropped4 ,at the bottom of each spring is a little platinum knob that is brought against a platinum plate as each spring is raised1 so as to make electric contact4 ,two batteries 7single cells of 8sawdust-,daniell's0 answer admirably for short distances7 are used1 the pole of one being put in contact with the upper attachment of one spring and the - pole of the other battery in contact with the other spring4 ,the other poles are put to earth1 or connected to the return wire from the governed clock4 ,the plate against which the springs are lifted is put in connection with the line wire going to the regulated clock4 ,then1 as either spring is lifted up during the swing of the pendulum from side to side1 a or - current is sent through the line wire from one of the batteries4 ,it is not absolutely necessary to use two batteries1 one being sometimes sufficient1 and in this case one spring is thrown out of action1 and a current sent only during every other second in the same direction4 ,the battery may in this case be placed close to the regulated clock1 or anywhere in the circuit1 so long as a current flows whenever the standard clock completes the circuit at the other end4 ,this method has the advantage that the amount of current sent can be regulated at will by a person at the regulated clock1 so that it is possible by putting on more battery power to get sufficient current through the wire to work a bell ringing at every other second1 or a galvanometer1 showing when the seconds hand of the standard clock is at the ,os1 for there is one tooth cut from the wheel in such a position that when the seconds hand is at ,os no current is sent for two or more following seconds according as one or both springs are acting2 knowing this1 the observer watches for the first missing current or 8dropped second10 and so finds if his clock is being correctly regulated4 ,we see now the necessity for correcting the standard clock by gradually increasing or decreasing the rate1 for if it were done rapidly1 the controlled clocks would break away from the control1 and not be slowed and accelerated with the standard4 ,at ,greenwich the correction1 usually only a fraction of a second1 is made a little before the hours of #aj ,a4,m4 and #a ,p4,m41 since at those instants a distribution of time is made throughout the country4 ,this distribution is made as follows3-- ,an electric circuit is broken in two places at the standard clock1 one place of which is connected for some seconds on either side of each hour1 while the other is connected at each sixtieth second2 both breaks can therefore be only connected at the commencement of each hour1 and then only can the current pass4 ,we will call this1 therefore1 the hourly current3 it acts on the magnet discharging the ,greenwich time ball at one o'clock daily1 and on the magnet of the hourly relay shown in ,fig4 #abi1 which completes various circuits4 ,one goes to the ,london ,bridge station of the ,south-,eastern ,railway ,co41 and the other to the ,general ,post ,office for further distribution4 ,the bell and galvanometer in the figure marked 8,s4 ,e4 ,r4 hourly signal and ,deal ball10 and 8,post ,office ,telegraphs0 show the passage of these signals4 ,we have now got the hourly signal at the ,post ,office1 and this is distributed by means of the ,chronopher1 or rather ,chronophers1 for there are two1 the old one originally constructed by ,mr4 ,yarley1 and brought from ,telegraph ,street on the removal to ,st4 ,martin's-le-,grand1 and a new one1 much larger1 shown in the accompanying ,fig4 #acj4 ,it is to this that the ,greenwich wire is led1 and the current transmitted to the different lines4 ,the lines are divided into four groups1 7#a7 the metropolitan1 7#b7 short provincial1 7#c7 medium provincial1 7#d7 long provincial2 the first being wires passing to points in ,london only1 the second to places within about #ej miles of ,london1 the third to more distant places1 and the fourth to the more distant places still1 requiring signals4 ,the ends of each of the four groups are brought together1 and each group has its separate relay4 ,these four relays--the left-hand four shown in ,fig4 #acj--;are all acted upon by the ,greenwich signal and therefore act simultaneously1 each relay sending a portion of the current of its battery through each wire of its group4 ,illustration3 ,,fig4 #acj4--,the ,chronopher4 ,the metropolitan group1 being used only for time purposes1 is always connected with the relay1 but to the country1 signals are sent only twice a day1 namely1 at #aj ,a4,m4 and at #a ,p4,m41 and as the ordinary wires are used for this purpose1 they must be switched into communication with ,nos4 #b1 #c1 and #d relays4 ,the action at each hour is as follows3--,the wires leading to the respective towns are connected with their speaking instruments through a contact spring2 these contact springs are shown in the figure in a row1 like the keys of a piano2 along the keys runs a flat bar which at a short time before #aj ,a4,m4 and #a ,p4,m4 is turned on its axis by the clockwork above1 by so doing it presses back all the keys from their respective studs1 and so cuts off communication with the speaking instruments1 and puts the wires into communication with the bar1 which is divided into three insulated portions1 each in communication with a relay and battery2 the batteries and relays become connected with their respective groups1 and a constant current flows through all the wires to the distant stations serving as a warning4 ,when the ,greenwich current arrives the relays reverse the currents1 and this gives the exact time4 ,shortly afterwards the clock turns back the rod and the springs go into contact with their respective instruments1 and all goes on as before4 ,one of the remaining relays of the apparatus sends a current to ,westminster clock tower for the rating of the clock there1 but it is in no way mechanically governed by the current4 ,the apparatus is entirely automatic1 and to judge of the degree of accuracy obtained an experiment was made4 ,one of the distributing wires was connected with a return wire to ,greenwich1 and the outgoing current to the ,post ,office and the incoming one were passed round galvanometers1 when no sensible difference could be seen in the indications4 ,at #aj ,a4,m4 a considerable distribution goes on by hand4 ,at this instant a sound signal is heard from the chronopher1 and the clerks immediately transmit signals through the ordinary instruments to some #fjj places2 these again act as centres distributing the time to railway stations and smaller places4 ,the methods of signalling the time are various2 at some places1 as at ,edinburgh1 ,newcastle1 ,sunderland1 ,dundee1 ,middlesborough1 and ,kendal1 a gun is fired at #a ,p4,m4 ,the history of the introduction of time-guns is a somewhat curious one4 ,in ,august #ahfc1 during the meeting of the ,british ,association at ,newcastle1 ,mr4 ,n4 ,j4 ,holmes contrived the first electric time-gun4 ,this gun was fired by the electric current direct from the ,royal ,observatory at ,edinburgh1 #abj miles distant4 ,time-guns were afterwards experimentally fired at ,north ,shields and ,sunderland2 the ,sunderland gun was after a time withdrawn2 the ,newcastle and ,north ,shields time-guns are regularly fired every day at #a ,p4,m4 ,four time-guns were mounted in ,glasgow1 also to be fired by the electric current from ,edinburgh2 a large #cb-pounder was placed at ,port ,dundas1 on the banks of the ,forth and ,clyde ,canal2 a second small gun was placed near the ,royal ,exchange2 a third #ah-pounder at the ,bromielaw1 for the benefit of ,clyde ships in harbour2 and a fourth twenty-five miles further down the ,clyde1 at the ,albert ,quay1 ,greenock1 for the vessels anchored off the tail of the bank4 ,these four guns1 and the two at ,newcastle1 were regularly fired from the ,royal ,observatory1 ,edinburgh1 for some weeks4 ,a local jealousy springing up amongst a few of the ,glasgow ,college ,professors and the ,edinburgh ,observatory1 against the introduction of mean-time into ,glasgow from the ,royal ,observatory ,edinburgh1 instead of deriving it from the ,glasgow ,observatory clock 7the longitude of which was undetermined at that time71 the originator of the guns1 ,mr4 ,holmes1 was cited before the police-court1 charged under the ,act with discharging firearms in the public streets4 ,the jealousy ended in the withdrawal of the guns1 and ,glasgow1 from then until now1 has been without any practical register of true time4#ae ,another system of time signalling is to expose a ball to view on the top of a building1 and drop it1 as in the case of the ball automatically dropped at ,greenwich every day4 ,we have already mentioned that one of the wires from the ,greenwich ,observatory connects it with the ,london ,bridge ,station1 and this is used for dropping the time-ball at ,deal4 ,in return for the hourly signals the ,company give up the use of the wires to ,deal for two or three minutes about #a ,p4,m41 when the ,deal wire is switched into communication with the ,greenwich wire by a clock1 just in the same manner as at the ,post ,office1 and communication is also made at ,ashford and ,deal1 in order that the current shall go to the time-ball4 ,in order that they shall know at ,greenwich that the ball has fallen correctly1 arrangements are made so that the ball on falling sends a return current back to ,greenwich4 ,it appears that erroneous drops are rare1 but1 if such is the case1 a black flag is immediately hoisted and the ball dropped at #b ,p4,m4 ,hourly signals are distributed on the metropolitan lines and to the 8,british ,horological ,institute0 for ,clerkenwell2 the leading ,london chronometer makers also receive them privately4 ,we now come to deal with one of the practical uses of the clock and transit instrument with reference to determining longitudes4 ,the earth rotates once every twenty-four hours1 and if at any time a star is directly south of ,greenwich it is also due south of all places on the meridian of ,greenwich north of the equator1 and north of all places on the same meridian south of the equator2 then1 as the earth rotates1 the meridian of ,greenwich will pass from under the star1 and others to the west will take its place1 and in an hours time1 at #a ,p4,m41 a certain meridian to the west of ,greenwich will be under the star1 and in that case all places on this meridian will be an hour west of ,greenwich1 and so on through all the twenty-four hours1 the meridian being called so many hours1 minutes1 or seconds1 west1 as it passes under any star that length of time after the meridian of ,greenwich4 ,it is immaterial whether we reckon longitude in degrees or in time1 for since there are #cfj degrees or twenty-four hours into which the equator is divided1 each hour corresponds to #ae4 ,we also express the longitude of a place by its distance east of ,greenwich in hours1 so instead of calling a place twenty-three hours west1 it is called one hour east4 ,suppose we wish to find the longitude of any place1 all that is required to be known to an observer there is the exact time that a certain star is on the meridian of ,greenwich2 he then observes the time that elapses before the star comes to his meridian1 and this time is the longitude required4 ,this1 of course1 only shows the principle1 for in practice it is not absolutely necessary for the star to be on either meridian1 provided its distance on either side is known1 when1 of course1 the difference between the times when it actually crosses the meridian can be reckoned4 ,in practice a difficulty arises in finding out at a distance from ,greenwich what time it is there4 ,it is of course twelve o'clock at ,greenwich when the sun crosses the meridian1 and it is also twelve o'clock at all the other places when the sun crosses their meridian3 but if a place is two hours west of ,greenwich1 the sun crosses the meridian two hours later than it does at ,greenwich1 and consequently their clock is two hours slower than ,greenwich time1 hence the term 8local time10 which is different for different places east or west of ,greenwich4 ,we have taken above a star for our fixed point1 but obviously the sun answers the same purpose4 ,it will appear from this1 that if we know the difference between the local times of two places1 we also know the longitude of one place from the other1 which is the same4 ,a great number of ways have been tried in order to make it known at one observing station what time it is at the other4 ,rockets are sent up1 gunpowder fired1 and all kinds of signals made at fixed times for this purpose2 but these1 of course1 only answer for short distances1 so for long ones carefully adjusted chronometers have to be carried from one station to the other to convey the correct time2 unless telegraph wires are laid from one place to another1 as from ,england to ,america2 then it is easy to let either station know what time it is at the other4 ,for ships at sea chronometers answer well for a short time1 but they are liable to variation4 ,there are certain astronomical phenomena the instant of occurrence of which can be foretold--and published in the nautical almanacs--such as the eclipses of ,jupiter's moons1 and the position of our own moon amongst the stars4 ,suppose then an eclipse of one of ,jupiter's moons is to take place at #a ,p4,m4 ,greenwich time1 and it is observed at a place at #b ,p4,m4 of the observer's local time1 i4e41 two hours after the sun has passed his meridian1 then manifestly the clock at ,greenwich is at #a ,p4,m4 while his is at #b ,p4,m41 and the difference of local time is one hour1 and the place is one hour1 or #ae1 east of ,greenwich4 ,if1 however1 the eclipse was observed at #ab noon1 then the place must be one hour west of ,greenwich4 ,the local time being one hour slower than ,greenwich shows that the sun does not south till an hour after it does at ,greenwich1 or1 in reality1 the place does not come under the sun till after the meridian at ,greenwich has passed an hour before1 clearly showing it to be west of ,greenwich4 ,we shall now see how easy it is to find the longitude when the two stations are electrically connected4 ,suppose we wish to determine the difference of longitude of two places in ,england1--this can be determined with the utmost accuracy in a short time if the observers have a chronograph1 of the kind just described1 to record the transit of a star at these two places4 ,the observers at each station arrange that the observer at ,station ,a shall observe the transit of a certain star on his chronograph1 and the observer at ,station ,b shall observe the transit of the same star on his1 and then with the faithful clock1 beating seconds and marking them on the surface of both chronographs simultaneously1 the difference of sidereal time between the transit of the same star over ,station ,a and ,station ,b will be an absolute distance to be measured off in as delicate a way as possible by comparison of the roller of each chronograph1 and will give exactly how much time elapses between the two transits4 ,this is the longitude required4 ,there are various methods of utilizing the same principle1 as1 for instance1 one chronograph only may be used1 and both observers then register their transits on the same cylinder4 ,but when we have to deal with considerable distances1 such as between ,england and the ,united ,states1 then we no longer employ this method4 ,from ,valentia we telegraph to ,newfoundland in effect 8,our time is so-and-so10 and then the observer at ,newfoundland telegraphs to ,valentia 8,our time is so-and-so40 ,in this way the absolute longitude of the ,west of ,ireland and ,america and the different observatories of ,europe has been determined with the greatest accuracy4 ,so it appears there are two methods1 the first showing one time1 say ,greenwich time1 at both places1 and showing the difference in times of transit of stars2 or secondly1 having the clock at each place going to its own local time1 so that a certain star transits at the same local time at each place1 and finding the difference between the two clocks4 ----- ,footnote #ae3 ,it was found1 that between the passing of the spark into the gun1 and the ignition of the powder and discharge of the piece1 one tenth of a second elapsed4 ,,chapter ,,xix4 ,,other ,,instruments ,,used ,,in ,,astronomy ,,of ,,precision4 ,in former chapters we have described the transit circle as it now exists as the result of the thought of ,tycho1 ,picard1 ,rmer1 and ,airy4 ,this1 though the fundamental instrument in a meridional observatory1 is by no means the only one1 and we must take a glance at the others4 ,in ,rmer's 8,observatorium ,tusculaneum10 near ,copenhagen1 built in #agjd1 there was not only a transit circle in the meridian of course1 but a transit instrument in the prime vertical1 i4e4 swinging in a vertical plane at right angles to the former one1 so that while the optical axis of one always lies in a ,n4,s4 plane1 that of the other lies in an ,e4,w4 one4 ,rmer did not use this instrument much2 it remained for the great ,bessel to point out its value in determinations of latitude4 ,this instrument is1 so to speak1 self-correcting1 because between the transit of a star over its wires while pointing to the east of the meridian1 and that while pointing to the west its telescope can be reversed in its ,ys1 or one position may be taken for one night's observations1 and the other for the next1 and so on4 ,in ,struve's form of this instrument the transit of stars can be observed at an interval of one minute and twenty seconds1 this time only being required to raise it from the ,ys1 to rotate it through #ahj1 and lower it again4 ,this rapid reversal1 and consequent elimination of instrumental imperfections1 enable observations of the most extreme precision to be made in such delicate matters as the slight differences of declination of stars due to aberration1 nutation1 and the like4 ,the intersection of the meridian with the prime vertical marks the zenith4 ,to determine this3--first1 there is the zenith sector1 invented by ,hooke2 it consists of a telescope1 carried by an axis on one side of the tube1 and at right angles to it1 so that the telescope swings exactly as a transit does1 and it is provided with cross wires in the same manner2 instead1 however1 of having a whole circle1 it has only two segments of a circle2 and as it is never required to swing the telescope far from its vertical position1 there is a diagonal reflector at the eyepiece1 so that the observer can look sideways1 instead of upwards1 in an awkward position4 ,its use is to determine the zenith distance of stars as they pass near that point4 ,these distances are read off on the parts of the circle by verniers or microscopes1 as in the transit circle4 ,the zenith telescope1 chiefly designed by ,talcott1 is the modern equivalent of the sector1 and both instruments are more used in geodetical operations than in fixed observatories4 ,at ,greenwich1 however1 there is an instrument for determining zenith distances of very special construction4 ,this is called the reflex zenith tube1 shown in ,fig4 #aca4 ,it is a sectional drawing of one of those instruments showing the path of the rays of light4 ,a1 ,b1 is an object-glass1 fixed horizontally1 and below it is a trough of mercury1 ,c1 the surface of which is always of course horizontal4 ,the light from a star near the zenith is allowed to fall through the object-glass1 which converges the rays just so much that they come to a focus at ,f1 after having been reflected from the surface of the mercury1 and also by the diagonal mirror or prism1 ,g2 at ,f1 therefore1 we have an image of the star1 which can be examined together with the cross-wires at the eyepiece1 ,m4 ,there is in this instrument no necessity for the accurate adjustments that there is in the case of the transit1 the surface of the mercury being always horizontal1 and so giving an unaltering datum plane4 ,illustration3 ,,fig4 #aca4--,reflex ,zenith ,tube4 ,when the star is perfectly vertical1 its image will fall on a certain known part in the eyepiece2 but1 as it leaves the vertical1 the angle of incidence of its light on the mercury alters1 and likewise that of reflection1 so that the position of the image changes1 and this change of position in the eyepiece is measured by movable cross-wires and a micrometer screw1 similar to that employed for reading the circle in the transit circle4 ,at the present time ,draconis is the star which passes very nearly through the zenith of ,greenwich1 and observations of this star are accordingly made at every available opportunity4 ,we now pass to an enlargement of the sphere of observation of the transit circle in order that any object can be viewed at all times when above the horizon2 in this case the transit circle passes into the alt-azimuth1 or altitude and azimuth instrument1 astronomical theodolite1 or universal instrument4 ,a reference to ,fig4 #acb--;a woodcut of an ordinary theodolite--will show the new point introduced by this construction4 ,imagine the upper part of the theodolite fixed with its telescope and circle in the plane of the meridian--we have the transit circle2 swing the theodolite round through #ij--we have the prime vertical instrument4 ,now instead of having the upper part fixed let it be free to rotate on the centre of the horizontal circle--we have the alt-azimuth4 ,in the description of the instruments used in ,tycho's observatory 7,chapter ,,iv471 we described another instrument by which ,tycho and the ,landgrave of ,hesse-,cassel endeavoured to make observations out of the meridian2 and we may remember that they almost had to give the matter up in despair1 because they could not find any clocks sufficiently good to enable them to fix the position of the star4 ,illustration3 ,,fig4 #acb4--,theodolite4 ,illustration3 ,,fig4 #acc4--,portable ,alt-azimuth4 ,if we refer again to ,fig4 #ah1 we see the method by which ,tycho tried to get the two co-ordinates4 ,on the horizontal circle there are the graduations for azimuth1 or the measurement from the south along the horizon1 and on the vertical quadrant are the graduations for altitude4 ,now let us turn to the modern equivalent of that instrument4 ,fig4 #acc shows this in a portable form4 ,the upper part of the instrument is1 as one sees1 nothing more than a transit circle exactly equivalent to the one described4 ,we have a telescope carried on a horizontal axis1 supported by a pillar2 we have the reading microscopes1 and the like2 but the support of the horizontal axis1 instead of being on the solid ground1 as it is in the transit circle1 rests on a movable horizontal circle1 which is also read by microscopes arranged round it1 so that all errors may be eliminated4 ,with this instrument we can get the altitude of an object at any distance from the meridian1 and at the same time measure its distance east and west of it4 ,the arrangements designed by the ,astronomer ,royal for observations of the moon at ,greenwich are more elaborate4 ,in the ,greenwich alt-azimuth1 the telescope is swung on pivots between two piers1 just as in the case of the transit1 these piers being fixed to the horizontal circle4 ,the great advantage of this instrument is that the true place of a heavenly body can be determined whenever it is above the horizon2 we have neither to wait for a transit over the meridian nor over the prime vertical4 ,nevertheless its use is not general in fixed observatories4 ,reduce the dimensions of the horizontal circle and increase those of the vertical one1 and we have the vertical circle designed by ,ertel1 and largely used in foreign observatories4 ,,book ,v4 ,,the ,,equatorial4 ,,chapter ,,xx4 ,,various ,,methods ,,of ,,mounting ,,large ,,telescopes4 ,we have already gone somewhat in detail into the construction of the transit circle1 which is almost the most important of modern astronomical instruments4 ,we then referred to the alt-azimuth1 in which1 instead of dealing with those meridional measurements which we had touched upon in the case of the transit circle1 we left1 as it were1 the meridian for other parts of the sphere and worked with other great circles1 passing not through the pole of the heavens1 but through the zenith4 ,we now pass to the 8optick tube10 as used in the physical branch of astronomy1 and we have first to trace the passage from the alt-azimuth to the ,equatorial1 as the most convenient mounting is called4 ,this equatorial gives the observer the power of finding any object at once1 even in the day-time1 if it be above the horizon2 and1 when the object is found1 of keeping it stationary in the field of view4 ,but although this form is the most convenient1 it is not the one universally adopted1 because it is expensive1 and because1 again1 till within the last few years our opticians were not able to grapple with all its difficulties4 ,hence it is that some of the instruments which have been most nobly occupied in investigations in physical astronomy have been mounted in a most simple manner1 some of them being on an alt-azimuth mounting4 ,of these the most noteworthy example is supplied by the forty-feet instrument erected by ,sir ,william ,herschel at ,slough4 ,illustration3 ,,fig4 #acd4--,the #dj-;feet at ,slough4 ,lord ,rosse's six-feet reflector again is mounted in a different manner4 ,it is not equatorially mounted2 the tube1 supported at the bottom on a pivot1 is moved by manual power as desired between two high side walls1 carrying the staging for observers1 and so allowing the telescope a small motion in right ascension of about two hours4 ,our amateurs then may be forgiven for still adhering to the alt-azimuth mounting for mere star-gazing purposes4 ,illustration3 ,,fig4 #ace4--,lord ,rosse's #f-;feet4 ,illustration3 ,,fig4 #acf4--,refractor mounted on ,alt-azimuth ,tripod for ordinary ,stargazing4 ,we must recollect that1 with the alt-azimuth1 we are able to measure the position of an object with reference to the horizon and meridian2 but suppose we tip up the whole instrument from the base1 so that1 instead of having the axis of the instrument vertical1 we incline it so as to make the axis1 round which the instrument turns in azimuth1 absolutely parallel to the earth's axis4 ,of course1 if we were using it at the north pole or the south pole1 the axis would be absolutely vertical1 as when it is used as an alt-azimuth1 or otherwise it would not be absolutely parallel to the axis of the earth4 ,on the other hand1 if we were using it at the equator1 it would be essential that the axis should be horizontal1 since to an observer at the equator the earth's axis is perfectly horizontal2 but1 for a middle latitude like our own1 we have to tip this axis about #ea from the horizontal1 so as to be in proper relationship with1 i4e4 parallel to1 the earth's axis4 ,having done this1 we can1 by turning the instrument round this axis1 called the polar axis1 keep a star visible in the field of view for any length of time we choose by exactly counteracting the rotation of the earth1 without moving the telescope about its upper1 or what was its horizontal1 axis4 ,the lower circle of the instrument will then be in the plane of the celestial equator1 and the upper one1 at right angles to it1 will enable us to measure the distance from that plane1 or the declination of an object1 while the lower circle will tell us the distance of the object from the meridian in hours or degrees4 ,with the aid of good circles and good clocks1 we can thus determine a star's position4 ,fig4 #acg shows an ,equatorial ,stand1 one of the first kind of equatorials used by astronomers4 ,we see at once the general arrangements of the instrument4 ,in the first place1 we have a horizontal base1 ,d1 and on it1 and inclined to it1 is a disc of metal1 ,c2 again on this disc lies another disc1 ,a1 ,b1 which can revolve round on ,c1 being held to it by a central stud1 so that when ,a ,b is in the plane of the earth's equator its axis points to the pole and is parallel to the axis of the earth4 ,on the upper disc there are two supports for the axis of the telescope1 ,e1 which is at right angles to the polar axis and is called the declination axis of the telescope2 round it the telescope has a motion in a direction from the pole to the equator4 ,illustration3 ,,fig4 #acg4--,simple ,equatorial ,mounting4 ,in the equatorial mounting1 clockwork is introduced1 and after the instrument has been pointed to any particular star or celestial body1 the clock is clamped to the circle moving round the polar axis1 and so made to drive it round in exactly the time the earth takes to make a rotation4 ,by a clock is meant an instrument for giving motion1 not with reference to time1 but so arranged that1 if it were possible to use it continuously1 the motion would exactly bring the telescope round once in the twenty-four sidereal hours which are necessary for the successive transits of stars over the meridian4 ,there is an objection to the form of instrument given above1--the telescope cannot be pointed to any position near the pole1 since the stand comes in the way4 ,this is obviated in the various methods of mounting1 which we shall now pass under review4 ,the ,german ,mounting4 ,this is the form now almost universally adopted for refractors and reflectors under #bj inches aperture4 ,the polar axis has attached to it at right angles a socket through which the declination axis passes1 and this axis carries the telescope at one end and a counterweight at the other4 ,the polar axis lies wholly below the declination axis1 and both are supported by a central pillar entirely of iron1 or partly of stone and partly of iron4 ,by the courtesy of ,messrs4 ,cooke and ,sons1 ,mr4 ,howard ,grubb1 and ,mr4 ,browning1 we are enabled to give examples of the various forms of this mounting now in use in this country for instruments of less than #bj inches aperture4 ,in ,fig4 #ach1 we have the type form of ,equatorial ,refractor introduced some #cj years ago by the late ,mr4 ,thomas ,cooke4 ,the telescope is represented parallel to the polar axis1 which is inclosed in the casing supported by the central pillar1 and carries one large right ascension circle above and another smaller one below1 the former being read by microscopes attached to the casing4 ,the socket or tube carrying the declination axis is connected with the top of the polar axis4 ,to this the declination circle is fixed1 while an inner axis fixed to the telescope carries the verniers4 ,illustration3 ,,fig4 #ach4--;,cooke's form for ,refractors4 ,illustration3 ,,fig4 #aci4--,mr4 ,grubb's form applied to a ,cassegrain ,reflector4 ,the clock is seen to the north of the pillar4 ,while this is driving the telescope1 rods coming down to the eyepiece enable the observer to make any small alterations in right ascension or declination2 indeed in all modern instruments everything except winding the clock is done at the eyepiece1 so that the observer when fairly at work is not disturbed4 ,the lamp to illuminate the micrometer wires is shown near the finder4 ,the friction rollers1 which take nearly all the weight off the surfaces of the polar axis1 are connected with the compound levers shown above the casing of the polar axis4 ,in ,fig4 #aci we have ,mr4 ,grubb's revision of the ,german form4 ,the pillar is composite1 and the support of the upper part of the polar axis is not so direct as in the mounting which has just been referred to4 ,there are1 however1 several interesting modifications to which attention may be drawn4 ,the lamp is placed at the end of the hollow polar axis1 and supplies light not only for the micrometer wires1 but for reading the circles2 the central cavity of the lower support is utilised for the clock1 which works on part of a circle1 instead of a complete one1 as in the instrument already described4 ,in the case of ,newtonian reflectors the observer requires to do his work at the upper end of the tube2 this therefore should be as near the ground as possible4 ,this is accomplished by reducing the support to a minimum4 ,figs4 #adj and #ada show two forms of this mounting1 designed by ,mr4 ,grubb and ,mr4 ,browning4 ,the two largest and most perfectly mounted refractors on the ,german form at present in existence are those at ,gateshead and ,washington1 ,u4,s4 ,the former belongs to ,mr4 ,newall1 a gentleman who1 connected with those who were among the first to recognise the genius of our great ,english optician1 ,cooke1 did not hesitate to risk thousands of pounds in one great experiment1 the success of which will have a most important bearing upon the astronomy of the future4 ,illustration3 ,,fig4 #adj4--;,grubb's form for ,newtonians4 ,illustration3 ,,fig4 #ada4--;,browning's mounting for ,newtonians4 ,in the year #ahfj the largest refractors which had been turned out of the ,optical ,institute at ,munich under the control1 first1 of the great ,fraunhofer1 and afterwards of ,merz1 were those of #agg square inches area at ,poulkowa and ,cambridge 7,u4,s474 ,our own ,cooke1 who was rapidly bringing back some of the old prestige of ,dollond and ,tulley's time to ,england--a prestige which was lost to us by the unwise meddling of our excise laws and the duty on glass1#af which prevented experiments in glass-making--had completed a #i inch for ,mr4 ,fletcher and a #aj inch for ,mr4 ,barclay2 while in ,america ,alvan ,clarke had gone from strength to strength till he had completed a refractor of #ah inches for ,chicago4 ,the areas of these objectives are #fg1 #ghe1 and #bfh inches respectively4 ,those who saw the great ,exhibition of #ahfb may have observed near the ,armstrong ,gun trophy two circular blocks of glass some #bf inches in diameter and about two inches thick standing on their edges4 ,these were two of the much-prized 8discs0 of optical glass manufactured by ,messrs4 ,chance of ,birmingham4 ,at the close of the ,exhibition they were purchased by ,mr4 ,newall1 and transferred to the workshops of ,messrs4 ,cooke and ,sons at ,york4 ,the glass was examined and found perfect4 ,in time the object-glass was polished and tested1 and the world was in possession of an astronomical instrument of nearly twice the power of the #ah inch ,chicago instrument--#dhe inches area to #bfh4 ,such an achievement marks an epoch in telescopic astronomy1 and the skill of ,mr4 ,cooke and the munificence of ,mr4 ,newall will long be remembered4 ,the general design and appearance of this monster among telescopes will be gathered from the general view given in the frontispiece1 for which we are indebted to ,mr4 ,newall4 ,it is the same as that of the well-known ,cooke equatorials2 but the extraordinary size of all the parts has necessitated the special arrangement of most of them4 ,the length of the tube1 including dew-cap and eye-end1 is #cb feet1 and it is of a cigar shape1 the diameter at the object-end being #bi inches1 at the centre of the tube #cd inches1 and at the eye-end #bb inches4 ,the cast-iron pillar supporting the whole is #ai feet in height from the ground to the centre of the declination axis1 when horizontal2 and the base of it is #e feet #i inches in diameter4 ,the trough for the polar axis alone weighs #ad cwt41 the weight of the whole instrument being nearly #f tons4 ,the tube is constructed of steel plates riveted together1 and is made in five lengths screwed together with bolts4 ,the flanges were turned in a lathe1 so as to be parallel to each other4 ,it weighs only #ac cwt41 and is remarkably rigid4 ,inside the outer tube are five other tubes of zinc1 increasing in diameter from the eye to the object-end2 the wide end of each zinc tube overlapping the narrow end of the following tube1 and leaving an annular space of about an inch in width round the end of each for the purpose of ventilating the tube1 and preventing1 as much as possible1 all interference by currents of warm air with the cone of rays4 ,the zinc tubes are also made to act as diaphragms4 ,the two glasses forming the object-glass weigh #add lb41 and the brass cell weighs #hj lb4 ,the object-glass has an aperture of nearly #be inches1 or #dhe inches area1 and in order as much as possible to avoid flexure from unequal pressure on the cell1 it is made to rest upon three fixed points in its cell1 and between each of these are arranged three levers and counterpoises round a counter-cell1 which act through the cell direct on to the glass1 so that its weight in all positions is equally distributed among the twelve points of support1 with a slight excess upon the three fixed ones4 ,the focal length of the lens is #bi feet4 ,attached to the eye-end of the tube are two finders1 each of #abe inches area2 they are fixed above and below the eye-end of the main tube1 so that one may be readily accessible in all positions of the instrument4 ,it is also supplied with a telescope having an object-glass of #cc inches area4 ,this is fixed between the two finders1 and is for the purpose of assisting in the observations of comets and other objects for which the large instrument is not so suitable4 ,this assistant telescope is provided with a rough position circle and micrometer eyepieces4 ,two reading microscopes for the declination circle are brought down to the eye-end of the main tube2 the circle--#ch inches in diameter--is divided on its face and edge1 and read by means of the microscopes and prisms4 ,the slow motions in declination and ,r4 ,a4 are given by means of tangent screws1 carrying grooved pulleys1 over which pass endless cords brought to the eye-end4 ,the declination clamping handle is also at the eye-end4 ,the clock for driving this monster telescope is fixed to the lower part of the pillar1 and is of comparatively small proportions1 the instrument being so nicely counterpoised that a very slight power is required to be exerted by the clock1 through the tangent screw1 on the driving-wheel 7seven feet in diameter71 in order to give the necessary equatorial motion4 ,the declination axis is of peculiar construction1 necessitated by the weight of the tubes and their fittings1 and corresponding counterpoises on the other end1 tending to cause flexure of the axis4 ,this difficulty is entirely overcome by making the axis hollow1 and passing a strong iron lever through it having its fulcrum immediately over the bearing of the axis near the main tube1 and acting upon a strong iron plate rigidly fixed as near the centre of the tube as possible1 clear of the cone of rays4 ,this lever1 taking nearly the whole weight of the tubes1 c41 off the axis1 frees it from all liability to bend4 ,the weight of the polar axis on its upper bearing is relieved by anti-friction rollers and weighted levers2 the lower end of the axis is conical1 and there is a corresponding conical surface on the lower end of the trough2 between these two surfaces are three conical rollers carried by a loose or 8live0 ring1 which adjust themselves to equalize the pressure4 ,the hour-circle on the bottom of the polar axis is #bf inches in diameter1 and is divided on the edge1 and read roughly from the floor by means of a small diagonal telescope attached to the pillar2 a rough motion in ,r4 ,a4 by hand is also arranged for1 by a system of cogwheels1 moved by a grooved wheel and endless cord at the lower end of the polar axis1 so as to enable the observer to set the instrument roughly in ,r4 ,a4 by the aid of the diagonal telescope4 ,it is also divided on its face1 and read by means of microscopes4 ,the declination and hour-circle will probably be illuminated by means of ,geissler tubes1 and the dark and bright field illuminations for the micrometers will be effected by the same means4 ,illustration3 ,,fig4 #adb4--,the ,washington ,great ,equatorial4 ,so soon as the success of the ,newall experiment was put beyond all question by ,cooke1 ,commodore ,b4 ,f4 ,sands1 the superintendent of the ,u4,s4 ,naval ,observatory1 sent a deputation1 consisting of ,professors ,s4 ,newcomb1 ,asaph ,hall1 and ,mr4 ,harkness1 accompanied by ,mr4 ,alvan ,clarke1 to examine and report upon the ,newall telescope1 and the result was that they commissioned ,alvan ,clarke to construct a large telescope for that country4 ,in the ,washington telescope the aperture of the object-glass is #bf inches--that is1 one inch larger than the ,english type-instrument4 ,the general arrangements are shown in the accompanying woodcut4 ,it will be seen that the mounting is much lighter than in the ,english instrument1 and a composite pillar gives place for the clock in the central cavity4 ,the ,english ,mounting4 ,in the ,english mounting the telescope1 like a transit instrument1 has on each side a pivot1 and these pivots rest on a frame somewhat larger than the telescope1 pointing to the pole and supported by two pivots1 one at the bottom resting on bearings near the ground1 and the other carried by a higher pillar clear of the observer's chair4 ,the motions of the telescope are similar to those given by the ,german mounting in all essentials2 the ,greenwich equatorial is mounted in this manner4 ,it is carried in a large cylindrical frame1 supported at both ends by two pillars--above by a strong iron pillar1 while the other end rests on a firm stone pillar1 going right to the earth1 independently of the flooring4 ,this mounting1 though preferred for the large instrument at ,greenwich1 has been discarded generally1 as the long polar axis is necessarily a serious element of weakness2 the telescope is supported on its weakest part1 and it is liable to great changes from contraction and expansion of the frame4 ,the ,forked ,mounting4 ,it is now getting more usual to mount ,newtonians of large dimensions equatorially1 in spite of the immense weight to be carried4 ,one of the first methods was to use a polar axis in the same manner as for a refractor1 only that it bifurcated at the top1 forming there a fork1 and between this fork the telescope is swung1 after the same manner as a transit4 ,this method of mounting was adopted by ,m4 ,foucault in the case of his first large silvered-glass reflector4 ,the height of the bifurcation is dependent on the distance between the centre of gravity of the tube and the speculum1 and if we use an extremely light tube1 or if1--as it is the fashion to abolish them now altogether for reflectors1--we use a skeleton tube of iron lattice work1 this bifurcation of the polar axis need not be of any great length4 ,the polar axis being entirely below the telescope and being driven by the clock1 we have a perfect method of mounting a speculum of any weight we please4 ,this arrangement was first suggested and carried into effect by ,mr4 ,lassell for his four-foot ,newtonian1 which was mounted at ,malta4 ,the polar axis was a heavy cone-shaped casting resting on its point below1 and moving on its largest diameter just below the base of the fork4 ,lord ,rosse has recently much improved upon the original idea4 ,as the observer must be at the mouth of the tube1 he is in a very bad position as far as comfort goes1 especially as the eye-end changes its position rapidly in consequence of the great length of the tube from its centre of gravity outwards4 ,the platform on which he stands is raised on supports1 extending from the floor and going up to the opening through which the telescope points to the heavens1 and the whole platform is sometimes fixed to the dome of the observatory1 so that it travels round with it4 ,with ,mr4 ,lassell's four-foot the observer stood in a gigantic reading box1 about thirty feet high1 with openings in it at different elevations4 ,this structure was supported on a circular platform movable on rails round the base of the mounting4 ,almost continual variations1 both of the observing height and of the circular platform1 were necessary1 as the distance from the centre of motion of the tube and the eyepiece was no less than #cd feet4 ,in ,lord ,rosse's recent adaptation of this form the observer is placed in a swinging basket1 at the end of an arm almost as long as the telescope tube4 ,he is here counterpoised1 and moves round a railway which surrounds the mounting at the height of the tip of the fork4 ,the ,composite ,mounting4 ,illustration3 ,,fig4 #adc4--;,general view of the ,melbourne ,reflector4 ,there is still another form of mounting which promises to be largely used for reflectors in the future1 whether the tube be lightened by its being constructed of only a framework of iron or not4 ,this mounting is neither ,german nor ,english1 but in part imitates both of these methods3 hence ,i give it the name of ,composite4 ,there is a short polar axis supported at both ends4 ,illustration3 ,,fig4 #add4--,the mounting of the ,melbourne ,telescope4 ,c1 polar axis 7cube #a yard square1 cone #h feet long72 ,d1 ,clock sector2 ,u1 ,counterpoise weights 7#b tons74 ,within the last few years two large reflectors have been erected1 equatorially mounted in this composite manner--the great ,melbourne ,equatorial1 constructed by ,mr4 ,grubb1 and the new ,paris ,equatorial1 constructed by ,mr4 ,eichens4 ,of the former1 ,fig4 #adc gives a general view1 showing how the construction of this instrument differs from other equatorials which we have seen4 ,fig4 #add shows the mounting in more detail4 ,c is the polar axis1 ,t ,p is the declination axis1 and ,t the small portion of the tube of the telescope1 the remainder of the tube being represented by delicate lattice work1 which is as light as possible1 and used merely for supporting the reflector1 by means of which the light is thrown back again1 according to the suggestion of ,cassegrain1 and comes through the hole in the centre of the speculum into the eyepiece1 which is seen at y1 so that the observer stands at the bottom of the telescope in exactly the same way as if he were using a refractor4 ,in this enormous instrument1 the tube and speculum of which alone weigh nearly three tons1 the system of counterpoises is so perfect that we describe the method adopted in order to give an idea of the general arrangement of the bearing and anti-frictional apparatus4 ,the series of weights hanging behind the support of the upper end of the polar axis are intended to take a great part of the weight of that axis off the lower support2 beside which there are friction-rollers pressed upwards against the axis by the weights inside the support4 ,all the bearings are constructed on the same principle as the ,y bearings of a theodolite--that is1 the pivots rest on two small portions of their arc1 #ij or #ajj apart4 ,if allowed to rest on these bearings without some anti-frictional apparatus1 the force required to move such an instrument would render it simply unmanageable and destroy the bearings4 ,the plan adopted by ,mr4 ,grubb is to allow the axis to rest in its bearings with just a sufficient portion of its weight to insure perfect contact1 and to support the remainder by some anti-frictional apparatus4 ,generally #a_/ej to #a_/ajj of the weight is quite sufficient to allow the axis to take its bearing1 and the remainder #di_/ej to #ii_/ajj can thus be supported on friction rollers1 and reduced to any desired extent1 without injuring in the slightest degree the perfection of steadiness obtained by the use of the ,y's4 ,this is the plan used in the bearings of the polar axis1 and the result is that the instrument can be turned round this axis by a force of #e pounds at a leverage of #bj feet4 ,the bearings of the declination axis are supported on virtually the same principle2 but the details of that construction are necessarily much more complicated1 on account of the variability of direction of the resolved forces with respect to the axis4 ,we may now turn to the four-foot silver-on-glass ,newtonian now in course of completion at the ,paris ,observatory4 ,the illustration which we give represents the telescope in a position for observation4 ,the wheeled hut under which it usually stands1 a sort of waggon seven metres high by nine long and five broad1 is pushed back towards the north along double rails4 ,the observing staircase has been fitted to a second system of rails1 which permits it to circulate all round the foot of the telescope1 at the same time that it can turn upon itself1 for the purpose of placing the observer1 standing either on the steps or on the upper balcony1 within reach of the eyepiece4 ,this eyepiece itself may be turned round the end of the telescope into whatever position is most easily accessible to the observer4 ,illustration3 ,,fig4 #ade4--;,great ,silver-on-,glass ,reflector at the ,paris ,observatory4 ,the tube of the telescope1 #gcj metres in length1 consists of a central cylinder1 to the extremities of which are fastened two tubes three metres long1 consisting of four rings of wrought-iron holding together twelve longitudinal bars also of iron4 ,the whole is lined with small sheets of steel plate4 ,the total weight is about #b1djj kilogrammes4 ,at the lower extremity is fixed the cell which holds the mirror2 at the other end a circle1 movable on the open mouth of the telescope1 carries at its centre a plane mirror1 which throws to the side the cone of rays reflected by the great mirror4 ,the weight of the mirror in its barrel is about #hjj kilogrammes2 the eyepiece and its accessories have the same weight4#ag ,it will be quite clear from what has been said that the manipulation of these large telescopes at present entails much manual and even bodily labour1 and when we come in future to consider the winding of the clock1 the turning of the dome1 and the adjustment of the observing chair1 it will be seen that the labour is enormous4 ,to save this1 in all the best instruments everything is brought to the eye-end of the telescope1 movements both in right ascension and declination1 reading of circles1 and adjustment of illumination4 ,mr4 ,grubb has suggested that everything should be brought to this point1 and that1 by the employment of hydraulic power1 8the observer1 without moving from his chair1 might1 by simply pressing one or other of a few electrical buttons1 cause the telescope to move round in right ascension1 or declination1 the dome to revolve1 the shutters to open1 and the clock to be wound40 ,he very properly adds1 8,this is no mere ,utopian idea4 ,such things are done1 and in common use in many of our great engineering establishments1 and it is only in the application that there would be any difficulty encountered40 ,the ,driving ,clock4 ,in a previous chapter it was stated that in all large telescopes used for the astronomy of position1 whether a transit circle or the alt-azimuth1 what we wanted to do was to note the transit of the star across the field--the transit due to the motion of the earth2 but that when we deal with other phenomena1 such1 for instance1 as those a large equatorial is capable of bringing before us1 we no longer want these objects to traverse the field1 we want to keep them1 if possible1 absolutely immovable in the field of view of the eyepiece1 so that we may examine them and measure them1 and do what we please with them4 ,hence it was that we found driving clocks applied to equatorials2 and our description would not be complete did we fail to explain the general principles of their construction4 ,they are instruments for counteracting the motion of the earth by supplying an exactly equal motion to the tube of the telescope in an opposite direction4 ,without such a clock we may get an image of the object we wish to examine2 but before we should be able to do anything with it1 either in the way of measurement or observation1 it would have gone from us4 ,a glimpse of a planet or star with a large telescope will give a general notion of the extreme difficulty which any observer would have to deal with if he wanted to observe any heavenly body without a driving clock4 ,we can easily see at once that it would not do to have an ordinary clock regulated by a pendulum for driving the telescope1 it would be driven by fits and starts1 which would make the object viewed jump in the field at each tick of the pendulum4 ,the most simple clock is therefore one in which the conical pendulum is used in the form of the governor of a steam-engine1 so that when the balls ,a ,a1 ,fig4 #adf1 fly up by reason of the clock driving too fast1 they rub against a ring1 ,b1 or something else that reduces their velocity4 ,illustration3 ,,fig4 #adf4--;,clock ,governor4 ,illustration3 ,,fig4 #adg4--;,bond's ,spring ,governor4 ,there is another form made by ,alvan ,clarke1 in which a pendulum regulates the clock1 but not quite in the ordinary way4 ,the drawing will perhaps make it clear3 ,a ,a1 ,fig4 #adg1 is one of the wheels of the clock-train driving a small weighted fan1 ,b1 which is regulated so as to allow the clock to drive a little too fast4 ,now let us see how the pendulum regulates it4 ,on the axis of ,a ,a is placed an arm1 ,c1 which is of such a length that it catches against the studs ,s ,s1 and is stopped until the pendulum1 ,p1 swings up against one of the studs1 ,r1 which moves the piece ,d1 like a pendulum about its spring at ,e1 until the stud1 ,s1 is sufficiently removed to let the arm1 ,c1 pass1 so that the clock is under perfect control4 ,if1 however1 the arm ,c were fixed rigidly to the axis of the wheel ,a ,a1 there would be a jerk every time ,c touched one of the studs4 ,the wheel is therefore attached to the axis through the medium of a spring1 ,f1 so that when the arm is stopped the wheel goes on1 but has its velocity retarded by the pressure of the spring4 ,the pendulum is kept going in the following manner3--,there is a pin fixed to the axis on the same side of the centre as ,c1 which1 as the arm approaches either stud ,s1 raises the piece ,d1 but not sufficiently to liberate the arm2 the pendulum has then only a very little work to do to raise ,d and disengage the arm1 ,c2 but as soon as it is free it starts off with a jerk1 due to the tension of the spring on the axis1 and leaves ,d by means of its stud1 ,r1 to exert its full force on the pendulum and accelerate its return stroke1 so that the pendulum is kept in motion by the regulating arrangement itself4 ,the late ,mr4 ,cooke of ,york constructed a very accurately-going driving clock4 ,this differs in important particulars from ,bond's form1 though the control of the pendulum is retained4 ,the following extracts from a description of it will show the principal points in its construction3-- ,the regulator adopted is the vibrating pendulum1 because amongst the means at the mechanician's command for obtaining perfect time-keeping there is none other by which the same degree of accuracy can be obtained4 ,the difficulty in this construction is the conversion of the jerking or intermittent motion produced by such pendulums into a uniform rotatory motion which can be available with little or no disturbing influence on the pendulum itself1 when the machine is subject to varying frictions and forces to be overcome in driving large equatorials4 ,the pendulum is a half-second one1 with a heavy bob1 adjusted by sliding the suspension through a fixed slit4 ,it is drawn up and let down by a lever and screw1 the acting length of the pendulum being thus regulated4 ,the arrangement of the wheels represents something like the letter ,u4 ,at the upper end of one branch is the scape-wheel4 ,at the upper end of the other branch is an air-fan4 ,the large driving-wheel and barrel are situated at the bottom or bend4 ,all the wheels are geared together in one continuous train1 which consists of eight wheels and as many pinions4 ,the scape-wheel and the two following wheels have an intermittent motion2 all the others have a continuous and uniform one4 ,the change from one motion to the other is made at the third wheel1 which1 instead of having its pivot at the end of the arbor where the wheel is fixed--fixed to the frame like the others--is suspended from above by a long arm having a small motion on a pin fixed to the frame2 the pivot at the other end of the arbor is fixed to the frame as the others are1 but its bole and its pivot are arranged so as to permit a very small horizontal angular motion round them1 as a centre1 without interfering with the action of the gearing of the wheel itself4 ,if the weight is applied to the clock1 and the pendulum is made to vibrate1 the moment it begins to move1 the scape-wheel moves its quantity for a beat2 the remontoire wheel1 by the very small force outwardly caused by the reaction of the break-spring1 relaxes its pressure against a friction-wheel1 and sets at liberty the train of the clock4 ,the spring is now driven back to the break-wheel1 but before it can produce more than the necessary friction to keep the train in uniform motion1 another beat of the clock again releases it4 ,the repetition of these actions produces a series of impulses on the break-wheel of such a force and nature as to keep the train freely governed by the pendulum4 ,the uniform rotatory motion obtained by this clock as far as experiments can be made by applying widely different weights1 and comparing the times with a chronometer1 is perfectly satisfactory4 ,a clock constructed on the same principle1 connected1 and giving motion to a cylinder1 will1 it is presumed1 make an excellent chronograph4 ,illustration3 ,,fig4 #adh4--;,foucault's governor4 ,the form of governor most usually employed will be seen in figures previously given4 ,the governor raises a plate and thus becomes a frictional governor1 by which all overplus of power is used up in frictions1 or by that doubling the driving power no1 or only a small1 difference should be brought about in the rate4 ,other forms of driving clocks or governors invented by ,foucault and ,yvon ,villarceau are now being largely employed4 ,in them the rapid motion of a fan and other devices are introduced4 ,a driving clock adjusted to sidereal time requires adjustments for observations of the sun and moon4 ,this 7as at z in ,fig4 #add7 is sometimes done once for all by differential gearing thrown into action by levers when required4 ,mr4 ,grubb has lately made a notable improvement upon the usual form by controlling the motion of the governor by a sidereal clock and an electric current4 ,there are various methods of attaching the clock to the polar axis4 ,one is to make the clock turn a tangent screw1 gearing into a screw-wheel on the axis of the telescope1 which can be thrown in and out of gear for moving the telescope rapidly in right ascension4 ,another method is to have a segment of a circle on the polar axis which can be clamped or unclamped at pleasure by means of a screw attached to it4 ,a strip of metal is attached to each end of the segment and is wound round a drum turned by the clock1 so that the two are geared together just as wheels are geared by an endless strap passing round them4 ,this arrangement gives a remarkably even motion to the telescope4 ,when the strap is wound up to the end of the segment1 which is done in about two or three hours' work1 the drum is thrown out of gear and the arc pushed back to its starting-place again4 ,,the ,,lamp4 ,illustration3 ,,fig4 #adi4--;,illuminating lamp for equatorial4 ,in the description of the transit circle we saw how the ,astronomer-,royal had contrived to throw light into the axis of the telescope1 so that the wires were either rendered visible in a bright field1 or1 the field being kept dark1 the wires were visible as bright lines in a dark field4 ,that is the difference between a bright field1 and a dark field of illumination4 ,now a bright field of illumination in the case of equatorials is managed by an arrangement as follows4--,a ,a1 ,fig4 #adi1 is a section of the tube of the telescope4 ,near the eyepiece is a small lamp1 ,d1 swung on pins on either side which rest on a circular piece of brass swinging on a pin at ,c1 and a short piece of tube at ,e1 through which the light passes into the telescope and falls on a small diagonal reflector1 ,f4 ,this reflects the rays downwards into the eyepiece4 ,when the telescope is moved into any position the lamp swings like a mariner's compass on its gimbals1 and still throws its light into the tube1 and the light mixes up with that coming from the star1 but spreads all over the field of view instead of coming to a point1 so that the star is seen on a bright field1 and the wires as black lines4 ,now if the star which is observed is a very faint one1 we defeat our own object1 for the light coming from the lamp puts out the faint star4 ,illustration3 ,,fig4 #aej4--;,cooke's illuminating lamp4 ,we have seen how the illumination of the wires1 instead of the field1 is carried out in the ,greenwich transit4 ,the same method can be adopted in the case of equatorials1 the light from the diagonal reflector being thrown on other diagonal reflectors or prisms on either side the wires in the micrometer so as to illuminate them4 ,messrs4 ,cooke and ,sons have devised a lamp of very great ingenuity1 ,fig4 #aej4 ,it is a lamp which does for the equatorial1 in any position1 exactly what the fixed lamp does for the transit circle4 ,it is impossible to put it out of order by moving the telescope4 ,there is a prism at ,p reflecting the light into the telescope tube1 and at whatever different angle of inclination1 or whatever may be the size of the telescope on which this lamp is placed1 it is obvious that the lamp never ceases to throw its light into the reflector inside the telescope2 and any amount of light1 or any colour of light required can be obtained by turning the disc containing glass of different colours or the other having differently sized apertures1 in order to admit more or less light1 or give the light any colour4 ,in both these arrangements the lamp is hung on the side of the telescope1 while ,mr4 ,grubb prefers to hang it at the end of the declination axis1 as shown in ,figs4 #aci and #adj4 ,the function of the lamp then is to illuminate the wires of the micrometer eyepiece1 of which more presently2 but ,mr4 ,george ,bidder places the micrometer itself outside the tube of the telescope1 the light of a lamp being thrown on the wires4 ,this is done as follows3--,on the same side of the wires as the lamp is a convex lens and reflector so arranged that the rays from the wires are reflected through a hole in the tube1 and again down the tube to the eyepiece1 where the images of the wires are brought to a focus at the same place as the stars to be measured1 so that any eyepiece can be used4 ,the wires show as bright lines in the field1 and they are worked about in the field just as real wires might be by moving the wires outside the tube4 ,a sheet of metal can be moved in front of the distance-wires so as to obstruct the light from them at any part of their length1 and their bright images appear then abruptly to terminate in the field of view1 so that faint stars can be brought up to the terminations of the wires and be measured without being overcome by bright lines4 ----- ,footnote #af3 ,it is not too much to say that the duty on glass entirely stifled1 if indeed it did not kill1 the optical art in ,england4 ,we were so dependent for many years upon ,france and ,germany for our telescopes1 that the largest object-glasses at ,greenwich1 ,oxford1 and ,cambridge are all of foreign make4 ,footnote #ag3 ,these details are given from the ,forces of ,nature 7,macmillan74 ,,chapter ,,xxi4 ,,the ,,adjustments ,,of ,,the ,,equatorial4 ,as the equatorial is par excellence the amateur's instrument1 and as in setting up an equatorial it is important that the several adjustments should be correctly made1 they are here dwelt upon as briefly as possible4 ,they are six in number4 #a4 ,the inclination of the polar axis must be the same as that of the pole of the heavens4 #b4 ,the declination circle must read #j when the telescope is at right angles to the polar axis4 #c4 ,the polar axis must be placed in the meridian4 #d4 ,the optic axis of the telescope1 or line of collimation must be at right angles to the declination axis1 so that it describes a great circle on moving about that axis4 #e4 ,the declination axis must be at right angles to the polar axis1 in order that the telescope shall describe true meridians about that axis4 #f4 ,the hour circle must read #j;h4 #jm4 #jsec4 when the telescope is in the meridian4 ,when these are correctly made the line of collimation will1 on being turned about the declination axis1 describe great circles through the pole1 or meridians1 and when moved about the polar axis1 true parallels of declination2 and the circles will give the true readings of the apparent declination1 and hour angles from the meridian4 ,to make these adjustments1 the telescope is set up by means of a compass and protractor1 or otherwise in an approximately correct position1 the declination circle put so as to read nearly #ij when the telescope points to the pole1 and the hour circle reading #j;h4 #jm4 #jsec4 when the telescope is pointing south4 ,first1 then1 to find the error in altitude of the polar axis4 ,take any star from the ,nautical ,almanac of known declination on or near the meridian1 and put an eyepiece with cross wires in it in the telescope1 and bring the star to the centre of the field as shown by the wires4 ,then read the declination circle1 note the reading down and correct it for atmospheric refraction1 according to the altitude#ah of the star by the table given in the ,nautical ,almanac1 turn the telescope on the polar axis round half a circle so that the telescope comes on the other side of the pier4 ,the telescope is then moved on its declination axis until the same star is brought to the centre of the field1 and the circle read as before and corrected4 ,the mean of the two readings is then found1 and this is the declination of the star as measured from the equator of the instrument1 and its difference from the true declination given by the almanac is the error of the instrumental equator and of course1 also of the pole at right angles to it4 ,it is obvious that if the declination circle were already adjusted to zero1 when the telescope was pointing to the equator of the instrument1 one observation of declination would determine the error in question2 and it is to eliminate the index error of the circle1 as it is called1 that the two observations are taken in such a manner that the index error increases one reading just as much as it decreases the other1 so that the mean is the true instrumental declination4 ,index ,error4--,from what has just been stated it follows that half the difference of the two readings is the index error1 which can be at once corrected by the screws moving the vernier1 giving correction ,no4 #b4 ,to correct the error in altitude of the pole1 the circle is then set to the declination of the star given by the almanac1 corrected for refraction1 and the telescope brought above or below the star as the error may be1 and the polar axis carrying the telescope is moved by the setting screws1 until the star is in the centre of the field4 #crd ,adjustment4--,a single observation of any known star1 about #f hours to the east or west will give the error of the polar axis east and west1 the difference between the observed and true declination being this error1 and it can be corrected in the same manner as the last4 ,these observations should be repeated1 and stars in different parts of the heavens observed1 in order to eliminate errors of division of the circle until the necessary accuracy is obtained4 ,for example3 ,observed dec4 of ,capella #dc #ej #cj ,telescope west4 #dg #j #j ,telescope east4 ------ ------ ------ #b7 #ij #ej #cj ------ ------ ------ #de #be #ae #dg #j #j ,error due to refraction #j #j #g #dc #ej #cj ------ ------ ------ ------ ------ ------ ,instrumental declination #de #be #h #b7 #c #i #cj ,true declination #de #eb #j ------ ------ ------ ------ ------ ------ ,index error #a #cd #de #bf #eb ,this indicates that the pole of the instrument is pointing below the true pole1 and index error #a #cd #de4 ,observed declination of ,pollux #f;h4 west #bh #ai #ah ,refraction #j #j #df ------ ------ ------ #bh #ah #c ,true declination #bh #bj #aj ------ ------ ------ #j #a #ch ,this shows the pole to be #a #ch east of true pole4 #dth ,adjustment4--,for the estimation and correction of the third error1 that of collimation1 an equatorial star is brought to the centre of the field of the telescope1 the time by a clock noted1 and the hour circle read4 ,the polar axis is then turned through half a circle1 and the star observed with the telescope on the opposite side 7say the west7 of the pier1 the time noted1 and the hour circle read4 ,subtract the first reading from the second 7plus twenty-four hours if necessary7 and subtract the time elapsed between them1 and the result should be exactly twelve hours1 and half the difference between it and twelve hours is the error in question4 ,if it is more than twelve hours the angle between the object end of the telescope and the declination axis is acute1 and if less then it is obtuse4 ,this error can then be corrected by the proper screws4 ,a little consideration will show1 that if the angle between the object end of the telescope and the declination axis be acute1 and the telescope is on the east side of the pier1 and pointing to a star1 say on the meridian1 the hour circle will not read so much as it would do if the line perpendicular to the declination axis were pointing to the meridian4 ,when the telescope is on the wrest side of the pier1 the circle will read higher for the same reason1 and therefore the difference between the angle through which the hour circle is moved and #ahj is equal to double the angle between the line perpendicular to the declination axis and the collimation axis of the telescope2 allowance being made for the star's motion4 ,for example ,virginis1 ,dec4 #j #dfe4 ,time by clock4 ,hour circle reading4 #aa;h4 #bcm4 #ebs4 #aa;h4 #eem4 #cjs4 ,telescope east4 #aa;h4 #cam4 #ees4 #bd;h4 #hm4 #bds4 ,telescope west4 -------- -------- -------- -------- -------- ------------ #hm4 #cs4 #ab;h4 #abm4 #eds4 #hm4 #cs4 -------- ------------ #b7 #dm4 #eas4 -------- ------------ ,collimation error at #bm4 #bees4 dec4 #dfe angle between object glass and declination axis acute4 ,if this error is not corrected1 it must be added when the telescope is on the east side of the pier1 and subtracted when on the west4#ai #eth ,adjustment4--,place a striding level on the pivots of the declination axis and bring the bubble to zero by turning the polar axis2 read off the hour circle and note it2 then reverse the declination axis east and west and replace the level2 bring the bubble to zero and again read the circle4 ,the readings should show the axis to be turned through half a circle1 and the difference shows the error4 ,if the second reading minus the first be more than half a circle or #ab hours1 it shows that the pivot at the east at the first observation is too high1 and therefore in bringing the declination axis level1 the first reading of the hour circle is diminished from its proper amount and increased on the axis being reversed4 ,to adjust the error1 find half the difference of circle readings and apply it1 with the proper sign1 to each of the two circle readings1 which will then differ by exactly twelve hours2 bring the circles to read one of the corrected readings and alter the declination axis until the bubble of the level comes to zero4 ,if the pivots of the declination axis are not exposed1 so that the level can be applied1 the following method must be adopted3--,fasten a small level on any part of the declination axis or its belongings1 say on the top of the counterpoise weight2 bring the axis apparently horizontal and the bubble to zero2 turn the telescope on the declination axis1 so that by the turning of the counterpoise the level comes below it2 if then the bubble is at zero1 the axis of the level is parallel to the declination axis1 and both are horizontal1 and if not it is clear that neither of these conditions holds2 therefore bring the bubble to zero by the two motions of the level with reference to the counterpoise and the motion of the declination axis on the polar axis1 so that the error is equally corrected between them2 repeat the proceeding until the level is parallel with the axis1 when it will show when the axis is horizontal as well as the striding level4 ,for example3-- ,hour circle reading when #aa;h4 #egm4 #egs4 ,telescope east4 declination axis is horizontal4 #bc;h4 #eim4 #dgs4 ,telescope west4 -------- -------- -------- #ab;h4 #am4 #ejs4 ,error #j;h4 #am4 #ejs4 ,or this error can be found and corrected without a level by taking two observations of a star of large declination in the same manner as in estimating the collimation error1 for example3-- ,,urs ,,majoris4 ,time by clock4 ,hour circle reading4 #ab;h4 #hm4 #egs4 #j;h4 #bhm4 #dds4 ,telescope east4 #ab;h4 #ahm4 #ecs4 #ab;h4 #dfm4 #dbs4 ,telescope west4 -------- -------- -------- -------- -------- -------- #im4 #efs4 #ab;h4 #agm4 #ehs4 #im4 #efs4 -------- -------- #b7 #hm4 #bs4 -------- -------- ,error of hour circle due to error of #dm4 #as4 inclination of axes#bj #fth ,adjustment4--,bring the declination axis to a horizontal position with a level and set the hour circle to zero1 or obtain the sidereal time from the nearest observatory1 or again find it from the solar time by the tables1 and correct it for the longitude of the place 7subtracting the longitude reduced to time when the place is west and adding when east of the time-giving observatory7 and set a clock or watch to it4 ,take the time of transit of a known star near the meridian and then the sidereal time by the clock at transit minus the right ascension of the star will give the hour angle past the meridian1 and its difference from the circle reading is the index error1 which is easily corrected by the vernier4 ,if the star is east of the meridian the time must be subtracted from the right ascension to give the circle reading4 ,in the above examples we have assumed1 for the sake of better illustration1 that the hour circle is divided into twenty-four hours1 but more usually they are divided into two halves of twelve hours each4 ,a movement through half a circle1 therefore1 brings the hour circle to the same reading again instead of producing a difference of twelve hours1 as in the above example4 ,when the equatorial is once properly in adjustment1 not only can the co-ordinates of a celestial body be observed with accuracy when the time is known1 but a planet or other body can easily be found in the day-time4 ,the object is found by the two circles--the declination circle and the hour or right-ascension circle4 ,the declination of the required object being given1 the telescope is set by the circle to the proper angle with the equator4 ,the ,r4,a4 of the object is then subtracted from the sidereal time1 or that time plus twenty-four hours1 which will give the distance of the object from the meridian1 and to this distance the hour-circle is set4 ,the object should then be in the field of the telescope1 or at least in that of the finder4 ,we subtract the star's ,r4,a4 from the sidereal time because the clock shows the time since the first point of ,aries passed the meridian1 and the star passes the meridian later by just its ,r4,a41 so that if the time is #b;h41 or the first point of ,aries has passed #b;h4 ago1 a star of #a;h4 ,r4,a41 or transiting #a;h4 after that point1 will have passed the meridian #b;h4 - #a;h4 #a;h4 ago2 so if we set the telescope #a;h4 west of the meridian we shall find the star4 ,the moment the object is found the telescope is clamped in declination1 and the clock thrown into gear1 so that the star may be followed and observed for any length of time4 ----- ,footnote #ah3 ,the altitude of the star in this case is its declination plus the co-latitude of the place1 but this only applies when the star is on the meridian4 ,when the altitude of a star in another situation is required1 it is found sufficiently accurately by means of a globe4 ,a sextant1 if at hand1 will of course give it at once4 ,footnote #ai3 ,since the velocity of the star varies as the cosine of the declination1 the error of collimation at the equator #bm4 #bees4 cos4 #j #dee #bm4 #bejhs42 and for non-equatorial stars1 #bm4 #bejhs4 sec4 dec4 ,footnote #bj3 ,this error varies as the tangent of the declination1 and therefore to find the constant for the instrument1 in case the parts do not admit of easy adjustment1 we divide #dm4 #as4 by #aah the tan4 of ,dec4 of ,urs ,majoris1 giving #c min4 #bh sec4 ,,chapter ,,xxii4 ,,the ,,equatorial ,,observatory4 ,we have now considered the mounting and adjustment of the equatorial1 be it reflector or refractor4 ,if of large dimensions it will require a special building to contain it1 and this building must be so constructed that1 as in the case of the ,melbourne and ,paris instruments1 it can be wheeled away bodily to the north1 leaving the instrument out in the open2 or the roof must be so arranged that the telescope can point through an aperture in it when moved to any position4 ,this requirement entails 7#a7 the removal of the roof altogether1 by having it made nearly flat1 and sliding it bodily off the ,observatory1 or 7#b7 the more usual form of a revolving dome1 with a slit down one side1 or 7#c7 the ,observatory maybe drum-shaped1 and may run on rollers near the ground4 ,the last form is adopted for reflectors whose axis of motion is low2 but with refractors having their declination axis over six or seven feet from the ground1 the walls of the ,observatory can be fixed1 as the telescope1 when horizontal1 points over the top4 ,the roof1 which may be made of sheet-iron or of wood well braced together to prevent it altering in shape1 is built up on a strong ring which runs on wheels placed a few feet apart round the circular wall1 or1 instead of wheels1 cannon balls may be used1 rolling in a groove with a corresponding groove resting on them4 ,a small roof1 if carefully made1 may be pulled round by a rope attached to any part of it1 but large ones generally have a toothed circle inside the one on which the roof is built1 or this circle itself is toothed1 so that a pinion and hand-winch can gear into it and wind it round4 ,if the roof is conical in shape the aperture on one side can be covered by two glazed doors1 opening back like folding-doors2 but if it is dome-shaped1 the shutter is made like a ,venetian blind or revolving shop-window shutter1 and slides in grooves on either side of the opening4 ,illustration3 ,,fig4 #aea4--;,dome4 ,illustration3 ,,fig4 #aeb4--;,drum4 ,illustration3 ,,fig4 #aec4--,new ,cincinnati ,observatory--,front elevation1 showing exterior of ,drum4 ,illustration3 ,,fig4 #aed4--;,cambridge 7,u4,s47 ,equatorial1 showing ,observing ,chair and rails4 ,the equatorial and the building to contain it have now been described1 but there is another piece of apparatus which is required as much as any adjunct to the equatorial1 and that is the chair or rest for the observer4 ,since the telescope may be sometimes horizontal1 and at other times vertical1 the observer must be at one time in an upright position1 and at another lying down and looking straight up4 ,a rest is required which will carry the observer in these or in intermediate positions4 ,a convenient form of rest for small telescopes consists of a seat like that of a chair1 with a support moving on hinges at the back of the seat2 a rack motion fixes this at any inclination1 so that the observer's back can be sustained in any position1 between upright and nearly horizontal4 ,the seat with its back slides on two straight bars of wood1 sloping upwards from near the ground at an angle of about #cj1 and about #h;ft4 long2 these are supported at their upper ends by uprights of wood1 and at their lower ends in the same manner by shorter pieces4 ,these four uprights are firmly braced together1 and have castors at the bottom4 ,a rack is cut on one of the inclined slides1 and a catch falls into it1 so as to fix the seat at any height to which it is placed4 ,in larger observatories a more elaborate arrangement is adopted1 the rails1 on which the seat moves1 are curved to form part of a circle1 having the centre of motion of the telescope for its centre2 as the seat with its back is moved up or down on the curved slides1 its inclination is changed1 so that the observer is always in a favourable position for observing4 ,the seat on its frame runs on circular rails round the pier of the telescope1 so that the eyepiece can be followed round as the telescope moves in following a star4 ,a winch by the side of the observer1 acting on teeth on one of the rails1 enables him to move the chair along1 and a similar arrangement enables him to raise or lower the seat on the slides without removing from his place4 ,a steady mounting for the telescope1 and a comfortable seat for the observer1 are the two things without which a telescope is almost useless4 ,the observing chair is well seen in the engravings of ,mr4 ,newall's and the ,cambridge telescopes4 ,the eyepieces and micrometer can be carried on the rest1 close to the observer1 when much trouble is saved in moving about for things in the dark2 and for the same reason there should be a place for everything in the observatory1 and everything in its place4 ,illustration3 ,,fig4 #aee4--,section of ,main ,building--,united ,states ,naval ,observatory1 showing support of ,equatorial4 ,the very high magnifying power employed upon equatorials in the finest states of the air necessitates a very firm foundation for the central pillar4 ,the best position for such an instrument is on the ground1 but it is almost always necessary to make them high in order to be able to sweep the whole horizon4 ,the accompanying woodcut will give an idea of the precautions that have to be taken under these circumstances4 ,a solid pillar must be carried up from a concrete foundation1 and there must be no contact between this and the walls or floors of the building1 when the dome thus occupies the centre of the observatory4 ,the other rooms1 generally built adjoining the equatorial room1 radiate from the dome1 east and west1 not sufficiently high to interfere with the outlook of the equatorial4 ,in one of these the transit is placed2 an opening is made in the walls and roof1 so that it has an unimpeded view when swung from north through the zenith to south1 and this is closed when the instrument is not in use by shutters similar to those of the dome4 ,,chapter ,,xxiii4 ,,the ,,siderostat4 ,at one of the very earliest meetings of the ,royal ,society1 the difficulties of mounting the long focus lenses of ,huyghens being under discussion1 ,hooke pointed out that all difficulties would be done away with if instead of giving movement to the huge telescope itself1 a plane mirror were made to move in front of it4 ,this idea has taken two centuries to bear fruit1 and now all acknowledge its excellence4 ,one of the most recent additions to astronomical tools is the ,siderostat1 the name given to the instrument suggested by ,hooke4 ,by its means we can make the sun or stars remain virtually fixed in a horizontal telescope fixed in the plane of the meridian to the south of the instrument1 instead of requiring the usual ponderous mounting for keeping a star in the field of view4 ,it consists of a mirror driven by clockwork so as to continually reflect the beam of light coming from a star1 or other celestial object1 in the same direction2 the principle consisting in so moving the mirror that its normal shall always bisect the angle subtended at the mirror by the object and the telescope or other apparatus on which the object is reflected4 ,illustration3 ,,fig4 #aef4--;,foucault's ,siderostat4 ,it was ,foucault who1 towards the end of his life1 thought of the immense use of an instrument of this kind as a substitute for the motion of equatorials2 he1 however1 unfortunately did not live to see his ideas realized1 but the ,commission for the purpose of carrying out the publication of the works of ,foucault directed ,mr4 ,eichens to construct a siderostat1 and this one was presented to the ,academy of ,science on ,december #acth1 #ahfi1 and is now at the ,paris ,observatory4 ,since that date others have been produced1 and they have every chance of coming largely into use1 especially in physical astronomy4 ,fig4 #aef shows the elevation of the instrument1 the mirror of which1 in the case of the instrument at ,paris1 is thirty centimetres in diameter1 and is supported by a horizontal axis upon two uprights1 which are capable of revolving freely upon their base4 ,the back of the mounting of the mirror has an extension in the form of a rod at right angles to it1 by which it is connected with the clock1 which moves the mirror through the medium of a fork jointed at the bottom of the polar axis4 ,the length of the fork is exactly equal to the distance from the horizontal axis of the mirror to the axis of the joint of the fork to the polar axis1 and the direction of the line joining these two points is the direction in which the reflected ray is required to proceed4 ,the fork is moved on its joint to such a position that its axis points to the object to be viewed1 and1 being carried by a polar axis1 it remains pointing to that object as long as the clock drives it1 in the same manner as a telescope would do on the same mounting4 ,then1 since the distance from the axis of the mirror to the joint of the fork is equal to the distance from the latter point to the axis of its joint to the sliding tube on the directing rod1 an isosceles triangle is formed having the directing rod at its base2 the angles at the base are therefore equal to each other4 ,further1 if we imagine a line drawn in continuation of the axis of the fork towards the object1 then the angle made by this line and that from the axis of the mirror to the elbow joint of the fork 7the direction of the reflected ray7 will be equal to the two angles at the base of the isosceles triangle2 and1 since they are equal to each other1 the angle made by the directing rod and the axis of the fork 7or the incident ray7 from the object1 is equal to half the angle made by the latter ray and the direction of the reflected ray2 and if lines are drawn through the surface of the mirror in continuation of the directing rod and the line from the elbow joint to the axis of the mirror2 and a line to the point of intersection be drawn from the object1 this last line will be parallel to the axis of the fork1 and the angle it makes with the continuation of the directing rod1 or normal to the surface of the mirror1 will be half the angle made by it and the line representing the reflected ray4 ,therefore the angle made by the incident ray and the required direction of the reflected ray is always bisected by the normal1 so that the reflected ray is constant in the required direction4 ,the clock is driven in the usual manner by a weight4 ,a rod carries the motion up to the system of wheels by which the polar axis is rotated4 ,as this axis rotates it carries with it the fork1 which transmits the required motion to the mirror4 ,and as the fork alters its direction the tube slides upon the directing rod1 thus altering the inclination of the mirror4 ,in order to vary the position of the mirror without stopping the instrument there are slow motion rods or cords proceeding from the instrument which may be carried to any distance desirable4 ,illustration3 ,,fig4 #aeg4--,the ,siderostat at ,lord ,lindsay's ,observatory4 ,the polar axis is set in the meridian similarly to an equatorial telescope1 the whole apparatus being firmly mounted upon a massive stone pillar which is set several feet in the ground1 and rests upon a bed of concrete1 if the soil is light4 ,a house upon wheels1 running upon a tramway1 is used to protect the instrument from the weather1 and when in use this hut is run back to the north1 leaving the siderostat exposed4 ,in the north wall of the observatory is a window1 and the telescope is mounted horizontally opposite to it3 so the observer can seat himself comfortably at his work1 and by his guide rods direct the mirror of the siderostat to almost any part of the sky1 viewing any object in the eyepiece of his telescope without altering his position4 ,in spectroscopy and celestial photography its use is of immense importance1 for in these researches the image of an object is required to be kept steadily on the slit of the spectroscope or on the photographic plate1 and for this purpose a very strongly-made and accurate clock is required to drive the telescope and mounting1 which are necessarily made heavy and massive to prevent flexure and vibration4 ,the siderostat1 on the other hand1 is extremely light1 without tube or accessories1 and a light1 delicate clock is able to drive it with accuracy1 while the heavy telescope and its adjuncts are at rest in one position4 ,the sun and stars can1 therefore1 as it were1 be 8laid on0 to the observer's study to be viewed without the shifting of the observatory roof and equatorial1 or of the observing chair1 which brings its occupant sometimes into most uneasy positions4 ,we figure to ourselves the future of the physical observatory in the shape of an ordinary room with siderostat outside throwing sunlight or rays from whatever object we wash into any fixed instrument at the pleasure of the observer4 ,there are1 however1 inconveniences attending its use in some cases2 for instance1 in measuring the position of double stars1 the diurnal motion gradually changes their position in the field of the telescope1 so that a new zero must be constantly taken or else the time of observation noted and the necessary corrections made4 ,,chapter ,,xxiv4 ,,the ,,ordinary ,,work ,,of ,,the ,,equatorial4 ,the equatorial enables us to make not only physical observations1 but differential observations of the most absolute accuracy4 ,first we may touch upon the physical observations made with the eyepiece alone--star-gazing1 in fact4 ,the ,sun first claims our attention3 our dependence on him for the light of day1 for heat1 and for in fact almost everything we enjoy1 urges us to inquire into the physics of this magnificent object4 ,precautions must however be taken2 more than one observer has already been blinded by the intense light and heat1 and some solar eyepiece must be used4 ,for small telescopes up to two inches1 a dark glass placed between the eye and the eyepiece is sufficiently safe2 for larger apertures1 the diagonal reflector1 or ,dawes' solar eyepiece1 already described1 comes into requisition4 ,another method of viewing the sun is to focus the sun's image with the ordinary eyepiece on a sheet of paper or card1 or1 better still1 on a surface of plaster of ,paris carefully smoothed4 ,the bright ridges or streaks1 usually seen in spotted regions near the edge1 called the facul1 and the mottled surface1 appearing1 according to ,nasmyth1 like a number of interlacing willow-leaves--the minute 8granules0 of ,dawes1 are best seen with a blue glass2 but for observing the delicately-tinted veils in the umbr of the spots a glass of neutral tint should be used4 ,the ,moon is a fine object even in small telescopes4 ,the best observing time is near the quarters1 as near full moon the sun shines on the surface so nearly in the same direction as that in which we look1 that there is no light and shade to throw objects into view4 ,hours may be spent in examining the craters1 rilles1 and valleys on the surface1 accompanied with a good descriptive map or such a book as that which ,mr4 ,neison has recently published4 ,the planets also come in for their share of examination4 ,mercury is so near the sun as seldom to be seen4 ,venus in small telescopes is only interesting with reference to her changes1 like the moon1 but in larger ones with great care the spots are visible4 ,mars is interesting as being so near a counterpart of our own planet4 ,on it we see the polar snows1 continents and seas1 partially obscured by clouds1 and these appearances are brought under our view in succession by the rotation of the planet4 ,with a good six-inch glass and a power of #bjj when the air is pure and the opposition is favourable1 there is no difficulty in making out the coast-lines1 and the various tones of shade on the water surface may be observed1 showing that here the sea is tranquil1 and there it is driven by storms4 ,up to very lately it was the only planet of considerable size further off the sun than ,venus that was supposed to have no satellite2 two of these bodies have however been lately discovered by ,hall with the large ,washington refractor of twenty-six inches diameter1 and they appear to be the tiniest celestial bodies known1 one of them in all probability not exceeding #aj miles in diameter4 ,jupiter and ,saturn are very conspicuous objects1 and the eclipses1 transits1 and occultations of the moons1 and the belts of the former and rings of the latter1 are among the most interesting phenomena revealed to us by our telescopes1 while the delicate markings on the third satellite of ,jupiter furnish us with one of the most difficult tests of definition4 ,uranus and ,neptune are only just seen in small telescopes1 and even in spite of the use of larger ones1 we are in ignorance of much relating to these planets4 ,the amateur will do well to attack all these with that charming book1 the ,rev4 ,t4 ,w4 ,webb's ,celestial ,objects for ,common ,telescopes1 in his hand4 ,to observe the fainter satellites of the brighter planets1 or1 indeed1 faint objects generally1 near very bright ones1 the bright object may be screened by a metallic bar1 or red or blue glass placed in the common focus4 ,so much with regard to our own system4 ,when we leave it we are confounded with the wealth of nebul1 star-clusters1 and single or multiple systems of stars1 which await our scrutiny4 ,with the stars1 not much can be done without further assistance than the eyepiece alone4 ,the colours of stars may however be observed1 and for this purpose a chromatic scale has been proposed1 and a memoir thereon written1 by ,admiral ,smyth1 for comparison with the stars4 ,the colour of a star must not be confused with the colours--often very vivid--produced by scintillations1 these rapid changes of brightness and colour depending on atmospheric causes4 ,of the large stars1 ,sirius1 ,vega and ,regulus are white1 while ,aldebaran and ,betelgueux are red4 ,in many double and multiple stars however the contrast of colours shows up beautifully2 in ,cygni for instance we have a yellow and blue star1 in ,leonis1 a yellow and a green star2 and of such there are numerous examples4 ,interesting as all these observations are1 a new life and utility are thrown into them when instead of using a simple eyepiece the wire micrometer is introduced4 ,this1 as we have before stated1 generally consists of one wire1 or two parallel wires1 fixed1 and one or two other wires at right angles to these1 movable across the field4 ,this micrometer is used in connection with a part of the eyepiece end of the telescope1 which has now to be described4 ,this is a circle1 the fineness of the graduation of which increases with the size of the telescope1 read by two or four verniers4 ,the circle is fixed to the telescope1 while the verniers are attached to the eyepiece1 carrying the micrometer1 which is rotated by a rack and pinion4 ,the whole system of position circle 7as it is called7 and wire micrometer1 is in adjustment when 7#a7 the single or double fixed wires and the movable ones cross in the centre of the field1 and 7#b7 when with a star travelling along the single fixed or between the two fixed wires1 the upper vernier reads #ahj and the lower one reads zero4 ,this motion across the field gives the direction of a parallel of declination2 that is to say1 it gives a line parallel to the celestial equator1 and1 knowing that1 one will be able at once1 by allowing the object to pass through the field of view1 to get this datum line4 ,for instance1 supposing the whole instrument is turned round on the end of the telescope1 so that one of the two wires x and y1 ,fig4 #ajd1 at right angles to the thin wires for measuring distance1 shall lie on a star during all its motion across the field of view2 then those two wires1 being parallel to the star's motion1 will represent two parallels of declination2 and we use the direction of the parallels of declination to determine the datum point at right angles to them1 that is1 the north point of the field4 ,we have then a position micrometer1 that is1 one in which the field of view is divided into four quadrants1 called north preceding1 north following1 south preceding1 and south following1 because if there be an object at the central point it will be preceded and followed by those in the various quadrants4 ,the movable wires lie on meridians and the fixed ones on parallels when adjusted as above4 ,illustration3 ,,fig4 #aeh4--,position ,circle4 ,the position circle is often attached to1 and forms part of1 the micrometer instead of being fixed to the telescope1 and in screwing it on from time to time1 the adjustment of the zero changes1 and the index error must be found each time the micrometer is put on the telescope4 ,in practice it is usual to take the north and south line as the datum line1 and positions are always expressed in degrees from the north round by east #ij1 south #ahj1 and west #bgj1 to north again in the direction contrary to that of the hands of a clock4 ,the angle from the east and west line being found by the micrometer1 #ij is either added or subtracted1 to give the angular measurement from north4 ,but to make these measurements we want a clock2 a clock which1 when we have got one of these objects in the middle of the field of view1 shall keep it there1 and enable the telescope to keep any object that we may wish to observe fixed absolutely in the field of view4 ,but in the case of faint objects this is not enough4 ,we want not only to see the object1 but also the wires we have referred to4 ,now then the illuminating-lamp and bright wires1 if necessary1 come into use4 ,the following1 ,fig4 #aei1 will show how we proceed if we merely wish to measure a distance1 the value of the divisions of the micrometer screw having been previously determined by allowing an equatorial star to transit4 ,it represents the position of the central and the movable wire when the shadow thrown by the central hill of the the lunar crater ,copernicus is being measured to determine the height of the hill above the floor of the crater4 ,it has been necessary to let the fixed wire lie along the shadow2 this has been done by turning the micrometer2 but there is no occasion to read the vernier4 ,illustration3 ,,fig4 #aei4--;,how the ,length of a ,shadow thrown by a ,lunar ,hill is measured4 ,except on the finest of nights the stars shake in the field of view or appear woolly1 and even on good nights the readings made by a practised eye often differ1 inter se1 more than would be thought possible4 ,in measuring distances we have supposed for simplicity that we find the distance that one wire has to be moved from coincidence with the fixed wire from one point to another1 and theoretically speaking the pointer should point to ,o on the screw head when the wires are over each other1 and then when the wires are on the points1 the reading of the screw head divided by the number of divisions corresponding to #a will give the distance of the points in seconds of arc4 ,but in practice it is unnecessary to adjust the head to ,o when the wires coincide1 and the unequal expansion of the metals of the instrument1 due to changes of temperature1 would soon disarrange it4 ,it is also somewhat difficult to say when the wires exactly coincide1 and an error in this will affect the distance between the points4 ,it is therefore found best to only roughly adjust the screw head to ,o1 and then open out the wires until they are on the points and take a reading1 say twenty-two2 the screw is then turned1 in the opposite direction and the movable wire passed over to the other side of the fixed one1 and another reading taken1 say eighty-two2 now the screw has to be moved in the direction which decreases the readings on its head from one hundred downwards1 as the distance of the wires increases1 so that we must subtract the reading eighty-two from a hundred to give the number of divisions from the ,o through which the screw is turned1 and the reading in this direction we will call the indirect reading1 in contradistinction to the direct reading taken at first4 ,so far we have got a reading of twenty-two direct and eighteen indirect1 which means that we have moved the screw from twenty-two on one side of ,o to eighteen on the other side1 or through forty divisions1 and in doing so the movable wire has been moved from the distance of the two points on one side of the fixed wire to the same distance on the other1 or through double the distance required4 ,therefore forty divisions is the measure of twice the distance1 and the half of forty1 or twenty divisions1 is the measure of the distance itself between the two points to which our attention has been directed1 whether stars1 craters in the moon1 spots on the sun1 and the like4 ,let us consider what is gained by this method over a measure taken by coincidence of the wires as a starting-point1 and opening out the wires until they cut the points4 ,in the method we have just described there are two chances of error in taking the measurements--the direct and indirect2 but the result obtained is divided by two1 so that the error is also halved in the final result4 ,now by taking the coincidence of the wires as the zero1 or starting-point1 the measure is open to two errors1 as in the last case--the error of measurement of the points1 plus the error of coincidence of wires1 an error often of considerable amount1 especially as the warmth of the face and breath causes considerable alteration in the parts of the instrument1 making a new reading of coincidence necessary at each reading of distance4 ,as the result is not divided by two1 as in the first case1 the two errors remain undivided1 so we may say that there is the half of two errors in one case and two whole errors in the other4 ,here then we use the micrometer to measure distances2 but from a very short acquaintance with the work of an equatorial it will at once be seen that one wants to do something else besides measure distances4 ,for instance1 if we take the case of the planet ,saturn1 it would be an object of interest to us to determine how many turns1 or parts of a turn1 of the screw will give the exact diameter of the different rings2 but we might want to know the exact angle made by the axis with the direction of the planet's motion1 across the field1 or with1 the north and south line4 ,if we have first got the reading when the wires are in a parallel of declination1 and then bring ,saturn back again to the middle of the field and alter the direction of the wires until they are parallel to the major axis of the ring1 we can read off the position on the circle1 and on subtracting the first reading from this1 we get the angle through which we have moved the wires1 made by the direction of the ring with the parallel of declination1 which is the angle required4 ,we are thus not only able to determine the various measurements of the diameter of the outer ring by one edge of the ring falling on one of the fine wires1 and the other edge on the other wire1 but1 by the position circle outside the micrometer we can determine exactly how far we have moved that system1 and thus the angle formed by the axis of the ring of the planet at that particular time4 ,illustration3 ,,fig4 #afj4--,the ,determination of the ,angle of ,position of the axis of ,saturn's ,ring4 ,the uses of the position micrometer as it is called are very various4 ,in examination of the sun it is used to ascertain the position of spots on the surface1 and the rate of their motion and change4 ,the lunar craters require mapping1 and their distances and bearing from certain fixed points measuring1 for this then the position micrometer comes into use4 ,the varying diameters and the inclinations of the axes of the planets and the periods of revolution of the satellites are determined1 and the position of their orbits fixed1 in like manner4 ,when a comet appears it is of importance to determine not only the direction of its motion among the stars1 but the position of its axis of figure1 and the angles of position and dimensions of its jets4 ,the following diagram gives an example of the manner in which the position of its axis of figure is determined4 ,first the nucleus is made to run along the fixed wire1 so that it may be seen that the north vernier truly reads zero under this condition2 if it does not its index error is noted4 ,the system of wires is then rotated till one of the wires passes through the nucleus and fairly bisects the dark part behind the nucleus4 ,illustration3 ,,fig4 #afa4--,measurement of the ,angle of ,position of the ,axis of ,figure of a ,comet1 a a1 positions of fixed wire when the north vernier is at zero2 d d position of movable wire under like conditions2 a a1 d d1 positions of these wires which enable the angle of position of the comet's axis to be measured4 ,the angle a a or d d is the angle required4 ,it need scarcely be said that these observations are also of importance with reference to the motion of the binary stars1 those compound bodies1 those suns revolving round each other1 the discovery of which we owe to the elder ,herschel4 ,we may thus have two stars a small distance apart2 at another time we may have them closer still2 and at another we may have them gradually separating1 with their relative position completely changed4 ,by means of the wire micrometer and the arrangement for turning the system of wires into different positions with regard to the parallel of declination1 we have a means of determining the positions occupied by the binary stars in all parts of their apparent orbit1 as well as their distances in seconds of arc4 ,it is found1 however1 by experience that the errors of observation made in estimating distances are so large1 relatively to the very small quantities measured1 that it is absolutely necessary to make the determination of the orbit depend chiefly on the positions4 ,and this is done in the following way4 ,illustration3 ,,fig4 #afb4--;,double ,star ,measurement1 a a1 b b1 first position of fixed1 double wire when the vernier reads #j1 and the star runs between the wires2 c c1 d d1 first position of movable wires4 a a1 b b1 new position of fixed double wire which determines the angle of position2 c c1 d d1 new positions of the movable wires which measure the distance4 ,it is possible1 by knowing the position angles at different dates1 to find the angular velocity1 and since the areas described by the radius vector are equal in equal times1 the length of the radius vector must vary inversely as the square root of the angular velocity1 and by taking a number of positions on the orbit of known angular velocity1 we can set off radii vectores1 and construct an ellipse1 or part of one1 by drawing a curve through the ends of the radii vectores2 and from the part of the ellipse so constructed it is possible to make a good guess at the remainder4 ,the angular size of this ellipse is obtained from the average of all the measures of distance of the stars4 ,this ellipse is then the apparent ellipse described by the star1 and the form and position of the true ellipse can be constructed from it from the consideration of the position of the larger star 7which must really be the focus71 with reference to the focus of the apparent ellipse2 for if an ellipse be seen or projected on a plane other than its own1 its real foci will no longer coincide with the foci of the projected ellipse4 ,the methods adopted in practice1 for which we must refer the reader to other works on the subject1 are1 however1 much more laborious and lengthy than the above outline1 which is intended merely to show the possibility1 or the faint outline of a method of constructing the real ellipse4 ,when the real ellipse or orbit is known1 it is then of course possible to predict the relative positions of the two components4 ,let us consider in some little detail the actual work of measuring a double star4 ,a useful form for entering observations upon1 as taken1 is the following1 which is copied from one actually used4 ,,temple ,,observatory4 ,no4 #a4 ,april #ab1 #ahgebgf4 ,,double ,,stars4 ,,struve #acch4 ,r4,a4--#i;h4 #acm4 #bhs4 ,,decl4 #ch #da #bj4 ,magnitudes--#fg1 #gb4 ,,position4 ,zero1 #ajih4 ,illustration ,,distance4 ,direct4 ,indirect4 ,diff4 #ag #ig #aj #af #ig #ie -------------- #ige mean4 ,readings4 #agja #agj #afie #afih ---------- #d7 #fgid ---------- #afih #ajih #ijj ---------- #aih #afih ,position #aej #aih ---------- ,distance #ahbh4 #aej 99 99 99 99 99 ,no4 #b4 ,feb4 #eth1 #ahgeji4 ,,double ,,stars4 ,,struve #egg4 ,r4 ,a4--#d;h4 #cdm4 #is4 ,,decl4 #cg #ag ,magnitudes--#g1 #h4 ,,position4 ,zero1 #hhi4 ,illustration ,,distance4 ,direct4 ,indirect4 ,diff4 #abe #iie #fe #abf #iib #fg -------------- #ff mean4 ,readings4 #gie #hae #hab ---------- #c7 #bdbb ---------- #haa mean4 #hhi #ijj ---------- -#aa #haa -#aa ---------- #hbb ,position #bfbb4 #ahjj ---------- ,distance #abcg4 #bfbb ,the star having been found1 the date and decimal of the year are entered at the top1 and a position taken by bringing the thick wires parallel to the stars4 ,a distance--say direct--is then taken1 and the degrees of position #agja1 and divisions of the micrometer screw seventeen1 read off with the assistance of a lamp and entered in their proper columns4 ,the micrometer is then disarranged and a new measure of position and an indirect distance taken1 and so on4 ,at the end of the readings1 or at any convenient time1 the zero for position is found by turning the micrometer until the wires are approximately horizontal1 and then allowing a star to traverse the field by its own motion1 or rather that of the earth1 and bringing the thick wires parallel to its direction of motion2 this may be more conveniently done by means of the slow-motion handle of the telescope in ,r4 ,a41 which gives one the power of apparently making the star traverse backwards and forwards in the field4 ,the position of the wires is altered until the star runs along one of them4 ,the position is then read off and entered as the zero4 ,in describing the adjustments of the position circle we made the vernier read #j when the star runs along the wire1 for that is practically the only datum line attainable2 since1 however1 the angles are reckoned from the north1 it is convenient to set the circle to read #ij when the star runs along the wire1 so that it reads #j when the wires are north and south4 ,now as positions are measured from north #j in a direction contrary to that of the hands of a watch1 and an astronomical telescope inverts1 we repeat the bottom of the field is #j1 the right #ij1 and so on2 now the reading just taken for zero is the reading when the wires are ,e4 and ,w41 so that we must deduct #ij from this reading1 giving #aih as the reading of the circle when the wires were north and south1 or in the position of the real zero of the field4 ,of course theoretically the micrometer ought to read #j when the wires are north and south1 but in screwing on the instrument from night to night it never comes exactly to the same place1 so that it is found easier to make the requisite correction for index error rather than alter the eye end of the telescope to adjustment every night4 ,the readings of position must therefore be corrected by the number of degrees noted when the wires are at the real zero1 which in the case in point is #aih1 which may be called the index error4 ,it is also obvious that the micrometer may be turned through #ahj and still have its wires parallel to any particular line4 ,the position of the stars also depends upon the star fixed on for the centre round which our degrees are counted2 for in the case of two stars just one over the other in the field of view1 if we take the upper one as centre1 then the position of the system is #j1 but if the lower one1 then it is #ahj2 in the case of two equal or nearly equal stars1 it is difficult to say which shall be considered as centre1 and so the position given by two different persons might differ by #ahj4 ,there are also generally two verniers on the position circle1 one on each side1 and these of course give readings #ahj different from each other1 so that #ahj has often to be added or subtracted from the calculated result to give the true position4 ,all that is really measured by the position micrometer is the relative position of the line joining the stars with the ,n4 and ,s4 line4 ,in order1 therefore1 to find1 whether #ahj should be added or not1 a circle is printed on the form1 with two bars across for a guide to the eye1 and the stars as seen are roughly dotted down in their apparent position--in the case in point about #aej4 ,our readings being now made1 we first take a mean of those of position1 which is #afih1 nearly1 and the zero is #ajih2 deduct #ij from this to give the reading of the ,n4 and ,s4 line #aih1 then we deduct this from the mean of position1 #afih1 giving us #aej as the position angle of the stars4 ,it often happens that the observed zero is less than #ij1 and then we must add #cfj to it before subtracting the #ij1 or what is perhaps best1 subtract the observed zero from #ij1 and treat the result as a minus quantity1 and therefore add it to the mean of position readings instead of subtracting as usual4 ,the observations of the second star give a case in point3 the zero is #hhi1 and subtracting this from #ij1 we get #aa2 we put this down as -#aa to distinguish it from a result when #ij is subtracted from the zero2 it is then added to the mean of position readings #haa1 giving #hbb1 but on reference to the dots showing the approximate position of the stars1 it is seen that #ahj must be added to their result1 giving #bfbb as the position of the stars4 ,now as to distance1 take the case of the second star4 ,subtract the first indirect reading from #ajj1 giving #je1 and add this to the direct reading1 #abe1 making #acj1 which is the difference between the two readings taken on either side of the fixed wire2 the half of this1 #fe1 is placed in the next column1 and the same process is repeated with the next two readings3 a mean of these is then taken1 which is #ff for the number of divisions corresponding to the distance of the stars4 ,in the micrometer used in this case1 #ec divisions go to #a1 so that #ff is divided by #ec1 giving #abcg as the distance4 ,a table showing the value in seconds of the divisions from one to twenty or more1 saves much time in making distance calculations2 the following is the commencement of a table of this kind where #ec divisions correspond to #a4 ,divi- #j #a #b #c #d #e #f #g #h #i sions of micro- meter4 #j #jjjjjahjcgjefjgejicaabacaaejafh #a #jahgbjebbdbdcbfbbhjbiicahccgcef #b #jcgecicdabdcadejdfhdhgejfebeedc ,in the first column are the divisions1 and in the top horizontal line the parts of a division1 and the number indicated by any two figures consulted is the corresponding number of seconds of arc4 ,in the case of a half difference of #bc we look along the line commencing at #b until we get under #c1 when we get #jdca as the seconds corresponding to #bc divisions4 ,it is necessary to adjust the quantity of light from the lamp in the field1 so that the wires are sufficiently visible while the stars are not put out by too much illumination2 for the majority of stars a red glass before the lamp is best4 ,this gives a field of view which renders the wires visible without masking the stars1 but a green or blue light is sometimes very serviceable4 ,a shaded lamp should be used for reading the circles on the micrometer1 so as not to injure the sensitiveness of the eye by diffused light in the observatory4 ,a lamp fixed to the telescope1 having its light reflected on the circles1 but otherwise covered up1 is a great advantage over the hand-lamp4 ,in very faint stars1 which are masked by a light in the field sufficient to see the wires1 the wires can be illuminated in the same manner as in the transit1 but there is this disadvantage--the fine wires appear much thickened by irradiation1 so that distances1 especially of close stars1 become difficult to take4 99 99 99 99 99 ,we come now to the differential observations made with the equatorial4 ,let us explain what is meant4 ,suppose it is desired to determine with the utmost accuracy the position of a new comet in the sky4 ,if we take an ordinary equatorial1 or an extraordinary equatorial 7excepting probably the fine equatorial at ,greenwich71 and try to determine its place by means of the circles1 its distance from the meridian giving its right ascension and its distance from the equator giving its declination1 we shall be several seconds out1 on account of want of rigidity of its parts2 but if we do it by means of such an instrument as the transit circle at ,greenwich1 we wait till the comet is exactly on the meridian1 and determine its position in the way already described4 ,as a matter of fact1 however1 the transit circle is not the instrument usually used for this purpose1 but the equatorial4 ,we do not however just bring the comet or other object into the middle of the field and then read off the circles1 but we differentiate from the positions of known stars2 so that all that has to be done in order to get as perfect a place for the comet as can be got for it by waiting till it comes to the meridian--which perhaps it will do in the day-time1 when it will not be visible at all--is to determine its distance in right ascension and declination from a known star1 by means of a micrometer4 ,of course one will choose the brightest part of the comet and a well-known star1 the place of which has been determined either by its appearance in one of the catalogues1 or by special transit observations made in that behalf4 ,we then by the position micrometer determine its angle of position and distance from the known star at a time carefully noted1 or we measure the difference in right ascension and the difference in declination4 ,illustration3 ,,fig4 #afc4--,ring ,micrometer4 ,continental astronomers have another way of doing this which we will attempt to explain4 ,suppose we wish to find the difference in declination of a star and ,jupiter1 we place the ring1 ,a ,d1 ,fig4 #afc1 in the eyepiece of the telescope and watch the passage of ,jupiter and the star over this ring micrometer4 ,it will be clear that1 as the motion of the heavens is perfectly uniform1 it will take very much less time for the star to travel over the ring from ,b to ,c than it will for ,jupiter to travel over the ring from b to c1 because the star is further from the centre2 and by taking the time of external and internal contact at each side of the ring1 the details of which we need not enter upon here1 the ,continental astronomers are in the habit of making differential observations of the minutest accuracy by means of this ring micrometer1 whilst we prefer to make them by the wire micrometer4 ,,book ,,vi4 ,,astronomical ,,physics4 ,,chapter ,,xxv4 ,,the ,,general ,,field ,,of ,,physical ,,inquiry4 ,we have now gone down the stream of time1 from ,hipparchus to our own days4 ,we find now enormous telescopes which enable us to see and examine celestial bodies lying at distances so great that the mention of them conveys little to the mind4 ,we find also perfect systems of determining their places4 ,the following chapters will show1 however1 that modern astronomy has not been contented with annexing those two branches of physics which have enabled us to make the object-glass and the clock1 and another still which enables us to make that clock record its own time with accuracy4 ,these applications of ,science have been effected for the purpose either of determining with accuracy the motion and positions of the heavenly bodies or of enabling us to investigate their appearances under the best possible conditions4 ,the other class of observations to which we have now to refer1 have to do with the quantity and the quality of the vibrations which these bodies impart to the ether1 by virtue of which vibrations they are visible to us4 ,we began by measurement of angles1 we end with a wide range of instruments illustrating the application of almost every branch of physical as well as of mathematical science4 ,in modern observatories applications of the laws of ,optics1 ,heat1 ,chemistry and ,electricity1 are met with at every turn4 ,each introduction of a new instrument1 or of a new method of attack1 has by no means abolished the preexisting one2 accretion rather than substitution has been the rule4 ,on the one hand1 measurement of angles goes on now more diligently than it did in the days of ,hipparchus1 but the angles are better measured1 because the telescope has been added to the divided arc4 ,time is as necessary now as it was in the days of the clepsydra1 but now we make a pendulum divide its flow into equal intervals and electricity record it4 ,on the other hand1 the colours of the stars are noted as carefully now as they were before the spectroscope was applied to the telescope1 but now we study the spectrum and inquire into the cause of the colour4 ,the growth of the power of the telescope as an instrument for eye observations has gone on1 although now almost all phenomena can be photographically recorded4 ,the uses to which all astronomical instruments may be put may be roughly separated into two large groups3-- ,i4 ,they may be used to study the positions1 motions1 and sizes of the various masses of matter in the universe4 ,here we are studying celestial mechanics or mechanical astronomy1 and with these we have already dealt4 ,,ii4 ,they maybe used to study the motions of the molecules of which these various masses are built up1 to learn their quality1 arrangement1 and motions4 ,here we are studying celestial physics1 or physical astronomy4 ,it is with this latter branch that we now have to do4 ,first we have to deal with the quantity and intensity of the ethereal vibrations set up by the constituent molecules of these distant bodies4 ,we wish to compare the quantity of light given out by one star with that given out by another4 ,we wish1 say1 to compare the light of ,mars with the light of ,saturn2 we are landed in the science of photometry1 which for terrestrial light-sources has been so admirably investigated by ,rumford1 ,bouguer1 and others4 ,here we deal with that radiation from each body which affects the eye--but by no means the total radiation4 ,this is a point of very considerable importance4 ,modern science recognises that in the radiation from all bodies which give us white light there is so great a difference of length of wave in the vibrations that different effects are produced on different bodies4 ,thus white light is a compound thing containing long waves with which heat phenomena are associated1 waves of medium length to which alone the eye is tuned1 and short waves which have a decided action on some metallic salts which are unaffected by the others4 ,to thus examine the constituents of a beam of light a lantern1 with a lime-light or electric light1 may be used for throwing a constant beam2 we may then produce an image of the cylinders of lime or the carbon points in the lantern on a piece of paper or a screen1 and our eyes will tell us that this is an instance of how the radiations from any incandescent substance are competent to give us light4 ,we receive all the rays to which our eyes are tuned and we see a white image on the screen4 ,we shall see also that the light is more intense than that of a candle1 in other words that the radiation from the light-sources we have named is very great4 ,illustration3 ,,fig4 #afd4--,thermopile and ,galvanometer4 ,now let us insert in front of the lantern a piece of deep red glass1 that is1 glass which allows only the red constituents of the white light to pass4 ,now if a thermo-electric pile1 ,fig4 #afd1 be introduced into the beam we shall see that the needle of the galvanometer will alter its position4 ,now1 why does the needle turn8 ,this is not the place for giving all the details of this instrument1 but it is sufficient to say 7#a7 that the needle moves whenever a current of electricity flows through the coil of wire surrounding the needles1 and 7#b7 that the pile consists of a number of bars of antimony and bismuth joined at the alternate ends1 and whenever one end of the pile is heated more than the other1 a current of electricity is caused to flow4 ,such is the delicacy of the instrument1 that the heat radiated from the hand1 held some yards away from it1 is sufficient to set the needle swinging violently2 this then acts as a most delicate thermometer4 ,in this case it shows that heat effects are produced by the red constituents of the light from the lamp4 ,now replace the thermopile by a glass plate coated with a salt of silver in the ordinary way adopted by photographers4 ,no effect will be produced4 ,replace the red glass by a blue one4 ,if the light is now allowed to fall on the photographic plate1 its effect is to decompose1 or alter the arrangement of1 the atoms of silver1 so that on applying the developing solution1 the silver compound is reduced to its metallic state on the places where the light has acted2 and thus1 if the image of the light-source has been focussed on the plate1 a photograph of it is the result4 ,if the thermopile is brought into the beam it will be now as insensitive to the blue light as the photographic plate was to the red light in the former case4 ,we have therefore three kinds of effects produced1 viz41 light1 heat1 and chemical or actinic action1 and when light is passed through a prism1 these three different radiations1 or energies1 are most developed in three different portions of the spectrum4 ,if indeed a small spectrum be thrown on the screen and the different colours are examined with the thermopile1 it will be found that as long as we allow it to remain at the blue end of the spectrum1 there will be no effect on the galvanometer1 but if instead of holding it at the blue end we bring it towards the red1 the galvanometer needle is deflected from its normal position1 to that it had when the red rays fell on it1 showing that it is beyond all doubt the red rays and not the blue to which it is sensitive4 ,where then in the spectrum are the rays which affect the photographic plate8 ,we can at once settle this point4 ,if one be placed in the spectrum for a short time1 and then developed1 it will be found to be affected only in the part on which the blue rays have fallen4 ,indeed to demonstrate this no lamp is necessary4 ,if for half-an-hour or so two pieces of sensitive paper are placed in the daylight1 one covered with red glass1 and the other with violet1 so that the sunlight is made to travel1 in the one case1 through red glass1 and in the other through violet1 it will be found that the violet light will act1 and produce a darkening of the paper1 while the red glass will preserve the paper below it from all action4 ,this is a proof that the blue end of the spectrum has another kind of energy1 a chemical energy1 by means of which certain chemicals are decomposed1 this is the basis of photography4 ,these different qualities of light have been utilized by the astronomer4 ,he attaches a thermopile to his telescope and establishes a celestial thermometry4 ,the radiations repay a still more minute examination1 and aided by the spectroscope1 he is able to study with the utmost certitude the chemical condition of the heavenly host1 while the polariscope enables him to acquire information in still another direction4 ,nor does he end here4 ,he replaces his eye by a sensitive plate1 which not only enables him to inquire into the richness of the various bodies in these short waves1 but actually to obtain images of them of most marvellous beauty and exactness4 ,these various lines of work we have to consider in the remaining chapters4 ,,chapter ,,xxvi4 ,,determination ,,of ,,the ,,light ,,and ,,heat ,,of ,,the ,,stars4 ,one branch of observatory work is that of determining the relative magnitude of stars1 the word magnitude being of course used in a conventional sense for brightness4 ,there are1 moreover1 stars which vary in brightness or magnitude from time to time2 these are called variable stars1 and the investigation of the amount and period of variation opens up another use for the equatorial1 and an instrument is required for finding the value of the amount of light given by a star at any instant2 in fact1 a photometer is necessary4 ,the methods of determining the brilliancy of stars are so similar in principle to those employed for ordinary light-sources that the ordinary methods of photometry may be referred to in the first instance4 ,we may determine the relative brilliancy of two or more lights1 or we may employ a standard light and refer all other lights to that4 ,rumford's photometer1 ,fig4 #afe1 is based upon the fact that if the intensity of the shadows of an opaque body be equal1 the lights throwing the shadows are equal4 ,hence the lights are moved towards or from a screen until the shadows are equal2 then if the distances from the screen are unequal the lights are unequal1 and the intensities vary in the inverse ratio of the squares of the distances4 ,this method is practically carried out in the telescope by reducing the aperture till the stars become invisible1 and noting the apertures at which each vanishes in turn4 ,the most simple method of doing this is that used by ,dawes1 which is simply an adjustable diaphragm limiting the available area of the object-glass2 we can thus view a star1 and gradually reduce the aperture until the star is just visible1 or until it just disappears1 the latter limit being perhaps the most accurate and most usually used2 the aperture is read off on the scale attached4 ,illustration3 ,,fig4 #afe4--,rumford's ,photometer4 ,the photometer of ,mr4 ,knobel is1 however1 a very handy one2 it consists of a plate of metal having a large ,v-shaped piece with an angle of #fj cut out of it2 another plate slides over the first in such a manner that its edge forms a base for the ,v-shaped opening1 thus forming an equilateral triangular hole1 which is adjustable at pleasure by moving the second plate4 ,the edge of the moveable plate is divided so that the size of the base of opening is known at once1 and its area easily calculated4 ,the annexed woodcut will give an idea of the second method which is possible4 ,illustration3 ,,fig4 #aff4--;,bouguer's ,photometer4 ,let the gas flame be supposed to represent a constant light at constant distance2 then the intensity of the light to be experimented upon 7represented by the candle7 is determined by moving it towards or from the mirror till the illumination of both the halves of the porcelain screen is equal4 ,the instrument by which this kind of investigation is carried out by astronomers has been introduced by ,zllner1 and is called the ,astrophotometer4 ,in this the star is compared with a small image of a portion of the flame of a lamp attached to the telescope4 ,it being found that1 though the total light emitted by the flame varies with its size1 the intensity of the brightest part does not1 appreciably4 ,two artificial stars are formed by means of a pin-hole1 a double concave lens1 and a double convex lens4 ,these appear in the field by reflexion from the front and back faces of a plate of glass alongside the image of the real star1 the light of which passes through the plate4 ,the intensity of the artificial star is varied1 first by changing the pin-hole1 and finally by two ,nicol's prisms1 the colour being first matched with that of the star by means of a third ,nicol1 with a quartz plate between it and the first of the other two ,nicols4 ,the instrument is provided with object-glasses of various sizes 7and diaphragms7 up to #b inches1 and1 if fainter stars are to be examined1 it can be screwed on to the eyepiece of an equatorial instrument4 ,a second arrangement1 like the first1 but without the quartz plate arrangement1 forms an artificial star from moonlight1 for comparison of the light of that body with the artificial star4 ,so far there is no difficulty1 but this measure must be interpreted into magnitude1 and we must know what magnitude a star is which just disappears with a given aperture of1 say1 one inch1 and secondly1 the ratio of light between the magnitudes1 or how much less light is received from a star of the next magnitude in proportion to the given one4 ,if now we were able to start a new scale of magnitude1 it would be easy to say that a star just visible with an inch aperture on a fine night shall be called a ninth magnitude star1 and fix a certain number of ninth magnitude stars for reference1 so that the errors induced by hazy nights and variable eyes might be eliminated4 ,an observer on a bad night could limit his aperture on a known star1 when he might find that double the area given by an aperture of one inch was required as a limit for one of the stars of reference1 and in that case he would know that half the usual amount of light from every star was stopped by atmospheric causes1 and he would make the requisite corrections throughout his observations4 ,we might also say that a star of a whole magnitude1 greater or less than another1 shall give us half or double the amount of light--in fact1 that this shall be the ratio between magnitudes4 ,we are not1 however1 able to make these rules1 for an arbitrary scale has been adopted for years1 and we can only reduce this scale to a law1 in such a manner as not to interfere greatly with the generally received magnitudes4 ,amongst the brighter stars there is a close agreement in the estimate of magnitude by different observers1 but amongst the higher magnitudes a difference appears4 ,sir ,j4 ,herschel and ,admiral ,smyth1 for instance1 go into much higher numbers of magnitudes than ,struve2 the limit of ,admiral ,smyth's vision with his #f-;inch telescope was a #afth magnitude1 while the limit of ,struve's vision with a #i-;inch telescope he calls a #abth magnitude2 the estimates of the latter observer are1 however1 gaining greater adoption4 ,in order to reduce the relative magnitude to a law1 ,mr4 ,pogson#ba took stars differing largely in magnitude1 and compared the amount of light from each1 and so reduced the ratio between the magnitudes given by ,knott and all the best observers4 ,from this he found that a mean of #bd represented the ratio1 and for reasons given he adopted the quantity #beab as a convenient ratio2 as he states1 8the reciprocal of log4 ,r 7in his paper ,r the ratio #beab71 a constant continually occurring in photometric formul1 is in this case exactly #e40 ,so far the ratio is established4 ,the next thing is the basis from which to commence reckoning2 this ,mr4 ,pogson fixed by reference to ,argelander's catalogued stars1 estimated by him at about the #ith magnitude1 and with these1 comparison is made with the star whose light is measured1 and the above constant of ratio applied1 which at once gives the magnitude of the measured star4 ,to do this1 in ,mr4 ,pogson's words3 8,if then any observer will determine for himself the smallest of ,argelander's magnitudes1 just visible by fits1 on a fine moonless night1 with an aperture of one inch1 and call this quantity ,l1 or the limit of vision for one inch1 the limit l1 for any other aperture1 will be given by the simple formula1 l ,l #e log4 aperture40 ,the value of ,l founded by ,mr4 ,pogson is #ib2 that is1 a star of #ib magnitude1 according to ,argelander1 is limited by #a-;inch aperture1 with ,mr4 ,pogson's eye4 ,on different nights and with different eyes1 this number1 or the magnitude limited1 must vary1 and it varies from exactly the same causes that produce variation in the light of the stars to be measured1 so that we are independent of transparency of the air1 at least within considerable limits4 ,having found the value of ,l for any night1 we turn the telescope on a star to be measured1 then alter the aperture if we employ the first method1 until the limit is found1 and insert the value in the equation1 the value of l1 or the star's magnitude1 then at once appears4 ,by this means a number of well-known stars of all magnitudes may be settled for future reference and comparison with variable stars4 ,the comparison stars then being fixed upon1 and their magnitude accurately known1 there is not much difficulty in comparing any variable star with one or more of those of approximately the same magnitude4 ,by this means a number of independent estimates of the magnitude of the variable is obtained free from errors from the disturbing effects of mist or moonlight1 which affects both the stars of comparison and variable alike4 ,if we call the stars of comparison ,a ,b ,c ,d1 we enter the comparisons somewhat as follows2 7variable7 #b ,a1 #d ,b1 #a ,c1 #g ,d1 the number showing how many tenths of a magnitude the variable is more or less bright than each comparison star1 and the magnitude of the latter being known1 we get several values of the magnitude of the variable1 a mean of which is taken for the night4 ,in order to show clearly to the eye the variations of a star1 and to compute the periods of maximum and minimum1 a graphical method is adopted3 a sheet of cross-ruled paper is prepared1 on which the dates of observation are represented by the absciss1 and the corresponding observed magnitudes by the ordinates4 ,dots are then made representing the several observations1 and a free-hand curve drawn amongst the dots1 which at once gives the probable magnitude at any epoch in the period of observation1 the change of the curve from a bend upwards to downwards1 or vice vers1 indicating a maximum or minimum of magnitude4 ,so much then for the method of determining the intensity of the visible radiation4 ,the next point to consider is the intensity of the thermal radiations--we pass from photometry to thermometry4 ,the thermopile will in the future be an astronomical instrument of great importance4 ,we need not go into its uses in other branches of physics1 we shall here limit ourselves to the astronomical results which have been already obtained4 ,lord ,rosse used a pile of this kind1 made of alternate bars of bismuth and antimony4 ,he attacked the moon1 and by observing it from new to full1 and from full to new1 he got a distinct variation of the amount of heat1 according as the moon was nearest to the epoch of full moon1 or further from that epoch4 ,as the moon was getting full1 he found the needle moved1 showing heat1 and1 after the full1 it went down again and found its zero again at new4 ,by differential observations ,lord ,rosse showed that this little instrument1 at the focus of his tremendous reflector1 was able to give some estimate of the heat of the moon1 which may be #ejj degrees ,fahr4 at the surface4 ,it may be said that the moon is very near us1 and we ought to get a considerable amount of heat from it2 but the amount is scarcely perceptible without delicate instruments4 ,still the instrument is so delicate1 that the heat of the stars has been estimated4 ,a pile of very similar construction to the one just mentioned has been attached by ,mr4 ,stone to the large equatorial at ,greenwich4 ,the instrument consists of two small piles about one-tenth of an inch across the face2 the wires from each are wound in contrary directions round a galvanometer1 so that when equal currents of electricity are passing they counteract each other1 and the needle remains stationary4 ,it only moves when the two currents are unequal2 we have then a differential galvanometer1 showing the difference of temperature of the faces of the two piles2 the image of a star is allowed to fall half-way between the two piles--then on one pile and then on another2 then matters are reversed1 and a mean of the galvanometer readings taken1 beginning with zero when the image of a star was exactly between the two piles4 ,the result was this1 that the heat received from ,arcturus1 when at an altitude of #be1 was found to be just equal to that received from a cube of boiling water1 three inches across each side1 at the distance of #djj yards4 ,arcturus is not the only star which has been observed in this way2 in another star1 ,vega1 which is brighter than ,arcturus1 it has been demonstrated that the amount of heat which it gives out1 when at an altitude of #fj1 is equal to that from the same cube at #fjj yards1 so that ,mr4 ,stone shows beyond all question1 that ,arcturus gives us more heat than ,vega4 ,this opens a new field1 for if we get heat effects different from the effects on the eye1 the stars ought to be catalogued with reference to their thermal relations as well as their visual brightness4 ,another valuable application of this method is due to ,professor ,henry1 of ,washington4 ,professor ,henry imagined that1 by means of a thermo-electric pile placed at the eyepiece of the telescope1 so that a sun-spot1 or a part of the ordinary surface1 could be brought on the face of the pile1 he could tell whether there was a greater1 or less radiation of heat from a spot1 than from any other part2 and he was able with the thermopile to show that there was a smaller radiation of heat from the spots than from the other parts of the sun's surface4 ----- ,footnote #ba3 ,monthly ,notices1 ,r4,a4,s41 vol4 xvii41 p4 #ag4 ,,chapter ,,xxvii4 ,,the ,,chemistry ,,of ,,the ,,stars3 ,,construction ,,of ,,the ,,spectroscope4 ,in the addition of chemical ideas to astronomical inquiries1 we have one of the most fruitful and interesting among the many advances of modern science1 and one also which has made the connection between physics and astronomy one of the closest4 ,to deal properly with this part of our book1 as the constitution of one of the heavenly bodies can be studied in the laboratory as well as in the observatory1 we have to describe physical instruments and methods1 as well as the more purely astronomical ones4 ,in a now rare book published in ,london in the year #afec1 that is to say1 some years before ,sir ,isaac ,newton made his important observations on the action of a prism on the rays of light--observations which have been so very rich in results--is given ,kepler's treatise on ,dioptrics4 ,from this one finds that the great ,kepler had done all he could to try to investigate the action of a three-cornered piece of glass4 ,it has been considered1 that1 because ,newton was the first to teach us much of its use1 he was the first to investigate the properties of the prism4 ,this is not so4 ,fig4 #afg is an illustration taken from this book1 by which ,kepler shows that if we have a prism and pass light through it1 we get three distinct results when a ray 7,f7 falls on the prism4 ,he shows that the first surface reflects a certain amount of light1 7,d ,i71 and that this is uncoloured1 because it does not pass through the glass1 and that the remainder is refracted by the glass and part emerges at ,e1 coloured like the rainbow4 ,then he goes on to show that the second surface of the prism also reflects some light internally1 and that there is a certain amount of light leaving the prism at ,m1 and going to ,k4 ,illustration3 ,,fig4 #afg4--,kepler's ,diagram4 ,by means of a very few experiments ,newton was able to show how much knowledge could be got by examination of the prism4 ,the first proposition in ,newton's ,optics is an attempt to prove that light1 which differs in colour1 differs also in degree of refrangibility4 ,we shall recollect from the fifth chapter what this term means1 for it was there shown that whenever a ray of light enters obliquely a medium denser than that in which it had been travelling1 it is bent towards the perpendicular to the surface1 in fact it is refracted1 and those rays which are most refracted by the same substance with the same angle are said to be more refrangible than others4 ,newton's experiment was very simple4 ,he took a piece of paper1 one half of which was coloured red and the other half blue2 and this was placed on a stand horizontally1 in the light from a window1 with a prism between it and the eye4 ,illustration3 ,,fig4 #afh4--,newton's ,experiment showing the different ,refrangibilities of ,colours4 ,he went on to show1 that when he allowed the beam of sunlight to fall upon the paper1 strongly illuminating the red and blue portions1 making at the same time all the rest of the room as dark as possible 7so that the operation was not impeded by extraneous light71 when he held a prism in a particular way1 he found that the red and the blue occupied different positions when looked at through the prism4 ,when the prism is held as shown1 the red is seen below and the blue above4 ,if the prism be turned with the refracting edge downwards1 the red is seen above and the blue below4 ,when the refracting edge is upwards1 it is very clear that if the violet is seen uppermost it must be because the violet ray is more refracted1 and when the red ray is uppermost1 with the refracting edge of the prism downwards1 it is because the red ray is the least refracted4 ,there are other experiments to which he alludes1 and by which ,sir ,isaac ,newton considered he had proved that lights which differ in colour differ also in degrees of refrangibility4 ,newton at one step went to the sun1 and his second theorem is 8,the light of the sun consists of rays of different refrangibility10 and then he enters into the proof by experiment4 ,the light from the sun passes through a hole in the window-shutter and through the prism which throws a spectrum on a screen4 ,we now see the full meaning of the different degrees of refrangibility4 ,there he had a long band of light of all colours1 the red at one end and the blue at the other1 showing that the different colours are unequally refracted1 or turned from their course4 ,in this way ,sir ,isaac ,newton determined whether the law1 that light which differed in colour differed also in refrangibility1 held true with regard to the sun2 and he clearly showed that in this case also the light differs in refrangibility1 in exactly the same way as the red light and the blue light had done in his experiment with the pieces of paper4 ,he was soon able to prove to himself that the circular aperture was not the best thing he could use1 because in the spectrum he had a circle of colour representing every ray into which the light could be broken up4 ,if we put a bit of red glass in the path of the rays we get an image of the hole in red2 if we use other coloured glasses1 we have a circle for each particular colour2 all these images overlap1 and the sum total gives us an extremely mixed spectrum1 something quite different from what is seen when we introduce a slight alteration1 which curiously enough was delayed for a great many years4 ,sir ,isaac ,newton recognised the difficulties there were in getting a pure spectrum by means of a circular aperture1 but although he used afterwards an oblong opening instead of a circular aperture1 in which we had something more or less like what we now use1 namely1 a 8slit0--a narrow line of light2 he does not seem to have grasped the point of the thing1 because in one of his theorems he says he also tried triangular openings4 ,we shall show how important it is that we should not only have an oblong opening as proposed by ,newton1 but that that oblong opening should be of small breadth4 ,the moment we exchange the circular aperture for the oblong opening of ,newton1 we get a spectrum of greater purity1 and1 as in the case of the circular opening the purity depended on the size of the circle1 so also in the case of the oblong opening the purity of the spectrum depends very much on the breadth of the oblong opening4 ,we thus sort out the red1 orange1 yellow1 green1 blue1 and violet2 they are no longer mixed as they are when we employ a circular opening4 ,if we attempt the same experiment with red glass interposed we get something more decided than before2 we have no longer a circular patch of light1 but an oblong one in the red2 in fact1 the exact form of the aperture1 or slit1 through which we have allowed the light to pass through the prism and lens to form an image4 ,illustration3 ,,fig4 #afi4--,wollaston's first ,observation of the ,lines in the ,solar ,spectrum4 ,now although ,newton made these important observations on sunlight1 he missed one of the things1 in fact we may say the thing1 which has made sunlight and starlight of so much importance to ,astronomy4 ,the oblong opening which ,newton used varied from one-tenth to one-twentieth of an inch in width2 but ,dr4 ,wollaston in #ahab--we had to wait from #afgb till #ahab to get this apparently ridiculously small extension--used such a narrow slit as we have mentioned1 and he found that when he examined the light of the sun with a prism before the eye1 he got results of which ,newton had never dreamt4 ,dr4 ,wollaston not only found the light of the sun differing in refrangibility2 but in the different colours of the solar light he found a number of dark lines1 which are represented by the black lines across the spectrum in ,fig4 #afi4 ,illustration3 ,,fig4 #agj4--;,copy of ,fraunhofer's first ,map of the ,lines in the ,solar ,spectrum4 ,illustration3 ,,fig4 #aga4--,student's ,spectroscope4 ,in the year #ahad ,fraunhofer examined the spectrum by means of the telescope of a theodolite1 directing it towards a distant slit1 with a prism interposed4 ,in this manner he observed and mapped #egf lines1 the appearance of the spectrum to him being represented in ,fig4 #agj4 ,from this time they were called the 8,fraunhofer lines40 ,it need scarcely be said that from the time of ,wollaston until a few years ago these strange mysterious lines were a source of wonder to all observers who attempted to attack the problem4 ,the difference between the simple prism and slit which ,newton1 ,wollaston1 and ,fraunhofer used to map these lines1 and the modern spectroscope1 as used with or without the telescope1 is due to a suggestion of ,mr4 ,simms in #ahcj4 ,let us refer to a modern spectroscope4 ,fig4 #aga represents a form usually used for chemical analysis4 ,the only difference between the spectroscope and the simple prism in ,newton's experiment is this1 that in the one case the light falls directly from the slit through the prism on a screen and is viewed there2 and in the other the eye is placed where the screen is1 and looks through the prism and certain lenses at the slit4 ,the great improvement which ,mr4 ,simms suggested was this simple one4 ,he said1 8,it would surely be better that the light which passes through the prism or prisms independently of the number ,i use1 should1 if possible1 pass through them as a parallel beam of light2 and therefore1 instead of putting the slit merely on one side of a prism and the eye on the other1 ,i will1 between the slit and the prism1 insert an object-glass10 as shown in ,fig4 #agb2 so that the slit of the spectroscope is the representative of the hole in the shutter4 ,illustration3 ,,fig4 #agb4--,section of a ,spectroscope1 showing the ,path of the ,ray from the ,slit4 ,the slit is exactly in the focus of the little object-glass1 ,c1 or collimating lens1 as it is called2 so that naturally the light is grasped by this lens1 and comes out in a parallel beam1 and travels among the prism or prisms1 quite irrespective of course of their number4 ,this parallel beam1 in order to be utilized by the eye after it has passed through the system of prisms1 is again taken up by another object-glass and reduced from its parallel state into a state of convergence1 and brought to a focus which can be examined by means of an eyepiece4 ,the red rays from the slit come to a focus at ,r1 and the blue at ,b1 forming there their respective images of the slit1 and between ,b and ,r are a number of other images of the slit1 painted in every colour that is illuminating it1 thus forming a spectrum which is viewed by the eyepiece4 ,in fact1 the object-glass and eyepiece constitute a telescope1 through which the slit is viewed1 and the collimating lens makes the light parallel1 just as if it had come from a distant object1 and fit to be utilized in the telescope4 ,this is the principle to be observed in the construction of every spectroscope4 ,we have now given an idea of the general nature of the instrument depending on this important addition made by ,mr4 ,simms1 which is the basis of the modern spectroscope1 and it is obvious that if we want considerable dispersion1 we can either increase the number of prisms1 or increase their dispersive power4 ,we have already shown in a previous chapter that the dispersion depends on the angle of the prisms1 and that the calculations necessary for making the object-glass of a telescope were based upon an observation made by passing light through a prism of a particular angle made of the same glass as that of which the proposed object-glass was to be constructed4 ,then1 again1 we took the opportunity of showing that with very dense substances greater dispersion could be obtained4 ,we showed how the prism of dense flint glass overpowered the dispersion of the prism of the crown glass1 and how the combination gave us refraction without dispersion4 ,illustration3 ,,fig4 #agc4--,spectroscope with ,four ,prisms4 ,fig4 #agc is a drawing of a spectroscope containing four prisms4 ,it is a representation of that used by ,bunsen and ,kirchhoff when they made their maps of the solar spectrum3 it is so arranged that the light after passing through the slit goes through the collimating lens1 and then through the prisms2 it is afterwards caught by the telescope lens and brought to a focus in front of the eyepiece4 ,it is very important1 when we have many prisms1 to be able to arrange them so that whether we use one part of the spectrum or the other1 each prism shall be in the best condition for allowing the light to traverse it2 that is to say1 that it shall be in the position of minimum deviation1 when the angles of incidence and emergence are equal1 and each surface refracts the ray equally4 ,they can be arranged so1 that as the telescope is moved to observe a new part of the spectrum1 every prism will be automatically adjusted4 ,to insure this the prisms are united to form a chain so that they all move together1 and each has a radial bar to a central pin which keeps them at the proper angle4 ,illustration3 ,,fig4 #agd4--;,automatic ,spectroscope 7,grubb's form74 ,there is another arrangement which is very simple1 in which we get the condition of minimum deviation by merely mounting the prisms on a spring1 and then moving the spring with the telescope1 in the same way as the telescope moves the other automatic arrangement4 ,illustration3 ,,fig4 #age4--;,automatic ,spectroscope 7,browning's form74 ,for some observations1 especially solar observations1 in which the light is very intense1 it is extremely important1 in fact essential1 to reduce the brilliancy of the spectrum2 and of course this enables us1 in the case of the sun especially1 to increase the dispersion almost without limit1 by having a great number of prisms1 or even using the same twice over1 in the following manner3 ,on the spectroscope there is a number of prisms so arranged that the light comes from the slit1 and travels through the lower portion of the prisms2 it then strikes against the internal reflecting surface of a right-angled prism at the back of the last prism1 ,fig4 #agf1 and is sent1 up to another reflecting surface1 and then comes back again through the same prisms along an upper storey1 and then is caught by means of a telescope above the collimator1 on the slit of which the sun's image is allowed to fall4 ,illustration3 ,,fig4 #agf4--,last ,prism of ,train for returning the ,rays4 ,this contrivance1 suggested by the author and ,prof4 ,young independently1 is now largely used4 ,fig4 #agg shows an ordinary spectroscope so armed4 ,the light from the slit traverses the upper portions of the prisms2 it is then thrown down by the reflecting prism seen behind the collimator1 then1 returning along the lower part1 it is received by a right-angled prism in front of the object-glass of the observing telescope4 ,instead of the rays of light being reflected back through the upper storey of the prisms1 another method has been adopted2 the last prism is in this case a half prism1 and the last surface on which the rays of light fall is silvered2 the rays then are returned on themselves1 and1 when the instrument is adjusted1 come to a focus on the inside of the slit plate1 forming there a spectrum1 any part of which can1 by moving the prisms1 be made to fall on a small diagonal reflecting prism on one side of the slit1 by which it is reflected to the eyepiece4 ,in this arrangement the collimating lens becomes its own telescope lens on the return of the ray4 ,illustration3 ,,fig4 #agg4--,spectroscope with returning ,beam4 ,there is another form of spectroscope1 called the direct vision1 which is largely used for pocket instruments4 ,the principle of it is that the light passing through it is dispersed but not turned from its course1 just the reverse of the achromatic combination of the object-glass2 a crown-glass prism is cemented on a flint one of sufficient angle that their deviative powers reverse each other but leave a certain portion of the flint-glass dispersion uncorrected2 since1 however1 the dispersive power of the flint-glass is to a great extent neutralized1 therefore1 in order to make the instrument as powerful as one of the ordinary construction1 a number of flint-glass prisms are combined with crown-glass ones1 as shown in ,fig4 #agh4 ,illustration3 ,,fig4 #agh4--;,direct ,vision ,prism4 ,there is another form of direct-vision prism1 called the ,herschel-,browning1 in which the ray is caused to take its original course on emerging by means of two internal reflections4 ,,chapter ,,xxviii4 ,,the ,,chemistry ,,of ,,the ,,stars 7,,continued73 ,,principles ,,of ,,spectrum ,,analysis4 ,we have next to say something about the principles on which the use of the spectroscope depends2 if we look through one we can readily observe how each particular ray of light paints an image of the slit4 ,thus1 if we are dealing with a red ray of light1 that ray1 after passing through the prisms1 will paint a red image of the slit2 if the light be violet1 the ray will paint a violet image of the slit1 and these images will be separated1 because one colour is refracted more than the other4 ,now it follows from this that when the slit is illuminated by white light1 white light being white because it contains all colours1 we get an infinite number of images of slits touching or overlapping each other1 and forming what is called a continuous spectrum4 ,hence it is that if we examine the light of a match or candle1 or even the electric light1 we get such a continuous spectrum1 because these light sources emit rays of every refrangibility4 ,modern science teaches us that they do so because the molecules--the vibrations of which produce1 through the intermediary of the ether1 the sensation of light on our optic nerve--are of a certain complexity4 ,in the preceding list of light sources the sun was not mentioned1 because its light when examined by ,wollaston and ,fraunhofer1 was found to be discontinuous4 ,now it is clear that if in a beam of light there be no light of certain particular colours1 of course we shall not find the image of the slit painted at all in the corresponding regions of the spectrum4 ,this is the whole story of the black lines in the spectrum of the sun and in the spectra of the stars4 ,here and there in the spectrum of these there are colours1 or refrangibilities1 of light which are not represented in light which comes from those bodies1 and therefore there is nothing to paint the image of the slit in that particular part of the spectrum2 we get what we call a dark line1 which is the absence of the power of painting an image4 ,but then it may be asked1 ,how comes it that the prism and the spectroscope are so useful to astronomers8 ,in answer we may say1 that if we knew no more about the black lines in the spectra of the sun and stars than we knew forty years ago1 the spectroscope ought still to be an astronomical instrument1 because it is our duty to observe every fact in nature1 even if we cannot explain it4 ,but these dark lines have been explained1 and it is the very explanation of them1 and the flood of knowledge which has been acquired in the search after the explanation1 which makes the spectroscope one of the most valuable of astronomical instruments4 ,many of us are aware of the magnificent generalizations by which our countrymen1 ,professors ,stokes and ,balfour ,stewart1 and ngstrm1 ,kirchhoff and ,bunsen1 were enabled to explain those wonderful lines in the solar spectrum4 ,these lines in the solar spectrum are there because something is at work cutting out those rays of light which are wanting1 and they explained this want by showing to us that around the sun and all the stars there are absorbing atmospheres containing the vapours of certain substances cooler than the interior of the sun or of the stars4 ,these philosophers also showed us1 that we can divide radiation and absorption into four classes1 and that we can have general radiation and selective radiation1 and general absorption and selective absorption1 so that the phenomena that we see in our chemical and physical laboratories and our observatories may all be classed as general and selective radiation1 or general and selective absorption4 ,let us explain these terms more fully4 ,kirchhoff showed us that from incandescent solid and liquid bodies we get a continuous spectrum2 thus from the carbon poles of an electric lamp we get a complete spectrum4 ,that is called a continuous spectrum1 and it is an instance of continuous radiation1 which we get from the molecular complexity of solids or liquids1 and likewise1 from dense gases or vapours4 ,when we examine vapours or gases which are not very dense we get an indication of selective radiation--that is to say1 the light one gets from these substances1 instead of being spread broadcast from the red to the violet1 will simply fall here and there on the spectrum2 in the case of one vapour we may get a yellow line--a yellow image of the slit--and in the case of another vapour1 we may get a green one2 the light selects its point of appearance1 and does not appear all along the spectrum4 ,illustration3 ,,fig4 #agi4--;,electric ,lamp4 y1 z1 wires connecting battery of #ej ,grove or ,bunsen elements2 ,g1 ,h1 carbon holders2 ,k1 rod1 which stops a clockwork movement1 which when going makes the poles approach until the current passes2 ,a1 armature of a magnet which by means of ,k frees the clockwork when not in contact2 ,e1 electro-magnet round which the current passes when the poles are at the proper distance apart1 causing it to attract the armature ,a4 ,this selective radiation is due to a simplification of the molecular structure of the vapours1 the simpler states are less rich in vibrations1 and therefore instead of getting rays of all refrangibilities we only get rays of some4 ,illustration3 ,,fig4 #ahj4--;,electric ,lamp arranged for throwing a spectrum on a screen4 ,d1 lens2 ,e ,e1 bisulphide of carbon prisms4 ,very striking experiments showing the spectra of bodies may be made with an electric lamp armed with a condenser and a narrow slit2 by means of a lens this slit is magnified on a screen4 ,then one or two prisms of glass containing bisulphide of carbon are placed in the beam after it has traversed the lens1 which draw out the image of the slit into a spectrum4 ,we can then place a piece of sodium on the lower carbon pole1 and when the poles are brought together it will be volatilized1 and its vapour rendered luminous4 ,its spectrum on the screen will be seen to consist of four lines only1 the yellow line being for more brilliant than the rest4 ,sodium was selected on account of the simplicity of its spectrum4 ,illustration3 ,,fig4 #aha4--;,comparison of the line spectra of ,iron1 ,calcium1 and ,aluminium1 with ,common ,impurities4 ,copy of a photograph1 in which by dividing the slit of the spectroscope into sections1 and admitting light from the various light sources through them in succession1 spectra of different elements are recorded on the same photographic plate4 ,if we put another metal1 say calcium1 in the place of the sodium1 there will appear on the screen the characteristic lines of that metal4 ,a number of distinct images of the slit in different colours is seen2 if we are well acquainted with the spectrum of any metal1 and see it with the spectroscope1 it is easy to at once recognise it4 ,fig4 #aha shows at one glance the spectra 7#a7 of iron1 7#b7 of calcium1 and 7#c7 of aluminium2 and will clearly indicate the great difference there is between the radiation spectra of the rare vapours of each of the metallic elements4 ,illustration3 ,,fig4 #ahb4--;,coloured ,flame of ,salts in the flame of a ,bunsen's ,burner4 ,the electric light is only required where great brilliancy is essential1 as for showing spectra on a screen4 ,a ,bunsen's burner is the best instrument for studying the spectra of metallic salts4 ,by its means the nature of a salt can be easily studied with a hand spectroscope1 and in this way an almost infinitesimal quantity can be detected4 ,these are instances of selective radiation4 ,we will now turn to absorption4 ,if we first get a continuous spectrum from our lantern and then interpose substances in the path of the beam1 we can examine their effects on the light4 ,if we first use a piece of neutral-tinted glass1 which is a representative of a great many substances which do1 for stopping light1 what solids and liquids do for giving light--namely1 it cuts off a portion of every colour2 the spectrum on the screen will be dimmed2 here we have a case of general absorption4 ,if1 instead of this1 we hold in the beam a vessel containing magenta1 a dark band in the spectrum is seen1 and if we put a test-tube in its place containing iodine vapour1 a number of well-defined lines pervading the spectrum is observed4 ,in these cases clearly1 the magenta in one case1 and the iodine vapour in the other1 have cut off certain colours1 and so the slit is not painted in these colours1 and dark lines or bands appear4 ,these are instances of selective absorption1 certain rays are selected and absorbed1 while others pass on unheeded4 ,the easiest method of performing these absorption experiments in the case of liquids is to place the substance in a test-tube in front of the slit of the spectroscope1 as shown in ,fig4 #ahc1 and point the collimator to a strong light4 ,besides the absorption by liquids1 the vapours of the metals also absorb selectively1 and if a tube containing a piece of sodium and filled with hydrogen 7so that the metal will not get oxidized7 is placed in the path of the rays1 and the sodium heated1 the spectrum is at first unaffected1 but as the sodium gets hot and its vapour comes off1 we can mark its effect on the spectrum4 ,we see a dark line beginning to appear in the yellow1 finally the whole light of that particular colour is absorbed1 and we have a dark line in its place4 ,to sum up then3-- ,we get from solids1 when heated1 general radiation1 and when they act as absorbers1 we get general absorption2 from gases and vapours we get selective radiation and selective absorption4 ,illustration3 ,,fig4 #ahc4--,spectroscope arranged for showing ,absorption4 ,now it at once strikes any one performing these experiments that the dark line of yellow sodium appears in the same place in the spectrum as the bright one1 and this is so4 ,when the absorption by sodium vapour is examined by the spectroscope1 it is then seen to consist of two well-defined lines close together1 and when the radiation is examined1 it is found to consist of two bright ones1 and the absorption and radiation lines1 the dark and bright ones1 are found to exactly agree in position in the spectrum1 showing that the substance that emits a certain light is able to absorb that same light1 so that it matters not whether a body is acting as an absorber or radiator1 for still we recognize its characteristic lines4 ,in #ahad ,fraunhofer strongly suspected the coincidence of the two bright sodium lines with the dark lines in the sun2 afterwards ,brewster1 ,foucault1 and ,miller showed clearly the absolute coincidence2 and ,professor ,stokes in #aheb came to the conclusion that the double line ,d1 whether bright or dark1 belonged to the metal sodium1 and that it absorbed from light passing through it the very same rays which it is able1 when incandescent1 to emit4 ,the phenomena rendered visible to us by the spectroscope have their origin1 as we have said1 in molecular vibration1 and the reason of the identical position of the light and dark lines1 and indeed the whole theory of spectrum analysis1 may be shortly stated as follows3-- ,the spectroscope tells us that when we break a mass of matter down to its finest particles1 or1 as some people prefer to call them1 ultimate molecules1 the vibrations of these ultimate parts of each different kind of matter are absolutely distinct2 so that if we get the ultimate particle1 say of calcium1 and observe its vibrations we find that the kind of vibration or unrest of one substance--of the calcium1 for instance--is different from the kind of unrest or mode of vibration--which is the same thing--of another substance1 let us say sodium4 ,mark well the expression1 ultimate molecule1 because the vibrations of the larger molecular aggregations are absolutely powerless to tell us anything about their chemical nature4 ,when we bring down a substance to its finest state1 and observe1 by means of the prism1 the vibrations it communicates to the ether1 we find that1 using a slit in the spectroscope and making these vibrations paint different images of the slit1 we get at once just as distinct a series of images of the slit for each substance as we should get a distinct sequence of notes if we were playing different tunes on a piano4 ,next1 this important consideration comes into play--whenever any element finds itself in this state of fineness1 and therefore competent to give rise to these phenomena1 it will give rise to them in different degrees according to certain conditions4 ,the intensest form is observed when we employ electricity4 ,in a great many cases the vibrations may be rendered very intense by heat4 ,the heat of a furnace or of gas will1 for instance1 in a great many cases1 suffice to give us these phenomena2 but to see them in all their magnificence--their most extreme cases--we want the highest possible temperatures1 or better still1 the most extreme electric energy4 ,what we get is the vibration of these particles rendered visible to our eye by the bright images of the slit or by their bright 8lines40 ,but that is not the only means we have of studying these states of unrest4 ,we can study them almost equally well if1 instead of dealing with the radiation of light from the particles themselves1 we interpose them between us and a light source of more complicated molecular structure1 and hotter or more violently excited than the particles themselves4 ,from such a source the light would come to us absolutely complete2 that is to say1 a perfectly complete gamut of waves of light1 from extreme red to extreme violet4 ,when we deal with these particles between us and a light-source competent to give us a continuous spectrum1 then we find that the functions of these molecules are still the same1 but that their effect upon our retinas is different4 ,they are not vibrating strongly enough to give us effectively light of their own1 but they are eager to vibrate1 and1 being so1 they are employed1 so to speak1 in absorbing the light which otherwise would come to our eyes4 ,so that whether we observe the bright spectrum of calcium or any other metal1 or the absorption spectrum under the conditions above stated1 we get lines exactly in the same part of the chromatic gamut1 with the difference that when we are dealing with radiation we get bright lines1 and when dealing with absorption we get dark ones4 ,it was such considerations as these by which the presence of sodium was determined in the sun4 ,soon followed the discovery of coincidence of other dark lines with the bright lines of numbers of our elements1 and we had maps made by ,kirchhoff1 and ,bunsen1 and ngstrm1 in which almost every dark line is mapped with the greatest accuracy4 ,the dark lines in the spectra of the stars1 and the light ones in nebul1 comets1 and meteorites have also yielded to us a knowledge more or less accurate of the elements of which these celestial bodies are built up4 ,these radiations and absorptions are the ,a ,b ,c of spectrum analysis1 and they have their application in every part of the heavens which the astronomer studies with the spectroscope4 ,but although it is the ,a ,b ,c it is not quite the whole alphabet4 ,after ,kirchhoff and ,bunsen had made their experiments showing that we might differentiate between solids1 liquids1 gases1 and vapours1 by means of their spectra1 and say1 here we have such a substance1 and there another1 either by its spectrum when it is incandescent or from the absorption lines produced by it on a continuous spectrum when it is absorbing1 ,plcker and ,hittorf showed that not only were the spectra very different among themselves1 but there were certain conditions under which the spectrum of the same substance was not always the same2 and although they did not make out clearly what it was1 they showed that it depended either on the pressure of the gas or vapour1 or the density1 or the temperature4 ,and other observations since then indicate that we get changes in spectra which are due to pressure1 and not to temperature per se2 so that we have another line of research opened to us by the fact1 that not only are the spectra of different substances different1 but that the spectra of the same substances are different under different conditions4 ,illustration3 ,,fig4 #ahd4--;,geissler's ,tube4 ,fig4 #ahd represents a hydrogen tube1 called a ,geissler's tube--a glass tube with hydrogen in it and two platinum wires1 one passing into each bulb1 by which a current of electricity can be passed through the gas4 ,in this case we use hydrogen gas in a state of extreme tenuity4 ,if now one of these tubes be connected with a ,sprengel pump1 we can alter the condition of tenuity at pleasure1 either reducing the contents of the tube or increasing them by admitting hydrogen from a receiver1 by a tap connected to the tubing of the air-pump2 we can thus considerably increase the amount of gas in the tube and bring it to something like atmospheric pressure4 ,we shall find the colour of the gas through which the spark passes varies considerably as we increase the pressure of the hydrogen in the tube4 ,the hydrogen at starting is nearly as rare as it can be1 and if more hydrogen be let in we shall see a change of colour from greenish white to red2 the hydrogen admitted has increased the pressure and the colour of the spark is entirely changed4 ,it is a very brilliant red colour1 the colour of the prominences round the sun4 ,it may be asked1 probably1 whether there are any applications of this experiment to astronomical observation4 ,it is of importance to the astronomer to get the differences of the spectra of the same substance under different conditions1 and it is found as important to get these differences between the spectra of the same substance1 as those between the spectra of different substances4 ,there is another experiment which will show another outcome of this kind of research4 ,change of colour in the spark is accompanied by a considerable difference in the spectrum--that is to say1 it is clear1 to refer back to the colour of the hydrogen when the light was green1 that we should get some green in the spectrum1 and when the light became red1 there would be some change or increase of light towards the red end of the spectrum4 ,we see that that is perfectly true2 but there is not only a change produced by the different pressures1 as shown by the different colours2 but if we carry the analysis still further--if1 instead of dealing with the whole of the spectrum1 we examine particular lines1 we find in some cases that there are very great changes in them4 ,if1 for instance1 we examine the bluish-green line given by hydrogen1 we shall find it increase in width as the pressure increases4 ,this kind of effect can be shown on the screen by means of the electric lamp4 ,we place some sodium on the carbon poles in the lamp1 and have an arrangement by which we can use either twenty or fifty cells at pleasure4 ,the action of a number of cells upon the vapour of sodium in the lamp is this3 the more cells we work with1 the greater is the quantity of the sodium vapour thrown out1 and associated with the greater quantity of vapour is a distinct variation of the light--in fact1 an increase in the width and brightness of the yellow lines on the screen4 ,illustration3 ,,fig4 #ahe4--,spectrum of ,sun-,spot4 ,now just to give an illustration of the profitable application of this3 we know1 for instance1 from other sources1 strengthened by this1 that in certain regions of the sun1 called sun-spots1 there are greater quantities of sodium vapour present than in others1 or it exists there at greater pressure4 ,if that be so1 we ought to get the same sort of result from the sun as we get on the screen by varying the density of the sodium vapour4 ,that is so4 ,we do get changes exactly similar to the changes on the screen1 only of course it is the dark lines we see1 and not the bright ones3 the dark lines of sodium are widened out over a sun-spot1 ,fig4 #ahe1 showing its presence in greater quantity1 or at greater pressure4 ,illustration3 ,,fig4 #ahf4--;,diagram explaining ,long and ,short ,lines4 ,besides the widening of the lines due to pressure1 there is something else which must be mentioned4 ,while experimenting with the spark taken between two magnesium wires focussed on the slit of the spectroscope by a lens1 the lines due to the metal were found to be of unequal lengths4 ,now1 as the lines are simply images of the slit1 the lengths of the lines depend on the length of the slit illuminated1 so that in this case it appeared that the slit was not illuminated to an equal extent by all the colours given out by magnesium vapour1 but that the vapour existed in layers round the wires1 the lower ones giving more colours1 and so also more lines1 than the upper ones further from the wire1 as is represented in ,fig4 #ahf2 this is only meant to give an idea of the thing1 and is not1 of course1 exactly what is seen4 ,s is the slit of the spectroscope1 ,p the image of one of the magnesium poles2 the other1 being at some little distance away1 does not throw its image on the slit1 and therefore does not interfere4 ,the circles shown are intended to represent the layers of vapour giving out the spectrum2 on the right the lower layers give ,a1 ,b1 and ,c1 the next ,a and ,b1 and the upper ones only ,b4 ,now we may reason from this that the layers next the poles are denser than those further off1 and give a more complicated spectrum than the others2 and also1 if the quantity of vapour of any metal is small1 we may only get just these longest lines4 ,of late1 experiments have been made in ,england on other metals--for instance1 aluminium and zinc1 and their compounds2 and it is found that1 when the vapour is diluted1 as it were1 one gets only the longest line or lines2 and in the compounds1 where the bands due to the compound compose the chief part of the spectrum1 the longest line or lines of the metal only appear4 ,now what is the application of this8 ,in the sun are found some of the dark lines of certain metals1 but not all2 for instance1 there are two lines in the solar spectrum corresponding to zinc1 but there are twenty-seven bright lines from the metal when volatilized by the electric spark4 ,why should not these also have their corresponding dark lines in the sun8 ,the answer is1 that the non-corresponding lines of the metal are the short ones1 and only exist close to the metal where the vapour is dense2 and in the sun the density is not sufficient to give these lines4 ,here1 then1 we have at once a means of measuring the quantity of vapour of certain metals composing the sun4 ,it was thought that aluminium was not in the sun1 as only two lines of the metal out of fourteen corresponded to black lines in the solar spectrum4 ,it is now known that these two are the longest lines1 and that aluminium probably exists in the sun1 and zinc1 strontium1 and barium must also be added4 ,these probably exist in small quantities1 insufficiently dense to give all the lines seen from a spark in the air4 ,illustration3 ,,fig4 #ahg4--;,comparison of the ,absorption ,spectrum of the ,sun with the ,radiation ,spectra of ,iron and ,calcium1 with ,common ,impurities4 ,there is also another quite distinct line of inquiry in which the spectroscope helps us4 ,imagine yourself in a ship at anchor1 and the waves passing you1 you can count the number per minute2 now let the vessel move in the direction whence the waves come1 you would then meet more waves per minute than before2 and if the vessel goes the other way1 less will pass you1 and by counting the increase or decrease in the number passing1 you might estimate the rates at which you were moving4 ,again1 suppose some moving object causes ripples on some smooth water1 and you count the number per minute reaching you1 then if that object approach you1 still moving1 and so producing waves at the same rate1 the number of ripples a minute will increase1 and they will be of course closer together2 for as the object is approaching you1 every subsequent ripple is started1 not from the same place as the preceding one1 but a little nearer to you1 and also nearer to the one preceding1 on whose heels it will follow closer4 ,by the increase in the number of ripples1 and also the decrease in the distance between them1 one can estimate the rate of motion of the object producing them1 for the decrease in distance between the ripples is just the distance the object travels in the time occupied between the production of two waves1 which was ascertained when the object was stationary4 ,now let us apply this reasoning to light4 ,light1 we now hold1 is due to a state of vibration of the particles of an invisible ether1 or extremely rare fluid1 pervading all space2 and the waves of light1 although infinitesimally small1 move among these particles4 ,now we know that it is the length of the waves of light which determines their refrangibility or colour1 and therefore anything that increases or diminishes their length alters their place in the spectrum2 and as waves of water are altered by the body producing them moving to or from the observer1 so the waves of light are changed by the motion of the luminous body2 and this change of refrangibility is detected with the spectroscope4 ,by measuring the wave-length of let us say the ,f line1 and the new wave-length as shown by the changed position1 we can estimate the velocity at which the light source is approaching or receding from us4 ,this application1 as we shall see in the next chapter1 enables us to determine the rate at which movements take place in the solar atmosphere4 ,it also gives us the power of measuring the third co-ordinate of the motion of stars4 ,we can1 by the examination of their positions1 measure the motion at right angles to our line of sight1 and so determine their motion with reference to the two co-ordinates1 ,r4,a4 and ,dec41 or ,lat4 and ,long41 and just in the same way as we can measure the velocity of the solar gases to or from us1 so we can measure the motion of the stars to or from us1 thereby giving us the third co-ordinate of motion4 ,it need scarcely be said that by the introduction of the spectroscope a new method of observation1 and a new power of gaining facts1 has dawned1 and the sooner it is used all over the world with the enormous instruments which are required1 the better it will be for science4 99 99 99 99 99 ,these then are some of the chief points of spectroscopic theory which makes the spectroscope one of the most powerful instruments of research in the hands of the modern astronomer4 ,,chapter ,,xxix4 ,,the ,,chemistry ,,of ,,the ,,stars 7,,continued73 ,,the ,,telespectroscope4 ,we have now to speak of the methods of using these spectroscopes for the purpose of astronomical observations4 ,for a certain class of observations of the sun no telescope is necessary1 but some special arrangements have to be made4 ,thus while ,dr4 ,wollaston and ,fraunhofer were contented with simple prisms1 when ,kirchhoff observed the solar spectrum1 and made his careful maps of the lines1 he used an instrument like ,fig4 #agc1 and for the purpose of comparing the spectrum of the sun with that of each of the chemical elements in turn1 he used a small reflecting prism1 covering one-half of the slit1 ,fig4 #ahh1 so that any light thrown sideways on to the slit would be caught by this prism1 and reflected on to the slit as if it came from an object near the source of light at which the spectroscope is pointing1 so that one-half of the slit can be illuminated by the sun1 while the other is illuminated by another light2 and on looking through the eyepiece one sees the two spectra1 one above the other2 so that we are able to compare the lines in the two spectra4 ,the sunlight1 whether coming from the sun itself or a bright cloud1 is reflected1 into the comparison prism1 ,fig4 #ahi1 of the spectroscope4 ,an instrument called a heliostat can be used for this1 reflecting the light either directly into the prism or through the medium of other reflectors4 ,illustration3 ,,fig4 #ahh4--;,comparison ,prism1 showing the path of the ,ray4 ,the heliostat is a mirror1 mounted on an axis1 which moves at the same rate as the sun appears to travel1 so that wherever the sun is1 the reflector1 once adjusted1 automatically throws the beam into the instrument1 so that the light of the moving sun can be observed without moving the spectroscope4 ,illustration3 ,,fig4 #ahi4--;,comparison ,prism fixed in the ,slit4 ,an average solar spectrum is thus obtained1 and1 by means of a prism over one-half of the slit1 it was quite possible for ,kirchhoff and ,bunsen to throw in a spectrum from any other source for comparison1 and so they compared the spectra of the metals and other elements with the solar spectrum1 and tested every line they could find in the spectra4 ,they first found that the two lines of sodium corresponded with the two lines called ,d in the spectrum1 then that the #dfj lines of iron corresponded in the main with dark lines in the solar spectrum2 and so they went on4 ,illustration3 ,,fig4 #aij4--;,foucault's ,heliostat4 ,there is1 however1 a method of varying the attack on this body altogether1 by means of the spectroscope and telescope4 ,we saw that ,kirchhoff and ,bunsen contented themselves with an average spectrum of the sun--that is to say1 they dealt with the general spectrum which they got from the general surface of the sun1 or reflected from a cloud or any other portion of the sky to which they might direct the reflector2 but by means of some such an arrangement as is shown in ,fig4 #aib1 we can arrange our spectroscope so that we shall be able to form an image of the sun by the object-glass of a telescope1 on the slit1 and allow it to be immersed in any portion of the sun's image we may choose4 ,we then have a delicate means of testing what are the spectroscopic conditions of the spots and of those brighter portions of the sun which are called facul1 and the like4 ,and it is known that1 by an arrangement of this kind1 it is even possible to pick up1 without an eclipse1 those strange things which are called the red prominences1 or the red flames1 which have been seen from time to time during eclipses4 ,if we wish to observe any of the other celestial bodies1 we must employ a telescope and form an image on the slit1 or else use the heavenly body itself as a slit4 ,in the former case spectroscopes must be attached to telescopes1 and hence again they must be light and small1 unless a siderostat is employed4 ,in the latter case the prism is placed outside the object-glass1 and the true telescope becomes the observing telescope4 ,fraunhofer1 at the beginning of the present century1 was the first to observe the spectra of the stars by placing a large prism outside the object-glass1 three or four inches in diameter1 of his telescope1 and so virtually making the star itself the slit of the spectroscope2 and in fact he almost anticipated the arrangement of ,mr4 ,simms1 and satisfied the conditions of the problem4 ,the parallel light from the star passed through the prism1 and by means of the object-glass was brought to a focus in front of the eyepiece1 so that the spectrum of the star was seen in the place of the star itself4 ,this system has recently been re-invented1 and the accompanying woodcut1 ,fig4 #aia1 shows a prism arranged to be placed in front of an object-glass of four inches aperture4 ,it is seen that the angle of the prism is very small4 ,the objection to this method of procedure is that the telescope has to be pointed away from the object at an angle depending upon the angle of the prism4 ,illustration3 ,,fig4 #aia4--,object-glass ,prism4 ,in the other arrangement we have the thing managed in a different way3 we have the object-glass collecting the light from the star and bringing it to a focus on the slit1 and it then passes on to the prisms1 through which the light has to pass before it comes to the eye4 ,in this combination of telescope and spectroscope we have what has been called the telespectroscope2 one method of combination is seen in the accompanying drawing of the spectroscope attached to ,mr4 ,newall's great refractor2 but any method will do which unites rigidity with lightness and allows the whole instrument to be rotated with smoothness4 ,illustration3 ,,fig4 #aib4--,the ,eyepiece ,end of the ,newall ,refractor 7of #be inches aperture71 with ,spectroscope attached4 ,for solar observation1 as there is light enough to admit of great dispersion1 many prisms are employed1 as shown in ,fig4 #aib2 or the prisms may be made so tall that the light may be sent backwards and forwards many times by means of return prisms1 to which reference has been already made4 ,for the observation of those bodies which give a small amount of light1 fewer prisms must be used1 and arrangements are made for the employment of reference spectra1 i4e41 to throw the light coming from different chemical elements into the spectroscope1 in order that we may test the lines2 whether any line of ,sirius1 for instance1 is due to the vapour of magnesium1 as ,kirchhoff tested whether any line in the sunlight was referable to iron or the other vapours which he subsequently studied4 ,illustration3 ,,fig4 #aic4--,solar ,spectroscope 7,browning's form74 ,illustration3 ,,fig4 #aid4--,solar ,spectroscope 7,grubb's form74 ,illustration3 ,,fig4 #aie4--,side view of ,spectroscope1 showing the arrangement by which the light from a spark is thrown into the instrument by means of the reflecting prism1 e1 by a mirror ,f4 7,huggins47 ,illustration3 ,,fig4 #aif4--,plan of ,spectroscope4 ,t1 eyepiece end of telescope1 ,b interior tube1 carrying ,a1 cylindrical lens2 ,d1 slit of spectroscope2 ,g1 collimating lens2 h h1 prisms2 ,q1 micrometer4 7,huggins47 ,illustration3 ,,fig4 #aig4--;,cambridge ,star ,spectroscope ,elevation4 ,illustration3 ,,fig4 #aih4--;,cambridge ,spectroscope ,plan4 ,these are shown in ,fig4 #aie4 e is a reflecting prism1 and ,f is another movable reflector to reflect the light from a spark passed between two wires of the metal to be compared1 and to throw it on the prism1 which reflects the light through the slit of the spectroscope to the prisms and eye2 if the instrument were in perfect adjustment and turned on a star1 and a person were to place his eye to the spectroscope1 he would see in one-half of the field of view the spectrum of the star with dark lines1 and in the other half the spectrum of the vapour with its bright lines2 and if he found the bright lines of the vapour to correspond with any particular dark line of the spectrum of the star1 he would know whether the metal exists at that star or not2 so this little mechanical arrangement at once tells him what there is at the star1 whether it be iron or anything else4 ,in ,figs4 #aig and #aih is shown another form of stellar spectroscope1 that of the ,cambridge 7,u4,s47 observatory2 it is the same in principle as that just described4 ,a direct vision star spectroscope is shown in ,fig4 #aii4 ,illustration3 ,,fig4 #aii4--;,direct-vision ,star ,spectroscope4 7,secchi47 ,a new optical contrivance altogether has to be used when star spectra are observed4 ,the image of a star is a point1 and if focussed on the slit will of course give only an extremely narrow spectrum2 to obviate this a cylindrical lens is employed1 which may be placed either before the slit or between the eyepiece and the eye4 ,if placed before the slit1 it draws out the image of the star to a fine line which just fits the slit1 so that a sufficient portion of the slit is illuminated to give a spectrum wide enough to show the lines1 or the slit may be dispensed with altogether4 ,in stellar observations1 when the cylindrical lens is used in front of the slit1 special precautions should be taken so as to secure that the position of the cylindrical lens and slit in which the spectrum appears brightest should be used4 ,in any but the largest telescopes the spectra of the stars are so dim that unless great care is used the finer lines will be missed4 ,a slit is not at all necessary for merely seeing the spectra2 indeed they are best seen without one4 ,if a slit be used1 it should lie in a parallel and not in a meridian2 under these circumstances slight variations in the rate of the clock are of no moment4 ,in this and in other observational matters it is good to know what to look for1 and there are great generic differences between the spectra of the various stars4 ,in ,fig4 #bjj are represented spectra from the observations of ,father ,secchi4 ,in the spectrum of ,sirius1 a representative of ,type ,i41 very few lines are represented1 but the lines are very thick2 and stars of this class are the easiest to observe4 ,next we have the solar spectrum1 which is a representative of ,type ,,ii41 one in which more lines are represented4 ,in ,type ,,iii4 fluted spaces begin to appear2 and in ,type ,,iv41 which is that of the red stars1 nothing but fluted spaces is visible1 and this spectrum shows that there is something different at work in the atmosphere of those red stars to what there is in the simpler atmosphere of the first--of ,type ,i4 ,these observations were first attempted1 and carried on with some success1 by ,fraunhofer1 and we know with what skill and perseverance ,mr4 ,huggins has continued the work in later years1 even employing reference spectra and determining their chemical constitution as well as their class4 ,illustration3 ,,fig4 #bjj4--,types of ,stellar ,spectra 7,secchi74 ,we need scarcely say that the same arrangement1 minus the cylindrical lens1 is good for observing the nebul and such other celestial objects as comets and planets4 ,for all spectrum work1 it has to be borne in mind that the best definition is to be had when the actual colour under examination is focussed on the slit4 ,with reflectors1 of course1 there is no difference of focus for the different colours4 ,as the best object-glasses are over-corrected for chromatic aberration1 the red focus is generally inside and the blue one outside the visual one4 ,it is not necessary to move the whole spectroscope to secure this2 all collimators should be provided with a rack and pinion giving them a bodily movement backwards and forwards4 ,this precaution is of especial importance in the case of solar observations1 to which we have next to refer4 ,if in any portion of the sun's image on the plate carrying the slit we see a spot1 all we have to do is to move the telescope1 and with it of course the sun's image1 so that the slit is immersed in the image of the spot2 if1 however1 we wish to observe a bright portion of the sun1 we can immerse this slit in the bright portion4 ,again1 if we wish to examine the chromosphere of the sun1 we simply have to cover half the slit with the sun1 and allow the other part of the slit to be covered by any surroundings of the sun1 and1 so to speak1 to fish round the edge2 the lower half of the slit1 say1 is covered by the sun itself1 and therefore we shall get from that half the ordinary solar spectrum2 the upper half is1 however1 immersed in the light reflected from our atmosphere1 giving a weak solar spectrum1 so that we get a bright and feeble spectrum side by side4 ,but besides the atmospheric light falling on the upper part of the slit1 the image of anything surrounding the sun falls there also1 and its spectrum is seen with the faint solar spectrum1 and we find there a spectrum of several bright lines4 ,now1 as an increase of dispersive power will spread out a continuous spectrum and weaken it1 we may almost indefinitely weaken the atmospheric spectrum1 and so practically get rid of it1 still leaving the bright-line spectrum with the lines still further separated2 so that if it were not for our atmosphere1 we should get only the spectrum of the sun and that of its surroundings2 one a continuous spectrum with black lines1 and the other consisting of bright lines only4 ,now if we suppose these observations made--if the precaution to which we have alluded be not taken1 the spectrum of the sun-spot will differ but little from that of the general surface1 and the chromospheric lines will scarcely be visible4 ,if the precaution be taken1 in the case of the spot it will be found that every one of the surrounding pores is also a spot2 and if the air be pure the spectrum will be full of hard lines running along the spectrum1 just like dust lines1 but emphatically not dust lines1 because they change with every movement of the sun4 ,the figure of the spot spectrum on p4 #dae will show what is meant4 ,fig4 #bja will show the appearance of the chromospheric line when the blue-green light is exactly focussed2 the boundary of the spectrum of the photosphere approaches in hardness that at the end of the slit4 ,by measuring the lengths of the lines we can estimate the height of the vapours producing them2 we find from this that magnesium is usually present to a height of a few hundred miles1 and that hydrogen extends to between #c1jjj and #d1jjj miles2 in some positions of the slit the hydrogen lines are seen to start up to great heights1 showing the presence of flames or prominences extending in height to sometimes #ajj1jjj miles4 ,illustration3 ,,fig4 #bja4--,part of ,solar ,spectrum near ,f4 ,if1 without changing the focus1 we open the slit wider1 and throw the sun's image just off the slit1 so that the very bright continuous spectrum no longer dazzles the eye1 we shall be able to see these flames whenever they cross the opening1 for the image of the slit is focussed on the eye1 and the sun and its flames are focussed on the slit1 so if we virtually remove the slit by opening it wide1 we see the flames2 still the limit of opening is soon approached1 and the flood of atmospheric light soon masks them4 ,the red hydrogen line of the spectrum is the best for viewing them1 although the yellow or blue will answer4 ,we may also place the sun's image so that the slit is tangential to it1 in which case a greater length of the hydrogen layer1 or chromosphere1 as it is called1 is visible1 although its height is limited by the opening of the slit4 ,by these means we are able to view a small part of the chromosphere at a time1 and to go all round the sun in order to obtain a daily record of what is going on4 ,if1 however1 we throw the image of the sun on a disc of metal of exactly the same size1 we eclipse the sun1 but allow the light of the chromosphere to pass the edge of the disc2 this of course is masked by the atmospheric light1 but if the annulus1 or ring of chromosphere1 be reduced sufficiently small1 it can be viewed with a spectroscope in the place of a slit1 in fact it is virtually a circular slit on which the chromosphere rests4 ,by this means nearly the whole of the chromosphere can be seen at once4 ,this is accomplished as follows3-- ,the image of the sun is brought to focus on a diaphragm having a circular disk of brass in the centre1 of the same size as the sun's image1 so that the sun's light is obstructed and the chromospheric light is allowed to pass4 ,the chromosphere is afterwards brought to a focus again at the position usually occupied by the slit of the spectroscope2 and in the eyepiece is seen the chromosphere in circles corresponding to the 8,c0 or other lines4 ,a lens is used to reduce the size of the sun's image1 and keep it of the same size as the diaphragm at different times of the year2 and other lenses are used in order to reduce the size of the annulus of light to about inch1 so that the pencils of light from either side of it may not be too divergent to pass through the prisms at the same time1 in order that the image of the whole annulus may be seen at once4 ,there are mechanical difficulties in producing a perfect annulus of the required size1 so one inch in diameter is used1 and can be reduced virtually to any size at pleasure4 ,from what has been said it is easy to see that we really now get a new language of light altogether1 and a language which requires a good deal of interpretation4 ,illustration3 ,,fig4 #bjb4--;,distortions of ,f line on ,sun4 ,we have still1 indeed1 to consider some curious observations which are now capable of being made every day when anything like a sun-storm is going on1 by means of the arrangement in which the spectroscope simply deals with the light that comes from a small portion of the sun instead of from all the sun4 ,if we make the slit travel over different portions of the sun on which any up-rushes of heated material1 or down-rushes of cold material1 or other changes1 are going on from change of surface temperature1 the ,fraunhofer lines1 which we have before shown to be straight1 instead of being so1 appear contorted and twisted in all directions4 ,on the other hand1 if we examine the chromosphere under the same conditions1 we find the bright lines contorted in the same manner4 ,the usually dark lines1 moreover1 sometimes appear bright1 even on the sun itself2 sometimes they are much changed in their relative positions with reference to the solar spectrum4 ,the meaning of these contortions has already been hinted at 7p4 #dbj74 ,it was there shown that every colour1 or light of every refrangibility1 is placed by the prisms in its own particular position1 so if a ray of light alters its position in the spectrum it must change its colour or refrangibility1 so the light producing the ,f line in the one case1 and the absent light producing the dark line in the other1 differ slightly in colour1 or are rather more or less refrangible than the normal light from hydrogen4 ,in the case when the ,f line is wafted towards the blue end of the spectrum1 the light falling on the slit is rather more refrangible than usual2 and in the middle drawing1 ,fig4 #bjc1 where the ,f line bifurcates1 the slit is supplied with two kinds of light differing slightly in refrangibility4 ,not only does the light radiated by a substance change in this way1 but the light absorbed by that substance also changes1 hence the contortions of the black lines are due to a similar cause4 ,illustration3 ,,fig4 #bjc4--;,displacement of ,f line on edge of ,sun4 ,here1 therefore1 we have evidence of a change of refrangibility1 or colour1 of the light coming from the hydrogen surrounding the sun4 ,this change of refrangibility is due to the motion of the solar gases1 as explained in the last chapter4 ,so we find that the hydrogen producing the light giving us one of the forms of the ,f line1 shown in ,fig4 #bjc1 is moving towards us at the rate of #abj miles a second1 while that giving the other form is moving away from us4 ,let us see how these immense velocities are estimated4 ,by means of careful measurements1 ngstrm has shown on his map of the solar spectrum the absolute length of the waves of light corresponding to the lines2 thus the length of the wave of light of hydrogen giving the ,f line is #dhfj_/ajjjjjjj of a millimeter4 ,in ,fig4 #bjc the dots on either side of the ,f line show the positions1 where light would fall1 if it differed from the ,f light by #a1 #b1 #c1 or #d ten-millionths of a millimeter1 so that in the figure the light of that part of the line wafted over the fourth dot is of a wave-length of #d ten-millionths of a millimeter less than that of the normal ,f light1 which has a wave-length #dhfj_/ajjjjjjj of a millimeter4 ,the ,f light therefore has had its wave-length reduced by #d_/dhfj #a_/abae part2 and in order that each wave may be decreased by this amount1 the source of the light must move towards us with a velocity of #a_/abae of the velocity of light1 which is #ahf1jjj miles per second1 and #a_/abae of #ahf1jjj is about #aej2 this then is the velocity1 in miles per second1 at which the hydrogen gas must have been moving towards us in order to displace the light to the fourth dot1 as shown in the figure4 ,,chapter ,,xxx4 ,,the ,,telepolariscope4 ,in previous chapters we have considered the lessons that we can learn from light--from the vibrations of the so-called ether--when we put questions to it through various instruments as interpreters4 ,there is still another method of putting questions to these same vibrations1 and the instrument we have now to consider is the ,polariscope4 ,the spectroscope helped us to inquire into the lengths of the luminiferous waves2 from the polariscope we learn whether there is any special plane in which these waves have their motion4 ,the polariscope is an instrument which of late years has become a useful adjunct to the telescope in examining the light from a body in order to decide whether it is reflected or not1 and to ascertain indirectly the plane in which the rays reflected to the eye lie4 ,the action of the instrument depends upon the fact that light which consists solely of vibrations perpendicular to a given plane is said to be completely polarized in that plane4 ,light that contains an excess of vibrations perpendicular to a given plane is said to be partially polarized in that plane4 ,it was ,huyghens that discovered the action of ,iceland spar in doubly refracting light2 and the light which passed the crystal was called polarized light at the suggestion of ,newton1 who1 it must be remembered1 looked upon light as something actually emitted from luminous bodies2 these projected particles were supposed1 after passage through ,iceland spar1 to be furnished with poles analogous to the poles of a magnet1 and to be unable to pass through certain bodies when the poles were not pointing in a certain direction4 ,it was not until the year #ahjh that ,malus discovered the phenomenon of polarization by reflection4 ,he was looking through a double-refracting prism at the windows of the ,luxembourg ,palace1 on which were falling the rays of the setting sun4 ,on turning the prism he noticed the ordinary and extraordinary images alternately become bright and dark4 ,this phenomenon he at once saw was in close analogy to that which is observed when light is passed through ,iceland spar4 ,at first he thought it was the air that polarized the light1 but subsequent experiments showed him that it was due to reflection from the glass4 ,let us examine some of the phenomena before we proceed to show the use astronomers make of them4 ,it is the property of some crystals1 such as tourmaline1 when cut parallel to a given direction1 called the optic axis of the crystal1 to absorb all vibrations or resolved parts of vibrations perpendicular to this line1 transmitting only vibrations parallel to it4 ,a similar absorption of vibrations perpendicular to a given direction may be effected by various other combinations1 of which one1 ,nicol's prism1 is in most common use4 ,any of these arrangements may be used as an analyzer with the telescope1 for determining whether the light is completely or partially polarized1 and in either of these cases which is the plane of polarization4 ,the plane containing the direction of the rays and the line in the analyzer to which the transmitted vibrations are parallel1 is called the plane of analyzation3 all the light which reaches the eye consists of vibrations in the plane of analyzation4 ,as we rotate the analyzer1 we rotate equally the plane of analyzation4 ,if we find a position of the plane of analyzation for which the light received by the eye is a maximum1 we know that the light from the object is partially or completely polarized in a plane perpendicular to the plane of analyzation when in this position4 ,to determine whether the polarization is partial or complete1 we must turn the analyzer through an angle of #ij from this position3 if we now obtain complete darkness1 we know that there are no vibrations having a resolved part parallel to the plane of analyzation in this position1 or that the light is completely polarized in this plane3 if there be still some light visible1 the polarization is only partial4 ,to explain this a little more fully1 we may compare the vibrations or waves of light to waves of more material things3 we may have the vibrating particles of the ether moving up and down as the particles do in the case of a wave of water1 or the particles may move horizontally as a snake does in moving along the ground4 ,we may consider that ordinary light consists of vibrations taking place in all planes1 but if it passes through or is reflected by certain substances at certain angles1 the vibrations in certain planes are1 as it were1 filtered out1 leaving only vibrations in a certain plane4 ,this light is then said to be polarized1 and its plane of polarization is found by its power of passing through polarizing bodies only when they are in certain positions4 ,if1 for instance1 a ray of ordinary light is passed through a crystal of tourmaline1 the vibrations of the filtered ray will only lie in one plane2 if then a second crystal of tourmaline be held in a similar position to the first1 the ray will pass through it unaffected2 but if it be turned through a quarter of a circle about the ray as an axis1 the ray will no longer be able to pass1 for being in a position at right angles to the first1 it will filter out just the rays that the first allows to pass4 ,for illustration1 take a gridiron3 if we attempt to pass a number of sheets of paper held in all positions through it1 only those in a certain plane1 viz41 that of the rods forming the gridiron1 could be passed through1 and those that would go through would also go through any number of gridirons held in a similar position4 ,but if another gridiron be placed so that its bars cross those of the first1 the sheets of paper could no longer pass1 and it is evident that if we could not see or feel the paper1 we could tell in what plane it was by the position in which the gridiron must be held to let it pass1 and having found the paper to be1 say horizontal1 we know that the bars of the first gridiron are also horizontal4 ,so with light1 we can analyze a ray of polarized light and say in what plane it is polarized4 ,the example of the gridiron1 however1 does not quite represent the action of the second crystal2 for if the bars of the second gridiron are turned a very small distance out of coincidence with those of the first1 the sheets of paper would be stopped2 but with light1 the intensity of the ray is only gradually diminished1 until it is finally quenched when the axes of the crystals are at right angles to each other4 ,illustration3 ,,fig4 #bjd4--;,diagram showing the ,path of the ,ordinary and ,extraordinary ,ray in ,crystals of ,iceland ,spar4 ,light is polarized by transmission and by reflection4 ,we have already1 when we were discussing the principle involved in the double-image micrometer1 seen how a crystal of ,iceland spar divides a ray into two parts at the point of incidence4 ,now these two rays are oppositely polarized1 that is to say1 the vibrations take place in planes perpendicular to each other2 the vibrations of the incident light in one plane are refracted more than the vibrations in the opposite plane1 and we have therefore two rays1 one called the ordinary ray1 and the other the extraordinary ray4 ,fig4 #bjd shows a ray of light1 ,s ,i1 incident on the first crystal at ,i2 it is then divided up into the ordinary ray ,i ,r and the extraordinary one ,i ,r2 a screen is then interposed1 stopping the extraordinary ray and allowing the ordinary one to fall on the second crystal at ,i4 ,if then this crystal be in a similar position to the first1 this ray1 vibrating only in one plane1 will pass onwards as an ordinary ray1 ,i ,r2 there being no vibrations in the perpendicular plane to form an extraordinary ray1 there will be only one circle of light thrown on the screen at ,o by the lens4 ,but1 if the second crystal be turned round the line ,s ,s as an axis1 the plane of vibration of the ray falling on its surface will no longer coincide with the plane in which an ordinary ray vibrates in the crystal1 and it therefore becomes split up into two1 one vibrating in the plane as an ordinary ray1 and the other in that of an extraordinary ray2 we have therefore the ray ,i ,r in addition to the first1 and consequently a second circle on the screen at ,e4 ,as the crystal rotates1 the plane of extraordinary refraction becomes more and more coincident with the plane of vibration of the incident ray1 until1 when it has revolved through #ij1 it coincides with it exactly2 it then passes through totally as an extraordinary ray1 and as the refractive power of the crystal is greater for vibrations in this plane1 we get all the light traversing the direction ,i ,r and falling on the screen at ,e1 and there being then no light ordinarily refracted1 the circle ,o disappears4 ,fig4 #bje shows the relative brightness of the circles ,e and ,o as they revolve round the centre ,s of the screen1 the images produced by the ordinary and the extraordinary ray becoming alternately bright and dark as the crystal is rotated4 ,fig4 #bjf shows the images on the screen when the ordinary ray is stopped by the first screen instead of the extraordinary one4 ,illustration3 ,,fig4 #bje4--;,appearance of the ,spots of ,light on the ,screen shown in the preceding ,figure1 allowing the ordinary ray to pass and rotating the second ,crystal4 ,illustration3 ,,fig4 #bjf4--;,appearance of ,spots of ,light on ,screen on rotating the second ,crystal1 when the extraordinary ray is allowed to pass through the first ,screen4 ,a crystal of tourmaline acts in a like manner to ,iceland spar1 but the ordinary ray is rapidly absorbed by the crystal1 so that the extraordinary ray only passes4 ,there is an objection to the use of it1 as it is not very transparent1 and a ,nicol's prism is now generally used for polarizing light4 ,it is constructed out of a rhombo-hedron of ,iceland spar cut into two parts in a plane passing through the obtuse angles1 and the two halves are then joined by ,canada balsam4 ,the principle of construction is this3 the power of refracting light possessed by ,canada balsam is less than that possessed by ,iceland spar for the ordinary ray1 and greater in the case of the extraordinary ray2 in consequence1 the ordinary ray is reflected at the surface of junction1 while the extraordinary ray passes onwards through the crystal4 ,illustration3 ,,fig4 #bjg4--;,instrument for showing ,polarization by ,reflection4 ,it is manifest then that if two ,nicols are used instead of two simple crystals1 represented in ,fig4 #bjd1 there will be only one spot of light on the screen1 which is due to the extraordinary ray1 and as in certain positions this no longer passes 7for the ordinary ray1 which appears in the place of the extraordinary when the crystal is used1 cannot pass through the ,nicol71 no light at all passes in such positions1 so that we can use the second ,nicol as an analyzer to ascertain in what plane the light is polarized4 ,light is also polarized by reflection from the surface of a transparent medium4 ,when a ray of ordinary light falls on a plate of glass at an angle of #ed #ee with the normal1 the reflected ray is perfectly polarized1 and at other inclinations the polarization is incomplete4 ,here then is polarization by reflection4 ,fig4 #bjg shows an apparatus for producing this phenomenon4 ,the light foiling on the first mirror from ,e is reflected through the tube as a polarized beam1 and this is analyzed by the other mirror 7,i71 whose plane can be rotated round the axis of the tube4 ,the angle of polarization differs with different substances according to their refractive power1 for polarization of the reflected ray is perfect only when the angle of incidence is such that the reflected ray is at right angles to the refracted one4 ,as a result of what we have said1 the light of the sun reflected from the surface of water or from the glass of a window is polarized1 and although it may be dazzling to the eye1 it is reduced1 or even entirely cut off1 when falling at the polarizing angle1 by looking through the transparent ,nicol's prism or plate of glass held in certain positions and acting as an analyzer4 ,on rotating the analyzer there is an alternation of intensity1 and by looking at the window through a crystal of ,iceland spar as an analyzer1 two images would be seen which would alternate in brightness as the crystal is rotated4 ,so also there is a difference in the intensity of the light from the sky when the analyzer is rotated1 showing that the light reflected from the watery and dust particles in the air is polarized1 and by the position of the analyzer we find that it is polarized in the plane we should expect if it be1 as it is1 reflected from the sun4 99 99 99 99 99 ,it will be asked1 however1 what is the astronomical use of determining whether light has an excess of vibrations in any given direction8 ,to this we may reply that light that is reflected from any body is generally partially polarized in the plane of reflection1 and that if we find that the light received from any body is partially polarized in a given plane1 we may conclude that it has very likely been reflected in that plane4 ,hence then in the case of any celestial body the origin of the light of which is doubtful1 the polariscope tells us whether the light is intrinsic or reflected4 ,it tells us more than this1 it tells us the plane in which the reflection has taken place4 ,as the polarization takes place1 when it does take place1 at the celestial body1 all we have to do is to attach an analyzer to the telescope4 ,a careful application of the above principles has shown that the light from the sun's corona is partially polarized1 and in the same plane as it would be if reflected from small particles in the neighbourhood of the sun3 so also a portion of the light of ,coggia's ,comet was found to be polarized1 and therefore we say that it reflected sunlight in addition to its own proper light4 ,in what has been hitherto said we have only considered the use of a ,nicol1 or glass plates1 or crystal of ,iceland spar as an analyzer1 and by the variation of brightness the presence and plane of polarization have been determined2 but unless the polarization is somewhat decided1 it could not be detected by this method4 ,advantage is therefore taken of the fact that a plate of quartz rotates the plane of polarization of a ray passing through it1 and it rotates the more refrangible colours more than the others1 and some crystals rotate the plane one way1 and others in the opposite direction3 the crystals are therefore called respectively right- and left-handed quartz2 the thicker the quartz the greater the angle through which the plane of polarization is twisted4 ,this supplies us with a most delicate apparatus1 which we next describe4 ,a crystal of right- and a crystal of left-handed quartz are taken and cut to such thickness that a ray of any colour1 say green1 has its plane turned through #ij on passing through each of them4 ,they are then cut into the form of a semicircle and placed side by side4 ,any change of the angle of polarization will now affect each plate differently4 ,in one plate the colours will change from red to violet1 in the other from violet to red4 ,if now a ray of polarized light1 say vibrating in a vertical plane1 falls on them1 the green rays will have their plane of vibration turned through #ij by each crystal1 and the vibration of the green from both crystals will then be in the horizontal plane4 ,nicol's prism interposed between the quartz plates and the eye1 so as to allow horizontal vibrations to pass1 will show the green from both crystals of equal intensity2 the rays of other colours1 being turned through a greater or less angle than #ij1 will not be vibrating horizontally1 and will therefore only partially pass through1 so green will be the prevailing colour4 ,if now the plane of vibration of the original ray be turned a little out of the vertical1 the ray1 on the red side of the green1 will appear in one half1 and that on the violet side of the green in the other3 so that immediately the plane of polarization changes1 the plates transmit a different colour1 and the apparatus must be twisted round through just the same angle as the polarized ray in order to get the crystals of the same colour4 ,it is therefore obvious that the angle made by a polarized ray with a fixed plane is easily ascertained in this manner4 ,there is also another instrument for detecting polarization which is perhaps more commonly used than the biquartz3 it is generally called ,savart's analyser1 and is extremely sensitive in its action4 ,on looking through it at any object emitting ordinary light1 the white circle of light limited by the aperture of the instrument only is seen2 but if any polarized light should happen to be present1 a number of parallel bands1 each shaded from red to violet1 make their appearance2 on rotating the instrument a point is found when a very slight motion causes the bands to vanish and others to appear in the intermediate spaces1 and knowing the position required for the change of bands with light polarized in a known plane1 say the vertical plane1 it is easy to find how far the plane of polarization of any ray is from the vertical1 by the number of degrees through which the instrument must be turned to change the bands4 ,the construction of the instrument1 and especially its action1 is not easy to understand without a considerable knowledge of optics1 but it may be stated that a plate of quartz is cut1 in a direction inclined at #de to its axis1 into two parts of the same thickness2 one part is then turned through a right angle and placed with the same surfaces in contact as before2 these are fixed in the instrument so that the light shall traverse them perpendicularly to the plane of section2 the light then passes through a ,nicol's prism as an analyser to the eye4 ,the lines observed1 8black centred0 in one position1 and 8white centred0 in the position at right angles to this1 are always in the direction before referred to4 ,the delicacy of the test supplied by this arrangement increases as this direction is more nearly parallel or perpendicular to the plane of polarization of the ray under examination4 ,,chapter ,,xxxi4 ,,celestial ,,photography4--,,the ,,ways ,,and ,,means4 ,we come now last of all to that branch of the work of the physical astronomer which bids fair in the future to replace all existing methods of observation4 ,in the introductory chapter we referred to the introduction of photographic records of astronomical phenomena as marking an epoch in the development of the science4 ,in the last ones we have to dwell briefly on the modus operandi of the various methods by which the eye is thus being gradually replaced4 ,the point of celestial photography is that it not only enables us to determine form and place1 absolutely irrespective of personal equation so far as the eye is concerned1 but that1 properly done1 it gives us a faithful and lasting record of the operation1 so that it is not forgotten2 ,mr4 ,de ,la ,rue has called the photographic plate the retina which does not forget1 and an excellent name it is4 ,we may pass over altogether the ordinary photographic processes1 which have been carried on with a degree of skill and patience which is beyond all praise1 and confine our attention exclusively to the instrumental processes4 ,be it remembered1 we have no longer to consider the visual rays1 but the so-called chemical rays1 which lie at the violet end of the spectrum4 ,we must also recollect that1 in a former chapter1 we have seen that the optician's business was to throw aside the violet rays altogether--to discard them1 caring nothing for them1 because1 so far as the visible form of the objects is concerned1 they help very little4 ,but we shall see in a moment that1 if we wish to use refractors for photographing1 we must abolish this idea1 and undo everything we did to get a perfect telescope to see the body1 because in the case of the photographic processes employed at present1 the visible rays have as little to do with building up the image on the photographic plate as the blue rays have to do with building up the image on the retina of the eye4 ,we shall see presently how admirably this has been done by ,mr4 ,rutherfurd4 ,if1 however1 we use reflectors instead of refractors1 we are able to utilize all the rays by means of the same mirror without alteration1 as the focus is the same for all rays1 so that a reflector is equally good for all classes of observation4 ,let us first consider the cases in which the plate is made to replace the retina with the ordinary telescope4 ,we shall see in the sequel that whether the spectroscope1 polariscope1 or other physical instrument be added to the telescope--when we pass1 that is to say1 from mechanical to physical astronomy--the plate can still replace the eye with advantage4 ,the body of the telescope1 with the object-glass or mirror at one end and the plate at its focus in place of the eyepiece1 forms the camera1 corresponding to those we find in photographic studies4 ,the plate-holder shown in section in the accompanying figure is therefore the only addition required to make a telescope into a camera for ordinary work4 ,fig4 #bjh4 ,illustration3 ,,fig4 #bjh4--,section of ,plate-holder4 ,a is a screw of such a size that it can be inserted into the eyepiece end of the telescope2 the sensitive plate is held between a lid at the back1 which opens for the plate to be inserted1 and a slide in front1 which is drawn out so as to expose the face of the plate to the object4 ,a piece of ground glass of extreme fineness is inserted in the slide1 on which the object is focussed before the sensitive plate is put in4 ,it is easy then by the eyepiece focussing-screw to put this nearer or further away from the object-glass1 so that the image is thrown sharply on the ground glass4 ,when that is done the ground glass is taken away1 and the sensitive plate put there in its place1 and then exposed as required1 so that the methods are similar to the ordinary photographic process4 ,we have here an arrangement that enables us to photograph the moon1 stars1 and planets4 ,m4 ,faye has proposed that for the transit circle also the photographic method should be applied1 the chronograph registering the time of the instantaneous opening of the slide1 instead of the time the star is seen to transit1 so that the position of the star with respect to the wires is registered at a certain known time2 therefore1 not only for physical astronomy have we the means of making observations without an observer at all1 but also for position observations4 ,every one knows sufficient of photography to be aware that1 if we wish to secure the image of a faint object1 such as a faint star or a faint part of the moon1 we must expose the plate for some little time1 as we have to do in ordinary photography if the day is dull1 and therefore the larger the aperture of the telescope the more light passes2 and the shorter the focus is1 and the more rapid the process1 the shorter will be the exposure2 if the focus is short1 the image will be small2 but as we can magnify the image afterwards1 rapidity becomes of greater moment1 as the shorter the time of exposure is the less atmospheric and other disturbances and errors in driving the telescope come into play4 ,still1 if we photograph the moon or other object1 we do not wish to limit ourselves to the size of the original negative obtained at the focus4 ,if the negative is well defined--that is1 if it possesses the quality of enlargeableness--there is no difficulty in getting enlarged prints4 ,the method of enlarging photographs is very simple2 all that is required is a large camera1 the negative to be copied being placed nearer the lens than the prepared paper1 so that the image is larger than the original4 ,fig4 #bji shows an enlarging camera3 the body1 ,a1 can be made of wood1 or better still1 of a soft material1 bellows-fashion1 so that the length can be altered at pleasure4 ,in the end1 at ,b1 is fixed a lens--an ordinary portrait lens will do1 but a proper copying lens is preferable2 and ,e is a piece of wood with a hole in its centre1 over which the negative is placed1 the distance of ,e to ,b being also adjustible2 then1 by altering the lengths of ,b ,e and ,b ,c1 the image of the negative can be made to appear of suitable size4 ,at the end1 ,c1 a piece of sensitive paper is placed1 and the light of the sun being allowed to fall through the negative and lens1 the paper soon becomes printed1 and can be toned and fixed as an ordinary paper positive4 ,the camera may be carried on a rough equatorial mounting1 consisting of an axis pointing to the pole1 and pulled round with the sun by attaching a string to an equatorial telescope1 moved by clockwork2 or a heliostat can be used with more advantage1 thereby allowing the camera to be stationary2 a good enlarging lens is a very desirable thing1 for most lenses seem to distort the image considerably4 ,illustration3 ,,fig4 #bji4--;,enlarging ,camera4 ,f1 heliostat for throwing beam of sunlight on the reflector1 which throws it into the camera2 ,e1 negative2 ,b1 focussing-lens2 ,c1 plate- or paper-holder2 ,d1 focussing-screw4 ,if we wish to obtain a large direct image of the moon1 we must1 as said before1 employ a telescope of as long a focal length as possible2 for reasons just mentioned1 this is not always desirable4 ,if1 however1 large images can be obtained as good as small ones1 they can of course be enlarged to a much greater size4 ,the primary image of the moon taken by ,mr4 ,de ,la ,rue's exquisite reflector is not quite an inch in diameter4 ,in one of ,mr4 ,rutherfurd's telescopes of fifteen feet focus1 the image of the moon is somewhat larger--about one and a half inch in diameter4 ,in ,mr4 ,newall's magnificent refractor1 the focal length of which is thirty feet1 the diameter is over three inches4 ,in the ,melbourne reflector the image obtained is larger still4 ,in celestial photography we have not only to deal with faint objects4 ,with the sun the difficulty is of no ordinary character in the opposite direction1 because the light is so powerful that we have to get rid of it4 ,now there are two methods of doing this1 and as in a faint object we get more light by increasing the aperture1 so with a bright light like that of the sun we can get rid of a large amount of it by reducing the aperture of our telescope2 but it is found better to reduce infinitesimally the time of exposure1 and methods have been adopted by which that has been brought down to the one-hundredth part of a second4 ,let us show the simple way in which this can be done by the means of an addition to an ordinary plate-holder4 ,fig4 #bjh shows the ordinary plate-holder1 like those used generally for photography4 ,what is termed the instantaneous slide1 ,b1 ,fig4 #baj1 consists of a plate with an adjustible slit in it inserted between the object itself and the focus4 ,this can be drawn rapidly across the path of the rays by means of a spring1 ,d2 we can bring it to one side1 and fix it by a piece of cotton1 ,e1 and then we can release it by burning the cotton1 when the spring draws it rapidly across4 ,the velocity of the rush of the aperture across the plate1 and the time of exposure1 can be determined by the strength of the spring and the aperture of the slit4 ,if the velocity is too great1 we can alter the size of the slit1 ,c4 ,if we absorb some of the superabundant light by means of yellow glass1 or some similar material1 we can keep the opening wide enough to prevent any bad effects of diffraction coming into play4 ,illustration3 ,,fig4 #baj4--;,instantaneous ,shutter4 ,the light of the sun is so intense that another method may be employed4 ,instead of having the plate at the focus of the object-glass we may introduce a secondary magnifier in the telescope itself1 and thus obtain an enlarged image1 the time necessary for its production being still so short 7#a_/ejth of a second7 that nothing is lost from the disturbances of the air4 ,a telescope with this addition is called a photoheliograph4 ,the first instrument of this kind was devised by ,mr4 ,de ,la ,rue1 and for many years was regularly employed in taking photographs of the sun at ,kew4 ,illustration3 ,,fig4 #baa4--,photoheliograph as erected in a ,temporary ,observatory for ,photographing the ,transit of ,venus in #ahgd4 ,some astronomers object to this secondary magnifier1 and to obtain large images use very long focal lengths1 and of course a siderostat is employed4 ,in this way ,professor ,winlock obtained photographs of the sun which have surpassed the limits of ,mr4 ,newall's refractor2 the negatives have a good definition1 and show a considerable amount of detail about the spots2 they were taken by a lens1 inserted at the end of a gas-pipe forty feet long4 ,the pipe was fixed in a horizontal position1 facing the north1 and at the extreme north part of it was the lens1 a single one of crown glass1 with no attempt to correct it4 ,in front of it was a siderostat1 moved by a clock1 reflecting the light down the tube1 so that the image of the sun could be focussed on the ground glass at the opposite end4 ,one will see the importance of shortening the time for even the brightest object4 ,those who are favoured with many opportunities of looking through large telescopes know that the great difficulty we have to deal with is the atmosphere2 because we have to wait for definition1 and the sum total of the photograph of any one particular thing depends upon these atmospheric fits4 ,if we require to photograph an object1 it will be obvious that the more fits we have1 the worse it will be1 because we get a number of images partially superposed which would otherwise give as good an effect as we could get by an ordinary eye observation4 ,it is therefore most important to reduce the interval as much as possible4 ,,chapter ,,xxxii4 ,,celestial ,,photography 7,,continued74--,,some ,,results4 ,the process used should therefore be the most rapid attainable2 any work on photography will give a number of processes of different degrees of rapidity1 but a process that suits one person's manipulation may prove a failure in another's1 and the general principles are the only rules suitable for all4 ,first1 the glass plate should be carefully cleaned1 the collodion lightly coloured1 the bath strong and neutral1 certainly not acid1 and the developer fairly strong4 ,pyrogallic acid and silver should not be used for intensifying2 a good intensifier is made by adding to a solution of iodide of potassium1 strength one grain to the ounce of water1 a saturated solution of bichloride of mercury1 drop by drop1 until the precipitate at first formed ceases to be re-dissolved2 use this after fixing4 ,now let us inquire what has been done by this important adjunct to ordinary means of observing4 ,we may say that celestial photography was founded in the year #ahej by ,professor ,bond1 who obtained a daguerreotype of the moon about that date4 ,an immense advance has been made1 but not so great as there might have been if the true importance of the method had been recognized as it ought to have been2 and if we study the history of the subject we find that till within the last few years we have to limit ourselves to the works of two men who1 after ,bond1 set the work rolling4 ,several observers took it up for a time2 but the work requires much both of time and money1 and different men dropped off from time to time4 ,there remained always steadfast one ,englishman and one ,american--,mr4 ,de ,la ,rue and ,mr4 ,rutherfurd4 ,the magnificent work ,mr4 ,de ,la ,rue has done was begun in #aheb4 ,he was so anxious to see whether ,england could not do something similar to what had been done in ,america1 that1 without waiting for a driving clock1 he thought he would see whether photographs of the moon could be taken by moving the telescope by hand4 ,he soon found that he was working against nature--that nature refused to be wooed in this way2 the moon in quite a decided manner declined to be photographed1 and we waited five years till ,mr4 ,de ,la ,rue was armed with a perfect driving clock4 ,mr4 ,rutherfurd was waiting for the same thing in ,america4 ,at last1 in #aheg1 ,mr4 ,de ,la ,rue got a driving clock to his reflector of thirteen inches aperture1 and began those admirable photographs of the moon which are now so well known4 ,since the above date the moon has been photographed times without number1 and ,mr4 ,de ,la ,rue has made a series which shows the moon in all her different phases4 ,they are remarkable for the beautiful way in which the details come out in all parts of the surface4 ,we must recollect that these pictures of which we have spoken1 some of them a yard in diameter1 were first taken on glass about three inches across1 the image covering the central inch4 ,at the same time the ,british ,association granted funds for the photographic registration of sun-spots at the ,kew ,observatory1 where the sun was photographed every day for many years4 ,encouraged by success1 ,mr4 ,de ,la ,rue1 in #aheh1 attacked the planets ,jupiter and ,saturn1 and some of the stars4 ,he discovered that photographs of the moon can be combined in the stereoscope so that the moon shows itself perfectly globular4 ,to accomplish this result it was necessary to photograph her at different epochs1 so that the libration1 which gives it the appearance of being turned round slightly and looking as it would do to a person several thousand miles to the right or left of the telescope1 should be utilized4 ,these two views when combined give the appearance of solidity just as the image of a near object combined by the two eyes gives that appearance4 ,the reason of this appearance of solidity is easily seen by looking at an orange or ball first with one eye and then with the other1 when it is noticed that each eye sees a little more of one side than the other2 and it is the combination of these slightly dissimilar images that gives the solid appearance4 ,if we examine two of these photographs combined for the stereoscope1 we see that they have the appearance of being taken from two stations a long distance apart4 ,one shows a little more of the surface on one side than the other4 ,they are obtained in different lunations1 when the moon1 in the same phase1 has turned herself slightly round1 showing more of one side4 ,in this way we have a distinct effect due to libration4 ,in the year #ahei ,mr4 ,de ,la ,rue found that sun-pictures could be combined stereoscopically in the same manner4 ,when we turn to the labours of ,mr4 ,rutherfurd1 we find him in #aheg armed with a refractor of #aa inches aperture2 the actinic focus1 or rather the nearest approach to a focus1 was #g_/ajths of an inch from the visual focus4 ,with this telescope1 without any correction whatever1 he1 in #aheg and #aheh1 obtained photographs of the moon which1 when enlarged to five inches in diameter1 were well defined4 ,he also obtained impressions of stars down to as far as the fifth magnitude1 and also of double stars some #c apart--for instance1 ,virginis was photographed double4 ,the ring of ,saturn and belts of ,jupiter were also plainly visible1 but ill-defined4 ,the satellites of ,jupiter failed to give an image with any exposure1 while their primary did so in five or ten seconds4 ,the actinic rays1 instead of coming to a point and producing an image of a satellite1 were spread over a certain area and thereby rendered too weak to impress the plate4 ,in the summer of #aheh ,mr4 ,rutherfurd combined his first stereograph of the moon independently of ,mr4 ,de ,la ,rue's success in ,england4 ,mr4 ,rutherfurd then commenced an inquiry of the greatest importance1 which will in time bring about a revolution in the processes employed4 ,in #ahei he attempted1 by placing lenses of different curvatures between the object-glass and the focus1 to bring the chemical rays together1 leaving the visual rays out of the question2 this had the effect of shortening the focus considerably and improving the photographs2 but he found that1 except for the middle of the field1 this method would not answer4 ,he therefore in #ahfj attempted another arrangement1 and one which he found answered extremely well for short telescopes4 ,between the lenses of the object-glass of a #d-;inch refractor he put a ring which separated the lenses by three-quarters of an inch1 and reduced the power of the flint-glass lens1 which corrects the crown-glass for colour1 so that the combination became achromatic for the violet rays instead of for the yellow4 ,with this lens he was successful to a certain extent3 he obtained even better results than with the #aa inch2 but eventually he rejected this method1 which we may add has recently been tested by ,m4 ,cornu1 who thinks very highly of it4 ,he next attempted a silver-on-glass mirror in #ahfa2 in the atmosphere of ,new ,york it only lasted ten days2 he gave it up2 and he then very bravely1 in #ahfd1 attacked the project de novo1 and began an object-glass of a telescope which should be constructed so as to give best definition with the actinic rays1 just as ordinary object-glasses are made to act best with the visual rays4 ,he found that in order to bring the actinic portion of the rays to a perfect focus1 it was necessary that a given crown-glass lens should be combined with a flint1 which will produce a combined focal length of about shorter than would be required to satisfy the conditions of achromatism for the eye4 ,this combination was of course absolutely worthless for ordinary visual observation2 his new lens when finished was #aa inches aperture and a little less than #ad feet focal length4 ,with this he obtained impressions of ninth magnitude stars1 and within the area of a square degree in the ,prsepe in ,cancer twenty-three stars were photographed in three minutes' exposure4 ,castor gave a strong impression in one second1 and stars of #b distance showed as double4 ,but even with this method ,mr4 ,rutherfurd was not satisfied4 ,coming back to the #aa-;inch object-glass which he had used at first1 he determined to see whether or not the addition of a meniscus lens outside the front lens would not give him the requisite shortness of the focus and bring the actinic rays absolutely together4 ,by this arrangement he got a telescope which can be used for all purposes of astronomical research1 and he has also eclipsed all his former photographic efforts4 ,,chapter ,,xxxiii4 ,,celestial ,,photography 7,,continued7--,,recent ,,results4 ,having in the previous chapter dealt with some of the pioneer work1 we come finally to consider some of the applications which in the last years have occupied most attention4 ,with regard to the sun1 we need scarcely say that ,messrs4 ,de ,la ,rue and ,stewart have been enabled1 by the photographic method1 to give us data of a most remarkable character1 showing the periodicity of the changes on the sun's surface1 and so establishing their correlation with magnetic and other physical phenomena4 ,these photographic researches1 following upon the eye observations of ,schwabe1 ,sprer1 ,carrington and others1 have opened up to us a new field of inquiry in connection with the meteorology of the globe2 and it is satisfactory to learn that photoheliographs are now daily at work at ,greenwich1 ,paris1 ,potsdam1 and the ,mauritius1 and that shortly ,india will be included in the list4 ,quite recently1 the importance of these permanent records of the solar surface has been demonstrated by ,dr4 ,janssen1 the distinguished director of the ,physical ,observatory at ,meudon1 in a very remarkable manner4 ,it seems a paradox that discoveries can be made depending on the appearance of the sun's surface by observations in which the eye applied to the telescope is powerless2 but this is the statement made by ,dr4 ,janssen himself1 and there is little doubt that he has proved his point4 ,before we come to the discovery itself let us say a little concerning ,dr4 ,janssen's recent endeavours4 ,among the six large telescopes which now form a part of the equipment of the new ,physical ,observatory recently established by the ,french government at ,meudon1 in the grounds of the princely ,chateau there1 is one to which ,dr4 ,janssen has recently almost exclusively confined his attention4 ,it is a photoheliograph giving images of the sun on an enormous scale--compared with which the pictures obtained by the ,kew photoheliograph are1 so to speak1 pigmies1 while the perfection of the image and the photographic processes employed are so exquisite1 that the finest mottling on the sun's surface cannot be overlooked by those even who are profoundly ignorant of the interest which attaches to it4 ,this perfection of size and image have been obtained by ,dr4 ,janssen by combining all that is best in the principles utilised in one direction by ,mr4 ,de ,la ,rue1 and in the other by ,mr4 ,rutherfurd1 to which we have before referred4 ,in the ,kew photoheliograph1 which has done such noble work in its day that it will be regarded with the utmost veneration in the future1 we have first a small object-glass corrected after the manner of photographic lenses1 so as to make the so-called actinic and the visual rays coincide1 and then the image formed by this lens is enlarged by a secondary magnifier constructed1 though perhaps not too accurately1 so as to make the actinic and visual rays unite in a second image on a prepared plate4 ,mr4 ,rutherfurd's beautiful photographs of the sun were obtained in a somewhat different manner4 ,in his object-glass1 as we have seen1 he discarded the visual rays altogether and brought only the blue rays to a focus1 but when enlargements were made1 an ordinary photographic lens--that is1 one in which the blue and yellow rays are made to coincide--was used4 ,dr4 ,janssen uses a secondary magnifier1 but with the assistance of ,m4 ,pragmowski he has taken care that both it and the object-glass are effective only for those rays which are most strongly photographic4 ,nor is this all2 he has not feared largely to increase the aperture and focal length1 so that the total length of the ,kew instrument is less than one-third of that in operation in ,paris4 ,the largely-increased aperture which ,dr4 ,janssen has given to his instrument is a point of great importance4 ,in the early days of solar photography the aperture used was small1 in order to prevent over-exposure4 ,it was soon found that this small aperture1 as was to be expected1 produced poor images in consequence of the diffraction effects brought about by it4 ,it then became a question of increasing the aperture while the exposure was reduced1 and many forms of instantaneous shutters have been suggested with this end in view4 ,with these1 if a spring be used1 the narrow slit which flashes across the beam to pay the light out into the plate changes its velocity during its passage as the tension of the spring changes4 ,of this again ,dr4 ,janssen has not been unmindful1 and he has invented a contrivance in which the velocity is constant during the whole length of run of the shutter4 ,by these various arrangements the plates have now been produced at ,meudon of fifteen inches diameter1 showing details on the sun's surface subtending an angle of less than one second of arc4 ,so much for the modus operandi4 ,now for the branch of solar work which has been advanced4 ,it is more than fifteen years ago since the question of the minute structure of the solar photosphere was one of the questions of the day4 ,the so-called 8mottling0 had long been observed4 ,the keen-eyed ,dawes had pointed out the thatch-like formation of the penumbra of spots1 when one day ,mr4 ,nasmyth announced the discovery that the whole sun was covered with objects resembling willow-leaves1 most strangely and effectively interlaced4 ,we may sum up the work of many careful observers since that time by stating that the mottling on the sun's surface is due to dome-like masses1 and that the 8thatch0 of the penumbra is due to these dome-like masses being drawn1 either directly or in the manner of a cyclone1 towards the centre of the spot4 ,in fact the 8pores0 in the interval between the domes are so many small spots1 while the facul are the higher levels of the cloudy surface4 ,the fact that facul are so much better seen near the limb proves that the absorption of the solar atmosphere rapidly changes between the levels reached by the upper facul and the pores4 ,thus much premised1 we now come to ,dr4 ,janssen's discovery4 ,an attentive examination of his photographs shows that the surface of the photosphere has not a constitution uniform in all its parts1 but that it is divided into a series of figures more or less distant from each other1 and presenting a peculiar constitution4 ,these figures have contours more or less rounded1 often very rectilinear1 and generally resembling polygons4 ,the dimensions of these figures are very variable2 they attain sometimes a minute and more in diameter4 ,while in the interior of the figures of which we speak the grains are clear1 distinctly terminated1 although of very variable size1 in the boundary the grains are as if half effaced1 stretched1 stained2 for the most part1 indeed1 they have disappeared to make way for trains of matter which have replaced the granulation4 ,everything indicates that in these spaces1 as in the penumbr of spots1 the photospheric matter is submitted to violent movements which have confused the granular elements4 ,we have already referred to the paradox that the sun's appearance can now be best studied without the eye applied to the telescope4 ,this is what ,dr4 ,janssen says on that point4 8,the photospheric network cannot be discovered by optical methods applied directly to the sun4 ,in fact1 to ascertain it from the plate1 it is necessary to employ glasses which enabled us to embrace a certain extent of the photographic image4 ,then if the magnifying power is quite suitable1 if the proof is quite pure1 and especially if it has received rigorously the proper exposure1 it will be seen that the granulation has not everywhere the same distinctness2 that the parts consisting of well-formed grains appear as currents which circulate so as to circumscribe spaces where the phenomena present the aspect we have described4 ,but to establish this fact1 it is necessary to embrace a considerable portion of the solar disc1 and it is this which it is impossible to realise when we look at the sun in a very powerful instrument1 the field of which is1 by the very fact of its power1 very small4 ,in these conditions we may very easily conclude that there exist portions where the granulation ceases to be distinct or even visible2 but it is impossible to suppose that this fact is connected with a general system40 ,but it is not alone with the uneclipsed sun that the new method enables us to make discoveries4 ,the extreme importance of photography in reference to eclipse observations cannot be over estimated4 ,most of our best observations of eclipses have been wrought by means of photography4 ,the time of an eclipse is an exciting time to astronomers2 and it is important that we should have some mechanical operation which should not fail to record it4 ,illustration3 ,,fig4 #bab4--;,copy of ,photograph taken during the ,eclipse of #ahfi4 ,the first eclipse photograph was taken in #ahea4 ,in #ahfj1 chiefly owing to the labours of ,mr4 ,de ,la ,rue1 our knowledge was enormously increased4 ,the ,kew photoheliograph was the instrument used1 and the series of pictures obtained showed conclusively that the prominences belonged to the sun4 ,in #ahfh the prominences were again photographed4 ,in #ahfi the ,americans attacked the corona1 and their suggestion that the base of it was truly solar has been confirmed by other photographs taken in #ahgj1 #ahga1 and #ahge4 ,although to the eye the phenomena changed from place to place1 to the camera it was everywhere the same with the same duration of exposure4 99 99 99 99 99 ,it is not to be wondered at1 then1 that on the occasion of the last transit of ,venus1 which may be regarded as a partial eclipse of the sun1 photography was suggested as a means of recording the phenomena4 ,science is largely indebted to ,dr4 ,janssen1 ,mr4 ,de ,la ,rue1 and others for bringing celestial photography to aid us in this branch of work also4 ,while on the one hand astronomers have to deal with precious moments1 to do very much in very little time1 in circumstances of great excitement2 the photographer on the other goes on quietly preparing and exposing his plates1 and noting the time of the exposure1 and thus can make the whole time taken by the planet in its transit over the sun's disc one enormous base line4 ,his micrometrical measures of the position of the planet on the sun's disc can be made after all is over4 ,it was suggested by ,dr4 ,janssen that a circular plate of sufficient size to contain sixty photographs of the limb of the sun1 at the points at which ,venus entered and left it could be moved on step by step round its centre1 and so expose a fresh surface to the sun's image focussed on it1 say every second4 ,in this way the phenomena of the transit were actually recorded at several stations4 99 99 99 99 99 ,illustration3 ,,fig4 #bac4--,part of ,beer and ,mdler's ,map of the ,moon4 ,with reference to the moon1 we have said enough to show that if we wish to map her correctly1 it is now no longer necessary to depend on ordinary eye observations alone2 it is perfectly clear that by means of an image of the moon1 taken by photography1 we are able to fix many points on the lunar surface4 ,still1 although we can thus fix these and use them as so many points of the first order1 as one might say1 in a triangulation1 there is much that photography cannot do2 the work of the eye observer would be essential in filling in the details and giving the contour lines required to make a map of the moon4 ,the accompanying drawings on the same scale show that up to the present1 for minute work1 the eye beats the camera4 ,illustration3 ,,fig4 #bad4--,the same ,region copied from a ,photograph by ,de ,la ,rue4 ,the light of the moon is so feeble in blue rays that a long exposure is necessary for a large image1 and during the exposure all the errors in the rate of the clock are magnified4 ,we need not enlarge on the extreme importance of what ,mr4 ,rutherfurd has been doing in photographing star clusters and star groups4 ,it is doubly important to astronomy1 and starts a new mode of using the equatorial and the clock2 in fact1 it gives us a method by which observations may be photographically made of the proper motion of stars1 and even the parallax of stars may be thus determined independently of any errors of observers4 ,mr4 ,rutherfurd shows that the places of stars can be measured by a micrometer on a plate in the same way as by ordinary observation2 hence photography can be made use of in the measurement of position and distance of double stars4 ,as an instance of the extreme beauty of the photographs of stars produced by a proper instrument1 it may be stated that with the full aperture of the #aa-;inch object-glass corrected only for the ordinary rays1 ,mr4 ,rutherfurd found that he required an exposure of more than ten seconds to get an image of the bright star ,castor2 but now1 instead of requiring ten seconds1 he can get a better image in one4 ,the reason of this is1 that1 with the object-glass corrected only for the visual rays1 the chemical ones are spread over a certain small area instead of coming to a point1 and so1 of course1 the intensity is reduced2 but when the chemical rays all come to one point the intensity is greater1 since the image of the star is smaller and the action more intense4 ,let us follow ,mr4 ,rutherfurd a little in his actual work4 ,first1 a wet plate is exposed for four minutes4 ,this gives stars down to the tenth magnitude4 ,but there may be points on the plate which are not stars1 hence a second impression is taken on the same plate after it has been slightly moved4 ,all points now doubled are true stars4 ,now for measures of arc4 ,another photograph is taken1 and the driving clock is stopped2 the now moving stars down to the fourth magnitude are bright enough to leave a continuous line1 the length of this in a very accurately known interval1 say two minutes1 enables the arc to be calculated4 ,next comes the mapping4 ,the negative is fixed on a horizontal divided circle on glass illuminated from below4 ,above it is a system of two rails1 along which travels a carrier with two microscopes1 magnifying fifty diameters4 ,by the one in the centre1 with two cross wires in the field of view1 the photograph is observed2 by the other1 armed with a wire micrometer1 a divided scale on glass which is fixed alongside the rail is read4 ,suppose we wish to measure the distance between two stars on the plate4 ,the plate is rotated1 so that the line which joins them coincides with that which is described by the optical axis of the central microscope marked by the cross wires when the carrier runs along the rails4 ,this microscope is then brought successively over the two stars1 and the other microscope over the scale reads the nearest division1 while the fractions are measured by the micrometer4 ,hence1 then1 the fixed scale1 and not a micrometer screw1 is depended upon for the complete distance4 ,in this way the distance between the stars on the plate can be measured to the #a_/ejj part of a millimetre4 99 99 99 99 99 ,so far then we have shown how photography has been called in to the aid of the astronomer1 and how1 by means of photography1 pictures of the different celestial bodies have been obtained of surpassing excellence4 ,now1 photography is also the handmaiden to the spectroscope in the same way as it is the handmaiden to the telescope4 ,not only are we able to determine and register the appearance of the moon and planets1 but1 day by day1 or hour by hour1 we can photograph a large portion of the solar spectrum2 and not only so1 but the spectrum of different portions of the sun3 nay1 even the prominences have been photographed in the same manner2 while more recently still1 ,drs4 ,huggins and ,draper have succeeded in photographing the spectrum of some of the stars4 ,we owe the first spectrum of the sun1 showing the various lines1 to ,becquerel and ,draper2 the finest hitherto published we owe to ,mr4 ,rutherfurd4 ,illustration3 ,,fig4 #bae4--;,comparison between ,kirchhoff's ,map and ,rutherfurd's ,photograph4 ,this magnificent spectrum extends from the green part of the spectrum right into that part of the spectrum called the ultra-violet4 ,of course it had to be put together from different pictures1 because there is a different length of exposure required for the different parts2 the exposure of any particular part of the spectrum must be varied according to the amount of chemical intensity in that part4 ,if the line ,g was exposed1 say for fifteen seconds1 the spectrum near the line ,f would require to be exposed for eight minutes1 and at the line ,h1 which is further away from the luminous part of the spectrum than ,g1 there the exposure requisite would be two or three minutes4 ,illustration3 ,,fig4 #baf4--;,arrangement for ,photographically ,determining the ,coincidence of ,solar and ,metallic ,lines4 ,illustration3 ,,fig4 #bag4--,telespectroscope with ,camera for obtaining ,photographs of the ,solar ,prominences4 ,in order to obtain a photograph of the average solar spectrum1 the camera replaces the observing telescope1 and a heliostat is used1 as in the ordinary way4 ,the beam1 however1 should be sent through an opera-glass in order to condense it1 and thereby to render the exposure as short as possible4 ,further1 if an electric lamp be mounted as shown in ,fig4 #baf1 observations1 similar to those originally made by ,kirchhoff1 of the coincidence on the various metallic lines with the ,fraunhofer ones1 can be permanently recorded on the photographic plate4 ,the lens between the lamp and the heliostat is for the purpose of throwing an image of the sun between the carbon poles4 ,the lens between the lamp and spectroscope then focuses both the poles and the image of the sun on to the slit4 ,the spectrum of the sun is first obtained by uncovering a small part of the slit and allowing the image of the sun to fall on this uncovered portion1 the lamp not being in action4 ,when this has been done the light of the sun is shut off4 ,the metal to be studied is placed in the lower pole2 the adjacent portion of the slit is uncovered1 that at first used being closed in the process4 ,the current is then passed to render the metal incandescent4 ,after the proper exposure the plate is developed and the spectra are seen side by side4 ,fig4 #ahg is a woodcut of a plate so obtained4 ,if the spectrum of any special part of the sun1 or the prominences1 has to be photographed1 then either a siderostat must be employed1 or a camera is adjusted to the telespectroscope1 as shown in ,fig4 #bag4 ,for the stars1 of course1 much smaller dispersion must be used1 but the method is the same2 and what has already been said by way of precaution about the observation of stellar spectra applies equally to the attempt to obtain spectrum photographs of these distant suns4 ,,index4 ,a4 ,aberration 7see ,chromatic ,aberration1 ,spherical ,aberration7 ,absorption1 general and selective1 #djc1 #djh2 spectroscope arranged for showing1 #dji ,adjustment of the transit instrument1 #bch ,,adjustments ,,of ,,the ,,equatorial 7,chap4 ,,xxi471 #cbh ,achromaticity of ,huyghen's eyepiece1 #aaj ,achromatic lenses1 #hd1 #hf ,achromatism1 #abf ,airy's transit circle1 #bhd ,alexandrian ,museum1 astronomical observations1 #ai ,alt-azimuth1 #bhg1 #bhi ,altitudes1 instrument used by ,ptolemy for measuring1 #ce ,aluminium1 line spectrum of1 #djf2 the sun1 #dag ,analyser for polarization of light1 #ddc1 #dej ,anaximander1 his theory of the form of the earth1 #f2 invention of the gnomon ascribed to him1 #af1 #ag2 meridian observations by1 #be ,anchor escapement1 #aig ,angles of position1 measurement of1 #ceh-cff1 #cgb ngstrm1 spectrum analysis1 #djb1 #dab2 wave-lengths1 #djf ,annealing of lenses and specula1 #aba ,archimedes1 clocks used by1 #agf ,arcturus1 heat of1 #che ,argelander1 magnitudes of stars1 #chb ,aries1 its position in the zodiac1 #cd ,aristillus1 his observations in the ,alexandrian ,museum1 #ai ,armill quatori of ,tycho ,brahe1 #bf1 #da1 #de2 his ,armill ,zodiacales1 #bh ,ascension1 ,right 7see ,right ,ascension7 ,arctic circle1 ,euclid's observations of stars in the1 #aj ,astrolabe1 invented by ,hipparchus1 #be2 engraving of ,tycho ,brahe's1 #bf1 #da2 his ecliptic astrolabe1 #bh ,astronomical clock1 #bdj 7see ,clock7 ,,astronomical ,,physics 7,book ,,vi471 #cga ,,astronomy ,,of ,,precision1 ,,instruments ,,used ,,in 7,chap4 ,,xix471 #bhd-bij ,astrophotometer1 ,zllner's1 #cgi ,autolycus1 first map of the stars by1 #h1 #i ,automatic spectroscope1 #cig ,auzout1 invention of micrometer ascribed to1 #bai1 #bba ,axis of collimation1 #bah1 #bbj ,b4 ,barium1 in the sun1 #dai ,barlow1 correction of aberration in lenses1 #hh2 8,barlow lenses10 #hi1 #bbi ,barometrical pressure1 its effect on the pendulum1 #aic ,berthon's dynameter1 #aaf ,bessel's transit instrument1 #bhd ,binary stars1 #cea1 #cei1 #cfj ,blair 7,dr471 object-glasses1 #hh ,bloxam's improved gravity escapement1 #bja ,bond 7,prof471 spring governor1 #cbj1 #cba2 celestial photography1 #dfc ,bouguer's photometer1 #cgi ,brahe1 ,tycho 7see ,tycho ,brahe7 ,brewster 7,sir ,david71 his list of ,tycho ,brahe's instruments1 #ch2 spectrum analysis1 #daj ,british ,horological ,institute1 time signals1 #bhj ,browning's method of silvering glass specula1 #acg2 of mounting specula1 #add2 automatic spectroscope1 #cig2 solar spectroscope1 #dbh ,bunsen 7,ernest de71 on ancient astronomical observations1 #f ,bunsen 7,prof47 spectroscope1 #cif2 his burner1 flame of1 #djg2 his work in spectrum analysis1 #djb1 #dab1 #dbc ,c4 ,calcium1 line spectra of1 #djf1 #dah ,cambridge ,observatory 7,u4,s471 equatorial at1 #cci2 star spectroscope1 #dcj2 transit circle1 #bdg1 #bdh1 #bea ,camera1 enlarging1 for celestial photography1 #deh ,canada balsam1 its power of refracting light1 #ddg ,candles used to measure time1 #agf ,canopus1 observations of1 by ,posidonius1 #h ,cassegrain's reflecting telescope1 #ajc1 #adi1 #afi2 with ,mr4 ,grubb's mounting1 #cja ,casting lenses and specula1 #aba ,castor1 photograph of1 #dgh ,catalogues of stars 7see ,stars7 ,celestial globe1 #bc ,,celestial ,,photography 7,chap4 ,,xxxi41 ,,xxxii471 #ded ,chair1 observing1 for equatorial telescopes1 #cci ,chaldeans1 their observations of the motions of the moon1 #d2 early use of the gnomon1 #af ,chance and ,feil1 manufacture of glass discs1 #aai1 #cje ,,chemistry ,,of ,,the ,,stars 7,chap4 ,,xxvii4-,,xxx471 #chf-dec ,chinese1 observations of conjunctions of planets1 #d1 #e2 early use of the gnomon1 #af1 #ag ,chromatic aberration of object-glasses and eyepieces1 #hg1 #aji1 #abc ,,chronograph1 ,,the 7,chap4 ,,xvii471 #bec-bgj 8,chronographic method0 of transit observation1 #bei ,chronograph at ,greenwich ,observatory1 #bfj-bfd ,,chronometer1 ,,the 7,chap4 ,,xiii471 rise and progress of time-keeping1 #bjf-baj2 compensating balance1 #bjg2 detached lever escapement1 #bjh2 chronometer escapement fusee1 #bji ,chronometers used for determining 8local time10 #bha ,chronophers1 for distributing 8,greenwich time10 #bge1 #bgf ,cincinnati ,observatory1 #cch ,circle1 the2 its first application as an astronomical instrument1 #f1 #g1 #h1 #aj2 division into degrees1 #h1 #ag1 #ba ,circles1 great1 defined by ,euclid1 #ab ,,circle ,,reading 7,chap4 ,,xiv471 #baa-bag2 ,digges' diagonal scale1 #bac2 the vernier1 #bad ,,circle1 ,,transit 7see ,transit ,circle7 ,circle1 meridian1 at ,cambridge 7,u4,s471 #bdh2 mural1 #bda1 #bdb ,circumpolar stars1 #bci ,clarke 7,alvan71 improvement in telescope lenses1 #cje2 great equatorial at ,washington1 #cji1 #cai ,clement1 inventor of the anchor escapement1 #aig ,clepsydras1 #cf ,,clock1 ,,the 7,chap4 ,,xiii471 #age-bje2 ancient escapement1 #agg2 crown wheel1 #agh2 clock train1 #ahj2 winding arrangements1 #aha2 pendulum1 #ahc2 cycloidal pendulum1 #ahe2 compensating pendulums1 #ahg2 ,graham's1 ,harrison's1 and ,greenwich pendulums1 #ahh2 clock at ,royal ,observatory1 ,greenwich1 #aid2 escapements1 #aif2 anchor escapement1 #aig2 ,graham's dead-beat1 #aii2 ,mudge's gravity escapement1 #bjj2 escapement of clock at ,greenwich1 #bjc2 arrangements at ,edinburgh ,observatory1 #bfi2 astronomical1 #bdj1 #bdd1 #bde1 #cdf2 sidereal1 #bed1 #bef1 #bff2 solar1 #bed2 standard1 at ,greenwich1 #aid1 #bjc1 #bjd1 #bga1 #bgd ,clock1 driving1 for large telescopes1 #cah ,clocks driven and controlled by electricity1 #bgb ,clock stars1 #bfg ,clock tower at ,westminster1 #bgg ,coggia's comet1 its light polarized1 #dej ,collimation and collimation-error in the transit instrument and equatorial1 #bch1 #bdg1 #cbh ,colour1 amount produced by a lens1 #ha1 #hd1 #hf2 spectrum analysis1 #djg1 #djh1 #dad1 #daf2 of stars1 #afe1 #cea1 #dcc2 of waves of light1 #dbj2 refrangibility of1 #chg ,comet of #afgg1 discovered by ,tycho ,brahe1 #dg ,comet1 measurement of the angle of position of its axis1 #cei ,comparison prism of the spectroscope1 #dbc ,compensating balance1 #bjg ,compensating pendulums1 #ahg-aic ,composite mounting of large telescopes1 #caj ,concave lenses 7see ,lenses7 ,concave mirrors 7see ,mirrors7 ,conjugate images1 #fd ,conjunctions of planets1 first observations1 #d ,constellations1 first observations1 #e1 #i2 ,orion and its neighbourhood1 #aef ,convex lenses 7see ,lenses7 ,convex mirrors 7see ,mirrors7 ,cooke1 adjustment of object-glasses1 #ada2 improvement in telescope lenses1 #cje2 equatorial refractor1 #cjj2 driving clock for large telescopes1 #cba2 illuminating lamp for equatorial telescopes1 #cbf ,copernicus1 parallactic rules of1 #da ,copernicus 7lunar crater71 #ced ,cross wires for circle reading1 #bab1 #baf1 #bah2 in transit eyepiece1 #bcd1 #beg ,crown-glass prisms1 #hc1 #hd2 lenses1 #hf1 #hh ,crystals of ,iceland spar1 double refraction by 7see ,iceland ,spar7 ,culmination of stars1 first observations of1 #e ,cycloidal pendulum1 #ahe ,d4 ,dawes1 solar eyepiece1 #aad1 #aae1 #cdi2 photometry1 #cgh ,day1 solar and sidereal1 #bec1 #bed1 #bef ,day eyepiece1 #aac ,days1 first reckoning of1 #ai2 measurement of1 #agf ,dead-beat escapement1 #aih ,deal time-ball1 #bge1 #bgi ,declination1 #bd1 #bcd1 #bda1 #bdc1 #bea2 measured by ,tycho ,brahe1 #de ,declination axis of the equatorial1 #bii1 #cjh1 #cbg1 #cbh ,defining power of the modern telescope1 #afj1 #afd2 stars in ,orion a test of1 #afe ,degrees1 division of the circle into1 #h1 #ag1 #ba ,de ,la ,rue 7,warren1 ,f4,r4,s471 his reflecting telescope1 #ajh2 improvements in polishing specula1 #acd2 celestial photography1 #ded1 #dei1 #dfj1 #dfd1 #dfe1 #dge ,denderah1 the zodiac of1 #g ,dent 7,e4 ,co471 clock at ,royal ,observatory1 ,greenwich1 #aid1 #bjc1 #bjd1 #bga1 #bgd ,detached lever escapement1 #bjh ,deviation of light1 #gi1 #hb ,deviation error in the transit instrument1 #bdj1 #bdh ,dials of ancient clocks1 #beg ,diagonal scale1 ,digges'1 #bac ,differential observations made with the equatorial1 #cfg ,digges' diagonal scale1 #bac ,diogenes ,laertes1 on the invention of the gnomon1 #af ,dioptrics1 ,kepler's treatise on1 #chf ,direct vision spectroscope1 #dca ,dispersion of light by prism1 #gi1 #hj1 #hb ,dividing power of telescopes1 #afe ,dollond1 experiments with lenses1 #he2 correction of chromatic aberration1 #hi2 on manufacture of flint-glass discs1 #aah2 pancratic eyepiece1 #aac ,dome form of observatory1 #cch1 #cci ,double stars1 #cea1 #cei2 measurement of1 #cfj ,double-image micrometer1 #bbe1 #bbi ,double refraction by crystals of ,iceland spar 7see ,iceland ,spar7 ,driving clock1 for large telescopes1 #cah1 #cdf ,drum form of observatory1 #cch ,dundee time signal1 #bgh ,e4 ,earth1 ,the1 its position in ,ptolemy's system1 #c2 early theories of its form1 #f2 circumference measured by ,posidonius1 #h2 ,euclid's theory of its position1 #ab2 inclination of its axis1 #ad1 #ag2 size measured by ,eratosthenes1 #ai2 position in ,tycho ,brahe's system1 #df ,eclipses1 first observations of1 #d2 eclipses of ,jupiter's moons2 eclipses1 solar1 photograph of1 #dgd ,ecliptic1 plane of the1 #ac1 #ad2 discovery of its inclination1 #ag2 inclination measured by ,eratosthenes1 #ai ,ecliptic astrolabe of ,tycho ,brahe1 #bh ,edinburgh ,observatory1 clock arrangements at1 #bfi2 standard clock1 #bgb2 time signals1 #bgh ,egyptians1 their record of eclipses1 #d2 zodiac of ,denderah1 #g ,eichens1 his equatorial telescope at ,paris1 #cad1 #cae2 siderostat constructed by him1 #cdd ,electricity1 its application to the chronograph1 #bfe2 to driving and controlling clocks1 #bgb ,electric lamp1 #djd2 arranged for spectrum analysis1 #dje ,emery used in grinding lenses and specula1 #abg ,english mounting of large telescopes1 #caj ,equation of time1 #bed ,,equatorial1 ,,the 7,book ,v471 #bic-cfh 7see ,telescopes7 ,,equatorial ,,observatory1 ,,the 7,chap4 ,,xxii471 #ccg-cdb 7see ,observatories7 ,,equatorial1 ,,the2 its ordinary work1 7,chap4 ,,xxiv471 #cdi-cfh ,equinoctial circle1 observations of1 by ,euclid1 #aa ,equinoxes1 first observations of1 #ae1 #af1 #ag1 #bb2 precession of the1 #cc ,eratosthenes1 observations of1 #ag2 his measurement of the earth1 and inclination of the ecliptic1 #ai2 meridian circle invented by1 #bj ,erecting eyepiece1 #aac ,errors1 collimation and deviation1 in the transit instrument1 #bch1 #bdj1 #bdg1 #cbh ,errors2 personal equation1 #bei2 adjustments of the equatorial1 #cbi ,ertel1 vertical circle designed by1 #bij ,escapements of clocks1 #aif-bje2 ancient1 #agg2 anchor1 #aig2 ,graham's1 #aii2 ,mudge's1 #bjj2 ,greenwich clock1 #bjc2 detached lever1 #bjh2 chronometer escapement1 #bji ,ethereal vibrations1 #cgc1 #dja1 #daj1 #dbj1 #ddi1 #dej ,euclid1 his observations of the stars1 #h1 #i1 #aj2 of great circles1 horizon1 meridian and tropics1 #aa1 #ab2 theory of the earth's position1 #ab2 pole star1 #ad ,extra-meridional observations1 first employment of1 #bc1 #be 8,eye and ear0 method in transit observations1 #bei ,eyeball1 section of the1 #ff ,eyepieces1 ,huyghen's1 #aaj2 ,ramsden's1 ,dollond's1 #aab2 erecting or 8day eyepiece10 #aab2 ,dawes's solar eyepiece1 #aad2 magnifying power of1 #aaf ,eyepiece of ,greenwich transit circle1 #bdf2 of transit instrument1 #beg ,f4 ,faye1 ,m41 celestial photography1 #def ,feil and ,chance1 manufacture of flint glass discs1 #aai1 #cje ,fixed stars 7see ,stars7 ,flame of salts in a ,bunsen's burner1 #djg ,flint-glass prisms1 #hc1 #hd2 lenses1 #hf1 #agj ,flint-glass1 improvements in the manufacture of discs of1 #aah1 #aai1 #cje ,focal length of telescopes1 #hb1 #deh2 of lenses1 #fb1 #fc2 of convex mirrors1 #id ,foucault2 his reflecting telescope1 #ajh2 improvement of specula1 #aag2 mode of polishing specula1 #acd1 #acf2 mounting of his telescope1 #caa2 governor of driving clock for large telescopes1 #cbc2 siderostat1 #cdc2 spectrum analysis1 #daj2 heliostat1 #dbd ,fraunhofer2 manufacture of flint-glass discs1 #aah2 large telescopes1 #cjc2 lines in the solar spectrum1 #cib2 spectrum analysis1 #djb1 #daj1 #dbb1 #dbe1 #dcb1 #dch ,frederick ,,ii4 of ,denmark1 his patronage of ,tycho ,brahe1 #ch ,fusee for chronometers1 #bji ,g4 ,galileo2 his telescopes1 #gc1 #gh2 their magnifying power1 #gg2 the pendulum1 #ahc1 #ahd ,gascoigne1 eyepieces and circle reading1 #bab2 cross wires for 8telescopic sight10 #bai ,gateshead1 ,mr4 ,newall's refractor1 #cjb ,geissler's tubes1 #dac ,german mounting of large telescopes1 #bii ,gizeh1 great pyramid of1 an astronomical instrument1 #f ,glasgow1 electric time-gun1 #bgh ,glass1 injurious effects of the duty on1 #cje ,glass specula1 methods of silvering1 #acg ,globe1 celestial1 #bc2 terrestrial1 #bc ,gnomon2 its invention and early use1 #af2 improvements in1 #ah1 #age ,graham2 dead-beat escapement1 #aib1 #aii2 mercurial pendulum1 #ahh ,gravity escapement1 #bjj1 #bjb ,greeks1 their early use of the gnomon1 #af ,greenwich1 ,royal ,observatory2 perspective view and plan of transit circle1 #bdc1 #bde1 #bea2 transit room1 #bea1 #beg2 meridian of1 #beb2 chronograph1 #bfj-bfd2 computing room1 #bfg2 standard sidereal clock1 #bfg2 mean solar time clock1 #bfh2 standard clock1 #bgd2 pendulum1 #ahh2 reflex zenith tube1 #bhf2 alt-azimuth1 #bij2 equatorial1 #caj2 thermopile1 #chd2 photoheliograph1 #dfi 8,,greenwich ,,time0 ,,and ,,the ,,use ,,made ,,of ,,it 7,chap4 ,,xviii471 #bga-bhc ,gregorian telescope1 #adi ,gridiron pendulum1 #ahh1 #ahi1 #aib ,grinding of lenses and specula1 #abg ,grubb2 production and polishing of metallic specula1 #aba1 #acd2 adjustment of object-glasses1 #ada2 ,cassegrainian and ,newtonian reflectors1 #ajb1 #ajh1 #cja1 #cjc2 great ,melbourne equatorial telescope1 #ajh1 #cad1 #cae1 #cag1 #cbd1 #cbg2 mode of mounting its speculum1 #ade-adi2 automatic spectroscope1 #cig2 solar spectroscope1 #dbh ,guinand1 manufacture of flint-glass discs1 #aah ,guns fired as time-signals1 #bgh ,h4 ,haliburton1 on ancient astronomical observations1 #f ,hall2 experiments with lenses1 #he2 manufacture of flint-glass discs1 #aah ,harcourt1 ,vernon1 experiments with phosphatic glass1 #abc ,harrison's gridiron pendulum1 #ahh ,,heat ,,of ,,stars1 ,,determination ,,of 7,chap4 ,,xxvi471 #cgg-che ,heliometer1 #bbd ,heliostat1 #dbc1 #deh ,henry 7,prof471 radiation of heat from sun-spots1 #che ,herschel 7,sir ,john71 lenses corrected for aberration1 #hh2 table of reflective powers1 #afi2 star magnitudes1 #cha ,herschel1 ,sir ,william1 his reflecting telescopes1 #ajc1 #ajh2 his mode of polishing specula1 #abi2 great telescope at ,slough1 #afi1 #bid ,herschel-,browning direct-vision prism1 #djj ,hipparchus1 trigonometrical tables constructed by1 #ag2 discoveries of1 #be-ce2 his measurement of space1 #bac ,hittorf1 spectrum analysis1 #dac ,holmes 7,n4 ,j471 his proposal of the electric time-gun1 #bgh ,hooke1 improvement in clock escapements1 #aif2 micrometer1 #bba1 #bbb2 zenith sector invented by1 #bhe2 siderostat suggested by1 #cdc ,horizon1 the first astronomical instrument1 #d1 #g1 #h2 defined by ,euclid1 #ab ,horological ,institute1 time-signals1 #bhj ,hours1 first reckoning of1 #ai2 measurement of1 #agf ,hour circle of the equatorial telescope1 #cbh1 #cce ,huen1 island of1 granted to ,tycho ,brahe1 #ch ,huggins 7,dr471 telespectroscope1 #dbi1 #dcb ,huyghens2 telescopes used by1 #ha2 eyepiece1 #aaj1 #aaf1 #bab2 application of the pendulum to clocks1 #ahc2 his measurements of space1 #bai1 #bbc1 #cdc2 polarized light1 #ddb ,hydrogen in the sun1 #dce ,i4 ,iceland spar crystals2 double refraction by1 #bbf1 #bbh2 polarization of light1 #ddb1 #dde1 #ddg1 #ddi1 #dej ,illuminating power of the telescope1 #aeh1 #aff1 #afh1 #afi2 stars in ,orion1 a test of1 #afd ,images1 double1 seen through ,iceland spar1 #bbg ,inclination of the earth's axis1 #ad1 #ag ,inclination of the ecliptic1 #ag2 measured by ,eratosthenes1 #ai ,index error1 adjustments of the equatorial1 #ccj ,iron1 line spectrum of1 #djf1 #dah ,irrationality of the spectrum1 #hg ,j4 ,janssen 7,dr471 solar photography1 #dga2 discoveries in solar physics1 #dgb ,jupiter1 in ,ptolemy's system1 #c2 in ,tycho ,brahe's1 #df2 as a telescopic object1 #cea2 photographs of1 #dfe1 #dff ,jupiter's moons1 observation of their eclipses to determine 8local time10 #bhb ,k4 ,kepler's treatise on dioptrics1 #chf ,kew ,observatory1 photographs of the sun and sun-spots1 #dfj1 #dfe1 #dgj1 #dge ,kirchhoff2 spectroscope1 #cif2 spectrum analysis1 #djb1 #djc1 #dab1 #dbb1 #dbh ,kitchener 7,dr471 improved eyepiece1 #aac2 stars in ,orion1 #afd ,knobel's photometer1 #cgh ,knott1 star magnitudes1 #cha ,l4 ,lamp for equatorial telescope1 #cbe ,lamp1 electric 7see ,electric ,lamp7 ,lassell2 his ,newtonian telescope1 #ajh1 #caa2 production1 polishing1 and mounting metallic specula1 #aba1 #acb1 #add ,latitude2 observations of ,posidonius1 #h2 parallels of1 #bc ,lattice-work for tubes of telescopes1 #agb ,lenses2 action of1 #ee1 #eh1 #he2 concave and convex1 #fa1 #ga1 #ge2 amount of colour produced by1 #ha2 achromatic1 #hd2 ,hall and ,dollond's experiments1 #he2 correction for colour1 #hg2 correction for aberration in eyepieces1 #aji1 #aaf2 production of1 #aag ,lens1 crystalline1 of the eye1 #fg ,lewis 7,sir ,g4 ,c471 his 8,astronomy of the ,ancients10 #i ,liebig1 improvement in specula1 #aag ,light2 refraction1 #ee-gb2 deviation and dispersion1 #gi1 #hj1 #hb1 #hc2 decomposition and recomposition1 #hc2 reflection1 #ij-ii2 action of a reflecting surface1 #ia2 angles of incidence and reflection1 #ib2 concave and convex mirrors1 #id-ih2 velocity of1 #aei2 loss due to reflection1 #afh2 effective1 in reflectors1 #afi2 vibration of particles1 #cgc1 #dja2 polarization1 #dda-dec ,,light ,,of ,,stars1 ,,determination ,,of 7,chap4 ,,xxvi471 #cgg-che ,lindsay 7,lord71 siderostat at his observatory1 #cdg ,local time1 #bha ,longitude1 meridians of1 #bc2 as determined by ,hipparchus and ,tycho ,brahe1 #dd2 determined by clock and transit instrument1 #bhj2 expressed in degrees and time1 #bhj ,m4 ,magnesium vapour2 colour of1 #daf2 in the sun1 #dce ,magnifying power of large telescopes1 #aed1 #aee2 stars in ,orion1 a test of1 #afc ,magnitude of stars1 #cgg ,malus1 discovery of polarization by reflection1 #ddb1 #ddh ,malvasia 7,marquis71 his micrometer1 #bai1 #bba ,manlius1 gnomon erected by him at ,rome1 #ah ,maps of the stars 7see ,stars7 ,mars1 in ,ptolemy's system1 #c2 in ,tycho ,brahe's1 #df2 as a telescopic object1 #cej ,martin's method of silvering glass specula1 #ach ,mauritius1 photoheliograph at1 #dfi ,mean time1 #bed ,mean solar time clock at ,greenwich1 #bfh ,melbourne ,observatory1 great reflecting telescope1 #cab1 #cac1 #ccg2 composition and production of specula1 #abj1 #aba1 #abi2 view of optical part1 #adc2 mode of mounting speculum1 #add-adi2 photographs of the moon1 #dei ,mercurial pendulum1 #ahg1 #ahh1 #aib ,mercury1 in ,ptolemy's system1 #c2 in ,tycho ,brahe's1 #df2 as a telescopic object1 #cej ,meridian1 defined by ,euclid1 #ab ,meridional observations1 first employment of1 #bj ,meridian of ,greenwich1 #beb ,meridian circle1 the first1 #bj2 at ,cambridge 7,u4,s471 #bdh ,meridians of longitude 7see ,longitude7 ,,meridional ,,observations1 ,,modern 7,book ,,iv471 #bcc-bij ,merz 7,m471 manufacture of flint-glass discs1 #aai2 cost of large object-glasses1 #agb2 large telescopes1 #cjc ,metallic specula1 #abj1 #aga ,meton1 meridian observations by1 #be ,meudon ,observatory1 solar photography at1 #dgj ,,micrometer1 ,,the 7,chap4 ,,xv471 #bah-bcb2 wire micrometer1 #bba1 #ceb2 heliometer1 #bbd2 double image1 #bbi2 position1 #cec2 measurements made by1 #cee1 #cei-cff1 #cfh ,microscopes1 for reading transit circles1 #bdg2 for ,newall's telescope1 #cjg ,middlesborough1 time signal1 #bgh ,milky ,way1 observations of ,euclid1 #aa ,miller1 spectrum analysis1 #daj ,mirrors1 concave and convex1 #id-ih ,mirrors for reflecting telescopes 7see ,specula7 ,,modern ,,meridional ,,observations 7,book ,,iv471 #bcc-bij ,molecular vibration1 #cgc1 #dja1 #daj1 #dbi1 #ddi1 #dej ,months1 first observations of1 #e ,moon1 ,the1 in ,ptolemy's system1 #c2 motions observed by the ,chaldeans1 #d2 parallax observed by ,ptolemy1 #ce2 used by ,hipparchus to determine longitude1 #dd2 as a telescopic object1 #cej2 the lunar crater1 ,copernicus1 #ced2 measurement of shadow thrown by a lunar hill1 #cee2 photographs and stereographs1 #dei1 #dfd1 #dfe1 #dff2 part of ,beer and ,mdler's map1 #dgf2 of ,de ,la ,rue's photograph1 #dgg ,,mounting ,,of ,,large ,,telescopes 7,chap4 ,,xx471 #bic-cbg ,mounting of specula for reflecting telescopes1 #add1 #adi1 #afi ,mudge1 grinding and polishing specula1 #abi2 gravity escapement1 #bjj ,mural circle1 #bda1 #bdb ,mural quadrant1 ,tycho ,brahe's1 #bcc1 #bce ,multiple stars1 #cea ,n4 ,nebul1 #cea ,nebula of ,orion1 #aeg1 #aeh ,neptune1 as a telescopic object1 #cea ,newall's equatorial refractor1 #cjb2 with spectroscope1 #dbg2 flint-glass discs for1 #aai2 production of discs for object-glass1 #abh2 photographs of the moon1 #dei ,newcastle1 time signals1 #bgh ,newton 7,sir ,isaac71 on refracting telescopes1 #hb2 his reflecting telescope1 #aja1 #ajb2 use of pitch in polishing specula1 #abh2 refrangibility of light1 #chg2 polarized light1 #ddb ,newtonian reflector1 #adi2 view of optical part1 #adc2 effective light1 #afi2 ,grubb's form1 #cjc2 ,browning's form1 #cjd2 mounting of1 #caj ,nicols' prism1 #aae2 measurement of the light of stars1 #chj2 polarization of light1 #ddc1 #ddg1 #ddh1 #ddi1 #dej ,north pole1 diagram illustrating how it is found1 #bdi1 #bea ,o4 ,object-glasses1 production of1 #aah1 #aai2 correction of colour1 #hh2 correction for spherical aberration1 #abf2 mode of polishing1 #abh2 mode of centring1 #adj2 illustrations of defective adjustment1 #ada2 adjustment of1 #afc2 its perfection in modern telescopes1 #aff1 #cje2 cost of production1 #agb2 divided1 for duplication of image1 #bbe ,object-glass prism1 #dbf ,observatories see ,alexandrian ,museum1 ,cambridge 7,u4,s471 ,cincinnati1 ,edinburgh1 ,greenwich1 ,huen 7,tycho ,brahe's71 ,kew1 ,lord ,lindsay's1 ,mauritius1 ,melbourne1 ,meudon1 ,paris1 ,potsdam1 ,vienna1 ,washington ,observing chair for equatorial telescopes1 #cci ,optical action of the eye1 #fg2 long and short sight1 #fi1 #ga ,optical qualities of telescopes1 permanence of1 #agj ,optic axis in crystals of ,iceland spar1 #bbh 8,optick tube10 telescope so first called1 #ee1 #aci-aea ,orion1 first observations of1 #e2 ,orion and the neighbouring constellations1 #aef2 nebula of1 #aeg1 #aeh2 stars in1 a test for power of telescopes1 #afd-aff2 facilities for observing1 #afd ,p4 ,parallactic rules1 #ea2 used by ,ptolemy1 #ce2 by ,tycho ,brahe1 #ch1 #da ,parallax of the moon1 observed by ,ptolemy1 #ce ,paris ,observatory1 reflecting equatorial telescope1 #cad1 #cae1 #ccg2 siderostat1 #cdd2 photoheliograph1 #dfi ,pendulum1 #ahc1 #ahe1 #ahg1 #ahh ,personal equation1 #bei ,phosphatic glass for lenses1 #abc ,,photography1 ,,celestial 7,chap4 ,,xxxi41 ,,xxxii471 #ded-dhc ,photography1 stellar1 #agb ,photoheliograph1 for photographs of the sun1 #dfj1 #dgj2 for transit of ,venus 7#ahgd71 #dfa ,photometry1 #cgc1 #cgg ,,physics1 ,,astronomical 7,book ,,vi471 #cga ,,physical ,,inquiry1 ,,general ,,field ,,of 7,chap4 ,,xxv471 #cga-cgf ,picard1 transit circle1 #bhd ,pisces1 its position in the zodiac1 #cd ,pitch employed in polishing lenses and specula1 #abh1 #acb ,plane of the ecliptic1 #ac1 #ad ,planets1 in ,ptolemy's system1 #c2 first observations of conjunction1 #d1 #e2 motions observed by ,autolycus1 #i2 in ,tycho ,brahe's system1 #df2 ,saturn seen with object-glasses of #c and #bf inches1 #afj1 #afa2 as telescopic objects1 #cej2 photographs of1 #dfe ,pleiades1 the first observations of1 #e ,plcker1 spectrum analysis1 #dac ,pogson1 star magnitudes1 #cha1 #chb ,pointers of pre-telescopic instruments1 #ce1 #di1 #bad1 #baf ,polar axis of the equatorial1 #bii1 #cjb1 #cjh1 #caa1 #cab1 #cbd1 #cbh1 #cbi1 #cdf ,polariscope1 #dda-dec ,polarization of light1 #dda-dec ,pole1 ,north1 #bch2 diagram illustrating how it is found1 #bdi ,pole star1 first observations of1 #f2 observations of ,euclid1 #aj1 #ad2 its position1 #bch ,polishing lenses and specula1 #abh1 #aga2 ,lord ,rosse's polishing machine1 #aca2 ,mr4 ,lassell's1 #acb ,posidonius1 measurement of the earth's circumference1 #h ,position circle1 #cec ,position micrometer1 #cec1 #ceh ,post ,office ,telegraphs1 for distribution of ,greenwich time1 #bge ,potsdam1 photoheliograph at1 #dfi ,precession of the equinoxes1 #cc ,prime-vertical1 #bhe ,prime-vertical instrument1 #bhg ,primum mobile of ,ptolemy1 #c ,prisms1 action of1 #ee2 crown and flint-glass1 #hc1 #hd2 water1 #he2 doubly refracting1 for the micrometer1 #bbf2 direct vision1 #djj2 in the spectroscope1 #cic-djj2 object-glass prism1 #dbf ,ptolemy1 the ,heavens according to1 #c2 trigonometrical tables1 #ag2 sun's altitude1 #ba2 his discoveries1 #ce2 parallax of the moon1 #ce2 his measurement of time1 #cf2 parallactic rules1 #ch1 #ea ,purbach1 observation of altitudes by1 #cf ,pyramids1 the first constructed astronomical instruments1 #e1 #f ,q4 ,quadrants used by ,tycho ,brahe1 #ch2 his quadrans maximus1 #dh ,quadrant1 mural1 #bcc1 #bce ,quartz crystals for polarizing light1 #dej1 #deb ,r4 ,radiation of stars1 visual1 #chc2 thermal1 #che ,radiation1 general and selective1 #djc1 #djh ,ramsden's eyepiece1 #aab1 #bab ,reading microscopes1 for ,greenwich and ,cambridge 7,u4,s47 transit circles1 #bdg2 for ,newall's telescope1 #cjg ,red stars 7see ,colour of ,stars7 ,reflection of light 7see ,light7 ,reflecting telescopes 7see ,telescope7 ,reflective powers1 ,sir ,john ,herschel's table of1 #afh ,reflector1 diagonal1 for solar observations1 #aad ,reflecting and refracting telescopes compared1 #agj ,reflex zenith-tube at ,greenwich1 #bhf ,refracting telescopes 7see ,telescopes7 ,refracting and reflecting telescopes compared1 #agj ,refraction of light 7see ,light7 ,refraction1 double1 by crystals of ,iceland spar 7see ,iceland ,spar7 ,refrangibility of colours1 #chg2 of light1 #dbj ,regiomontanus1 altitudes measured by1 #cf ,regulation of clocks by electricity1 #bgb ,rising of stars 7see ,stars7 ,right ascension1 #bd1 #bcd1 #bda1 #bdi1 #beg2 measured by ,hipparchus1 #dd2 by ,tycho ,brahe1 #de ,ring micrometer1 #cfh ,robinson 7,dr471 specula of ,melbourne telescope1 #abi2 apertures of object-glasses1 #afh ,rockets fired as time signals1 #bha ,rmer1 wires in a transit eyepiece1 #bbj2 transit circle and transit instrument1 #bhd ,rosse 7,lord71 his reflecting telescope1 #ajh1 #bid1 #caa1 #cab2 composition of reflector1 #abj2 production of metallic specula1 #aba1 #aca2 nebula of ,orion as seen by his reflector1 #aeg1 #aeh2 illuminating power of his telescope1 #aei2 effective light1 #afi2 thermopile observations1 #chd ,royal ,observatory1 ,greenwich 7see ,greenwich7 ,rudolph ,,ii4 7,emperor71 his patronage of ,tycho ,brahe1 #db ,rumford's photometer1 #cgg ,rutherfurd1 his work in celestial photography1 #dee1 #dfd1 #dff1 #dga1 #dgg1 #dhj ,s4 ,salts1 flame of1 in a ,bunsen's burner1 #djg ,sand clocks and sand glasses1 #agf ,saturn1 in ,ptolemy's system1 #c2 in ,tycho ,brahe's1 #df2 as seen with a #c inch and #bf inch object-glass1 #afj1 #afa2 as a telescopic object1 #cea2 mode of measuring its rings1 #ceg2 photographs of1 #dfe1 #dff ,savart's analyser for polarization of light1 #deb ,scarphie1 employed by ,eratosthenes1 #ai ,scheiner's telescope1 #gh ,seasons1 ,the1 #ae1 #af ,secchi 7,father71 direct-vision star spectroscope1 #dca2 stellar spectra1 #dcc ,setting of stars 7see ,stars7 ,sextants used by ,tycho ,brahe1 #ch1 #ej ,sidereal clock1 #bed1 #bff 7see ,clock7 ,sidereal day1 #bef ,sidereal time1 #bdj1 #bed1 #cbd ,,siderostat1 ,,the 7,chap4 ,,xxiii471 #cdc-cdh1 #dfa2 at ,lord ,lindsay's ,observatory1 #cdg ,signals for distributing 8,greenwich time10 #bgh ,signals1 time1 #bha1 #bhc ,signs of the zodiac 7see ,zodiac7 ,silver-on-glass reflector at the ,paris ,observatory1 #caf ,silvering glass specula1 modes of1 #acg2 silvered glass reflectors1 #aga ,simms1 his introduction of the collimator in the spectroscope1 #cic1 #dbe ,sirius1 first observations of1 #e2 spectrum of1 #dcb ,slough1 ,sir ,wm4 ,herschel's telescope at1 #bid ,smyth 7,admiral71 stars in ,orion1 #afe2 colours of stars1 #cea2 star magnitudes1 #cha ,smyth 7,prof4 ,piazzi71 on the pyramids as astronomical instruments1 #f2 position of the vernal equinox1 #cd2 clock arrangements at ,edinburgh ,observatory1 #bfi ,sodium1 discovery of its presence in the sun1 #dab ,solar photography1 #dei1 #dfe ,solar spectroscope1 #dce2 ,browning's and ,grubb's forms1 #dbh ,solar spectrum1 #cij1 #cia1 #cib1 #dbc1 #dcc1 #dcf1 #dch1 #dci2 photographs of1 #dgi1 #dhj ,solar time1 #bec1 #bee ,solstices1 first observations of the1 #ae1 #af1 #ag1 #bb ,southing of stars1 #bcd ,,space ,,measurers 7,book ,,iii471 #ace-bcb2 circle reading1 #baa2 ,digges' diagonal scale1 #bac2 the vernier1 #bad2 micrometers1 #bah ,space-penetrating power of the telescope1 #aed2 stars in ,orion1 a test of1 #afe ,spectroscope1 construction of the1 #cic-djj2 automatic1 #cig2 arranged for showing absorption1 #dji2 attached to ,newall's refractor1 #dbg2 solar1 ,browning's and ,grubb's forms1 #dbh ,spectrum produced by prisms1 irrationality of the1 #hf1 #hg ,spectrum1 solar1 #cij1 #cia1 #cib ,spectrum analysis1 principles of1 #dja-dba ,specula1 production of1 #aag1 #abj2 casting1 annealing1 #aba2 curvature1 #abb2 grinding1 #abg2 polishing1 #abh2 silvering1 #acg2 mounting1 #adb1 #afi1 #agb2 effective light1 #afi2 repolishing1 #aga2 cost as compared with object-glasses1 #agb ,spherical aberration1 #hg2 diagram illustrating1 #ajd1 #aje2 its correction in eyepieces1 #aji1 #aaa2 of specula1 #abc1 #abd ,sprengel pump1 #dac ,spring governor of driving-clock for large telescopes1 #cai1 #cbj 8,spurious disc0 of fixed stars1 #afc ,standard clock at ,edinburgh ,observatory1 #bgb ,standard sidereal clock of ,greenwich ,observatory1 #bfg ,standard solar time clock of ,greenwich ,observatory1 #bfg ,,stars1 ,,chemistry ,,of ,,the 7,chap4 ,,xxvii4-,,xxx471 #chf-dec ,,stars1 ,,light ,,and ,,heat ,,of 7,chap4 ,,xxvi471 #cgg2 variable1 #cgg-che ,stars1 first observations of the1 #d1 #e1 #f1 #g2 first maps of1 #h2 observations of ,autolycus1 ,euclid1 and ,posidonius1 #h1 #aj2 first catalogues of1 #ai2 latitude and longitude of1 #bd1 #cj2 positions tabulated by ,hipparchus1 #cj2 ,tycho ,brahe's catalogue and map of1 #db1 #dd2 stars in ,gemini seen through a large telescope1 #aee2 nebula of ,orion1 #aeg2 ,orion and its neighbourhood1 #aef2 double1 as defined by telescopes of different power1 #afb1 #afd1 #afg1 #afg2 distance of stars from the earth1 #aei2 facilities for observing ,orion1 its stars1 a test for power of telescopes1 #afd2 stellar photography1 #agb1 #dfe1 #dff1 #dfg1 #dgh2 their rising and setting as measurers of time1 #agf2 double1 measurement of1 #cei1 #cfa1 #cfb2 spectrum of red star1 #dcc ,star-clusters1 double and multiple stars1 #cea ,star-spectra1 from ,father ,secchi's observations1 #dcc2 photographs of1 #dgi ,star spectroscopes1 at ,cambridge 7,u4,s471 #dcj2 direct vision1 #dca ,star-time 7see ,sidereal ,time7 ,steinheil1 improvement of specula1 #aag ,stellar day1 #bef ,stereographs of the moon1 #dfe1 #dff ,sternberg1 ,tycho ,brahe's ,observatory1 #ch ,stewart 7,prof4 ,balfour71 spectrum analysis1 #djb2 solar photography1 #dga ,stokes 7,prof471 experiments with phosphatic glass1 #abc2 spectrum analysis1 #djb1 #daj ,stone1 thermopile at ,greenwich1 #chd ,strontium in the sun1 #dai ,struve1 transit instrument1 #bhe2 double stars1 #cfb2 star magnitudes1 #cha ,sun1 ,the2 in ,ptolemy's system1 #c2 first determination of its yearly course1 #h1 #ae2 course in the zodiac1 described by ,autolycus1 #i2 altitude determined by the gnomon1 #af1 #ah2 and the ,scarphie1 #ai1 #bj2 telescopes for observing1 #aad2 8mean sun10 #bef2 as a telescopic object1 #cdi2 presence of sodium in1 #dab1 #dae2 vapour of other metals1 #dag2 absorption spectrum1 #dah2 telespectroscopic observations1 #dcf2 of the chromosphere1 #dcg2 sun-storms1 #dch1 #dci2 photographs1 #dei1 #dfi1 #dgj ,sun-dials1 #ah ,sun-spots observed by ,galileo and ,scheiner1 #gh2 examined by the position micrometer1 #ceh2 spectra of1 #dae1 #dce ,sunderland time signals1 #bgh ,t4 ,talcott1 zenith telescope designed by1 #bhe ,taurus1 its position in the zodiac1 #cd ,telegraph wires1 their application in determining 8local time10 #bha ,,telepolariscope1 ,,the 7,chap4 ,,xxx471 #dda-dec ,telespectroscope1 #dbf ,,telescope1 ,,the 7,book ,,ii471 #ee-agb ,,telescope1 ,,the ,,equatorial 7,book ,v471 #bic-cfh ,,telescope3--,,various ,,methods ,,of ,,mounting ,,large ,,telescopes 7,chap4 ,,xx471 #bic-cbg2 refracting1 #gc-hi2 ,galilean1 #gc2 magnifying power of the telescope1 #gf1 #gi2 ,scheiner's telescope1 #gh2 focal length of early telescopes1 #gi2 achromatic1 #hf2 reflecting1 #ajj-ajh2 ,gregory's telescope1 #aja2 ,newton's1 #ajb2 ,cassegrain's1 #ajc2 ,sir ,w4 ,herschel's #ajc1 #ajh2 ,lord ,rosse's1 ,de ,la ,rue's1 ,lassell's1 ,foucault's1 ,grubb's1 #ajh2 eyepieces1 #aji-aaf2 ,huyghen's eyepiece1 #aaj2 ,ramsden's eyepiece1 #aab2 magnifying power of eyepieces1 #aaf2 lenses and specula1 #aag-ach2 flint glass for lenses1 #aai2 the 8optick tube10 #aci-aea2 the modern telescope1 #aeb-agb2 magnifying and space penetrating power1 #aed1 #aee2 illuminating power1 #aeh2 defining power1 #afj2 reflecting and refracting compared1 #agj2 permanence of optical qualities1 #agj2 8telescopic sight10 #bai2 ,sir ,wm4 ,herschel's at ,slough1 #bid2 ,lord ,rosse's reflector1 #bid1 #caa1 #cab2 refractor on alt-azimuth tripod1 #bif2 simple equatorial mounting1 #bih2 the ,german mounting1 #bii2 ,washington great equatorial1 #cji2 ,english mounting1 #caj2 forked mounting1 #caj2 ,greenwich equatorial1 #caj2 ,melbourne reflector1 #cab1 #cac2 ,paris reflector1 #cad2 driving clock1 #cah2 ,newall's refractor with spectroscope1 #dbg2 ,de ,la ,rue's1 #dei2 ,rutherfurd's1 #dff2 ,newall's1 #dei2 ,melbourne1 #dei ,telescope1 zenith 7see ,zenith ,telescope7 ,temperature1 its effect on the pendulum1 #ahg1 #aic ,terrestrial globe1 #bc ,thales1 his employment of the gnomon1 #ag ,theodolite1 #bhh ,theodolite1 astronomical1 #bhg ,thermometry1 #cgd1 #chd ,thermopile1 #cgd ,time2 first reckoning of1 #ai2 early measurements1 #cf1 #dd1 #age2 modern measurement of1 #bec2 sidereal1 solar1 and mean1 #bed1 #bef ,,time ,,and ,,space ,,measurers 7,book ,,iii471 #age-bcb ,time1 ,greenwich 7see ,greenwich ,time7 ,time1 local1 #bha ,time balls for distributing ,greenwich time1 #bge ,time signals1 #bgh1 #bha1 #bhc ,timocharis1 his observations in the ,alexandrian museum1 #ai ,tourmaline1 in polarization of light1 #ddc ,,transit ,,circle1 ,,the 7,chap4 ,,xvi471 #bcc-beb2 system of wires in eyepiece1 #bbj2 at ,greenwich and ,cambridge 7,u4,s471 #bdg1 #bdh1 #bea2 mode of using1 #bec1 #bhd ,,transit ,,clock1 ,,the 7,chap4 ,,xvii471 #bec-bgj ,transit instrument1 #aga1 #bcd1 #bcf1 #bcg2 mode of using1 #bec2 ,rmer's1 #bhd2 ,struve's1 #bhe ,transit of ,venus1 photographic observations1 #dge ,trigonometrical tables1 first construction of1 #ag ,tropics1 defined by ,euclid1 #ab ,trouvelot1 ring of ,saturn observed with the ,washington refractor1 #afa ,tube of the telescope1 #aci-aea ,tycho ,brahe2 astrolabe1 #bf2 ecliptic astrolabe1 #bh2 discoveries of1 #cg-eb2 biography of1 #cg2 list of his instruments1 #ch2 portrait1 #ci2 catalogue of stars1 #db2 observatory 7engraving71 #dc1 #bhg2 his solar system1 #df2 discovery of comet of #afgg1 #dg2 instruments for measuring distances and altitudes of stars1 #ea2 clocks1 #agi1 #ahd1 #aif2 diagonal scale for measuring space1 #bac2 mural quadrant1 #bcc2 transit circle1 #bhd ,u4 ,united ,states ,naval ,observatory1 #cda ,uranus1 as a telescopic object1 #cea ,uraniberg1 ,tycho ,brahe's ,observatory1 #ch ,v4 ,variable stars1 #cgg ,velocity of gases in sun-storms1 #ddj ,venice1 ancient clock dials1 #beg ,venus1 in ,ptolemy's system1 #c2 in ,tycho ,brahe's1 #df2 employed by ,tycho ,brahe in determining longitude1 #dd2 as a telescopic object1 #cej2 transit of1 instrument used in the expedition of #ahgd1 #bcf2 photographic observations1 #dge ,vibrations1 ethereal1 #cgc1 #dja1 #daj1 #ddi1 #dej ,vienna1 refracting telescope1 #ada ,villarceau1 ,yvon1 driving clocks1 #cbd ,vega1 heat of1 #che ,vernal equinox1 its position in the constellations1 #cd ,vernier1 the1 #bad ,vertical circle1 ,ertel's1 #bij ,w4 ,walther1 altitudes measured by1 #cf ,washington ,observatory2 great refracting telescope1 #cjb1 #cji2 flint glass discs1 #aai2 ring of ,saturn seen through it1 #afa ,watches1 detached lever escapement for1 #bjg ,water clocks1 #agf ,wave-lengths of light of solar gases1 #ddj ,westminster clock-tower1 #bgg ,wheatstone 7,sir ,c472 8chronographic method0 of transit observation1 #bei2 apparatus for controlling clocks1 #bga ,winlock 7,prof471 photographs of the sun1 #dfa ,wires1 cross1 for circle reading1 #bab1 #baf2 system of wires in a transit eyepiece1 #bbj1 #bcd1 #beg2 in eyepiece of ,greenwich transit circle1 #bdf2 wires of the transit instrument1 #bcd ,wire micrometer1 #bba1 #ceb ,wolfius1 correction of chromatic aberration in lenses1 #hi ,wollaston 7,dr471 lines in the solar spectrum1 #cia2 spectrum analysis1 #djb1 #dbb ,wyck 7,henry de71 clock made in #acfd by1 #agh ,y4 ,ys of the transit instrument1 #bch1 #bhd ,years1 first observation of1 #e2 determination of their length1 #bb ,z4 ,zenith1 zenith sector1 zenith telescope1 reflex zenith tube1 at ,greenwich1 #bhe ,zenith distances1 measurement of1 #ea ,zodiac1 first defined1 #h1 #i2 observations of ,euclid1 #aa1 #ab2 of ,denderah1 #g ,zllner's astrophotometer1 #cgi ,zero of right ascension1 #bdi ,zinc in the sun1 #dai ,,the ,,end4 ,,london3 ,r4 ,,clay1 ,,sons1 ,,and ,,taylor1 ,,bread ,,street ,,hill1 ,e4,c4 ,,transcriber',s ,,notes #a4 ,silently corrected typographical errors4 #b4 ,retained anachronistic and non-standard spellings as printed4 #c4 ,enclosed italics font in underscores4 #d4 ,enclosed bold font in equals4 #e4 ,superscripts are denoted by a carat before a single superscript character or a series of superscripted characters enclosed in curly braces1 e4g4 ,mr4 or ,mister4 #f4 ,subscripts are denoted by an underscore before a series of subscripted characters enclosed in curly braces1 e4g4 ,h#b,o4