,trust7 ,the following typographical transcription has been used for this e-text3 text represents text printed in italics1 text represents text in bold face1 and text represents blackletter text4 ,superscript texts have been transcribed as text4 ,small capitals have been changed to capitals4 ,t represents a ,t shape rather than the letter ,t4 ,more ,transcriber's ,notes may be found at the end of the text4 ,,the ,,draughtsman',s ,,handbook ,,of ,,plan ,,and ,,map ,,drawing4 ,illustration3 ,,plate #a4 ,,plan ,,shewing ,,principal ,,characters ,,of ,,work ,,used ,,in ,,mapping4 ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,,the ,,draughtsman',s ,,handbook ,,of ,,plan ,,and ,,map ,,drawing1 ,,including ,,instructions ,,for ,,the ,,preparation ,,of ,,engineering1 ,,architectural1 ,,and ,,mechanical ,,drawings4 ,with ,numerous ,illustrations and ,coloured ,examples4 ,,by ,,george ,g4 ,,andr1 ,c4,e41 ,m4,s4,e4 ,illustration ,,london3 ,e4 ,f4 ,n4 ,,spon1 #dh1 ,,charing ,,cross4 ,,new ,,york3 #ddf1 ,,broome ,,street4 #ahgd4 ,,preface4 ,the main purpose of the present work is to be a handy book of reference for draughtsmen engaged chiefly in ,topographical ,drawings4 ,but to have limited its use to one class of draughtsmen1 and especially to the skilled members of that class1 would have necessitated the discovery of more cogent reasons for its publication than its author has yet been able to adduce4 ,works of such a character exist already1 and though their imperfections are numerous1 they fulfil their purpose in a fairly satisfactory manner4 ,but had the field been clear in this direction1 it is so restricted in extent that to have entered upon it would have been to undertake a labour that promised little fruit1 for such a work could be only of small utility even to those for whom it was specially intended4 ,it was1 therefore1 determined to make the present handbook generally useful by giving it a much wider scope4 ,and hence1 if the intention has been efficiently carried out1 it may claim a place in every drawing office1 be it that of the ,topographer1 the ,hydrographer1 the ,surveyor1 the ,military1 ,civil1 or ,mechanical ,engineer1 or the ,architect4 ,whether or not this degree of success has been achieved1 is not for the author to judge4 ,but should he have failed to reach the high mark at which he has aimed1 he hopes1 with some degree of confidence1 that he has at least succeeded in producing a book which the experienced draughtsman will find valuable as a book of reference1 and which the pupil may constantly consult with profit4 ,a want has long been felt by draughtsmen for some work of this kind to which they might refer their pupils in the office1 and it may not be presumptive to suppose that the present work has supplied that want4 ,to render it convenient for this twofold purpose1 it has been divided into two parts4 ,in the first part the principles and practices of the art have been clearly but briefly explained and illustrated2 while in the second part1 the application of the principles previously learned has been treated of1 and such information given as relates directly to the duties of the practitioner4 ,of course1 in a work of the present character1 originality in the matter is neither to be expected nor desired2 enough if the manner shows some novelty1 and is such as to add value to the matter4 ,although the preparation of maps and plans has received the chief share of attention1 engineering1 architectural1 and mechanical drawings have been largely treated of4 ,projection1 orthographic1 isometric and perspective1 has been altogether omitted as beyond the scope of the work2 but ,colouring and ,shading have been fully considered and profusely illustrated4 ,the ,plates appended as examples for reference are numerous and varied in character2 they have been specially prepared by ,b4 ,alexander1 to whom the author offers his warmest thanks for the truly admirable manner in which he has executed the work entrusted to him4 #af1 ,,craven ,,street1 ,,charing ,,cross1 ,september #gth1 #ahgd4 ,,contents4 ,,part ,i4--,,the ,,essential ,,elements4 ,,section ,i4--,,the ,,drawing ,,office ,,and ,,its ,,furnishings4 ,,page ,the ,drawing ,office #a ,instruments #b ,materials #e ,precautions and ,remarks #i ,,section ,,ii4--,,geometrical ,,problems4 #ae ,,section ,,iii4--,,lines1 ,,dots1 ,,and ,,their ,,combinations4 ,straight and ,curved ,lines #bg ,lines of uneven thickness #cj ,the ,broken ,line #cj ,the ,dotted ,line #ca ,combinations of ,straight1 ,broken1 and ,dotted ,lines #ca ,the ,wavy ,line #cc ,grass-land #cd ,swamps and ,marshy ,ground #ce ,sand and ,gravel #ce ,woodland #cf ,uncultivated ,land #cg ,contour ,lines #cg ,,section ,,iv4--,,colours4 ,flat-tints #dj ,conventional ,colours #dd ,water #de ,grass-land #de ,marsh #de ,sand and ,gravel #df ,mud #df ,woodland #df ,cultivated ,land #dg ,uncultivated ,land #dg ,buildings #dg ,roads and ,streets #dg ,fences #dg ,,section ,v4--,,shading4 ,application of ,shade ,lines #dh ,cylindrical ,surfaces #ej ,shading ,lines #ej ,shading ,lines on ,cylindrical ,surfaces #ea ,shading ,lines in ,topographical ,drawings #eb ,the ,vertical ,system of ,shading #eg ,shading in ,colours #fc ,hill ,slopes #fc ,cylindrical ,surfaces in ,mechanical ,drawings #fd ,,part ,,ii4--,,applications4 ,,section ,i4--,,lettering1 ,,bordering1 ,,and ,,north ,,points4 ,lettering #ff ,borders #fi ,north ,points #fi ,,section ,,ii4--,,scales4 ,scales of ,distances #gj ,scales of ,construction #gd ,,section ,,iii4--,,plotting4 ,reference ,lines and ,points #gh ,plotted ,points #gh ,to ,plot ,reference ,lines and ,points #gh ,to ,plot ,traverse ,reference ,lines #hd ,to ,plot ,detail #hi ,to ,plot ,contours #ij ,to ,plot ,sounded ,points in ,submerged ,districts #ij ,errors and ,error-sheets #ia ,to ,plot ,vertical ,sections #ib ,to lay down ,gradients #ie ,to ,plot a ,section from a ,contour ,map #if ,,section ,,iv4--,,civil ,,engineers' ,,and ,,surveyors' ,,plans4 ,standing ,orders of ,parliament #ih ,documents required #ii ,plans #ajj ,book of ,reference #aja ,sections #aja ,working ,sections #ajc ,regulations of ,local ,government ,board3-- ,boundary ,maps #ajd ,maps for ,division into ,wards #ajd ,plans of ,proposed ,works #aje ,general ,plan #aje ,detailed ,plan #ajf ,mining ,plans #ajf ,estate and ,town ,plans #ajg ,,section ,v4--,,map ,,drawing4 ,single ,stroke ,streams #aji ,double ,line ,streams and ,rivers #aaj ,colouring ,streams or ,rivers #aaj ,islands and ,sand-banks1 ,sandy and ,pebbly ,beds of ,rivers #aaj ,roads and ,pathways #aaa ,mountain ,passes #aaa ,fords and ,ferries1 ,toll-gates #aaa ,telegraph ,lines and ,stations #aab ,railways1 ,stations1 and ,termini #aab ,size of ,cities1 ,towns1 and ,villages #aab ,sketching1 ,shading1 and ,copying ,hills #aac ,field ,sketching #aad ,examination of ,maps in the ,field #aah ,,section ,,vi4--,,mechanical ,,and ,,architectural ,,drawings4 #aba ,,section ,,vii4--,,copying ,,and ,,reducing4 ,drawing from ,copy #abg ,copying by ,tracing #abh ,copying by ,transfer #abi ,reducing and ,enlarging #acj ,the ,pantograph #aca ,the ,eidograph #acf ,drawings for ,lithographers and ,engravers #ada ,,trigonometrical ,,formul #adb ,,inclined ,,measure #adc ,,curvature ,,and ,,refraction #adc ,,index #add ,,list ,,of ,,illustrations4 ---------------------------------------- -------------------------- ,page4 ,plate4 ---------------------------- ,,alphabets1 examples of 44 #d1 #e1 #f ,angle1 to bisect #af 44 ,angles1 to construct #af1 #ag 44 ,arch1 equilateral #bc 44 ----1 horse-shoe #bd 44 ----1 lancet #bd 44 ----1 obtuse #bd 44 ----1 ogee #be 44 ----1 semi-elliptical #bc 44 ----1 ,tudor #bd 44 ,architectural drawings1 colouring of4 44 #bd ,,borders 44 #a1 #c1 #h1 #i1 #ac ,boundaries1 parish1 c4 44 #c1 #ae ,,canal ,,locks 44 #a1 #aa ,chart1 example of 44 #ah ,cinquefoil1 ,gothic #bf 44 ,circle1 to describe through #ag 44 given points4 ----1 to find the centre of #ah 44 ,cliffs 44 #a1 #aa1 #ad ,colouring architectural drawings4 44 #bd ---- maps and plans 44 #a1 #c1 #ac1 #ag1 #bh1 #cc ---- mechanical drawings 44 #bb1 #bc1 #bg ,copse 44 #a1 #aj ,corners 44 #a1 #c1 #h1 #i1 #ac ,cylinders shaded #ea1 #eb 44 ,cyma recta #be 44 ---- reversa #be 44 ,,docks 44 #a1 #aa ,drawings1 architectural1 colouring of4 44 #bd ----1 isometrical 44 #bg ----1 mechanical1 colouring of4 44 #bb1 #bc1 #bg ,,eidograph 44 #bf ,ellipse1 to draw #bb 44 ,equilateral triangle1 to construct4 #af 44 ,,flourishes 44 #be ,fortifications1 plans 44 #cb ----1 sections 44 #ca ,,geological ,,maps 44 #bh ---- sections1 coloured 44 #bj1 #ba ,grass #cd #a1 #ag ,gravel #ce #a ,,harbours 44 #aa ,hexagon1 to describe #ba 44 ,hill shading #ec1 #ee1 #ef1 44 #eh1 #fa1 #fb1 #fc ,hills 44 #a1 #ab1 #ad1 #ag ---- in colour 44 #ab1 #ad ,,isometrical ,,drawings 44 #bg ,,lakes 44 #a1 #c1 #aa1 #ag ,land1 cultivated #cb #a1 #ac ----1 uncultivated #cg 44 ,lettering1 examples of 44 #d1 #e1 #f1 #g1 #h1 #be ,line1 to divide into equal parts4 #ae 44 ,lines1 broken #cj 44 ----1 contour #cg 44 ----1 dotted #ca 44 ----1 section #bi 44 ----1 shade #di 44 ----1 to bisect #ae 44 ,,maps1 geological 44 #bh ----1 ,ordnance1 example of4 44 #ah ---- and plans1 colouring of4 44 #a1 #c1 #ac1 #ag1 #bh1 #cc ,marsh #ce #a1 #aj1 #aa ,mechanical drawings1 colouring of4 44 #bb1 #bc1 #bg ,mining plans 44 #cc ,,north ,,points 44 #i ,,oval1 to construct #ah 44 ,,pantograph 44 #bf ,parabola1 to draw #ba 44 ,pentagon1 to describe #bj 44 ,perpendicular1 to erect #ae 44 ,plans1 estate 44 #c1 #ag ----1 fortifications 44 #cb ----1 mining 44 #cc ----1 office 44 #b ----1 parliamentary 44 #ac1 #ai ----1 reducing or enlarging 44 #bf ----1 town improvements 44 #ac ---- and maps1 colouring of4 44 #a1 #c1 #ac1 #ag1 #bh1 #cc ,plotting1 examples of #hb1 #he1 #hf1 44 #hh1 #ic ,,quarries 44 #a ,quatrefoil1 ,gothic #bf 44 ,,radii ,,of ,,circle1 to draw #ah 44 ,railways 44 #a1 #c ,rectangles1 similar1 to construct #bj 44 ,rivers 44 #a1 #aa1 #ab1 #ag ----1 outlines of #cj 44 ,roads 44 #a1 #c1 #ab1 #ag ,rocks 44 #a1 #aa ,roofs #cj 44 ,,sand #ce #a ---- banks 44 #a1 #aa ,scales #ga1 #ge1 #gf #b1 #c1 #h1 #i1 #ac ,section plotting1 example of #ic 44 ,sections1 fortifications 44 #ca ----1 parliamentary 44 #ai1 #ba ---- of strata1 examples of colouring4 44 #bj1 #ba ,shade1 scales of1 for hills #ec1 #eh 44 ,signs1 various1 used in ,indian and 44 #bi1 #cj ,colonial maps4 ----1 ----1 used in maps1 plans1 c4 44 #ae1 #af ----1 ----1 used in military maps and 44 #ca1 #cb fortifications4 ,soundings 44 #aa1 #ah ,square1 to construct #ai 44 ----1 multiple of1 to construct4 #ai 44 ,squares1 proportional1 to construct4 #ai1 #bj 44 ,swamps and marshy ground4 #ce #a1 #aj ,,tangent1 to draw #ah 44 ,titles1 examples of 44 #c1 #g1 #h ,towns 44 #a1 #c1 #aa1 #ac ,traverse plotting1 example of4 #he1 #hf1 #hh 44 ,trees #cf #a1 #c1 #aj1 #ac1 #ag ,trefoil1 ,gothic #be 44 ,triangles1 to construct #af1 #ag 44 ,,villages 44 #a ,,water1 flowing #cc #aa ----1 standing #bi #a1 #aa ---- in section #cj 44 ,wood-graining #cb 44 ,wood in section #cb 44 ,woods #cf #a1 #c1 #aj1 #ag ---------------------------------------- -------------------------- ,,plan ,,and ,,map ,,drawing4 ,,part ,i4--,,the ,,essential ,,elements4 ,,section ,i4--,,the ,,drawing ,,office ,,and ,,its ,,furnishings4 ,there are few occupations so dependent for their correct performance upon minute matters of detail as that of the draughtsman4 ,things apparently the most trivial are sufficient to render inaccurate or to mar the appearance of the otherwise most carefully and skilfully executed design1 and as the value of a drawing depends wholly upon its accuracy and its appearance1 it is obvious that such matters of detail1 however trivial they may be in themselves1 demand careful attention4 ,we have1 therefore1 deemed it desirable to preface our remarks on ,plan and ,map ,drawing with a brief description of the instruments and materials required1 and of the mode of using them which experience has shown to be the best4 ,the ,drawing ,office4--,the first essentials of a room for drawing in are--that it shall be quite free from damp and be well lighted4 ,the position of the windows is a matter of some importance1 and though persons have largely to accommodate themselves to circumstances in this respect1 it is desirable to know what are the most suitable conditions1 in order that they may be complied with as far as circumstances permit4 ,skylights are unsuitable1 because the light entering from above is liable to be intercepted by the body1 and especially by the hands of the draughtsman2 besides which1 the light from a skylight is seldom sufficient4 ,for the same reasons1 a window placed very high in the room is objectionable4 ,when possible1 a western aspect is to be preferred1 as the light from this direction is less variable and lasts later in the day than from other directions4 ,blinds of some kind are necessary to modify the light when the sun shines directly upon the window4 ,gaslights should be situate about #c feet above the drawing table1 and there should be two burners1 placed not less than #b feet apart1 as otherwise the hands and the instruments will cast shadows which will prevent fine lines and points from being seen4 ,the drawing table should be placed under the window2 it should have a breadth of about #b feet #f inches1 and its height should be #c feet #h inches at the back and #c feet #f inches at the front4 ,the front edge should be rounded over4 ,dusters and means for washing the hands must also be provided1 as it is requisite to frequently dust the paper and the instruments1 and to keep the hands perfectly clean4 ,instruments4--,all drawing instruments should be of the best workmanship1 for it is impossible to obtain accuracy with imperfect tools1 and they must be kept in order by careful handling4 ,for all kinds of drawing1 compasses of three sizes are required1 the ordinary compass1 the bows1 and the spring bows4 ,the best compasses are those which are sector-jointed4 ,the points should be kept sufficiently sharp not to slip on the paper1 but not so sharp as to readily penetrate it4 ,it is also important that the points be thin and round1 as otherwise1 when several arcs have to be struck from the same centre1 the compass leg is apt to make a large hole1 which is utterly destructive of accuracy4 ,the pencil leg should be kept exactly equal in length to the steel leg1 for true circles cannot be drawn when one leg is shorter than the other4 ,in removing the movable leg1 care should be taken to draw it straight out1 as nothing spoils the instrument so soon as wrenching the leg from side to side4 ,in using the compasses1 the instrument should be held lightly between the thumb and the forefinger only4 ,it should not be pressed upon the paper2 but it should rest equally upon both points4 ,if the weight of the hand be thrown upon the instrument the points will penetrate the paper4 ,care should also be taken to bend the joints so as to keep both legs perpendicular to the paper4 ,if attention be not given to this matter1 the steel leg will make a large hole in the paper1 and the ink leg will make a ragged line1 because only one of the nibs will touch4 ,next in importance to the compass1 and of more frequent use1 is the drawing pen4 ,the draughtsman should possess at least two of these instruments1 one for fine1 and another for medium lines4 ,when the proper opening of the nibs for fine lines has once been obtained1 it is desirable not to change it2 the pen can always be cleaned by passing a piece of drawing paper between the nibs4 ,the cleaning of the pen should be carefully attended to2 it should never be put away without having every particle of dried ink removed from it2 and frequently1 while in use1 it should be wiped out to remove the dust1 which is constantly settling in it1 as well as the particles of lead that are taken up from the paper4 ,the ink is supplied by breathing between the nibs and dipping them in the liquid1 or by means of a camel's hair brush4 ,when the latter method is adopted1 care should be taken to protect the brush from the dust floating in the atmosphere of the room4 ,after considerable wear1 the drawing pen will require setting4 ,the operation of setting requires some judgment and considerable practice1 and is one of those mechanical niceties which it is difficult to describe4 ,generally it will be found advantageous to have the pen set by an instrument maker4 ,as1 however1 this resource is not always at hand1 it is desirable that the draughtsman should be able to set his own pen4 ,the following description of the operation given by ,w4 ,binns1 in his admirable work on ,projection1 is the best we have seen4 8,the nibs must be precisely of the same length1 rounded in two directions1 and as sharp as it is possible to make them without producing to the touch a sensation of cutting1 and without scratching the surface of the paper when drawing a line1 which is generally the case when one nib is longer than the other4 ,this irregularity may be detected by placing alternately the sides of the pen at an acute angle with the forefinger1 and slipping the edge of the nail over the point1 when the difference in length will be at once perceived2 and it may be reduced by drawing a few lines1 as it were1 on a turkey stone1 with the pen applied to the edge of a set square in the same manner as if drawing lines upon paper1 but with this difference1 that during the longitudinal motion of the pen the handle must be turned over in a circular manner1 so as to give a rounded form to the point of the pen4 ,if the pen be now held with the point directed towards the eye1 and gently moved about so as to catch the angle of reflexion1 a bright speck on one or both nibs will be observed1 which must be reduced by rubbing the pen to and fro upon the stone1 giving at the same time a slight rotary motion to the handle1 which must be held at an angle of about #bj with the face of the stone3 the point of the pen being examined from time to time1 and the process of reducing the bright specks continued until the point is as fine as can be used without cutting or scratching the paper4 ,if at this stage the two nibs are of the same length1 a perfectly solid and fine line can be drawn4 ,the beginner1 however1 must not be disappointed if sixty minutes are thus expended before he can produce a satisfactory result2 whereas two minutes in the hands of a practitioner would suffice40 ,the instrument most frequently in the hands of the draughtsman is the lead pencil4 ,these are required of various degrees of hardness1 but for lines that are to be ruled an ,h ,h is the best4 ,the most suitable qualities of lead are those which are the most easily rubbed out2 these qualities are sometimes gritty1 but this defect is more than compensated by the facility with which a line may be removed from the paper4 ,there is some art in cutting a pencil properly4 ,if the point is intended for sketching1 it should be cut equally from all sides1 so as to produce a perfectly acute cone4 ,but for line-drawing a flat or chisel point should always be used4 ,this point is much stronger1 and will last much longer than the cone point4 ,to produce the chisel point1 first cut the pencil from two sides only with a long slope1 and afterwards cut the other sides away only just sufficiently to round the first edge a little4 ,this side wood is needed both to afford a support to the lead1 and to show in what direction the point stands4 ,to avoid breaking the lead1 the knife should be held at an acute angle with it4 ,a point cut in this manner may be kept in order for some time by rubbing it upon a fine file or upon a piece of glass-paper or fine sandstone4 ,of the other instruments used in drawing1 nothing need be said in this work1 as their use presents no difficulties4 ,it may1 however1 be well to remark that no straight-edge employed for ruling lines should be less than a fourteenth of an inch thick1 for if the edge be very thin1 it will be impossible to prevent the ink from escaping from the pen on to it4 ,materials4--,the drawing papers known as ,whatman's are the best prepared of any obtainable1 and they are almost universally employed4 ,of these there are two kinds1 the smooth and the rough2 the former is technically called not paper1 and is the more suitable for mechanical and architectural drawings2 the rough is more effective for perspectives and ,gothic elevations4 ,a third kind is known as the hot-pressed1 but as it does not take colour so well as the not and the rough1 it is not often used4 ,the various sizes are indicated by their names1 which are the following3-- ,antiquarian #ec #ca inches4 ,atlas #cd #bf ,columbier #cd #bc ,demy #bj #ae ,double ,elephant #dj #bf ,elephant #bh #bc ,emperor #fh #dh ,imperial #cj #bb ,medium #bb #ag ,royal #bd #ai ,super ,royal #bg #ai ,the sizes considered best1 and almost universally used for engineering and architectural drawings1 are the elephant1 the double elephant1 and the imperial4 ,if smaller sizes are required1 the half or quarter sheet is used4 ,antiquarian has generally a good surface to draw upon1 and it is preferred by some architects4 ,the atlas is also a very good paper4 ,besides the foregoing1 there is the machine-made or cartridge paper1 which is very commonly employed for detail drawings4 ,it has not so good a surface as the other kinds1 nor is it so white2 its chief advantage is found in its dimensions1 it being made uniformly #ec inches wide and continuous4 ,hence the exact length required may be obtained4 ,for large plans and competition drawings1 either cartridge or emperor paper is used4 ,paper that is to receive an elaborate drawing must be stretched and glued to the board4 ,this operation is one requiring a little skill and some practice to perform successfully4 ,the following is the best manner of proceeding4 ,the sheet to be strained is laid face upward upon the board1 and a wet sponge is passed rapidly along the margins1 and then across the face1 including the margins1 until the whole surface is sufficiently and uniformly wetted4 ,the object of wetting the margins first is to prevent cockling by allowing them a longer time to expand in than the middle of the paper4 ,the sheet must now be left for about ten minutes1 or until the wet gloss has entirely disappeared4 ,the process of glueing to the board is as follows4 ,a straight-edge is laid along one end of the sheet1 and about of an inch of the margin is turned up against it1 and glued by means of a brush4 ,the margin is then turned down and rubbed quickly with a knife-handle or1 still better1 a paper-knife4 ,the opposite end of the sheet is next pulled outwards and glued in the same way1 and the same method is afterwards applied to the top and bottom margins4 ,some draughtsmen prefer to glue down the adjoining edges1 but generally it will be found that laying down successively opposite edges will give more satisfactory results4 ,the contraction of the paper in drying should leave the face quite flat and solid4 ,during the process of drying1 it is important to keep the board in a perfectly horizontal position1 as otherwise the water will gravitate towards the lower side and soften the glue1 and as the sheet will dry unequally1 the lower edge will break away4 ,the thinner the glue used the better1 and for this reason the best quality should be obtained1 and care should be taken to keep the water supplied that is lost by evaporation4 ,when it becomes necessary to replenish the glue-pot1 the cake should be soaked in cold water for at least eight hours4 ,the removal of a drawing from the board presents no difficulty4 ,a pencil line is drawn along the margin at a sufficient distance from the edge to be clear of the glue1 and a pen-knife is guided along this line by a straight-edge not used for drawing4 ,as duplicates of drawings1 especially if they be working drawings1 are usually tracings1 tracing paper is an important material in every drawing office4 ,it is too well known to need a description4 ,it is sold in various sizes1 and of various prices1 but the most usual sizes are #cj #bj inches1 and #dj #cj inches1 the price of the former being #c;d4 and that of the latter #f;d4 a sheet4 ,it may also be purchased in continuous lengths of #bd yards1 #db inches wide1 for about #hs41 or if extra stout1 #afs4 ,a much less expensive mode of obtaining tracing paper is to make it one's self4 ,common silk or tissue paper may be purchased in quantities at less than a halfpenny a sheet of the ordinary size4 ,this may be prepared by placing a single sheet at a time flat upon a board or other smooth horizontal surface1 and applying a mixture of boiled linseed oil and turpentine4 ,this mixture should be composed of one part of oil to five of turpentine1 and it should be applied with a small sponge4 ,one coating is sufficient1 and it should not be put on too thickly4 ,each sheet as prepared should be hung over a string stretched across the room to dry1 and when all the clear oily marks have entirely disappeared1 it will be ready for use4 ,five gills of turpentine and one of oil is enough for two quires of double-crown tissue paper4 ,that tracing paper is best which is toughest1 most transparent1 and most free from greasiness4 ,the continuous papers are more economical than those in sheets1 because just the quantity required can always be taken from the roll4 ,for durability1 tracing cloth is to be recommended2 it is sold in continuous lengths of #bd yards1 and it may be had from #ah inches to #da inches in width4 ,that known as 8,sager's vellum cloth0 is of excellent quality1 both for transparency and strength4 ,some kinds of drawings1 such as specifications for ,letters ,patent1 plans upon deeds1 c41 have frequently to be made upon parchment4 ,special kinds of parchment can be obtained for these purposes4 ,there is a kind made which is quite transparent1 and which can be purchased cut to the ,patent ,office regulation size4 ,as parchment has always a more or less greasy surface1 before commencing to ink or to colour1 it should be pounced over with pouncet of finely-powdered ,french chalk4 ,besides this precaution1 it will be necessary to add a little ox-gall to the ink or colour4 ,blacklead and carbonic paper are used to transfer a drawing4 ,the former is prepared by rubbing thin paper over with a soft block of ,cumberland lead2 the latter by painting one side of the paper with lamp-black ground to perfect fineness in slow drying oil4 ,carbonic paper is used for coarser work than blacklead paper4 ,both may be purchased1 properly prepared1 at a trifling cost4 ,the drawing to be copied is laid over the sheet of paper which is to receive the copy1 with a sheet of the blacklead or carbonic paper interposed1 and a tracer is passed with a light pressure over the lines4 ,this method is mostly used to reproduce a drawing from a tracing1 to obtain a finished copy from a rough draught that has become soiled and marked in designing1 or to avoid errors or small alterations in the first drawing4 ,a very convenient kind of paper for small working drawings1 or for sketching to scale1 is that known as sectional paper4 ,this is paper ruled into small squares to a given scale with pale ink4 ,the spaces in ordinary use are 1 1 1 1 and inch4 ,thicker lines are drawn either to mark off the inches or to count the spaces in tens4 ,with this paper1 the scale may be dispensed with1 as the eye is capable of subdividing the spaces with sufficient accuracy for practical purposes4 ,sectional paper is much used for sections of railway cuttings and embankments1 as it affords a ready means of calculating the contents4 ,it is also made up into sketching books and architects' pocket-books1 for which purposes it is peculiarly convenient4 ,indian ink is used for all kinds of geometrical drawings4 ,being free from acid1 it does not corrode the steel points of the instruments1 and it preserves its colour unchanged4 ,it is difficult to get the genuine ink1 but even that1 as it is imported from ,china1 varies considerably in quality4 ,for line-drawing1 that is the best quality which will wash up least when other colours are passed over it4 ,this quality is ascertained in the trade1 though not with absolute certainty1 by breaking off a small portion4 ,if it be of the right quality1 it will show a very bright and almost prismatic-coloured fracture4 ,the ink is prepared for use by rubbing it with water on a slab or in a saucer4 ,the saucer should be quite smooth inside1 so as not to abrade the ink4 ,when mixed to the requisite thickness1 which may be ascertained by drawing a line with a common pen1 it should be covered to protect it from the particles of dust floating about the room4 ,ink should be rubbed up perfectly black1 for pale ink makes the boldest drawing look weak4 ,but after it has become black1 any further mixing will only injure it by rendering it viscid4 ,it is best to use it immediately after it is mixed1 for if re-dissolved1 it becomes cloudy and irregular in tone4 ,the addition of a little ox-gall will make it flow more freely from the pen4 ,for erasing ,cumberland lead-pencil marks1 native or bottle indiarubber is sufficient2 but for other kinds of pencils1 fine vulcanized indiarubber is better4 ,this1 besides being a more powerful eraser1 possesses the important quality of keeping clean1 as it frets away with the friction of rubbing1 and thus presents a continually renewed surface4 ,vulcanized rubber is also very useful for cleaning off drawings4 ,precautions and ,remarks4--,it is essential to the good appearance of a drawing that the paper be preserved perfectly clean4 ,the hands especially should be kept as much as possible from resting on it1 as the perspiration makes it greasy1 and when once it has acquired this defect1 clear1 sharp lines become impossible4 ,a sheet of clean paper should be constantly interposed between the draughtsman's hands and the drawing upon which he is working4 ,brown or printed paper is unfit for this purpose1 as the former is either greasy or tarry1 and the latter is apt to soil from the printed matter4 ,white paper can be had of large size1 or1 if necessary1 several sheets may be pasted together4 ,to prevent risk of smearing the lines when inking in1 it is well to begin at the top of the drawing and to work downwards1 also from the right to the left for vertical lines4 ,the ink slab or saucer should be kept on one side and never in front of the drawing4 ,should a drawing get a grease spot1 it may be removed by the application of a hot smoothing iron to a piece of clean blotting-paper laid over the spot1 but not sufficiently to be coloured over4 ,great care should be taken to correctly place the centre lines of a drawing2 these lines should be drawn very fine and distinct4 ,in working drawings the centre lines are of great importance1 as the dimensions are always measured from them2 in such cases it is customary to draw them in red or blue colour4 ,in all cases where a plane figure is symmetrical with respect to a given line1 whether the line exists in the figure or may be considered as existing in it1 that line should be drawn first1 and such a line is known as a centre line4 ,the centres of all arcs should be marked for the ink compasses at the time the arc is struck by the pencil1 by placing a small hand-drawn circle around it4 ,it is also necessary to mark distinctly by short intersecting straight lines the exact points at which the arc begins and ends4 ,when a number of concentric circles have to be struck1 the smaller ones should be struck first1 as it is more difficult when the hole in the paper becomes enlarged to draw a small circle than a large one4 ,whenever it is practicable1 lines should be drawn from a given point rather than to it2 and if there are several points in one of which two or more lines meet1 the lines should be drawn from that one to the others2 thus1 for example1 radii should be drawn from the centre to the points in the circumference of a circle4 ,when a point has to be determined by the intersection of circular arcs or straight lines1 these should not meet at an angle less than #cj4 ,in dividing a line into a number of parts1 instead of setting off the part repeatedly along the line1 it is better to set off a convenient multiple of the given part1 and subdivide it2 that is1 to work from the whole to the parts1 rather than from the parts to the whole4 ,this is an important principle in surveying as well as in plan drawing1 and in the construction of scales it ought always to be observed4 ,ink lines should never be erased with a knife1 nor should an ink-eraser be used1 especially if the drawing is to be coloured4 ,a needle point will take out a short line in a way that leaves little trace of the error4 ,a very good means of taking out a line is furnished by a piece of ,oakey's ,no4 #a glass-paper folded several times until it presents a round edge2 the application of this leaves the surface of the paper in a much better condition for drawing upon than it is left in by the knife4 ,when the drawing is to be coloured1 it is best to wash out a wrong line with a small hard brush1 and to slightly sponge over the place through a hole of the requisite size cut in a scrap of drawing paper1 to save the other parts of the drawing4 ,when a line has been drawn a little beyond the point at which it should terminate1 it will generally be found better to avoid erasure by laying a little ,chinese white over the line with a fine sable-brush4 ,sometimes1 when erasures are unavoidable upon a drawing that is to be coloured1 it will be found expedient to take the surface off the whole of the paper with glass-paper1 the colour will then flow equally4 ,in copying from a tracing1 it is well to put a sheet of drawing paper underneath the tracing1 for it not only shows up the lines more distinctly1 but it prevents the dividers from tearing the drawing while taking off measurements4 ,before commencing a drawing1 a cutting-off line should be drawn all round the sheet clear of the glued portion4 ,the portions outside of this line are useful to try the drawing pen upon before drawing a line1 or for trying a tint when colouring4 ,care should be taken not to leave too narrow a margin1 for nothing detracts more from the appearance of a good drawing4 ,for a drawing occupying a space of #a foot or #ae inches square over all1 there should be a margin of at least #e inches all round1 with the border line from #a to #b inches from the cut-off line4 ,other sizes should be in proportion4 ,this rule is given by ,maxton in his #8,engineering ,drawing1' who also has the following remarks on cutting off and preserving drawings4 8,the opposite side should never be cut first1 for if so cut1 upon nearly completing the cutting of the third side the paper undergoes contraction1 and the fourth side pulling against it1 is apt to snap off the remaining inch or so1 and generally in towards the sheet1 seldom in the margin on the outside of the cutting-off line4 ,the sheet should be cut off all round1 taking care1 by applying the knife-blade under the edge of the sheet1 that it is free from the board before proceeding to cut off the side or end adjoining4 ,when the sheet has been removed1 the strips of drawing paper left on the board should be simply sponged over two or three times1 and they will peel off easily4 8,for preserving a rolled drawing1 a common substitute for string1 and one less likely to crease the drawing1 is made as follows3--,take a strip of drawing paper from #a to #b inches wide and an inch longer than the circumference of the rolled drawing4 ,about half an inch from each end make incisions1 at one end in the middle and one-third of the breadth across1 and at the other end at the sides1 each one-third of the breadth across4 ,fold in these sides1 so that they may pass through the incision in the opposite end of the strip2 on being opened again after they have passed through1 the whole will form a hoop1 which1 when slipped over the drawing1 will keep it secure40 ,as cartridge paper is not always suitable1 it sometimes becomes necessary to join the smaller sizes end to end4 ,to do this neatly the edges should be cut straight1 and a straight-edge laid upon the paper1 allowing inch to project beneath it4 ,this portion of the paper should then be rubbed down with sand or glass-paper until the outer edge is quite thin4 ,the edges of both sheets to be joined must be treated in this way1 and covered with a thin coating of gum4 ,having placed these edges in contact1 a strip of paper #a or #b inches wide should be laid upon the joint1 and well rubbed with the handle of a paper-knife4 ,if the paper thus joined has afterwards to be stretched on a board1 it should be done while the joint is damp4 ,in sponging the paper1 care must be taken not to go over the joint4 ,in joining sheets of tracing paper1 the joint should never be made more than inch broad4 ,the gum used for this purpose should be very thin1 and a strip of drawing paper should be placed upon each side of the joint until it is quite dry4 ,it is a good plan to roll the joined sheet upon a roller with the joint in a line with the roller and the strips infolded over the joint4 ,when left to dry in this position1 the joint will be perfectly smooth4 ,drawings have frequently to be mounted on stretchers1 and the operation of mounting is one requiring some care and practice4 ,generally it will be found more convenient to purchase the stretcher ready made complete2 but when this is not done1 care must be taken to have the frame made of sufficient strength to resist the tension of the paper when dry4 ,the sides and the ends of a stretcher1 #h or #i feet long1 should be #d inches broad and not less than inch thick1 and for any length above #ah inches there should be one or more bars across4 ,a frame #f feet long should have two cross-bars dividing the length into three equal parts1 and they should be of such a thickness as not to come up flush with the sides and ends by about inch4 ,the inner edges on the face of the latter should be rounded down to the level of the cross-bars1 and the same degree of rounding should be given to the edges of the cross-bars themselves4 ,this is necessary to prevent the edges from showing a soiled mark on the paper4 ,when the frame has been thus prepared1 the linen or calico should be spread out on some flat surface and the frame laid upon it face downwards4 ,the ends of the linen should then be pulled over and nailed to the back2 next1 the middle of the sides should be pulled over and fixed in the same way4 ,the intermediate spaces are afterwards tacked down by placing a tack alternately on opposite sides1 care being taken to pull the linen tight and smooth before inserting the tack4 ,it is a good plan to fold the edge1 as the double thickness will hold the tacking better than if single4 ,to mount the paper on the stretcher1 it should be laid face downwards upon a clean flat surface1 which will be all the better if covered with a clean cloth1 and sponged with clean water4 ,when the water has soaked in1 apply with a flat brush some cold flour paste1 and1 if necessary1 remove all knots or particles of gritty matter1 as these would prevent the paper from lying close to the linen4 ,the addition of a little alum to the paste improves its adhesive property1 and also tends to make the drawing less stiff when dry4 ,when a good coating of paste has been well distributed over the paper1 place the stretcher upon the paper and rub the back of the linen well2 then turn the stretcher over and rub down the edges of the paper4 ,air-bubbles between the linen and the paper may be got rid of by puncturing the spot with a fine needle and rubbing it down4 ,paper thus mounted may be drawn upon nearly as well as when stretched on a board4 ,to give an edge for the ,t-square1 a strip of wood with parallel edges may be temporarily nailed on4 ,some drawings1 such as large plans of estates1 have frequently to be varnished4 ,this operation requires some skill1 and can be satisfactorily accomplished only by a practised hand4 ,the process generally adopted is to stretch the drawing upon a frame1 and to give it three or four coats of isinglass size with a flat broad brush1 taking care to well cover it each time1 and to allow it time to dry between each coat4 ,the best varnish is ,canada balsam1 diluted in oil of turpentine4 ,this requires to be put on evenly in a flowing coat with a fine flat brush1 and to be left in a warm room free from dust until it is thoroughly dry4 ,the drawing must be in a perfectly horizontal position while the size and the varnish are being applied4 ,in drawings to be varnished1 thick lines1 such as shade lines1 and chalky colours should never be put on before sizing1 as they are apt to blot during the process4 ,should a fir drawing-board get accidentally dented1 an application of water to the part will1 within certain limits1 bring it up to its proper level4 ,,section ,,ii4--,,geometrical ,,problems4 ,to bisect a given ,straight ,line4--,let ,a ,b 7,fig4 #a7 be the given line4 ,from ,a and ,b1 with any radius greater than ,a ,b1 draw arcs cutting each other in ,c and ,d2 then the line joining ,c ,d will bisect the line ,a ,b as at ,e4 ,illustration3 ,,fig4 #a4 ,illustration3 ,,fig4 #b4 ,to erect a ,perpendicular to a given ,straight ,line4--,let it be required to erect a line perpendicular to the point ,b 7,fig4 #b7 in the line ,a ,b4 ,from any point ,c above the line1 with radius ,b ,c1 describe an arc as ,a ,b ,d2 join ,a ,c and produce the line until it cuts the arc in ,d1 and join ,d ,b2 then will ,d ,b be perpendicular to ,a ,b4 ,illustration3 ,,fig4 #c4 ,to divide a ,line into any number of equal parts4--,let it be required to divide the line ,a ,b 7,fig4 #c7 into five equal parts4 ,from ,b1 at any angle1 draw ,b ,c1 and on the line ,b ,c lay off five equal parts1 #a1 #b1 #c1 #d1 #e2 then take a set square ,e1 and make one of the sides containing the right angle coincide with the points ,a and #e1 and to the other side apply a straight-edge ,d2 then by passing the set square along the edge of the straight-edge and drawing lines from the points #d1 #c1 #b1 #a1 through the line ,a ,b1 we shall have the line ,a ,b divided into five equal parts through the points #a1 #b1 #c1 #d4 ,to draw a ,line making1 with another line1 a given ,angle4--,let it be required to draw a line making with the line ,a ,b 7,fig4 #d7 an angle of #ce4 ,from a scale of chords1 which will be found on most scales supplied with a set of instruments1 take off #fj2 from the point ,a1 with this distance for radius1 describe an arc ,c ,d2 lay off on this arc the distance of #ce taken from the same scale of chords2 from ,a draw a line through this point4 ,then will the line ,a ,e make with the line ,a ,b an angle of #ce4 ,the same result may be more readily arrived at by means of a protractor4 ,if the centre point of the protractor be placed on the point ,a and its base made to coincide with the line ,a ,b1 we can from its circumference prick off the distance of #ce1 and a line drawn from ,a through the point thus found will make1 with the line ,a ,b1 the required angle of #ce4 ,illustration3 ,,fig4 #d4 ,illustration3 ,,fig4 #e4 ,to bisect an ,angle4--,let ,b ,a ,c 7,fig4 #e7 be the angle which it is required to bisect4 ,from ,a1 with any radius1 describe an arc cutting the lines ,a ,b and ,a ,c in ,d and ,e2 from ,d and ,e1 with the same or any other radius1 describe arcs cutting each other in ,f1 and from ,a draw a line through ,f2 this line will bisect the angle as required4 ,illustration3 ,,fig4 #f4 ,illustration3 ,,fig4 #g4 ,to construct an ,equilateral ,triangle on a given base4--,let ,a ,b 7,fig4 #f7 be the given base4 ,from ,a and ,b1 with radius ,a ,b1 describe arcs cutting each other in ,c2 join ,a ,c and ,c ,b1 which will complete the required triangle4 ,to construct a ,triangle1 the lengths of the ,sides being given4--,let it be required to construct a triangle whose sides shall be equal respectively to #f1 #e1 and #d4 ,lay down the base ,a ,b 7,fig4 #g71 making it equal to #f divisions of the scale2 from ,a with radius equal to #d divisions1 and from ,b with radius of #e divisions of the scale describe arcs cutting each other in ,c2 join ,a ,c and ,c ,b1 which will complete the required triangle4 ,illustration3 ,,fig4 #h4 ,to construct an ,angle equal to a given angle4--,it is required to draw a line making with the line ,d ,e 7,fig4 #h7 an angle equal to that contained by the lines ,b ,a ,c4 ,from ,a1 with any radius1 draw an arc ,f ,g1 and from ,d1 with the same radius1 draw the arc ,h ,i1 and make ,h ,i equal ,f ,g2 then a line drawn from ,d through ,i will make1 with the line ,d ,e1 an angle equal to the angle ,b ,a ,c4 ,illustration3 ,,fig4 #i4 ,to construct a ,triangle1 the length of the base and the angles at the base being given4--,it is required to construct a triangle whose base shall equal #a inch1 and the angles at the base be #cj and #de respectively4 ,having made the base ,a ,b 7,fig4 #i7 of the required length1 make the angles at ,a and ,b of the required magnitude in the manner already described 7see ,fig4 #d71 and the continuation of these lines meeting in the point ,g will complete the construction of the required triangle4 ,illustration3 ,,fig4 #aj4 ,to describe a ,circle which shall pass through three given points4--,let ,a ,b ,c 7,fig4 #aj7 be the points through which it is required to draw the circle4 ,from each of these points1 with any radius1 describe arcs cutting each other in ,d and ,e2 join the points ,d and ,e1 and the point where these lines intersect will be the centre from which to describe the circle which will pass through the points ,a ,b ,c as required4 ,illustration3 ,,fig4 #aa4 ,to draw a ,tangent to a circle4--,i4 ,let ,b 7,fig4 #aa7 be the point from which it is required to draw the tangent4 ,draw the radius ,o ,b1 and at ,b erect a perpendicular 7see ,fig4 #b72 then will the line ,b ,d be a tangent to the circle4 ,,ii4 ,it is required to draw a tangent from the point ,e in the same circle4 ,draw the radius ,o ,e extending beyond the circumference to ,f1 and make ,e ,g equal to ,e ,f4 ,from ,f and ,g1 with any radius1 describe arcs cutting each other in ,h and ,i2 then a line drawn through these points will be a tangent to the circumference at ,e4 ,illustration3 ,,fig4 #ab4 ,to find the ,centre of a circle4--,from any point in the circumference1 as ,b1 7,fig4 #ab71 describe an arc cutting the circumference in ,a and ,c1 and from ,a and ,c1 with the same radius1 describe arcs cutting the first arc in two points2 through the points of intersection draw lines to the interior of the circle1 and the point ,o where these lines intersect will be the centre of the circle4 ,illustration3 ,,fig4 #ac4 ,to draw lines which shall be ,radii of a circle1 the centre being inaccessible4--,having laid off on the circumference of the arc1 the distances apart of the radii1 as ,a1 ,b1 ,c1 c4 7,fig4 #ac71 from each of these points1 with radius greater than a division1 describe arcs cutting each other as at a1 b1 c1 c41 join ,a a1 ,b b1 ,c c1 c41 and the lines so drawn will be radii of the circle as required4 ,illustration3 ,,fig4 #ad4 ,to construct an ,oval1 the width being given4--,draw the line ,a ,b 7,fig4 #ad7 equal to the width1 and bisect ,a ,b by ,c ,d 7see ,fig4 #a74 ,from the point of intersection ,e1 with radius ,e ,a or ,e ,b1 describe the circle ,a ,c ,b ,f1 and from ,a and ,b through ,f1 draw the lines ,a ,g and ,b ,h4 ,from ,a1 with radius ,a ,b1 describe the arc ,b ,g1 and from ,b1 with the same radius1 describe the arc ,a ,h2 also from ,f1 with radius ,f ,g or ,f ,h1 describe the arc ,g ,d ,h1 which will complete the required oval4 ,illustration3 ,,fig4 #ae4 ,to construct a ,square on a given line4--,let ,a ,b 7,fig4 #ae7 be the given line4 ,at ,a erect a perpendicular 7see ,fig4 #b71 and from ,a1 with radius ,a ,b1 describe an arc cutting the perpendicular in ,c2 also from ,b and ,c1 with the same radius1 describe arcs cutting each other in ,d2 join ,c ,d and ,b ,d1 which will complete the required square4 ,illustration3 ,,fig4 #af4 ,to construct a square that shall be a ,multiple of any given square4--,let ,a ,b ,c ,d 7,fig4 #af7 be the given square1 and let it be required to construct a square that shall contain #b1 #c1 #d1 c41 times its surface4 ,draw the diagonal ,b ,c1 then the square described on ,b ,c will be double the square ,a ,b ,c ,d4 ,lay off ,d ,e1 equal to ,b ,c1 and draw ,c ,e2 then the square described on ,c ,e will be three times the square ,a ,b ,c ,d4 ,in the same manner lay off ,d ,f1 equal to ,c ,e1 and the square described on ,c ,f will be four times the square ,a ,b ,c ,d2 and so for any multiple of the square ,a ,b ,c ,d4 ,illustration3 ,,fig4 #ag4 ,to construct a square that shall be equal to 1 1 c41 of any given square4--,let ,a ,b ,c ,d 7,fig4 #ag7 be the given square4 ,on ,a ,b1 as a diameter1 describe the semicircle ,a ,g ,b1 and erect at the centre ,e the perpendicular ,e ,g4 ,draw ,g ,b1 which will be the side of a square equal to one-half of ,a ,b ,c ,d4 ,lay off ,b ,f1 equal to one-fourth of ,a ,b1 and erect the perpendicular ,f ,h2 then the square described upon ,h ,b will be equal to one-fourth of ,a ,b ,c ,d4 ,in the same manner a square may be constructed equal to any part of ,a ,b ,c ,d4 ,illustration3 ,,fig4 #ah4 ,to construct a square that shall be in any ,proportion to a given square4--,let ,a ,b ,c ,d 7,fig4 #ah7 be the given square4 ,it is required to construct a square which shall be to ,a ,b ,c ,d as #b is to #e4 ,upon the side ,a ,b as a diameter describe the semicircle ,a ,f ,b1 and divide the line ,a ,b into five equal parts4 ,at the second point of division erect the perpendicular ,e ,f and join ,a ,f2 the square described upon ,a ,f will be to the given square ,a ,b ,c ,d as #b is to #e4 ,illustration3 ,,fig4 #ai4 ,to construct1 upon a given base1 a ,rectangle1 which shall be similar to a given rectangle4--,let ,a ,e ,f ,g 7,fig4 #ai7 be the given rectangle4 ,it is required to construct upon the base ,a ,b1 one that shall be similar to ,a ,e ,f ,g4 ,produce ,a ,e and lay off the given base from ,a to ,b2 draw the diagonal ,a ,g and produce it indefinitely4 ,erect a perpendicular to ,a ,b at ,b1 and from the point ,d where it intersects the diagonal produced1 draw ,d ,c perpendicular to ,a ,f produced4 ,then ,a ,b ,c ,d will be similar to ,a ,e ,f ,g4 ,all rectangles having their diagonals in the same line are similar4 ,illustration3 ,,fig4 #bj4 ,to describe a regular ,pentagon on a given line4--,let ,a ,b 7,fig4 #bj7 be the given line4 ,bisect ,a ,b at ,c1 draw ,c ,f perpendicular to ,a ,b1 and make ,c ,d equal to ,a ,b4 ,draw ,a ,d and produce it indefinitely2 make ,d ,e equal to half ,a ,b4 ,from ,a as a centre1 with ,a ,e as a radius1 describe an arc cutting the perpendicular ,c ,d in ,f2 and from ,a ,f and ,b as centres1 with radius ,a ,b1 describe arcs cutting each other in ,g and ,h2 join ,a ,g1 ,b ,h1 ,f ,g and ,f ,h2 then ,a ,g ,f ,h ,b will be the pentagon required4 ,illustration3 ,,fig4 #ba4 ,to describe a regular ,hexagon4--,with a radius equal to the length of one side of the required hexagon1 describe a circle 7,fig4 #ba71 and set off the same radius round the circumference of the circle1 which will be thus divided into six equal parts4 ,join the points thus found1 and the required hexagon will be completed as ,a ,b ,c ,d ,e ,f4 ,illustration3 ,,fig4 #bb4 ,to draw a ,parabola1 the base and height being given4--,let ,c ,a 7,fig4 #bb7 equal half the base1 and ,c ,d the height4 ,from the point ,d draw ,d ,e parallel and equal to ,a ,c1 and from the point ,a draw ,a ,e parallel and equal to ,c ,d4 ,divide ,d ,e and ,a ,e similarly1 making the end ,e of ,a ,e correspond to the end ,d of ,e ,d4 ,through #a1 #b1 c41 in ,,de draw #a1 #a2 #b1 #b1 c41 parallel to ,d ,c4 ,join ,d to the several points #a1 #b1 c41 in ,a ,e4 ,the parabola will pass through the points of intersections of these lines with the verticals drawn from ,d ,e to ,c ,a4 ,illustration3 ,,fig4 #bc4 ,illustration3 ,,fig4 #bd4 ,illustration3 ,,fig4 #be a4 ,illustration3 ,,fig4 #be b4 ,to draw an ,ellipse4--,i4 ,by means of a piece of string and pins4 ,place the diameters ,a ,b and ,c ,d 7,fig4 #bc7 at right angles to each other1 and set off from ,c half the major axis at ,e and ,f2 then will ,e and ,f be the two foci in the ellipse4 ,fix a pin at ,e and another at ,f2 take an endless string equal in length to the three sides of the triangle ,e ,f ,c and pass it round the pins1 stretch the string with a pencil ,g1 which will then describe the required ellipse4 ,,ii4 ,from the centre ,o 7,fig4 #bd7 describe a circle of the diameter of the minor axis of the required ellipse4 ,from the same centre1 describe another circle with a diameter equal to its major axis4 ,divide the inner circle into any number of equal parts as #a1 #b1 c41 and through these points draw radii cutting the outer circle in #d1 #c1 c4 ,from #a1 #b1 c41 draw horizontals1 and from #c1 #d1 c41 draw perpendiculars cutting each other in ,e ,f1 c42 the curve traced from ,c through the points ,c ,e ,f ,a1 c41 will complete the curve of the required ellipse4 ,,iii4 ,let ,a ,b 7,fig4 #be a7 be the major and ,c ,d the minor axis of the required ellipse4 ,on any convenient part of the paper draw two lines ,f ,g1 ,f ,h 7,fig4 #be b7 at any angle with each other4 ,from ,f with the distance ,e ,c or ,e ,d1 the semi-axis minor1 describe an arc cutting the lines ,f ,g1 ,f ,h1 in ,i and ,k2 and from ,f with the distance ,e ,a or ,e ,b1 the semi-axis major1 describe the arc ,l ,m4 ,join ,i ,m1 and from ,l and ,k draw lines parallel to ,i ,m1 cutting ,f ,g1 ,f ,h1 in ,n and ,o4 ,from ,a and ,b 7,fig4 #be a7 set off the distance ,f ,n 7,fig4 #be b7 in points ,n1 and from these points as centres1 with ,f ,n as radius1 describe an arc of about #ae on each side of the major axis4 ,from ,c and ,d 7,fig4 #be a7 set off on the minor axial line the distance ,,fo 7,fig4 #be b7 in points ,o1 and from these points as centres1 with radius ,,fo1 describe arcs of about #ae on each side of the axis ,c ,d4 ,to obtain any number of intermediate points take a slip of paper 7,fig4 #be a7 and mark upon one edge1 with a sharp-pointed pencil1 #a1 #c1 equal to the semi-axis major1 and #b1 #c1 equal to the semi-axis minor4 ,if the slip of paper be now applied to the figure and moved over it in such a manner that the point #b is always in contact with the major axis1 and the point #a in contact with the minor axis1 the outer point #c will describe a perfect ellipse1 any number of points in which can be marked off as the 8trammel0 is moved into successive positions4 ,for this last method1 which in practice is by far the best1 we are indebted to ,binns' #8,orthographic ,projection4' ,illustration3 ,,fig4 #bf4 ,to construct a ,semi-,elliptical ,arch4--,the span ,a ,b 7,fig4 #bf7 and rise ,c ,d being given1 divide ,c ,a and ,c ,b into any number of equal parts4 ,through the point ,d1 draw ,e ,f parallel to ,a ,b1 and from the points ,a and ,b erect the perpendiculars ,a ,e and ,b ,f4 ,divide ,a ,e and ,b ,f similarly to ,c ,a and ,c ,b4 ,produce ,c ,d and make ,c ,g equal ,c ,d4 ,from ,d draw lines to the points #a1 #b1 #c1 c41 in the lines ,a ,e and ,b ,f2 also from ,g draw lines through the points #a1 #b1 #c1 c41 in the line ,a ,b1 and produce these lines until they cut those drawn from ,d to the corresponding numbers in ,a ,e and ,b ,f4 ,through the points thus obtained draw the curve of the ellipse4 ,illustration3 ,,fig4 #bg4 ,to draw the ,gothic ,equilateral ,arch4--,from the points ,a and ,b 7,fig4 #bg71 with radius ,a ,b equal to the span1 describe the arcs ,b ,c and ,a ,c4 ,by joining ,c to ,a and ,b we obtain an equilateral triangle from which this arch derives its name4 ,illustration3 ,,fig4 #bh4 ,to draw the ,gothic ,lancet ,arch4--,in this arch1 the centres ,e and ,d 7,fig4 #bh7 from which the arcs are struck1 are situate outside of and in a line with the points of springing ,a and ,b2 thus it is constructed on an acute-angled triangle1 as will be seen by joining ,c to ,a and ,b4 ,illustration3 ,,fig4 #bi4 ,to draw the ,gothic ,obtuse ,arch4--,this arch1 called sometimes the ,drop-,arch1 is constructed on an obtuse-angled triangle2 the centres ,e and ,d 7,fig4 #bi7 being situate below and within the points of springing ,a and ,b4 ,illustration3 ,,fig4 #cj4 ,to draw the ,gothic ,tudor ,arch4--,on the line of springing ,a ,b 7,fig4 #cj71 take any two points as ,f and ,g1 so that ,a ,f is equal to ,g ,b4 ,draw ,f ,e and ,g ,d cutting each other on the bisecting line through ,c2 from ,f and ,g1 with radius ,f ,a or ,g ,b1 describe the short arcs1 and from ,e and ,d1 with radius ,e ,c or ,d ,c1 describe the arcs meeting in ,c4 ,illustration3 ,,fig4 #ca4 ,to draw the ,moorish ,horse-,shoe ,arch4--,the centres ,e and ,d 7,fig4 #ca7 from which the arcs forming this arch are struck1 are situate above and within the points of springing ,a and ,b4 ,one of the most graceful forms of this arch is obtained when the height of the points ,e and ,d above the line of springing and their distance from the bisecting line through ,c are equal to one-third of the span ,a ,b4 ,illustration3 ,,fig4 #cb4 ,to draw the ,gothic ,ogee ,arch4--,the most pleasing form of this arch is that constructed on an equilateral triangle1 in the following manner4 ,having drawn the equilateral triangle ,a ,b ,c 7,fig4 #cb71 draw ,f ,g parallel to ,a ,b4 ,bisect the sides ,a ,c and ,c ,b and produce the bisecting lines to ,f ,g and ,h1 which will complete the triangle ,f ,g ,h similar and equal to the triangle ,a ,b ,c4 ,from ,h1 with radius ,h ,a or ,h ,b1 describe the arcs ,a ,e and ,b ,d1 and from ,f and ,g1 with the same radius1 describe the arcs ,e ,c and ,c ,d4 ,illustration3 ,,fig4 #cc4 ,illustration3 ,,fig4 #cd4 ,to draw the ,roman ,cyma ,recta and ,cyma ,reversa4--,join ,a ,b 7,fig4 #cc7 and bisect ,a ,b in ,c4 ,from the points ,c and ,b1 with the distance ,b ,c1 describe arcs cutting each other in ,e2 and from ,a and ,c1 with the same radius1 describe arcs cutting each other in ,d2 from ,d1 with the same radius1 describe the arc ,a ,c1 and from ,e describe the arc ,c ,b4 ,the projection of the upper end of the curve over the under1 as ,f ,b1 is generally equal to the height1 ,a ,f1 of the moulding4 ,the same description applies to the ,cyma ,reversa 7,fig4 #cd7 letter for letter4 ,illustration3 ,,fig4 #ce4 ,to draw the ,gothic ,trefoil4--,having drawn the equilateral triangle ,a ,b ,c 7,fig4 #ce71 bisect the angles and produce the bisecting lines ,d ,e ,f which will bisect the sides of the triangle in ,g ,h ,i4 ,from ,a ,b and ,c as centres1 with radius ,a ,h or ,a ,i1 equal to half the side of the triangle1 describe the arcs ,k ,l ,m1 and those concentric with them1 and from the centre ,o of the triangle describe the outer circles and concentric arcs1 which will complete the figure4 ,illustration3 ,,fig4 #cf4 ,to draw the ,gothic ,quatrefoil4--,draw the square ,a ,b ,c ,d 7,fig4 #cf72 bisect the sides of the square at ,i ,k ,l ,m and produce the bisecting lines to ,e ,f ,g ,h4 ,from the angles ,a ,b ,c ,d of the square as centres1 with radius ,a ,i or ,a ,m equal to half the side of the square1 describe the arcs ,p ,n ,r ,s1 and draw the outer concentric arcs4 ,the circles1 completing the figure1 are drawn from the centre ,o of the square4 ,illustration3 ,,fig4 #cg4 ,to construct the ,gothic ,cinquefoil4--,having drawn the regular pentagon ,a ,b ,c ,d ,e 7,fig4 #cg71 bisect the angles and produce the bisecting lines to ,f ,g ,h ,i ,k1 which will cut the sides of the pentagon in a1 b1 c1 d1 e4 ,from ,a ,b ,c ,d and ,e as centres1 with radius ,a a or ,a b1 equal to one-half of the side of the pentagon1 describe the arcs ,l ,m ,n ,p ,r1 and draw the outer concentric arcs and those concentric with them4 ,the circles are drawn from the centre ,o of the pentagon1 as in the preceding example4 ,,section ,,iii4--,,lines1 ,,dots1 ,,and ,,their ,,combinations4 ,all kinds of drawings are made up of lines and dots2 these are the constituent parts1 the materials which the draughtsman has to employ4 ,it is therefore essential that he should make himself acquainted with their various forms and uses1 and familiar with those means of producing them which experience has shown to be the best1 before commencing the study of the principles by which the representation of an object is delineated4 ,and moreover1 it is desirable that he should acquire a familiarity with the operations required in the delineation of isolated objects1 previously to making any attempt to place them in combination for the purpose of producing a complete drawing4 ,the student will1 therefore1 do well to study carefully and to practise diligently the forms and examples given in this ,section4 ,straight and ,curved ,lines4--,all straight lines1 however short1 should be ruled1 whether they be drawn with the pencil or the pen4 ,pencil lines1 which are intended to serve merely as guides to the pen1 should be drawn lightly1 as otherwise it will be difficult to rub them out without injuring the ink4 ,they should also be drawn a little beyond the point at which the line is required to terminate1 because the intersection of the lines at that point makes it more distinctly visible1 and there is1 consequently1 less danger of passing beyond that point or of stopping short of it when inking in4 ,it is very important not to stop short of the required length when ruling a straight line with a pen1 for it is extremely difficult to lengthen the line subsequently without leaving the join visible4 ,an accurate line cannot be drawn unless the point of the pencil or the pen be kept close up to the rule1 and to do this the top should be inclined a little outward4 ,before inking in a line that has been drawn in pencil1 the indiarubber should be passed lightly over it1 to remove the particles of lead adhering to the paper1 for if these particles are allowed to remain1 they get between the nibs of the pen and prevent the ink from flowing freely4 ,the chief difficulties in ruling a straight line with the pen are1 to keep it of a regular thickness throughout1 and1 when numerous parallel lines have to be drawn1 to keep them at equal distances apart4 ,to draw an even line1 a first requisite is that the pen be in good condition4 ,frequently it will be found when drawing fine lines that the pen ceases to mark before the end of the line is reached1 and as we have already said1 it is very difficult to join a line without leaving visible traces of the operation4 ,to remedy this defect1 the pen must be reset as described in ,section ,i4 ,if a very hard pencil has been used1 or if the pencil has been pressed heavily upon the paper1 the pencil line will lie in a groove in the paper1 and as the nib of the pen will not touch the bottom of this groove1 the line drawn will be ragged4 ,another cause of unevenness is unduly pressing the pen against the rule2 this pressure closes the nibs1 and besides producing an irregularity in the thickness of the line1 is very apt to cause a blot by forcing out the ink1 which adheres to the rule when brought into contact with it4 ,to prevent this1 care should be taken to press the pen very lightly against the edge of the rule4 ,a pen is manufactured by ,stanley1 of ,holborn1 ,london1 which has the back nib much stiffer than the other1 so that all danger of defect from this cause is removed by the construction of the instrument4 ,to ensure a good line1 the pen should rest lightly upon the paper1 and the handle of the pen should make the same angle with the paper from the beginning to the end of the line4 ,a considerable amount of practice is required to accomplish this1 and to acquire the habit1 the same attention should be given to the pencil as to the pen4 ,the ability to draw a number of parallel lines at equal distances apart without measuring requires considerable training of the eye1 and this training can be obtained from practice alone4 ,this ability must be acquired before anything further is attempted1 and the student who spends a good deal of time in its acquisition may have the satisfaction of knowing that while he is going through this somewhat monotonous practice1 besides exercising himself in drawing accurate lines1 he is acquiring a correctness of eye and a power of hand that will be of incalculable service to him later4 ,the straight line1 besides being used for the outlines of regular objects1 is employed conventionally for various purposes4 ,when it is required to show an object in section1 the part in section is covered with straight and parallel lines drawn at an angle of #de and at equal distances apart1 as in ,fig4 #ch4 ,to represent standing water1 as ponds and lakes1 horizontal straight lines are drawn parallel to each other and at equal distances apart over the surface1 as shown in ,fig4 #ci4 ,illustration3 ,,fig4 #ch4 ,illustration3 ,,fig4 #ci4 ,curved lines1 when arcs of circles1 are drawn by the compasses4 ,other curves are drawn by hand through points previously found4 ,to draw the curve correctly through these points1 unless they be very numerous1 a knowledge of the nature of the curve is necessary1 which the draughtsman should in all cases endeavour to obtain4 ,when the curved line is long1 it is usually inked in with the drawing pen1 with the aid of an instrument called the ,french curve1 or cardboard moulds cut for the purpose2 but for short lines an ordinary fine-pointed steel-pen point1 or better1 a good quill is used4 ,in general1 all lines drawn by hand should be drawn towards the body1 as a better command of the pen can be obtained in that direction than in any other4 ,in inking in curves by this means1 the draughtsman should proceed continuously along the pencil-drawn line by partly repeated touches with the pen point1 so held that the divided points of the pen may follow partly in the same track4 ,each touch should be made about one-thirtieth of an inch in length1 and it should begin and end fine4 ,each succeeding touch must begin half its length back1 so that the line is advanced by one-sixtieth of an inch4 ,in map drawing all irregular lines are drawn in this way4 ,tracing maps will afford the student excellent practice in this mode of using the pen4 ,illustration3 ,,fig4 #dj4 ,lines of uneven thickness4--,though generally a line is required to be of even thickness throughout1 cases sometimes occur in which a variation in the thickness may be made to express some feature or quality of the landscape4 ,the usual application of this kind of line is to mark the outline of rivers1 lakes1 and ponds1 as shown in ,fig4 #dj4 ,the drawing of such a line presents no difficulty2 the increased thickness is produced by going over those parts of the line again with the pen4 ,care must1 however1 be taken not to make a sudden increase in the breadth of the line1 but to begin and end imperceptibly4 ,illustration3 ,,fig4 #da4 ,illustration3 ,,fig4 #db4 ,illustration3 ,,fig4 #dc4 ,the ,broken ,line4--,the broken line1 shown in ,fig4 #da1 is of frequent occurrence in all kinds of drawings4 ,in architectural and engineering drawings it is usually employed in roofs1 as in ,fig4 #db1 and for water in sections1 as in ,fig4 #dc4 ,it is also used in combination with other lines for various purposes4 ,in drawing a succession of broken lines1 care must be taken not to allow the break in one line to be immediately over that in another4 ,the effect may be varied considerably by increasing or diminishing the extent of the break4 ,as in section lining1 the lines should be at regular intervals apart1 and be all of the same degree of fineness4 ,broken lines are sometimes used upon the face of stone buildings1 instead of marking in the joints and etching or colouring4 ,in such a case the breaks are long1 and the lines widely spaced4 ,illustration3 ,,fig4 #dd4 ,the ,dotted ,line4--,of still more frequent occurrence is the dotted line4 ,there are two kinds of dotted lines1 distinguished by the shape of the dot1 and known as the long and the round dotted line4 ,these are shown in ,fig4 #dd1 as well as a combination of the two4 ,the round dotted line is of very general application4 ,in architectural and mechanical drawings1 it is used to distinguish hidden parts1 and to mark the path of a moving piece in a machine4 ,in plans1 it is used to show the position of proposed works1 to denote the walks through pleasure grounds and gardens1 to indicate lines chained over in surveying1 and frequently for other purposes1 at the pleasure of the draughtsman4 ,the long dotted line is employed to mark the boundaries of a township1 the navigable channel of a river or creek1 and in large-scale maps to show farm and bridle roads1 footpaths1 and the divisions of land among different tenants4 ,the combination of the long and round dotted lines is used for the boundaries of a parish4 ,another combination of two round and one long dots1 or sometimes of three round and one long1 is used to denote proposed railways1 canals1 roads1 and other similar works4 ,to draw a good dotted line requires some care4 ,the difficulty lies in keeping the dots at equal distances apart1 and in making them equal in size2 and unless both these conditions are fulfilled1 the line will not present a pleasing appearance4 ,to obviate this difficulty1 an instrument is sold by mathematical instrument makers1 called the dotting or wheel pen4 ,but it requires very great care in using1 as otherwise it frequently happens that the ink escapes from it and spoils the drawing4 ,for this reason1 its use has been generally abandoned by draughtsmen4 ,but if the instrument were better constructed and carefully handled1 it might be made to do good service4 ,illustration3 ,,fig4 #de4 ,illustration3 ,,fig4 #df4 ,illustration3 ,,fig4 #dg4 ,illustration3 ,,fig4 #dh4 ,illustration3 ,,fig4 #di4 ,combinations of ,straight1 ,broken1 and ,dotted ,lines4--,combinations of the foregoing lines are used for various purposes4 ,some draughtsmen employ alternate1 full1 and dotted lines1 to denote wood in section1 as in ,figs4 #de and #df2 when wood is used in combination with iron or other metal1 this is a very good way of distinguishing it4 ,wood-graining1 though not made up of straight1 broken1 or dotted lines1 yet partakes somewhat of the nature of all three kinds1 and may therefore be introduced here4 ,oak-graining is shown in ,fig4 #dg1 and fir-graining in ,fig4 #dh4 ,the former is executed with the drawing pen1 and requires some care and practice2 the latter is most readily done with a common pen or a crow-quill4 ,end wood is grained as shown in ,fig4 #di4 ,the spring bows are very suitable for drawing in the circles1 as a certain degree of turn to the nut will open the ink leg to the required distance after drawing each circle4 ,a few broken wavy lines1 called shakes1 radiating from the centre1 produce a good effect4 ,when several pieces of end wood come together1 the centres in each should not be in the same relative position4 ,illustration3 ,,fig4 #ej4 ,cultivated land is represented by alternate broken and dotted lines1 suggesting furrows1 as shown in ,fig4 #ej4 ,for the sake of variety1 these lines are put in in sets1 and in different directions1 one set being usually parallel to one side of the enclosure4 ,the lines are first ruled in continuously with the pencil1 and the broken and dotted lines afterwards drawn in over them by hand4 ,the portions of the broken lines must in this case be short1 and the breaks still shorter4 ,the dots must be fine and close together2 they are made by touching the paper with the point of the pen1 and immediately lifting it off without dragging it over the paper4 ,all round dots must be made in this way4 ,the ,wavy ,line4--,the wavy line is very important in topographical drawings1 as it is employed to represent running water1 and frequently large bodies of standing water to which motion is communicated by the wind1 as lakes and the sea4 ,these rippled lines are intended to represent the ripples in the water1 a purpose which they fulfil in a very pleasing manner4 ,they must1 however1 be well executed1 or the pleasing effect will not be produced4 ,the operation of drawing these lines is usually regarded by the draughtsman as a tedious and an uninteresting one4 ,but such ought not to be the case1 for there is ample scope in it for the exercise of the taste and the judgment1 and in proportion to the taste displayed and the judgment exercised1 will be the effect of the work when executed4 ,illustration3 ,,fig4 #ea4 ,fig4 #ea shows the manner of employing these lines4 ,in representing water by this means1 the lines should be drawn from the shores towards the middle of the stream or lake1 and never from the middle outwards1 for if the latter mode of proceeding be adopted1 the proper graduation of the spaces between the lines becomes impossible4 ,the shore line1 or outline of the water1 should be a moderately thick line1 and of uniform thickness throughout4 ,the first shading line may be of nearly the same thickness as the shore line1 and it must be drawn as near to it as possible4 ,also this shade line1 as well as all subsequent ones1 must follow exactly all the windings of the shore line2 this is essential to a correct expression4 ,to effect this with accuracy1 care should be taken to make the space between the shore and the shade line a fine white line4 ,the second shade line must be drawn a little finer than the first1 and at a slightly increased distance from it4 ,this gradual diminution of the thickness of the lines1 and increase of the spaces1 must be continued to the middle of the current4 ,the last line in the middle of a piece of water must always return to itself4 ,when the shading lines meet the margin of the drawing1 they should terminate in it1 that is1 they should be drawn out to the margin as though they had been continued beyond and cut off4 ,these lines require to be drawn clean1 and to do this the hand must be kept steady4 ,this steadiness may be obtained by taking a very short hold of the pen1 and resting the middle finger upon the paper4 ,the lines1 as we have already said1 should be drawn towards the body1 the drawing being turned about as required to facilitate this1 and the last line drawn must be always kept on the left of the one being drawn4 ,by this means the last line and the point of the pen are kept constantly in sight4 ,it is also important that the lines should be completed successively1 rather than that several should be carried on at once1 because if the latter mode of working be adopted1 the eye is apt to become confused by the different intervals1 and an uneven distribution of the lines is the result4 ,a principle to be attended to is that every line shall return to itself1 spirals being altogether inadmissible4 ,the distance of the lines apart and their thickness are expressive of the character of the object2 thus1 in a small pond1 for example1 they will be fine and close together2 in a large pond or a lake they will be thicker and more widely spaced2 and in the open sea they will be made to present a bold appearance by increasing still more their thickness and the distance between them4 ,illustration3 ,,fig4 #eb4 ,grass-land4--,various combinations of lines and dots are used1 conventionally1 to represent certain natural features of common occurrence4 ,as far as convenient execution will allow1 these signs are made to resemble the objects denoted4 ,thus the sign for grass-land consists of groups of short lines1 arranged like tufts of herbage1 as shown in ,fig4 #eb4 ,each tuft is composed of five or seven lines converging towards a point situate below the base1 the middle line being the longest1 and the outside ones mere dots4 ,in drawing these groups1 the base must be kept quite straight1 and parallel to the base of the drawing whatever the shape of the enclosure may be4 ,beginners usually experience considerable difficulty in keeping the base straight1 the tendency being to make it curved4 ,great care is needed to distribute the groups evenly over the paper1 and to avoid the appearance of being in rows1 for the latter arrangement is destructive of that natural aspect which this sign otherwise possesses4 ,illustration3 ,,fig4 #ec4 ,swamps and ,marshy ,ground4--,as the surface of marshy ground consists of water and grass1 a combination of the signs for these objects is employed to represent it4 ,an illustration of this is given in ,fig4 #ec4 ,the lines representing the water should always be ruled parallel to the base of the drawing1 and they should be grouped in an irregular manner so as to leave small islands interspersed throughout the locality4 ,these islands should be covered with grass1 and to show them out more distinctly1 there should be nothing but water immediately around them4 ,the division between the land and the water should be sketched in lightly before proceeding to rule in the lines4 ,sometimes dotted lines are used for the water1 but full lines are to be preferred4 ,the addition of a tree here and there improves the appearance of a drawing4 ,a distinction is frequently made between a swamp and a marsh by watering the former more extensively than the latter4 ,in drawing in marsh land1 care should be taken to make the fineness of the lines in accordance with the scale of the map1 as otherwise an offensive appearance will be produced4 ,this caution applies equally to all signs4 ,illustration3 ,,fig4 #ed4 ,sand and ,gravel4--,sand and gravel are represented by dots1 the dots being made larger for the latter than for the former1 as shown in ,fig4 #ed4 ,simple as the operation of filling in these dots is1 it is one that requires some degree of care4 ,beginners are apt to mar the appearance of their drawings by inattention in this respect4 ,the dots should be made in the manner already described when speaking of the dotted line1 that is1 the point of the pen should be brought slowly down upon the paper1 and lifted without dragging it2 and no dot should be made without a deliberate intention respecting its position4 ,all arrangement in rows must be carefully avoided4 ,in sand-hills1 the slopes should be made darker than the level parts by placing the dots closer together4 ,mud in tidal rivers may be represented by very fine dots placed close together4 ,illustration3 ,,fig4 #ee4 ,illustration3 ,,fig4 #ef4 ,woodland4--,trees are generally shown in plan 7as in ,fig4 #ee74 ,the outline is circular in character1 and1 to have a good effect1 it should be made up of simple curves firmly drawn2 small indentations should be avoided as bad4 ,a few touches of the pen are given on the interior and towards the shadow4 ,the latter is cast by parallel rays of light inclined #de to the horizon1 and is detached from the outline of the tree4 ,when the scale is large1 the shadow will be elliptical in form1 but in small scales it will become a simple circle4 ,in representing woodland1 the trees and masses of trees should be disposed in every possible variety of position1 care being taken1 however1 to avoid all regular figures and arrangements in lines4 ,in parks and gardens1 where the arrangement of the trees is artificial1 it is usual to represent a grove in a rectangular form4 ,orchards are shown by placing single trees with their shadows at the points of intersection of two sets of equidistant parallel lines drawn at right angles to each other4 ,these lines are drawn in pencil and afterwards erased4 ,some draughtsmen prefer to draw trees in elevation1 as shown in ,fig4 #ef4 ,this method allows the various kinds of trees to be distinguished on the plan1 and gives scope to artistic skill4 ,illustration3 ,,fig4 #eg4 ,uncultivated ,land4--,uncultivated land1 other than woodland1 is represented by drawing bushes in plan1 similar to trees1 but of smaller dimensions1 and mixing tufts of grass with them1 as shown in ,fig4 #eg4 ,illustration3 ,,fig4 #eh4 ,contour ,lines4--,suppose a cone ,a ,b ,c 7,fig4 #eh7 cut at regular vertical intervals apart by a series of horizontal planes #a1 #b1 #c4 ,the intersections of these planes with the surface of the cone will give lines upon that surface2 and it is obvious that the cone may be represented in plan by the projection of these lines1 as shown in the figure4 ,to obtain this projection1 draw the horizontal line ,d ,e1 and from the apex of the cone and from the intersections of the cutting planes let fall vertical lines4 ,from the point where the line from the apex meets the line ,d ,e as a centre1 with radii equal to the distances from this point to those where the lines from the sections meet ,d ,e1 describe circles4 ,these circles will be the horizontal projections of the lines on the surface of the cone produced by the cutting planes2 and these lines are called contour lines4 ,also it is obvious that1 from the plan of the cone so obtained1 we may as readily project the elevation1 provided we know the vertical distance apart of the sections denoted by the contour lines4 ,to obtain the elevation1 we have only to draw horizontal lines at the given distance apart1 and from the points in ,d ,e erect perpendiculars to meet them4 ,lines drawn through the points of intersection will give the elevation of the cone4 ,to find the inclination of the surface of the cone1 upon a b1 a portion of the normal ,d ,e1 as a base1 erect a perpendicular b c1 equal in height to the distance of the sections apart1 and join a c4 ,the hypothenuse a c then represents that portion of the surface of the cone which is included between the two contour lines1 and of which the angle of inclination is b a c4 ,the space between two contour lines is called a horizontal zone4 ,the cone being a regular figure1 its contour lines are circles4 ,for irregular figures1 the contour lines will be irregular curves4 ,the regular inclination of the surface of the cone causes the projections of the contour lines to be at equal horizontal distances apart4 ,but when the inclination varies1 the horizontal distance between the contour lines also varies1 the distance decreasing as the inclination increases4 ,thus the method of representing objects in plan by contour lines1 not only gives the correct form of the object1 but shows the relative inclination of every portion of its surface4 ,this may be clearly seen in ,figs4 #ei and #fj1 the former of which is a representation in plan by contour lines of an irregularly shaped object1 and the latter an elevation of the same object projected from the plan4 ,illustration3 ,,fig4 #ei4 ,illustration3 ,,fig4 #fj4 ,the system of representation by contour lines is generally adopted by topographers to distinguish and define the variation of the surface of the ground in regard to hill1 valley1 and plain4 ,by intersecting a mountain1 for example1 by a sufficient number of horizontal planes1 its correct form may be delineated1 and the declivity of its surface accurately shown4 ,the relative declivity of any portion of its surface is indicated by the difference in the horizontal distance of the curves apart2 and by constructing a triangle upon a normal to the upper curve in the manner already described for the cone1 the absolute slope at any point between any two curves may be readily determined4 ,the ground is supposed to slope uniformly from one curve or contour line to the next4 ,such1 however1 is rarely the case2 but provided the curves are taken at frequent intervals1 the error is of no practical importance4 ,hollows are represented in the same way2 and whether the representation is that of a hill or a hollow1 is known from the other parts of the map4 ,thus1 if ,fig4 #ei represent a hill1 the vertical projection will be as shown in ,fig4 #fj2 but if it denote a hollow1 the outer curve must be projected highest1 and the vertical section will be ,fig4 #fj inverted4 ,in practice the contour lines are numbered1 the number of any contour indicating its height above a plane of reference called a datum plane4 ,the vertical distance of the contour lines apart varies with the character of the ground and the object of the survey2 but it is seldom less than #be feet4 ,the lines are obtained by the surveyor by fixing a number of points on the same level by means of instruments4 ,,section ,,iv4--,,colours4 ,the preceding ,section treats exclusively of representation by lines and dots1 or that mode of delineating objects and natural features known as line or pen drawing4 ,there is1 however1 another mode of representation by means of colours that is fast coming into general use4 ,this latter mode is far more expressive than the former1 and1 besides affording a wider scope for artistic effect1 shows with greater distinctness and precision the character of the object represented4 ,for these reasons it is almost always adopted for plans of estates and geological sections1 and also very frequently for other kinds of topographical as well as for engineering and mechanical drawings4 ,the colours used for this purpose are not applied in the way the artist applies them2 but they are laid on in thin washes to produce a faint tint rather than a body of colour4 ,the process is called tinting or flat-washing1 and though it cannot be described as a work of art1 considerable practice and skill are requisite to execute it properly4 ,flat-tints4--,a drawing to be coloured must be previously stretched and gummed to the board1 in the manner described in ,section ,i4 ,unless the paper be prepared in this way1 it will remain blistered after being wetted by the laying on of the tints4 ,the lines of the drawing must be very fine1 and the ink1 though black1 should not be thick4 ,great care should be exercised in drawing in the outlines1 that there be always a piece of clean paper between the hand and the drawing1 for the least degree of greasiness will prevent the colours from working freely4 ,should the surface of the paper1 however1 from inattention to this matter1 or from accident1 become slightly greasy1 the defect may be partially remedied by adding a little prepared ox-gall to the water with which the colours are mixed4 ,when all the outlines have been drawn in and the pencil lines erased1 the drawing is prepared for the colouring by being washed4 ,the washing is effected by passing a soft sponge well saturated with clean water gently and rapidly over the surface4 ,the purpose of this washing is twofold2 first1 to remove those portions of the ink which a wet brush would detach from the paper in laying on the colours1 and which1 by becoming mixed with the tint1 would injure its purity2 and second1 to damp the surface of the paper in order to prevent the colour from drying too rapidly4 ,the latter is an important matter1 for if the tint which is being applied dries quickly1 it is impossible to unite the edges properly1 and the tint1 especially if the surface be large1 will have a cloudy and blotchy appearance4 ,as the operation of washing renders the paper too wet to immediately receive the colour1 it must be allowed to remain in a perfectly horizontal position for a short time to dry1 and during this time any tendency to dry unequally must be corrected by means of blotting-paper4 ,while the paper is drying1 the tints may be prepared4 ,to ensure satisfactory results1 care must be taken in the preparation and preservation of the tints4 ,they should never be made by artificial light1 and a sufficient quantity should be made at first to cover all the portions required1 as it is very difficult to match a tint exactly4 ,when a drawing is several days in hand1 it is best to prepare a fresh tint for every coat1 for the colours will change in the course of a day or two1 even if protected from the light4 ,a few drops of water should be added now and then1 to make up for the loss by evaporation1 especially in warm weather4 ,tints left to dry upon the palette should never be wet up again for use1 but they should be washed clean out and a fresh tint made2 if this precaution be not attended to1 the colour will not be pure4 ,when a tint is to be mixed1 the end of the cake of colour should be moistened and allowed to soften for a minute or two1 as this will cause it to rub smooth and free from fragments4 ,the palette should then be moistened and the end of the cake rubbed gently and evenly upon it till a sufficient quantity of colour has been obtained1 which may be added to the requisite quantity of water by means of a brush4 ,a precaution necessary to be observed is never to rub one colour down upon another1 as it will probably be laid aside to dry with the other colour on it4 ,the brush used should be as large as the nature of the work will allow1 and it should be of the best sable hair2 the quality is judged by the length of the hair1 the longest and stiffest being the best4 ,draughtsmen frequently do all their work with a couple of sable brushes attached to one holder1 one being for colour and the other for water2 in this case the brushes should be of different colours to prevent mistakes4 ,the art of laying on a flat-tint consists in allowing the coloured water to flow equally over the paper1 which thus becomes uniformly tinged4 ,to facilitate this1 the surface of the drawing should be inclined towards the draughtsman at an angle of about five degrees during the process of laying on the colour4 ,having taken as much colour on the brush as it will safely carry without dropping1 the operation of applying it should be begun in the upper left-hand corner1 the brush being carried along towards the right1 so as to make the colour lie neatly along the upper outline4 ,the brush should then be struck unhesitatingly from right to left and from left to right alternately1 so as to bring the colour down in horizontal bands or stripes1 taking care not to pass the brush a second time over the same surface during the same wash1 and to control it neatly within the proper limits4 ,if the surface of the paper be in this way kept well wetted with the colour1 or if1 in other words1 a flow of colour be kept in motion with the point of the brush1 the tint can be carried on with perfect continuity4 ,it is important to keep as nearly as possible the same quantity of colour in the brush until the lower outline is nearly reached1 when the quantity must be diminished so as to finish at the lower outline without a great excess of tint1 for the excess must be taken up by a damp brush4 ,no accumulations should be allowed to take place anywhere1 as on drying1 these places would show a darker tint4 ,when the colour has once flowed over the surface1 the tint is finished1 and must not1 as we have said1 be touched a second time1 for any attempt to remedy defects while the colour is drying will only make them worse4 ,generally it will be found that the more quickly a tint is laid on1 the better is its appearance4 ,a little practice will enable the student to lay on a wash in the proper manner1 but to keep within the outlines is a matter of greater difficulty and one that requires some dexterity in the handling of the brush4 ,if the boundary should be exceeded1 a finger of the left hand should be instantly applied to brush the colour back4 ,though the foregoing directions can be followed strictly only on large surfaces1 the principles involved in them must in every case be observed4 ,the alternate or double tint consists of two colours applied alternately1 their edges being made to blend into each other4 ,the application of the double tint involves no particular difficulty4 ,having prepared two tints of equal intensity and provided a brush for each1 lay on one of the colours at the upper outline of the figure1 and before this dries1 take the brush charged with the other colour1 and run round its edge1 allowing them to blend together4 ,repeat the first tint in the same manner1 and continue the tints alternately till the surface is covered4 ,the forms of the masses of each colour should be varied1 and not made in stripes or spots1 but irregularly clouded4 ,all flat-tints should be made very light1 and intensity of colour should be produced by repeating the wash4 ,as every surface looks better with two washes than with only one1 the strength of the tint should be such as to allow two coats to be laid over the lightest parts4 ,if the colours have been laid on too dark1 or the general effect be uneven and disagreeable1 the defect may be remedied by sponging4 ,this operation should be performed with a close-grained #f-;inch sponge1 and be commenced at the upper end of the inclined board4 ,a basin of clean water having been provided1 and an empty basin to receive the dirty water from the sponge1 first moisten all the white surface of the paper to prevent the tint taken off by the sponge from adhering to it2 then1 having filled the sponge with water1 pass it gently to and fro across the sheet4 ,press out the dirty water into the basin1 refill the sponge1 and repeat the operation until hardly any tint comes off4 ,sponging after five or six coats have been laid on generally improves the appearance of a drawing2 it softens down asperities1 and makes the tints blend into each other2 the surface of the paper also takes the tints more readily after sponging4 ,small defects may frequently be remedied by a process called stippling4 ,this consists in making a number of dots with the point of a brush containing an almost imperceptible quantity of colour4 ,the process1 though a tedious one1 produces a very beautiful effect1 similar to that of dotted engravings4 ,excesses beyond the boundary lines may be washed out with the water-brush1 and the stains removed by a piece of clean blotting-paper4 ,white spots left in a tint may be filled up1 after the tint is dry1 with the point of the brush2 but care must be taken not to touch beyond the edges of the tint1 as that would double the intensity at the edges and produce a ring4 ,all flat surfaces in a drawing should be lighter or darker1 in accordance with their distance from the eye4 ,in laying on flat-tints when the surface is not in shade1 it must be borne in mind 7#a7 that all surfaces which are parallel to the plane of the picture1 and therefore equally distant from the eye1 should receive a tint of uniform intensity2 7#b7 that those surfaces which are farthest from the eye should receive the darkest tint2 and 7#c7 that surfaces which are inclined to the plane of the drawing should receive a tint of varying intensity1 the depth of the tint increasing as the surface recedes from the eye4 ,when the surfaces are in shade1 the converse of these rules holds good4 ,conventional ,colours4--,in representing objects by means of colours1 the natural colours of the objects are in some cases adhered to2 and in others1 for the sake of greater distinctness1 a conventional colour is adopted4 ,in engineering1 architectural1 and mechanical drawings1 the latter mode is nearly always resorted to1 while in plans of estates the former is very frequently employed4 ,unfortunately1 practice is not uniform among draughtsmen in the conventional use of colours2 but the following ,table shows the colours mostly employed1 and represents the general practice4 ,carmine or crimson lake ,for brickwork in plan or section to be executed4 ,prussian blue ,flintwork1 lead1 or parts of brickwork to be removed by alterations4 ,venetian red ,brickwork in elevation4 ,violet carmine ,granite4 ,raw sienna ,english timber1 not oak4 ,burnt sienna ,oak1 teak4 ,indian yellow ,fir timber4 ,indian red ,mahogany4 ,sepia ,concrete works1 stone4 ,burnt umber ,clay1 earth4 ,payne's grey ,cast iron1 rough wrought iron4 ,dark cadmium or orange ,gun metal4 ,gamboge ,brass4 ,indigo ,wrought iron--bright4 ,indigo1 with a little lake ,steel--bright4 ,hooker's green ,meadow land4 ,cobalt blue ,sky effects4 ,and some few others occasionally for special purpose4 ,sections are represented either by lines of the colour drawn with the pen or the point of the brush1 or by a darker shade of the colour4 ,in mechanical drawings1 sections are frequently shown by ink lines drawn over the colour4 ,in plans and maps1 as we have said1 some attempt is made to give the true appearance of things4 ,as this--which may be called the natural mode of representation--allows more scope for artistic skill than the conventional1 a great deal must be left to the judgment and the taste of the draughtsman4 ,but there are general principles and features that may be laid down and described1 and such are the following3-- ,water4--,for water1 a flat-tint of pure indigo is used4 ,to produce the clear1 transparent effect of water1 there should be two coats of the tint1 which1 to allow of this1 must be very light coloured4 ,grass-land4--,for grass or cleared land1 a flat-tint of green is employed4 ,this tint is composed of indigo and gamboge1 and should be of a lively hue1 which may be produced by giving predominance to the gamboge4 ,care must always be taken in preparing greens for maps and plans1 that the blue be kept subordinate to the yellow2 for a predominance of the former colour produces a cold quality1 which is utterly destructive of that natural appearance it is intended to give4 ,the intensity of the tint for this and for other purposes should be such as to distinguish it clearly from others1 and to allow somewhat for fading1 without masking any of the details of the drawing2 and it must be clear and transparent4 ,we may here remark that all tints which are much extended should be balanced1 that is1 no one should obtrude itself upon the eye by its relatively too great intensity4 ,marsh4--,marsh and swamp are represented1 as in line drawing1 by a combination of the signs for water and grass-land4 ,the tints are laid on horizontally1 that is1 parallel to the base of the drawing4 ,they are not1 however1 laid on in bands or strips across the drawing1 but are made to project in irregular points from each side1 with here and there a long and narrow patch to represent an island4 ,the land should cover a larger portion of the space than the water1 and it should be washed in first1 care being taken to make the white spaces left for the blue colour resemble the green in form1 which spaces should project their horizontal points into the green as the latter projects its points into the white4 ,the outer limits of a marsh should consist of an outline of projecting green points4 ,the land portion of the marsh is finished by drawing a light shading line of indigo and burnt sienna along the lower edge of the green4 ,this line must be drawn upon the edge and not against it upon the white space4 ,in washing in the water1 care must be taken not to overlay the edges of the green4 ,a good effect is produced by introducing a tree here and there upon the land4 ,sand and ,gravel4--,sand is shown by a flat-tint of yellow ochre4 ,sand and gravel are represented by dotting the flat-tint with burnt sienna by means of the point of the brush held in a vertical position4 ,stones and rocks in sand should be first outlined with the pen in burnt sienna and sepia in equal proportions1 and afterwards filled in with the brush with the same colour4 ,mud4--,in the survey of rivers1 creeks1 and coasts1 it frequently becomes necessary to show tracts of mud between the lines of high and low water4 ,for this purpose a flat-wash of sepia or ,indian ink may be used dotted with ,indian ink of greater intensity4 ,the dots in this case must be very minute and thinly placed1 and they should be evenly distributed4 ,a fine-pointed pen will be found more effective in putting in these dots than the point of the brush4 ,woodland4--,to represent woodland1 a flat-tint of green is first laid over the ground1 as for grass-land4 ,the groups and masses of trees are next drawn in outline1 in the manner described in the last ,section1 with a hard and sharp lead pencil1 or with a pen and pale ink4 ,to fill in these outlines1 a colour made up of indigo and gamboge in the same proportions as the ground tint1 but of greater intensity1 is laid on the lower and right-hand portion of each tree and mass of foliage1 so as to occupy about two-thirds of the figure4 ,the remaining portion1 which will be the side towards the light1 is then touched with an orange tint composed of gamboge and burnt sienna4 ,it only remains to add the shadow4 ,as the light is supposed to enter the drawing in parallel rays from the upper left-hand corner1 the shadow of every object will surround its lower and right-hand outlines4 ,it is laid close up to the outline in masses of foliage2 but for single trees1 as in orchards1 it is detached4 ,the form of the shadow was described in the last ,section4 ,to produce the shadow1 the same tint is used as for the ground1 two or three successive applications being sufficient to increase the intensity to the requisite degree2 or a neutral tint may be used1 composed of indigo1 burnt sienna1 and a little lake4 ,after the shadow has been put in1 the outlines on that side should be strengthened by going over them again with the pen4 ,by drawing the trees in elevation1 an opportunity is afforded for the display of artistic skill far greater than the foregoing method admits of4 ,when drawn in this way1 the work partakes somewhat of the nature of landscape painting4 ,cultivated ,land4--,cultivated land is represented by a flat-tint of burnt sienna4 ,uncultivated ,land4--,uncultivated land or brushwood is represented by a double tint of green1 as for grass-land1 and burnt sienna1 as for cultivated land1 laid on in the manner already described for the double tint4 ,as this is the only double tint used1 it may be made1 if thought desirable1 with alternate green and crimson lake4 ,buildings4--,buildings1 including all structures of masonry1 as bridges1 locks1 walls1 and such like1 are coloured with crimson lake1 and shadowed with a neutral tint composed of indigo1 burnt sienna1 and a little lake1 as given above for forest land4 ,roads and ,streets4--,roads and streets1 and generally all those portions of a drawing not particularly described1 are tinted with yellow ochre4 ,fences4--,hedges are represented by green dots1 varied in size for bushes2 stone or brick walls1 by a line ruled in red2 and wooden fences by lines of neutral tint1 either ruled or drawn in by hand1 according as the line is to be straight or otherwise4 ,in every case the shadow must be put in4 ,in determining the intensity of the various tints employed on a topographical drawing1 care must be taken that everything be 8in keeping40 ,a cardinal rule of art is that nothing shall unduly obtrude itself2 and in a coloured plan1 spottiness1 as it is called1 should be studiously avoided4 ,forest1 brushwood1 and cultivated land1 should be represented by tints of about equal intensity1 and the same equality may be observed for grass-land1 marsh1 water1 and sand1 but the intensity should be less than in the former case4 ,tints that are of small extent may be a little exaggerated in intensity for the purpose of giving them greater distinctness1 especially when the object represented is a building4 ,gardens and orchards require a little exaggeration in depth of tint1 to distinguish them from the surrounding country2 but care must be taken not to make the distinction too marked4 ,it will generally be found conducive to a maintenance of 8keeping10 to lay the lightest tints on first4 ,,section ,v4--,,shading4 ,in mechanical and architectural drawings1 shade lines must be considered rather as embellishments than constituent parts of the drawing4 ,they are1 however1 frequently employed2 and as their incorrect use may deceive the eye with respect to the intention of the designer1 it becomes an important matter to know when to apply them with propriety4 ,illustration3 ,,fig4 #fa4 ,illustration3 ,,fig4 #fb4 ,application of ,shade ,lines4--,as we have already explained1 the light is supposed to fall upon the objects in a drawing in parallel rays from the upper left-hand corner for elevations1 and from the lower left-hand corner for plans4 ,to determine whether or not a given line should be a shade line1 we have only to ascertain whether or not the light1 introduced in such a manner1 falls upon that edge of the object which the line represents4 ,all those parts of a body upon which the rays of light fall directly1 are said to be in light2 all those parts upon which the rays of light do not fall directly1 are said to be in shade2 and those parts of a surface which are deprived of light by another body intercepting the rays1 are said to be in shadow4 ,these definitions should be borne in mind4 ,lines representing the boundaries of surfaces in light should be fine lines1 and lines representing the boundaries of surfaces in shade should be thick or shade lines4 ,let it be required1 for example1 to determine the shade lines of the cube shown in elevation in ,fig4 #fa4 ,the extreme rays of light falling upon the cube meet the edges in b and c2 hence the surfaces a b1 a c1 are in light1 and the surfaces d b1 d c1 are in shade4 ,the foregoing rule will thus make a b and a c fine lines1 and d b and d c shade lines4 ,if the cube were turned so that a b should be at right angles to the rays of light1 the extreme rays would fall on the edges a and b1 and the middle ray which now falls on a would fall on the middle of the line a b4 ,the rays immediately beyond those which are arrested by the edges a and b1 may be considered to pass along in contact with the surfaces a c and b d2 and these surfaces must1 therefore1 be regarded as in light4 ,thus we shall have in this case the lines a b1 a c1 and b d1 fine lines1 and the line c d a shade line4 ,it is the practice of some draughtsmen to make a c and b d in such cases a medium line1 and the practice has propriety to recommend it4 ,the foregoing explanations of the shade lines in the elevation of the cube1 render any further remarks concerning those in the plan1 ,fig4 #fb1 unnecessary4 ,in practice1 whether or not a surface is in light may be determined by placing the set square of #de against it4 ,illustration3 ,,fig4 #fc4 ,illustration3 ,,fig4 #fd4 ,the same principles are observed in the end elevation of the hollow cylinder1 shown in ,fig4 #fc4 ,the extreme rays meet the circumference in the points a and b2 consequently the surface a c b is in light1 and the surface a d b is in shade4 ,the middle ray meets the surface perpendicularly at the point c1 which will be the lightest part of that surface2 similarly1 d will be the darkest part4 ,to show this1 the shade line must be gradually increased in thickness towards the point d4 ,the shading of the inner circle will be the converse of the outer4 ,fig4 #fd shows a plan of the same object4 ,illustration3 ,,fig4 #fe4 ,cylindrical ,surfaces4--,let a b c d1 ,fig4 #fe1 be a plan1 and k l n m an elevation of a cylinder4 ,the portion a c b is in light1 and the portion a d b is in shade1 of which latter portion a and b are the edges4 ,from the points a and c draw vertical lines e f1 g h4 ,then will e f be that part of the cylinder upon which the light falls perpendicularly1 or the lightest part1 and g h the edge of the surface in shade1 or that portion of the surface of the cylinder that would cast a shadow upon the plane of projection4 ,hence this will be the darkest part1 and consequently it is obviously improper to make the line k l a shade line4 ,this demonstration1 which is given by ,binns1 shows that shade lines must never be applied to cylindrical surfaces4 ,if this principle be observed1 cylindrical may be readily distinguished from flat surfaces4 ,illustration3 ,,fig4 #ff4 ,shading ,lines4--,shade lines are applied only to the edges or boundaries of surfaces2 when lines are put upon a surface to show the effects of light and shade1 they are called shading lines4 ,the use of the latter is determined by the same principles as that of the former2 indeed1 a shade line may be practically considered as an end view of a number of shading lines4 ,in ,fig4 #ff1 which is an elevation of a hexagon1 the surface c is in shade1 and to represent this surface correctly1 it must be made darker than the others4 ,this darkening of the surface is effected by drawing the shading lines heavier or closer together1 or by both of these means combined4 ,the surface b is in light1 but the rays fall upon it obliquely2 the shading lines on this surface will therefore be lighter and more widely spaced than on c4 ,the surface a is also in light1 and receives the rays normally1 that is1 the direction of the rays is normal to the surface4 ,hence this surface will reflect most1 or1 in other words1 will be the lightest4 ,this is shown by making the shading lines still lighter1 and spacing them still more widely than those on b4 ,the greatest care is needed in applying shading lines to keep their thickness and the spacing regular1 as an error in these respects will frequently produce an effect quite opposed to what is intended4 ,illustration3 ,,fig4 #fg4 ,shading ,lines on ,cylindrical ,surfaces4--,if the demonstration previously given concerning shade lines on cylindrical surfaces be understood1 the application of shading lines to these surfaces will present no difficulty4 ,the darkest and the lightest part of the cylinder having been determined1 and in practice this can be accomplished with sufficient exactness by the eye1 the shading lines are applied according to the principles explained above with respect to the hexagon4 ,the first shading line is drawn upon the darkest part2 and each successive line on each side of this first line is drawn lighter and spaced more widely than the preceding4 ,at the lightest part1 a clear space is left to represent the reflexion of the rays that occurs strongly there1 and beyond this part the shading is made equal to that of the corresponding part on the other side4 ,the thickening of the lines is effected by going over them a sufficient number of times4 ,fig4 #fg shows a vertical and a horizontal cylinder shaded in this manner4 ,in outline drawings of machinery1 this mode of shading with parallel lines is frequently resorted to4 ,illustration3 ,,fig4 #fh4 ,illustration3 ,,fig4 #fi4 ,illustration3 ,,fig4 #gj4 ,illustration3 ,,fig4 #ga4 ,it will be evident1 on reflection1 that when the cylindrical body stands parallel with the direction of the rays of light1 as shown in ,fig4 #fh1 the lightest part will be in the middle1 and the shade will increase in intensity as it approaches the edges4 ,the shading of the interior of a cylinder is1 as we have already remarked when treating of shade lines1 the converse of that of the exterior4 ,this is shown in the sectional elevation1 ,fig4 #fi4 ,when parallel with the direction of the rays of light1 as in ,fig4 #gj1 the internal shading is the same as the external4 ,on bright circular surfaces1 such as that of a circular saw1 or the polished end of a shaft1 the light is radiated from the centre1 as shown in ,fig4 #ga4 ,this mode of shading is strictly in accordance with the appearance presented by such surfaces4 ,it may be remarked here1 that if1 through inadvertence1 any part should be made too dark1 the error may be corrected by darkening all the other parts in a corresponding degree4 ,illustration3 ,,fig4 #gb4 ,shading ,lines in ,topographical ,drawings4--,the shading lines put upon mechanical drawings are merely accessories used for purposes of embellishment4 ,but in topographical drawings1 shading lines are applied to give expression1 and they constitute an essential element in the representation4 ,we have shown how undulations of the ground1 constituting hill and valley1 are represented by contour lines4 ,but it is obvious that these lines furnish information respecting the character of the surface only at those points through which they pass4 ,thus we are necessarily left in ignorance of the irregularities existing between any two successive contours4 ,to supply this information which the contours fail to give1 shading is resorted to4 ,another important object of hill shading is to represent the surface of the ground conventionally in a manner that will immediately afford an idea of its character without the aid of regular contours4 ,the method adopted consists in employing lines varying in their thickness and in their intervals apart according to the slope of the ground to be represented4 ,this method is based upon the principle of the horizontal contours1 which is to give to the same vertical interval the same absolute amount of shade1 whatever the inclination of the ground may be4 ,the shading lines are used1 as we have said1 to fill in the features of the ground between contours already fixed2 and to ensure accuracy and uniformity in the representation1 a 8scale of shade0 is employed4 ,the accompanying ,fig4 #gb shows the standard scale of shade adopted by the ,council of ,military ,education1 and made use of for all the ,government surveys4 ,the second and the fifth columns of this scale show the spacing of the hachures and their thickness for different angles of slope1 while the first and the last columns show the number of hachures to be interpolated between contours at every #be feet vertical intervals1 supposing the slope to be uniform4 ,the slope is denoted both by the number of degrees in the angle it makes with the horizontal1 and by a fraction showing the ratio of the vertical height to the base in a right-angled triangle1 the hypothenuse of which is the slope in question4 ,the scale of shade is constructed for a horizontal scale of six inches to the mile1 and the amount of shade has been chosen with a view of producing the best possible artistic effect4 ,of course1 the most satisfactory results1 both artistically and practically1 will be obtained when the ground is delineated to this scale1 but it can be readily applied to any other scale4 ,for example1 the horizontal interval for a slope of 1 corresponding to a vertical interval of #be feet1 will be #bj #be #ejj feet1 which1 on a scale of six inches to a mile1 will be represented by a length equal to #f #jeff inches4 ,in this case1 therefore1 supposing the slope of the ground to be uniform between two given contours #be feet apart1 we should represent it by means of the hachures shown opposite a slope of 1 continued over a space of #jeff inch4 ,illustration3 ,,fig4 #gc4 ,in topographical drawings1 the light is supposed to fall vertically upon the surface2 hence a level surface will reflect all the light that falls upon it1 while one of #de will not reflect any4 ,the drawing of the hachures presents certain difficulties of execution that can be overcome only by continued practice and careful attention to the modes of proceeding which experience has proved to be the most effectual4 ,thus an important rule is always to draw 8from left to right and downwards40 ,to allow this to be done1 the drawing must be placed with the summit of the hill to the left hand1 and be turned round as the work progresses4 ,the hachures should always be commenced at the crest of the hill1 working outwards towards the foot of the slope4 ,they should be drawn firmly1 and of a length varying from inch to inch1 according to the width of the zone1 that is1 according to the greater or less degree of the slope1 as shown in ,fig4 #gc1 at a1 b1 c1 d4 ,when the hill is steep1 the lines are made short and thick1 and when the declivity is less1 they are made longer and lighter1 becoming fine and clean as the level is approximated to4 ,a difficulty with beginners is to press upon the pen equally from the beginning to the end of the stroke1 the tendency being to press more heavily towards the end1 thus producing a whip-like appearance quite opposed to artistic effect1 and conveying a false impression of the character of the ground4 ,a good effect is produced by imparting a slightly tremulous motion to the pen when drawing the hachures4 ,the form of the hill being accurately defined by the pencil contour lines1 it is not necessary that the accessory curves formed by the shading lines should be rigorously continuous1 and indeed a much better effect1 artistically1 is gained by avoiding such a manner of drawing them4 ,the various sets of lines must be placed together1 end to end1 in such a way that the groups or sets shall not be separated by a vacant space1 nor overlap each other4 ,care must be taken that the junctions of sets in two contiguous zones do not form a continuous line from one zone to the other1 but everywhere 8break joint40 ,each zone must be filled in before the next lower one is commenced1 the drawing being turned as the work progresses to allow the rule enunciated above of 8from left to right and downwards0 to be complied with4 ,the distance between the shading lines must be increased or diminished according as the width of the zone varies1 so as to divide the space equally2 and on reaching the part where the lines were begun1 the ends must be brought neatly together4 ,as this can be most satisfactorily accomplished where the lines come close together1 it is best to begin at the steepest part of the slope4 ,in taking a set of hachures round a sharp bend1 as in the case of a spur or a ravine1 a practical difficulty occurs1 which difficulty is increased as the angle becomes more acute4 ,the most effective way of overcoming this difficulty is to draw a pencil line down the spur or re-entering angle1 as shown at ,a ,b and ,c ,d in ,fig4 #gd1 and to mark off on this line1 at the proper intervals1 small arcs of the same radius1 as near as can be judged by the eye1 as the curve of the contour line4 ,the sets of hachures on each side may then be drawn to these arcs4 ,guiding lines1 as a b1 c d1 e f1 and g h1 should be drawn at right angles to the general direction of the contours to ensure the hachures being correctly placed before and after rounding the angle4 ,for this method of carrying a set of hachures round a sharp curve1 we are mainly indebted to ,lieut4 ,r4 ,pulford's #8,theory and ,practice of ,drawing4' ,when this method is not employed1 the hachures must be drawn on each side of the angle first1 and those for the angle filled in separately4 ,illustration3 ,,fig4 #gd4 ,great care must be taken in filling in the zones formed by the contour lines1 that the drawing when finished do not present the appearance of separate layers or bands2 for such an appearance is not only quite opposed to artistic effect1 but it conveys a false notion of the character of the ground4 ,the successive zones are not separate portions of the surface1 but each is a continuation of the one adjoining it4 ,the great principle to be observed in this1 as in all matters of hill shading1 is that changes of slope are gradual4 ,when the contours are only pencilled in as guide lines to be afterwards erased1 the above-mentioned defect may be avoided by drawing the hachures over them1 without reference to exact spacing4 ,but when1 as is usually the case in regular surveys1 the contours are inked in in dotted lines1 the only means of avoiding it is to space the hachures on each side of a contour line at the same distance apart4 ,the student of map drawing should practise assiduously this system of shading in detached portions before undertaking the delineation of a complete hill4 ,for such exercises1 either a soft1 medium-pointed steel pen1 or a quill may be used4 ,the ,vertical ,system of ,shading4--,the foregoing system of shading is known as the ,horizontal1 and is now generally employed in this country for all kinds of surveys4 ,there is1 however1 another system much used abroad1 and frequently adopted here for engraved maps4 ,in this system1 which is known as the vertical1 the shading lines are made to radiate from or converge into the curved parts of a hill1 according as they project or re-enter4 ,such lines are called lines of greatest descent2 they are supposed to describe the same course that water would describe if allowed to trickle in streams down the slopes1 and hence they exhibit both the direction and the degree of the slope4 ,having the horizontal sections given1 we may obtain a complete knowledge of the direction in which the ground slopes by drawing perpendicular to them any number of lines of greatest descent2 the degree of declivity is expressed by purely conventional means4 ,the means adopted for this purpose are of two kinds4 ,one depends upon the principle of vertical illumination1 in which the maximum quantity of light is reflected upwards to the eye by a horizontal surface1 and a minimum by a surface inclined #de to the horizon4 ,this is the ,english and ,german convention1 and it lays more stress upon the proportions of black to white in indicating the degree of slope1 than upon the distance between the shading lines4 ,the other convention1 which is the ,french1 on the contrary1 makes its expression depend more upon the distance between the lines of greatest descent than upon the shade of colour produced1 though in this also the tint is graduated from dark to light1 according to the degree of declivity4 ,a scale of shade is used for this system1 founded upon the same principles as that already given for the horizontal system4 ,the scale adopted is due originally to ,major ,lehmann1 of the ,saxon ,infantry2 but it has received some modification to adapt it to the requirements of practice4 ,fig4 #ge shows ,lehmann's scale4 ,it is constructed for every #e1 from a level up to a slope of #de1 which is the steepest slope at which earth will stand4 ,each division of the scale corresponding to a given slope is subdivided into nine parts1 to show the proportions of black to white4 ,for a level1 the whole of these spaces are left white2 for a slope of #e1 the proportion is one black to eight white2 for a slope of #aj1 two black to seven white2 and so on up to #de1 for which slope we have all black4 ,the longitudinal divisions of the scale below that against the outer edge ,a ,b contain the same proportions of black to white1 but equally distributed to show the mode of applying it4 ,thus1 in the division o p r s1 corresponding to a slope of #e1 the single black space is1 in ,e ,f ,g ,h1 divided into two equal parts and distributed2 in ,g ,h ,i ,k1 these two parts are again equally divided and distributed2 and so on throughout the other longitudinal divisions4 ,if now the scale be cut off along the line ,l ,m1 the part ,l ,m ,c ,d will constitute a scale1 the graduated edge ,l ,m of which will furnish us with a means of marking off the distance between the centres of the shading lines4 ,illustration3 ,,fig4 #ge4 ,,lehmann',s ,,scale ,,of ,,shade4 ,to find the proportion of black to white in the foregoing scale for any given slope3--,subtract the given inclination from #de for a denominator1 and put the given inclination for a numerator4 ,in the scale1 as drawn in the figure1 the variations are by #e2 but it is obvious that a scale may be drawn in the same manner to mark smaller variations1 if thought desirable4 ,in applying this method in the ,united ,states' ,coast ,survey1 it was remarked that 8this scale of shade does not represent slopes greater than #de1 thereby limiting the graphic capabilities and effect of the map4 ,it also makes the slopes too dark as they approach the inclination of #de1 and does not well represent slopes of less than #e1 which latter it is often desirable and necessary to express distinctly40 ,the following modification was therefore made3-- ------------------------------ ,proportion of ,slope4 ------------ ,black4,white4 ----------------------------- #b or #b #a #aj #e #f #b #i #aj #aa #c #h #ae #af #d #g #be #bf #e #f #ce #f #e #de #g #d #fj #h #c #ge #i #b ----------------------------- ,by this scale1 the slighter slopes are represented distinctly4 ,for slopes less than #af1 the shades are darker than in ,lehmann's scale2 this makes their difference more noticeable4 ,above #be the shades are lighter4 ,a further modification1 which for ordinary purposes possesses the advantages of simplicity and facility of application1 has been made in ,england1 and very generally adopted4 ,this modification consists in fixing with accuracy only three proportions of black to white for three medium slopes1 as follows3-- -------------------- ,proportion of ,slope4------------ ,black4,white4 ------------------- ,level 44 all #ae #a #b #bb #a #a #cj #b #a #de all 44 ------------------- ,a scale of shade may at once be constructed from this ,table1 by assuming the thickness of the shading line for the medium slope of #bb1 which thickness must be suited to the scale1 and to the degree of fineness and finish it is intended to give the drawing4 ,generally1 if the lines have such a relation to the scale of the drawing as to present a well-connected appearance1 it will be found that fewer shading lines and a rather coarse texture will conduce more to clearness of expression than a finer texture1 which tends to produce a dryness of style4 ,in shading to this scale1 it should be applied to the drawing wherever the slope corresponds to one of the three on the scale4 ,intermediate slopes are indicated by graduating the thickness of the shading lines4 ,in all cases a good deal must be left to correctness of eye and skill of hand4 ,in the ,french method1 as we have said1 the inclination is expressed by the distances between the centres of the lines of greatest descent4 ,the limits of the slopes that can be represented by this method are1 or #de for the greatest and or #j #ec #dc for the smallest4 ,the largest scale that will admit of conveniently drawing the lines of greatest descent is full size1 or about #h feet to a mile4 ,the vertical distance between the horizontal sections is generally taken as #a yard4 ,hence to a scale of the least width of zone will be inch1 and the greatest #fd #c inches4 ,the distance between the shading lines is reckoned from centre to centre1 and is determined by the rule3--,to the distance between the upper and the lower curves of any zone add of an inch2 a sixteenth part of this sum will be the proper interval for the shading lines4 ,the distance is measured along the line of greatest descent4 ,thus1 if the inclination be and the scale 1 the width of zone will be #jf #fj #cfj inches1 and by the rule we have #cfj #c #ci --------- --- #jbdd inch4 #af #af ,another rule is3--,to a fourth of the distance between the upper and the lower curves of any zone1 add of an inch2 a fourth part of the sum will be equal to the interval4 ,the thickness or breadth of the lines is made to vary directly as the inclination to assist in expressing the declivity4 ,this thickness is determined by the following rule4 ,for a slope of the thickness of the shading lines is equal to of the distance between their centres1 and this thickness will diminish with the inclination down to 1 where the lines will be as fine as they can be drawn4 ,in a slope of this rule will always make the breadth of the shading lines twice that of the white space contained between them4 ,to represent declivities by the vertical system of shading a considerable amount of practice is required4 ,this practice should be commenced by drawing repeatedly the scale of shade1 and gradually applied1 as proficiency is attained1 to the varying inclinations of a hillside4 ,having the horizontal sections of the hill given1 the degree of slope should be written upon it in pencil in as many places as is necessary4 ,the distances between the centres of the shading lines may then be marked off upon the upper curve of the zone from the scale of shade1 and the lines of greatest descent drawn through the points thus determined4 ,the exact proportion of black to white being then adopted1 the colour will express the degree of the slope1 and the line of greatest descent will show its direction4 ,the principle of making the shading lines longer on a gentle slope than on a steep one should be adhered to generally2 but in this matter much must be left to the judgment and the skill of the draughtsman4 ,frequently on slight inclinations it will be desirable to divide and subdivide the zone by medial lines1 as shown in ,fig4 #gf1 and on very steep slopes the shading lines may be drawn over two or more zones4 ,for ordinary scales the extremes of length may be fixed at of an inch on the steepest slopes1 and of an inch on the gentlest4 ,illustration3 ,,fig4 #gf4 ,it is not necessary to repeat the process of construction for every line1 such a mode of proceeding would be too laborious and slow4 ,it will be sufficient to determine the lines in this exact manner at those parts where the greatest changes of slope occur4 ,thus a group should be constructed in each zone where the slope is greatest and another where it is least1 after which a few intermediate ones may be put in4 ,the vacancies may then be filled in1 taking care to graduate the changes in passing from group to group4 ,by this means we do not1 of course1 get a mathematically exact representation of the surface1 but it is sufficiently accurate for practical purposes4 ,when the preparatory pencil lines have been drawn in and the spaces for the shading lines laid off by dots1 the shading should be commenced at the steepest part of the upper zone4 ,the lines should be drawn firmly from curve to curve1 taking care to make each row terminate evenly at the lower edge2 they must always be drawn downwards and from left to right1 proceeding in this direction round the zone till the point of setting out is reached1 where the joining must be carefully effected4 ,this can always be done most neatly where the lines are thickest1 as we have previously pointed out4 ,the succeeding zones should be filled up in the same manner4 ,as changes must be gradual in every direction1 care must be taken to make the contiguous zones blend into each other4 ,when it is required to pass from a light zone to a darker one beneath it1 the lower ends of the lines in the light zone should be thickened a little1 so as to meet the upper ends of the lines in the dark zone with nearly the same colour4 ,the upper ends of these latter lines should also be slightly lightened4 ,the lines of one zone must not be continued into those of the next4 ,even on a uniform slope such a prolongation of the lines would produce a hard appearance1 which should be avoided4 ,but in the case of a conical hill1 like that shown in ,fig4 #gg1 it would give rise to an error in principle2 for soon after leaving the summit we should have too few lines of descent4 ,when the hill has been covered with shading lines1 the base and the summit must be softened off by tapering the lower end of each line at the base1 and the upper end of each line at the summit4 ,to give the taper to the latter1 the drawing should be turned upside down4 ,illustration3 ,,fig4 #gg4 ,when the curves are parallel or nearly so1 the shading lines are straight1 and also nearly parallel4 ,but when the curves depart widely from each other1 the shading lines will themselves have a slight curvature1 for being lines of greatest descent1 they must be normal to the curves4 ,in such cases1 a number of normals should be put in at short distances with the pencil1 as shown in ,fig4 #gh1 to serve as guides to the shading lines4 ,the foregoing directions for shading a hill apply equally to the shading of a hollow1 the shading lines in which are converging4 ,illustration3 ,,fig4 #gh4 ,occasionally short slopes steeper than the 8natural slope0 of #de will be met with4 ,such being exceptions to the law of slopes1 are marked in an exceptional manner4 ,when the surfaces of these slopes are of earth1 they are shown by black lines drawn parallel to the horizontal curves1 and when of rock1 by black lines drawn in all directions1 not intersecting1 but abutting abruptly upon each other in short heavy masses1 as shown in ,fig4 #gh4 ,shading in ,colours4--,frequently in topographical drawings1 and still more frequently in mechanical drawings1 colour is resorted to to produce the effect of shading lines4 ,as the principles according to which colour is applied for this purpose are the same as those which determine the use of shading lines1 there remains little to be said on this matter beyond describing the modes of applying the colour4 ,hill ,slopes4--,in representing slopes1 the tint employed to give the effect of that produced by the ink lines already described is composed of indigo and burnt sienna1 and is applied as a flat-wash4 ,a little lake is added to neutralize the greenish hue of this tint when it is to be laid over sand or cultivated ground4 ,the different degrees of intensity required to express the inclination are produced by repeating the wash over those parts which are darker than the rest4 ,to accomplish this neatly1 the darker portions must be washed in first1 so that the final washings may cover the whole surface1 and the edges of each successive wash must be softened off or blended into the next with a brush and clean water4 ,in shading hills1 the paper along the crest of the slope should be first moistened with the water-brush1 and before it dries1 the laying on of the colour should be begun on the moistened part1 and proceeded with down the slope4 ,the effect of representing hills by this method1 which is a very expeditious one1 is much improved by adding light shading lines with the pen1 either in pale ink1 or a mixture of indigo and burnt sienna4 ,the ground is always covered with its appropriate sign before the shading tint is laid on4 ,cylindrical ,surfaces in ,mechanical ,drawings4--,in shading cylindrical surfaces and drawings generally1 three methods are employed4 ,one of these is known as softening off1 and is employed on finished drawings of machinery4 ,for shading by this method1 a brush called a softener is required2 this has a brush at each end of the handle1 one being larger than the other4 ,having moistened the paper1 and filled the smaller brush with colour and the larger one with water1 a narrow strip of colour is laid along the darkest part of the cylinder1 and immediately after1 while the colour is quite moist1 the water-brush is drawn along one edge of the strip and then in like manner along the other1 so as to cause the colour to flow over that portion of the surface which has been damped4 ,the brush is then wiped upon a cloth and drawn lightly down the edge to take up the superfluous water4 ,the colour should be light to begin with1 and the quantity to be taken in the brush must be determined by experience4 ,the same remark applies to the water-brush1 for if too little be used the colour will not spread sufficiently1 and if too much1 the colour will be diluted and rendered uneven4 ,these operations of laying on the colour and softening off are continued until the cylindrical appearance has been produced4 ,each succeeding coat should be laid on before the preceding one is quite dry1 as the colour will spread more evenly over a damp surface4 ,the previously applied coat must1 however1 have been sufficiently absorbed not to wash up1 or a clouded appearance will be the result4 ,another method1 known as the ,french1 consists in applying a narrow strip of colour to the darkest part1 and overlaying this with other strips1 each wider than the one previously laid on4 ,to regulate the breadth of the strips1 a number of meridian lines are drawn upon the cylinder4 ,when shaded in this manner1 the cylinder presents the appearance of a polygon rather than that of a cylinder4 ,the third method1 by reason of the facility it affords of producing effect1 is very suitable for large drawings and diagrams for illustrating papers and lectures4 ,in shading according to this method1 a thick line or a narrow strip of very thick and black ,indian ink is laid on the darkest part of the cylinder with the point of the brush4 ,the breadth of the strip will be regulated by the diameter of the object1 and it should be previously lined out in pencil4 ,when dry1 a damp brush is passed over it so as to remove the sharp edges of the strip1 and to cause the ink to run slightly over the moistened surface of the paper4 ,the flat colour washes are then applied as required1 the washes being carried over the black strips1 which will be further reduced in tone by a portion of the ink mixing with the colour4 ,in shading1 it will be found convenient to keep the light side of the object next to the operator1 as it is easier to wash towards the body than from it with the water-brush4 ,the brush should be held in as nearly a vertical position as possible1 as it is more easy1 when that position is observed1 to keep within the boundary lines4 ,,part ,,ii4--,,applications4 ,,section ,i4--,,lettering1 ,,bordering1 ,,and ,,north ,,points4 ,lettering4--,the lettering of a plan1 map1 or drawing of any kind1 occupies a prominent and conspicuous position1 and may be considered as forming an essential part of the drawing4 ,it is1 therefore1 obvious that the character of the lettering1 and the degree of finish introduced into its execution1 will have an important influence on the general appearance of the drawing4 ,nothing detracts more from the value of a map1 considered as a work of art1 than a bad style of lettering1 while1 on the other hand1 a well-chosen and well-executed style is both pleasing to the eye1 and produces on the mind an impression of accuracy in the more important features of the work4 ,hence it is not merely desirable1 but necessary1 that the draughtsman should acquire the ability to form letters correctly and neatly1 especially if he be engaged on topographical drawings1 into which lettering enters very largely4 ,the formation of letters requires great attention and long practice4 ,it is not a matter in which much assistance is to be derived from descriptions or written instructions of any kind2 practice alone from good models will give the requisite skill4 ,the difficulty of forming the letters correctly and of uniform dimensions may1 however1 be considerably lessened by using guide lines drawn in pencil1 to be afterwards erased4 ,such lines are called construction lines1 and the mode of employing them is shown in ,plate #d4 ,a careful study of this ,plate will give the student a clear understanding of the use of these lines1 which could not be imparted by pages of description4 ,a reference to the letters ,b1 ,e1 and ,t1 in connection with the construction lines will show most readily the nature and the degree of assistance afforded by the latter4 ,in making capitals1 each letter must be sketched in pencil2 the outline must then be drawn in ink with a firm and steady line1 and afterwards filled up with the pen4 ,in forming the small roman and italic letters1 three construction lines are drawn1 the lower two to limit the height of the ordinary letters1 and the upper one to limit the height of such letters as d and l1 and the capitals4 ,the heavy parts of these letters are made at once by a bold pressure of the pen4 ,the curved portions should be carefully distinguished from the straight4 ,the letters a1 c1 g1 o1 s1 c41 for example1 are composed wholly of curved lines4 ,they should be drawn symmetrically1 and their width should be only a little less than their height4 ,the round portion of the g should not quite reach to the lower line4 ,a perfect regularity should be maintained throughout the letters1 as the beauty of their appearance depends greatly on this4 ,care must also be taken1 in italic writing1 to keep the inclination the same everywhere4 ,manuscript lettering should be more extended than the clear roman or italic type1 for crowding greatly mars its appearance4 ,the character of the letters employed should be in accordance with that of the drawing upon which they are to appear4 ,thus for engineering and mechanical drawings1 there is nothing more suitable generally than the plain block letter4 ,but on drawings of a more artistic and ornamental character1 a more elaborate form of letter may and should be used4 ,and of these elaborate forms1 there will always be one more suitable than the rest to the particular character of the drawing4 ,the choice of this form is a matter to be left entirely to the judgment and the taste of the draughtsman4 ,another matter on which the draughtsman will have to exercise his judgment is the size of the letters employed4 ,this must manifestly be in accordance1 first1 with the character of the object denoted1 and1 second1 with the scale of the drawing4 ,with regard to the former of these conditions1 it is obvious that propriety will demand a larger letter for the city than the town1 for the town than the village1 for the village than the farm1 and for the mansion than the gate-lodge4 ,this propriety of relative importance must be everywhere observed4 ,the different types of lettering are arranged in the order of importance as follows3--#a1 ,the upright capital2 #b1 the inclined capital2 #c1 the upright roman1 or ordinary small type2 and #d1 the small italic4 ,the draughtsman will have to exercise his judgment in suiting the size to the scale of the map1 but the following ,table may be taken as a general guide3-- ---------------------------------------- ------------------------- ,scale4 ,height of ,upright ,height of ,small ,roman4 ,capitals4 ---------------------------------------- ------------------------- 1 or one inch to fifty feet4 ,six-tenths of an inch4,twelve-hundredths of an inch4 1 or two feet to a mile4 ,four ,eight 1 or one foot to a mile4 ,three ,six 1 or four inches to a mile4 ,two ,four ---------------------------------------- ------------------------- ,the thickness of the capital should be one-seventh of the height4 ,as far as practicable1 the lines of lettering should be parallel to the base of the drawing4 ,frequently1 however1 cases will occur in which it will be desirable to letter in other directions and in curved lines4 ,in writing along a curved or very irregular outline1 the course of a river or the boundary of an estate1 for example1 an agreeable effect is produced by making the lines of lettering conform in some degree with the outlines against which they are written4 ,the arrangement of the letters in titles and the effective disposition of the words are also matters requiring great care and some taste4 ,the design and the execution of the title afford another opportunity of enhancing the beauty of a drawing by a display of striking arrangement and appropriate ornamentation4 ,plates #g and #h show some useful models for plans1 and ,plate #be contains some specimens of flourishes which may frequently be introduced with pleasing effect4 ,the form which the title shall assume and the space which it shall occupy must be determined before beginning to put it upon the drawing4 ,to avoid erasures1 it is well to sketch roughly upon a piece of paper1 a trial title1 emendations in which can be easily made4 ,when found satisfactory1 draw a vertical centre line1 which should pass through the middle letter of each line4 ,apply this centre line to the centre line of the title on the drawing1 and lightly mark in with the pencil the position of each letter4 ,when this method is not adopted1 the middle letters should be put in first upon the centre line1 and the others afterwards inserted from left to right1 and from right to left4 ,in maps1 the title may be placed outside the border if it consist of one line only1 but if it occupy more than one line1 it should be placed within the border4 ,generally1 it should be placed in one of the corners of the map1 and its size should bear some proportion to that of the map4 ,the letters composing the name of the locality1 which is usually the most important word1 should not exceed in height three-hundredths of the length of the short side of the border4 ,the letters of the other words will vary in size according to their relative importance4 ,borders4--,plain borders usually consist of two lines1 the outer one heavy1 and the inner one light4 ,the heavy line should be equal in breadth to the blank space between it and the light line1 and the total breadth of the border1 that is1 of the two lines and the space between them1 should be one hundredth part of the length of the shorter side4 ,ornamental corners may be made to embellish a drawing considerably1 and they afford some scope to the fancy and the taste of the draughtsman4 ,several examples of borders and ornamental corners will be found in the accompanying ,plates4 ,north ,points4--,the meridian or north and south line is an indispensable adjunct to every topographical drawing4 ,when the extent of country represented is considerable1 it is usual to make the top of the map the north1 and in such a case the side border lines are meridian lines4 ,frequently1 however1 in plans1 the shape of the ground does not admit of this arrangement1 and then it becomes necessary to mark a meridian on some part of the map4 ,this line is usually made a conspicuous one1 and its north extremity is often ornamented with some fanciful device4 ,the ornamentation of the meridian line should be in keeping with the rest of the map4 ,plate #i contains several examples which may be adopted or modified as deemed desirable4 ,,section ,,ii4--,,scales4 ,to all drawings which do not show the full size of the objects represented1 it is necessary to affix the scale according to which the objects are drawn4 ,such a scale is called a scale of lengths or distances1 because1 by means of it1 the distance from one point to another is ascertained4 ,the scale of distances does not contain very minute subdivisions1 and consequently is not suitable for use in constructing the drawing4 ,for the latter purpose1 another scale1 similarly but more minutely divided1 is employed1 and is known as the scale of construction4 ,a familiarity with the modes of constructing both of these scales should be early acquired by the young draughtsman4 ,scales of ,distances4--,one means of denoting the scale of a drawing is furnished by what is called its representative fraction1 the denominator of which shows how many times greater the actual length is than that in the drawing4 ,thus a scale of shows that #a inch on the drawing represents #bd inches on the object2 in other words1 that the object is twenty-four times larger than the drawing4 ,but in addition to this representative fraction1 it is usual to affix a graduated straight line1 termed a scale1 for the purpose of conveniently measuring distances upon it4 ,it is manifest that the unit of length in this scale must bear the same ratio to the real unit of length that a line in the drawing bears to the line which it represents4 ,thus if the representative fraction be 1 #a inch on the scale will represent #b feet4 ,scales of distances are usually of such a length as to be a multiple of #aj linear units of some kind1 as #ajj miles1 #ej chains1 #bj feet2 and this length should also be such as to allow of long lines being taken off at one measurement4 ,to construct the scale1 two light lines should be drawn at a suitable distance apart1 and below the lower of these lines and at a distance from it equal to one-third of the space between them1 a third and heavy line should be drawn4 ,the primary divisions may then be made with the compasses in the following manner4 ,supposing the number of divisions to be five1 open the dividers to what appears to be the fifth part of the line1 and step this distance along the line2 if the fifth step exceed or fall short of the end of the line1 close or open the dividers of the distance1 and repeat the trial4 ,this is the quickest and1 for large divisions1 the most accurate method of dividing a line4 ,to render the divisions more distinct1 draw a heavy line between the two light lines in alternate divisions4 ,the left-hand division must be subdivided into the units or lesser measures of which it is made up4 ,for example1 if the primary divisions are each of #aj feet1 the subdivisions will be feet2 if they represent feet1 the subdivisions will be inches1 and so on4 ,the subdividing should be performed in the following manner4 ,having erected a perpendicular of indefinite length from the left-hand extremity of the scale1 take with the compasses from any scale the number of divisions into which it is required to divide the part4 ,with this distance in the compasses1 strike1 from the first primary or zero division1 an arc cutting the perpendicular1 and join the point of intersection to the centre from which the arc is struck4 ,thus we shall have a right-angled triangle formed of the first primary division of the scale1 the perpendicular and the radius1 the latter being the hypothenuse 7see ,fig4 #gi74 ,mark on the hypothenuse the divisions to which it was made equal1 and from the points of division let fall perpendicular lines upon the scale4 ,these will divide the latter into the required number of equal parts4 ,the length of the hypothenuse should be so chosen as to make an angle not greater than #ej with the base4 ,illustration3 ,,fig4 #gi4 ,the total length of the scale will be determined by the greatest length which it is required to read off at once1 and in the following manner4 ,thus1 let it be required to construct a scale of 1 inch to the foot1 to show #ab feet4 ,here #e inch 3 x inches 33 #a inch 3 #ab inches2 whence x #ab #e #f inches4 ,this distance of #f inches must1 therefore1 be set off upon the lines intended for the scale1 and divided in the manner described above4 ,again1 to construct a scale of 1 #f inches to a mile1 to show #ajj chains4 ,since #f inches represents #ebhj feet or #hj chains1 the proportion becomes #f 3 x 33 #hj 3 #ajj2 whence x #g inches4 ,if the scale is #af inches to a mile1 #e chains to an inch1 and the distance to be shown is #cj chains1 we have #a 3 x 33 #e 3 #cj2 or x #f inches4 ,in a scale of #aj yards to the inch1 for example1 the representative fraction is #aj #c #ab 4 ,so1 on the contrary1 #aj yards to the inch4 ,sometimes it is required to construct a comparative scale1 that is1 a scale having the same representative fraction1 but containing other units4 ,thus suppose1 for example1 we have a ,russian plan on which is marked a scale of archines measuring a length of #ej archines4 ,it is required to draw upon this plan a comparative scale of yards1 upon which a distance of #ej yards may be measured4 ,the ,russian archine #ggg yard4 ,hence we have the proportion #ej 3 x 33 #ggg 3 #a1 whence x #fdce archines4 ,measure off this length from the ,russian scale1 and upon it construct the ,english scale in the manner already described4 ,this scale may then be used to measure distances on the plan4 ,amongst ,continental nations1 decimal scales are usually employed1 which are far more convenient in practice than those involving the awkward ratios of miles1 furlongs1 chains1 yards1 feet1 and inches4 ,the decimal scale has also been adopted for the ,united ,states' ,coast ,survey1 the smallest publication scale of which is 2 this is also the scale of the new map of ,france4 ,in choosing a scale1 regard must be had alike to the purposes for which the drawing is intended1 and to the nature and the amount of detail required to be shown4 ,thus a larger scale is required in plans of towns than in those of the open country2 and the smaller and more intricate the buildings1 the larger should the scale be4 ,also a plan to be used for the setting out of works should be to a larger scale than one made for parliamentary purposes4 ,the following ,tables1 given by ,rankine in his #8,civil ,engineering1' enumerate some of the scales for plans most commonly used in ,britain1 together with a statement of the purposes to which they are best adapted4 ,,horizontal ,,scales4 ---------------------------------------- ---------------------------- ,ordinary ,designation ,fraction ,use4 of ,scale4 of real ,dimen- sions4 ---------------------------------------- ---------------------------- #a4--a inch to a mile ,scale of the smaller ,ordnance maps of ,britain4 ,this scale is well adapted for maps to be used in exploring the country4 #b4--d inches to a mile ,smallest scale permitted by the ,standing ,orders of ,parliament for the deposited plans of proposed works4 #c4--f inches to a mile ,scale of the larger ,ordnance maps of ,great ,britain and ,ireland4 ,this scale1 being just large enough to show buildings1 roads1 and other important objects distinctly in their true forms and proportions1 and at the same time small enough to enable the eye of the engineer to embrace the plan of a considerable extent of country at one view1 is on the whole the best adapted for the selection of lines for engineering works1 and for parliamentary plans and preliminary estimates4 #d4--fcff inches to a mile ,decimal scale possessing the same advantages4 #e4--djj feet to an inch ,smallest scale permitted by the ,standing ,orders of ,parliament for 8enlarged plans0 of buildings and of land within the curtilage4 #f4--f chains to an inch ,scale answering the same purpose4 #g4--aehd inches to a mile ,scales well suited for the working surveys and land plans of great engineering works1 and for enlarged parliamentary plans4 #h4--e chains to an inch1 7,scale #h is that prescribed in or #af inches to a mile4 the ,standing ,orders of ,parliament for 8cross sections0 of proposed railways1 showing alterations of roads47 #i4--becdd inches to a mile ,scale of plans of part of the ,ordnance survey of ,britain1 from which the maps before mentioned are reduced4 ,well adapted for land plans of engineering works and plans of estates4 #aj4--bjj feet to an inch ,scale suited for similar purposes4 ,smallest scale prescribed by law for land or contract plans in ,ireland4 #aa4--c chains to an inch ,scale of the ,tithe ,commissioners' plans4 ,suited for the same purposes as the above4 #ab4--ajj feet to an inch ,scale suited for plans of towns1 when not very intricate4 #ac4--hh feet to an inch1 or ,scale of the ,ordnance plans of #fj inches to a mile4 the less intricately built towns4 #ad4--fccf inches to a mile ,decimal scale having the same properties4 #ae4--dd feet to an inch1 or ,scale of the ,ordnance plans of #abj inches to a mile4 the more intricately built towns4 #af4--abfgb inches to a ,decimal scale having the same mile properties4 #ag4--cj feet to an inch #ah4--bj feet to an inch ,scales for special purposes4 #ai4--aj feet to an inch ---------------------------------------- ---------------------------- ,,vertical ,,scales4 ---------------------------------------- -------------------------- ,ordinary ,fraction ,horizontal ,scales,exaggeration4 ,designation of real with which the ,use4 of ,vertical ,height4 ,vertical ,scale is ,scale4 usually combined4 ---------------------------------------- -------------------------- from #a4--ajj feet to #acb to #hh ,smallest scale to an inch permitted by the ,standing ,orders of ,parliament for sections of proposed works4 #b4--dj feet to #aj to #hbe ,smallest scale to an inch permitted by the ,standing ,orders of ,parliament for cross sections showing alterations of roads4 #c4--cj feet to #aa to #ff ,scales to an inch suitable for #d4--bj feet to #afe to #ii working to an inch sections4 ---------------------------------------- -------------------------- ,the vertical scale1 or scale of heights1 is always much greater than the horizontal scale or scale of distances1 and the proportion in which the vertical scale is greater than the horizontal1 is called the exaggeration of the scale4 ,this exaggeration is necessary1 because the differences of elevation between points on the ground are in general much smaller than their distances apart1 and would therefore1 without exaggeration1 be unapparent1 and also because1 in the execution of engineering works1 accuracy in levels is of more importance than accuracy in horizontal positions4 ,scales of ,construction4--,scales of construction are intended to afford means of measuring more minute quantities than scales of distances4 ,of the former there are two kinds1 known respectively as the ,diagonal and the ,vernier scale4 ,the diagonal is the more frequently employed4 ,its construction involves no peculiar difficulty1 as it consists simply of an ordinary scale of distances1 with the addition of a number of parallel lines crossed by other parallel lines drawn diagonally from the smaller points of division4 ,an example will best show the construction and mode of using this scale4 ,suppose it to be required to construct a scale of #aj miles to the inch1 showing furlongs diagonally2 the scale to measure #ej miles4 ,here #a 3 #aj 33 x 3 #ej1 whence x #e inches4 ,divide this length of #e inches into five equal parts1 and the first part into tenths to show miles1 in the manner already described for scales of distances4 ,then1 since it is required to show furlongs or eighths of a mile1 eight equidistant parallel lines must be drawn above the scale1 at a convenient interval apart1 as shown in ,fig4 #hj4 ,produce the primary points of division to meet the top parallel2 and from the last secondary point of division draw a line to the point in which the extreme primary division meets the top parallel4 ,draw from the other points of division1 lines parallel to this one1 and the scale will be complete4 ,it will be seen that the inclined lines are the diagonals of the rectangular figures formed by the top and bottom parallels and vertical lines drawn from the smaller points of division4 ,illustration3 ,,fig4 #hj4 ,to use this scale1 suppose a length of #bd miles #e furlongs is required4 ,place one leg of the dividers upon the point in which the fourth diagonal intersects the fifth parallel1 and extend the other to the point in which the primary division marked #bj intersects the same parallel4 ,in like manner1 if the distance required be #cc miles #c furlongs1 it must be taken from the intersection of the third diagonal with the third parallel1 to the intersection of the primary division marked #cj with the same parallel4 ,it is obvious that if a scale of feet showing inches diagonally be required1 twelve equidistant parallel lines must be drawn instead of eight as in the foregoing example where furlongs are required4 ,the diagonal scale possesses the important advantages of accuracy and distinctness of division which render it very suitable as a scale of construction4 ,another practical advantage is that it is less rapidly defaced by use than the other kinds1 in consequence of the measurements being taken on so many different lines4 ,the construction of the vernier scale is similar to that of the graduated arcs of surveying and astronomical instruments4 ,the principle of the vernier is as follows4 ,if a line containing n units of measurement be divided into n equal parts1 each part will1 of course1 represent one unit2 and if a line containing n #a of these units be also divided into n parts1 each part will be equal to 7n #a7_/n units2 and the difference between one division of the latter and one of the former will be 77x #a7_/n7 - #a #a_/n of the original unit4 ,similarly1 the difference between two divisions of the one and two of the other will be #b_/n of a unit1 between three of the one and three of the other1 #c_/n1 and so on4 ,hence1 to obtain a length of x_/n of a unit1 we have only to make a division on one scale coincide with one on the other scale2 the space between the two corresponding xth divisions from this on both scales will be the required length of x_/n of a unit4 ,the same reasoning will evidently hold good if a length equal to n - #a be taken4 ,illustration3 ,,fig4 #ha4 ,to show how the foregoing principle is applied in practice1 we will take an example4 ,it is required to construct a scale of to show feet and tenths of a foot4 ,construct a scale in the ordinary way1 and subdivide it throughout its whole length1 as shown in ,fig4 #ha2 then each division will show one foot4 ,above the first primary division1 draw a line parallel to the scale and terminating at the zero point4 ,from the zero point1 set off on this line towards the left a distance equal to eleven subdivisions1 and divide this distance into ten equal parts4 ,now1 as eleven divisions of the plain scale have been divided into ten equal parts on the vernier1 each division on the latter will represent #aa of that on the former2 and as the divisions of the plain scale represent feet1 those of the vernier will represent #aa foot4 ,consequently1 the distances from the zero of the scale to the successive divisions on the vernier are #aa1 #bb1 #cc1 #dd1 #ee1 #ff1 #gg1 #hh1 #ii1 and #aa feet4 ,it will be seen that the divisions of the two scales are made to coincide at the zero point4 ,the mode of using this scale will be seen from the following example4 ,let it be required to take off a distance of #bfg feet4 ,from zero to the #gth division of the vernier is1 as we have seen1 #gg feet4 ,therefore1 to ascertain how far to the right of zero we must go to obtain the distance of #bfg feet1 we must subtract #gg from that distance1 which gives #ai4 ,thus to take off the distance1 one leg of the dividers must be placed on the #gth division of the vernier1 and the other on the #aith division of the plain scale4 ,if the distance to be taken were #bgf feet1 one leg of the dividers would have to be placed on the #fth division of the vernier1 and the other on the 7#bgf7 - 7#ff7 #bast division of the plain scale4 ,to construct a scale to show feet and inches1 make the vernier equal to thirteen divisions of the plain scale and divide it into twelve equal parts4 ,each of these divisions will then represent #a of a foot4 ,scales of construction may be purchased upon box-wood or ivory1 but where great accuracy is important1 it is best to lay down the scale upon some part of the drawing1 as in such a case it expands and contracts with the drawing under the influence of moisture4 ,examples of scales of distances will be found on ,plates #h and #i4 ,,section ,,iii4--,,plotting4 ,the transference of the measurements determined by the survey from the field-book to the paper is termed plotting4 ,the operations of plotting are very simple1 and the ability to perform them properly may be acquired with a little practice4 ,but their due performance demands the same extreme care and attention as that of the operations in the field1 for it is obvious that the precautions taken to ensure accuracy in the latter may be rendered nugatory by inaccurate plotting4 ,the angular instrument used in plotting is the protractor1 and to ensure correct results this instrument must be accurately divided4 ,when1 however1 the survey has been made without the aid of an angular instrument1 the protractor is not required in laying down the results4 ,in such a case1 which frequently occurs in surveys of small extent1 the lines1 having all been chained and registered in the field-book1 are laid down directly from the scale by means of an ordinary straight-edge and a pair of compasses4 ,the several methods of plotting and the various operations involved have now to be considered4 ,reference ,lines and ,points4--,the lines chained over in a survey and recorded in the field-book are not usually the actual lines existing on the ground1 but imaginary straight lines chosen for the purpose of referring other lines and points to them4 ,they are1 therefore1 appropriately termed reference lines1 and all points situate in them to which other lines are referred1 in other words1 all points in a reference line in which other reference lines intersect it1 are termed reference points4 ,reference lines are generally made to form triangles for facility of computation1 and these triangles enclose the area to be surveyed4 ,but to determine the details included within them1 it is necessary to form other and smaller triangles within the larger ones first laid down4 ,the latter are1 therefore1 distinguished as ,primary and the former as ,secondary triangles1 and the lines of which they are composed are called primary and secondary reference lines4 ,plotted ,points4--,in laying down a line of definite length upon paper1 the positions of its extremities are determined and marked by pencil dots2 such dots1 or rather the points indicated by such dots1 are termed plotted points4 ,the line is drawn by joining the plotted points4 ,to ,plot ,reference ,lines and ,points4--,to plot a reference line of a given length when the position of neither of its extremities is given1 a light dot must be made upon the paper in a convenient part to indicate the position of one extremity4 ,the pencil-point mark should be as light and well defined as possible1 and hence it is essential that the pencil used should be hard1 and always kept pared to a fine conical point4 ,the scale must then be applied1 in the direction of the line to be drawn1 with its zero point coincident with the plotted point4 ,the scale should be lightly but firmly held in this position with the left hand4 ,the distance of the other extremity of the line must then be found upon the scale1 and the eye placed directly over the line of the graduation2 this is necessary to the correct placing of the point1 and it is well to train the eye to trace accurately the prolongation of the line of graduation upon the paper4 ,a dot must be placed in the prolongation of this line and close to the edge of the scale1 to mark the position of the other extremity4 ,the reference line is then to be drawn between these two plotted points with a sharp chisel-pointed pencil4 ,reference lines1 like reference points1 should be well defined1 but drawn as fine and light as possible4 ,the degree of fineness and lightness should be such that when the detail is finely but firmly outlined1 the reference lines and points may not be visible1 except on a close inspection of the surface4 ,to plot secondary reference lines1 as1 for example1 a number of offset lines1 apply the scale so that its edge may be parallel to and almost over the pencil trace of the primary line and its zero point coincident with the point at which the line begins4 ,care must always be taken to place the zero of the scale at the beginning of the line1 and not at the end of it4 ,at the distances recorded in the field-book as those at which the offsets were taken1 plot upon the line1 in the manner described above1 the points indicating the extremities of the offset lines4 ,all other points1 such as stations and intersection of fences1 roads1 and streams1 should be plotted at the same time4 ,around all stations1 a light1 hand-drawn circle should be placed1 and intersections marked by small cross lines4 ,this being done1 place the offset scale so that the zero may coincide with the plotted point in the reference line and the edge be perpendicular to the line4 ,to bring the edge into this position1 the end of the scale should be placed parallel to the reference line2 this is1 of course1 assuming the scale to be perfectly rectangular1 as it ought to be4 ,the other extremities of the lines may then be plotted in the same manner as those of the primary lines4 ,to illustrate the foregoing remarks1 let it be required to plot the following portion of a field-book4 ------ #jj #acdf or #jjj ,line #a4 #ge #aagj #if #ajjj #aje #fej #ff #djj #jj #jjj ------ ,line #c4 ,from #aidf last4 ------ ------ #aidf #jj #adbj #hh #abjj #add #ajjj #aaj #fjj #ge #ebj #ej #jjj #jj ------ ,line #b4 ,from #bejd last4 ------ ------ #bejd #jj #bjjj #fe #agij #ie #afaj #aae #addj #hg #abbj #aaj #ajjj #hej #bh #dbj #ajj ,line #a4 #jjj #jj or #acdf ,line #c4 ------ ,begin at south corner and range ,n4 ,having laid down in a convenient part of the paper the beginning of ,line #a1 place the edge of the scale so that the zero may coincide with the plotted point and the edge be parallel to one of the meridians4 ,holding the scale firmly in this position1 plot the distance #bejd links1 and join the plotted points4 ,then1 without removing the scale1 plot upon this reference line the distances at which the secondary or offset lines were taken1 that is at #dbj1 #hej1 #abbj1 #addj1 #afaj1 #agij1 and #bjjj links4 ,in this case we have nothing but offsets2 had there been stations or intersections of fences1 roads1 or streams1 these would have had to be plotted at the same time1 and distinguished by an appropriate mark4 ,line #b begins at the end of ,line #a1 and returns on the left at an acute angle1 as indicated by the arrow in the field-book4 ,but as the magnitude of this angle is not known1 the survey having been taken with the chain alone1 the exact direction of ,line #b must be ascertained in the following manner4 ,take the length of the line in the compasses1 and with this distance as a radius1 strike an arc from the end of ,line #a4 ,also with the length of ,line #c as a radius1 strike an arc from the beginning of ,line #a1 at which point ,line #c closes1 intersecting the former4 ,the point of intersection will be the end of ,line #b4 ,join this point to the end of ,line #a1 and plot the offset reference points upon this line in the manner already described for ,line #a4 ,line #c begins at the end of ,line #b1 and terminates at the beginning of ,line #a2 hence both extremities being determined1 we have only to join these points1 and to plot the offset reference points as before4 ,had a split line been taken for the sake of accuracy from the angle ,a ,c ,b to the base ,line #a1 the intersection of this line should have been plotted upon ,line #a1 and the position of the end of ,line #b found by striking an arc from this point also with a radius equal to the length of the split line4 ,if the distances have been correctly measured in the field and correctly taken from the scale1 the three arcs will intersect at the same point4 ,if they do not so intersect1 the error must be noted in an error-sheet1 and corrected in the field before proceeding further4 ,it may be remarked here that on account of the irregularities of the surface chained over1 all measured lines are liable to be recorded a little too long4 ,one link in ten chains may be allowed for this source of error4 ,assuming1 however1 that the primary reference lines 8close0 properly1 the offset lines may be plotted in the manner already described1 and the detail or boundary lines drawn in1 which in the present instance are hedges4 ,fig4 #hb shows the survey as laid down in the foregoing notes4 ,when the survey has been made with the aid of an angular instrument1 the method of plotting the primary reference lines differs somewhat from the foregoing4 ,in this case1 the paper should be first covered with a number of parallel straight lines ruled about an inch and a half apart to represent magnetic meridians4 ,the first station may then be marked upon one of these meridians in a convenient part of the paper4 ,to lay down the first reference line1 apply the protractor to this meridian with its centre point coincident with the plotted point1 and from the bearing recorded in the field-book1 lay off the given angle4 ,join the two plotted points and produce the line indefinitely2 and upon this line lay off a distance equal to the length of the measured line4 ,the second reference line must be drawn in the same manner1 from the end of the first1 by laying off from that point the recorded angle4 ,but as the end of the first line will probably not fall upon a meridian1 the protractor will have to be moved up to the point by means of a parallel ruler adjusted to the nearest meridian4 ,a more convenient and a more accurate method1 however1 is to make the left of the drawing represent the north while plotting1 and to use the ,t-square instead of the parallel ruler4 ,all subsequent lines are plotted in the same way4 ,instead of covering the paper with meridians before commencing to plot1 it may1 in some cases1 be found more convenient to draw with the set and ,t squares a short meridian through the point as required4 ,illustration3 ,,fig4 #hb4 ,to lay down ,fig4 #hb in this manner1 having fixed the first station ,a1 the length of the first primary reference line ,a ,b may be laid off upon the meridian1 because in this case the bearing being due north1 the reference line will be coincident with the meridian4 ,this done1 the protractor is to be placed over the plotted point ,b and the second bearing laid down4 ,having plotted the length of this line in the point ,c1 the third reference line ,c ,a will be determined both in length and direction by the plotted points ,c ,a1 which should be joined and the line measured to ascertain whether its length corresponds with the measured distance4 ,if these do not correspond1 the angle must be replotted and the lengths laid off anew to discover the source of the error4 ,assuming1 however1 that the lines close properly1 the offsets and other secondary points may be next plotted in the manner previously described4 ,angles may be more accurately laid down by means of a table of natural sines and cosines and a linear scale than by means of a protractor4 ,this is especially true when the angles are subtended by long lines1 as1 for example1 lines of #c1 #d1 and even #f feet4 ,in such cases1 a protractor is of little use4 ,this mode of laying down angles is also convenient in some cases where angles have been taken1 but some of the sides not measured4 ,in using the table1 it must be remembered that the radius of the sines and cosines is taken as unity2 therefore1 to find the sine and cosine for any other radius1 the sine and cosine in the tables must be multiplied by that radius4 ,to lay down the angle ,a ,b ,c in ,fig4 #hb1 the reduced cosine of the angle should be plotted from ,b in the point a1 according to some scale4 ,the scale length of the reduced sine should then be scribed from a1 and the scale length of the radius scribed from ,b4 ,a line drawn from ,b through the point of intersection of the scribes will lay down the angle corresponding to the sine and cosine in the table4 ,suppose the radius chosen to be #e chains1 the angle being #cb #cj4 ,the cosine of #cb #cj is #hdcd1 which multiplied by #e1 the assumed radius1 #dbagj4 ,lay off this distance from ,b on the base ,a ,b4 ,the sine of #cb #cj is #ecgc1 which multiplied by #e1 #bfhfe4 ,from the point a1 which is distant #dbagj chains from ,b1 with a radius equal to #bfhfe chains1 describe an arc2 and from the point ,b1 with a radius equal to #e chains1 describe another arc4 ,from ,b draw a line through the intersection of these arcs1 and lay off upon it the measured length of #aidf links as recorded in the field-book4 ,if only the length of the base ,a ,b and the magnitudes of the angles ,a ,b ,c and ,b ,a ,c were given1 the lengths of the sides ,b ,c and ,a ,c would have to be calculated by trigonometrical formul4 ,this method of calculating the lengths of the sides of triangles and plotting them with the beam compasses1 like chained triangles1 is the most accurate for laying down the great or primary triangles of a survey4 ,when it is required to plot according to this principle a solitary angle1 as1 for example1 that between a station line and the meridian1 a circle should be drawn with as large a radius as practicable round the station at which the angle is to be laid down4 ,the distance between the points at which the two lines enclosing the angle cut that circle is then found by multiplying the radius by the chord of the angle1 that is1 by twice the sine of half the angle4 ,it sometimes happens1 particularly in extensive surveys1 that all the angular points of some triangles cannot be plotted upon the same sheet of paper4 ,in such cases1 the plot of the outlying points and the sides of the triangles may be laid down in the following manner4 ,plot the intersected triangles independently and trace them on tracing paper4 ,then1 having drawn a fine line upon both sheets to represent the sheet edge1 lay the points on the trace corresponding to those already plotted on the first sheet down upon1 and make them to coincide with1 the latter4 ,secure the trace in this position and trace the sheet edge line upon it4 ,the intersected lines may now be plotted on the fair sheet with a pricker at points outside the sheet edge line4 ,next apply the trace to the second sheet and make the sheet edge lines coincide4 ,having secured the trace in this position1 the points and the intersected lines on this second sheet may be plotted upon the fair paper by means of the pricker4 ,to ,plot ,traverse ,reference ,lines4--,in plotting a traverse survey in which the angles have been measured from a fixed line of direction1 the magnetic meridian1 the direction of the lines may be all laid down at the first angular point4 ,an example will best show the method employed in this case4 ,it is required to lay down the traverse shown in ,fig4 #hc4 ,illustration3 ,,fig4 #hc4 ,in a convenient part of the paper draw the straight line ,n ,s to represent the magnetic meridian1 and plot upon it the first station ,a4 ,set the protractor with its centre accurately placed over this point and its #cfjth and #ahjth divisions coinciding with the meridian4 ,holding the instrument securely in this position1 lay off around it all the bearings as entered in the field-book1 numbering them in the order in which they were taken4 ,against each of these numbers it is well to place the page of the field-book on which the measurement of the angle and the survey of the line are entered4 ,the plotting must now be commenced by laying down the first line through the first bearing and determining its length from the recorded measurements4 ,the direction of the second line has next to be transferred from the first station ,a to the extremity of the first line1 or the second station ,b4 ,this is accomplished by means of the parallel ruler1 by placing the edge of the ruler through the plotted point and the point marked as bearing #b1 and extending it till the same edge intersects the point ,b4 ,a line is then to be drawn from this point and its length laid off from the field-book as before4 ,the direction of the third line will then be transferred from the first angular point to the end of the second line1 or station ,c1 in the same manner4 ,this will be continued for all the lines in the traverse1 and if all the measurements have been correctly laid down1 not only will the last line pass through the point ,a1 but it will be of the same length as the chained line4 ,also the bearings taken from ,a to ,e and ,h will pass through these latter stations4 ,these proof line bearings should be laid down at the same time as the reference line bearings1 from which they should be distinguished by some sign4 ,the directions of the reference lines should be consecutively transferred1 and the length of each line should be plotted in its proper place before the direction of the next is transferred4 ,to ensure the work closing properly1 great care must be taken to plot the points accurately and to draw the pencil lines fine4 ,illustration3 ,,fig4 #hd4 ,the degree of accuracy to be attained will depend in a great measure upon the extent of the traverse4 ,with long lines the difficulties increase1 and with a great number of angles the chances of error are multiplied4 ,if the angles are carefully taken1 it is probable that seconds have been read off in several instances1 and these if neglected1 especially upon long chain lines1 may lead to an error of some importance4 ,also when the lines are long1 the parallel ruler becomes practically useless1 and some other system has to be adopted4 ,one way of overcoming these difficulties is to draw a parallel to the first meridian through every third or fourth angle2 in such a case1 great care must be observed in drawing the parallels4 ,a more easily practicable method1 however1 is to use the ,t-square in the manner already described4 ,if the left-hand edge of the drawing board be made the north1 the blade will determine meridional lines1 and by laying the straight side of a semicircular protractor against the edge of the blade1 its zero will be adjusted to the fixed line of direction4 ,the first bearing having been laid down1 the line is drawn and made the scale length of the chain line2 the blade of the square is then pushed to the station thus found1 and the next bearing set off4 ,this operation is repeated until all the lines have been laid down4 ,if the work closes properly1 the plotting of the secondary lines may be proceeded with4 ,the most accurate method of plotting a traverse is by rectangular co-ordinates1 or1 as it is usually termed1 ,northings1 ,southings1 ,eastings1 and ,westings1 because the position of each station is plotted independently1 and is not affected by the errors committed in plotting previous stations4 ,this method consists in assuming two fixed lines or axes crossing each other at right angles at a fixed point1 computing the perpendicular distances or co-ordinates of each station from those two axes1 and plotting the position of each station by means of the ,t and set squares and a linear scale4 ,the meridian is usually made to represent one of the axes1 and in this case the co-ordinates parallel to one axis will be the distances of the stations to the north or south of the fixed point1 and those parallel to the other axis will be their distances to the east or west of the same point4 ,let ,n ,s1 ,fig4 #hd1 represent the meridian1 and ,a ,b the first bearing taken1 and the first line measured4 ,the angle in this case is ,n ,a ,b 4 ,if is an acute angle1 the second station ,b is to the north of the first station ,a2 if it is an obtuse angle1 ,b is to the south of ,a4 ,if the angle lies to the right of the meridian1 ,b is to the east of ,a2 if to the left1 to the west4 ,thus it will be seen that if the northernly and easternly directions are considered positive1 the southernly and westernly directions will be negative4 ,from the foregoing it is manifest that the co-ordinates of ,b are as follows3-- ,northing ,a a b ,b 7or if negative1 southing7 ,a ,b cos4 4 ,easting ,a b a ,b 7or if negative1 westing7 ,a ,b sin4 4 ,to plot the point ,b1 draw through the point ,a1 with the aid of the ,t-square1 a horizontal line4 ,multiply the chained length of the line ,a ,b by the sine of the angle ,n ,a ,b as entered in the field-book1 and set off this distance along the horizontal line4 ,from the point thus determined1 erect1 with the aid of the set square1 a perpendicular1 which will be parallel to the meridian4 ,multiply the chained length of ,a ,b by the cosine of the angle ,n ,a ,b1 and set off this distance along the perpendicular line4 ,the point thus determined will be the position of the second station ,b1 which may then be joined to ,a by a straight line4 ,illustration3 ,,fig4 #he4 ,the mode of laying down the survey in ,fig4 #he will now be obvious4 ,having determined the position of the second station ,b in the manner just described1 draw a horizontal line through ,b and determine the third station ,c in the same way4 ,the fourth station ,d being to the left of the meridian passing through ,c1 c d is a westing and is to be considered as negative4 ,therefore the horizontal line through ,c must be drawn to the left of that station1 and the station ,d determined in the same manner as the preceding stations4 ,the results of all these calculations should be entered in a book1 in four columns1 for northings1 southings1 eastings and westings respectively4 ,also in four other columns should be entered the total northing or southing1 and easting or westing1 of each station from the first station1 computed by adding all the successive northings and subtracting the southings made in traversing to the station1 the result being a northing if positive1 and a southing if negative4 ,the same treatment is applied to the eastings and westings4 ,this affords a means of testing the accuracy of the work4 ,it is also obvious that the position of the last or any station may be determined by this means without plotting the intermediate stations4 ,let it be observed that both and sin4 are positive or negative according as that angle lies to the east or to the west of the meridian2 and that the cosines of obtuse angles are negative4 ,to ,plot ,detail4--,by 8detail0 is meant outlines or objects whether natural or artificial1 such as fences1 walls1 rivers1 canals1 roads1 lakes1 water margins1 beach marks1 seas1 or imaginary boundary lines4 ,in plotting from the entries of measurements for detail1 these measurements should be laid down upon the paper in the order and manner indicated in the field-book4 ,the mode of plotting the perpendicular reference lines by means of which the position of the detail is fixed has already been fully described and illustrated4 ,the proper connections for detail1 as shown by the field-book1 should be made by drawing a firm pencil line through the detail points with the aid of an offset scale adjusted successively to the adjacent points4 ,all such connections should be clearly and elegantly made4 ,when all boundaries1 roads1 and streams have been drawn and inked in1 tracings should be taken in small portions of all that has been laid down for the use of the 8examiner40 ,the duties of the examiner are to make on the ground the necessary corrections for omissions and detail in error2 to give1 in position and character1 woods1 water1 marsh1 commons1 vegetable and geological features1 and permanent artificial structures2 and to furnish the descriptive names of places and things1 or any other desirable information4 ,the topographical character of mountains1 marshes1 bogs1 rough pasture1 woods and water1 should be drawn in character on trace and tinted4 ,if required1 hill sketching should also be supplied on the examiner's trace4 ,on being returned to the office1 the plotter should replot from the field notes the detail corrected1 and transfer the details from the trace to the map4 ,to ,plot ,contours4--,the student who has made himself familiar with the methods of laying down angles1 and plotting reference lines and points1 will find no difficulty in laying down contour traces4 ,when the contour points have been surveyed with the chain1 the contour is obtained by drawing a free line of feature through the plotted points4 ,but when the contour points have been surveyed by measuring magnetic angles to known points1 such angles must be laid down at these points1 and produced to meet in the contour point4 ,the drawing of contours differs from the drawing of ordinary detail insomuch as each contour point is shown by a small dot1 and each carrying point by a similar dot surrounded by a small hand-drawn circle to distinguish it4 ,the former should be so plotted as to be distinguishable in the trace or contour line1 which should be readily traceable1 but not conspicuous4 ,the line joining adjacent points should be true lines of feature4 ,colour is usually employed for these lines1 and it is well to give them a broken or somewhat undefined character4 ,when the ,french system is adopted1 contour lines are drawn continuous1 a broad but faint line of colour4 ,to ,plot ,sounded ,points in ,submerged ,districts4--,when the angles have been measured on dry land with the theodolite1 these angles should be laid down at the dry-land points1 and the lines produced to meet in the sounded point4 ,but when the angles have been measured on the water with a sextant1 a station pointer is required4 ,the arcs of the pointer should be adjusted to read the measured angles1 and the instrument applied to the plotted points of the observed objects so as to bring the hair lines accurately to their respective object points4 ,the sounded point may then be correctly plotted through the centre of the pointer4 ,if the angles have been measured by the magnetic compass1 that is1 if the angles are those made with the magnetic meridian1 the angles should be laid down at the plotted points of the observed land objects1 and the lines produced to meet in the sounded point4 ,instead of the station pointer1 a piece of tracing paper may be used in the following manner4 ,draw three straight lines radiating from one point so as to make with each other angles equal to the measured angles4 ,lay the paper on the plan and move it about till the three lines traverse the observed objects4 ,the point from which they diverge will then mark the position of the sounded point1 which may be plotted by being pricked off4 ,the sounded point determined by angles measured with the sextant may also be plotted by describing circles on the land-object lines as chords1 to contain segmental angles equal to the measured angles4 ,such circles will intersect in the common land-object point and the sounded point4 ,to plot the sounded point in this manner1 requires the solution by construction of the problem1 8to describe on a given line a segment of a circle that shall contain a given angle40 ,but this method is generally found too tedious in practice4 ,errors and ,error-sheets4--,there is a tendency1 as we have previously remarked1 for the measured lengths of lines to be a little too long1 by reason of the irregularities of the surface4 ,it is usual to allow for this source of error #a in #ajjj in fair open country1 and #a in #ajjj in close country4 ,when the measurements differ by an amount exceeding these limits1 the pencil trace should not be drawn between the reference points1 but the line should be entered on an 8office error-sheet40 ,the error-sheet should show the number of the plot-sheet1 the triangle1 the book and page in which the measurements are entered1 and the scale and measured lengths of the line4 ,to ascertain the source of the error1 other lines referenced to the reference point or points of the line in error should be plotted1 and the apparent source should be entered on the error-sheet4 ,if the lines referred to the same point be found to plot to another point in the reference line1 the scale measurement of this point should also be entered4 ,and if the reference point in error be not directly surveyed in the survey of their respective lines1 the measurements for reference and the arithmetical reductions will have to be examined4 ,besides the office error-sheet1 there should be a field error-sheet for each book and triangle1 upon which should be entered the book1 the page1 and the line in error1 and some indication of the source of the error4 ,this sheet will be forwarded with the field-book to the surveyor for correction4 ,the following are examples of a common and very good form of error-sheet1 but it may be varied in many ways if thought desirable3-- ,,office ,,error-,,sheet4 ,plotter's ,name ,date ---------------------------------------- ------------------------ ,book4,lines4 ,scale ,reference,apparent,triangles4 ,observations4 ----- ,measure- ,points ,correc- ,page4 ment4 of ,lines4 tions4 ---------------------------------------- ----------------------- #bjj #aaahaeea #afea ,examine reference ----- #aiec #aijg ---------------- point and line4 #bc #bjiddjbj #djbj #bjj #bhadacjh ,illus- ----- #cjjj #cjef -------- #cjef tra- ,examine line4 #bh #djbjcjhb tion #bjj #aeea #he #afea ,examine reference ----- #acad #acbc ---------------- point and line4 #db #djbjcjbh #djbj ---------------------------------------- ----------------------- ,,field ,,error-,,sheet4 ,to ,a4 ,b41 ,surveyor4 ,date ---------------------------------------- --------------------------- ,book4,lines4,triangles4 ,observations4 ----- ,page4 ---------------------------------------- --------------------------- ,examine reference points and line4 #bjj #afea ----- #aiec ---- ,reference point 7,august #ajth1 #ahgd74 #bc #djbj #bjj ,illus- ----- #cjjj tra- ,examine line4 ,line #cjef 7,august #ajth1 #ahgd74 #bh tion ,examine reference points and line4 #bjj #afea ----- #acad ---- 7,august #abth1 #ahgd74 #db #djbj ,corrected in the field1 ,a4 ,b4 ---------------------------------------- --------------------------- ,to ,plot ,vertical ,sections4--,in plotting a vertical section1 a fine and firm horizontal line is first drawn to represent the datum line4 ,the reference points are then plotted upon this line from the level-book by means of a linear scale1 in the manner already described for plotting such points4 ,the reference points to be plotted upon the datum line are the chain lengths entered in the field-book in the column headed ,distances4 ,these distances are the points at which the levels were taken1 and between them1 unless otherwise stated in the field-book1 the ground is supposed to slope uniformly4 ,moreover1 these distances are assumed to be measured horizontally1 and therefore care must be taken to ascertain whether or not they were so measured in the field2 if not1 they must be reduced before plotting1 or the section will be too long4 ,having plotted the reference points on the datum line1 a perpendicular must be erected from each of them1 and a length laid off upon this perpendicular equal to the vertical height above the datum line indicated by the entry in the column of the level-book headed ,reduced ,levels against the distance to which the perpendicular corresponds4 ,to render the differences of altitude more apparent1 these vertical distances are plotted to a much larger scale than the horizontal1 as explained in a preceding ,section4 ,to erect the perpendiculars1 the ,t and set square furnish the most convenient means4 ,the detail points thus determined upon the perpendiculars represent the points in the surface of the ground at which the levels were taken1 and by joining these points we obtain the surface line4 ,an example will clearly show the method pursued4 ,let it be required to lay down the section from the following level-book3-- ---------------------------------------- ----------------------- ,back ,fore ,rise4,fall4,reduced ,dis- ,remarks4 ,sights4,sights4 ,levels4tances4 ---------------------------------------- ----------------------- feet4 feet4 feet4feet4 feet4 chains4 #ajjjj 44 ,b4,m4 north-west corner of church tower4 #afda #icg #gjd 44 #ajgjd #bcj #aicf #ajdc #hic 44 #aaeig #dfe #afdb #aicf 44 #bid #aacjc #fdj #hcf #adcf 44 #fjj #ajgjc #gid #icg #abdi 44 #cab #ajcia #ajcj #aafd #aigf 44 #hab #iegi #abjj #aidf #icbajad 44 #ajeic #aefd #agfd #acfb #djb 44 #ajiie 44 ,centre of road at #abc links4 #ahgf #abfd #fab 44 #aafjg #ahbc #aihd #afib #bib 44 #aahii #aifd #aigf #aafd #hab 44 #abgaa #bajj ,forward station at corner of wood4 #agfd #aigb 44 #bjh #abejc #bbej #igc #ahfd 44 #hia #aafab #bcgf #hfd #agfd 44 #ijj #ajgab #beij #ahgf #afbd #beb 44 #ajifd #bgjj ------------------------ #bcagi #bbbaedihadjag #bbbae #djag #ajjjj ------- ----- ------- ,difference between datum and #ifd #ifd #ifdlast reduced level1 or height of ,b above ,a4 ---------------------------------------- ------------------------ ,illustration3 ,,fig4 #hf4 ,draw the datum line ,d ,l1 ,fig4 #hf1 and set off along it the distances #bcj1 #dfe1 #fdj1 #gid1 c41 links2 these points will be the reference points for the perpendiculars4 ,erect a perpendicular from each of these points1 and lay off1 to a suitable scale1 upon these lines successively the vertical heights #ajj1 #ajgjd1 #aaeig1 #aacjc1 #ajgjc1 c4 ,the points thus determined will be the surface detail points1 and by joining these we shall obtain the surface line4 ,then will ,a ,d ,l ,b represent a section of the ground between ,a and ,b4 ,a description of objects on the surface worthy of notice should be written over such objects4 ,in working sections1 where great accuracy is required1 larger scales are employed1 and the levels are taken at more frequent intervals4 ,thus1 in a railway working section1 for example1 the levels are taken at every chain's length1 and also over every little undulation in the surface of the ground4 ,in preparing such sections1 vertical lines are drawn in blue at every chain's length up to the surface of the ground from the datum line1 and on each vertical is written the reduced height above datum from the column of reduced levels in the level-book4 ,sections1 especially working sections1 are usually drawn upon ruled1 or1 as it is called1 8section0 paper1 the nature of which we have already described4 ,this method1 which was introduced by ,mr4 ,brunel1 possesses many practical advantages1 inasmuch as it obviates the necessity of plotting the 8distances0 and erecting perpendiculars1 the latter already existing4 ,it also greatly facilitates the computation of the contents of a given section4 ,its chief defect lies in the difficulty of making the horizontal lines coincide when joining the sheets end to end4 ,of course scales are not required upon section paper4 ,to lay down ,gradients4--,the method of laying down the gradients of railways and roads usually adopted in practice consists in applying one end of an extended silken thread to the section at the point in which the road commences1 and the other end in such a position that the thread may cut the profile of the earth's surface so as to leave equal portions of space above and below the thread1 as nearly as can be judged by the eye4 ,the cuttings from the parts above the thread will then furnish sufficient materials to form the embankments in the spaces below4 ,this is called 8balancing0 the cuttings and embankments4 ,when the first gradient has been determined in this way1 it may be found unfavourable to the second in respect to the extent of cuttings and embankments2 in such a case it must be modified to suit the requirements of the latter4 ,in this way the gradients must be modified successively until the compound result evidently gives a minimum of cuttings and embankments1 due regard1 of course1 being had to the limits imposed by the nature of the case1 both with respect to the ruling gradient and the proper heights for bridges4 ,to ,plot a ,section from a ,contour ,map4--,the mode of plotting a section from a contoured plan was explained when treating of contour lines4 ,the contour map used for this purpose should give the features of the surface configuration in sufficient detail without serious error4 ,having drawn a line of section on the map and a datum line upon the fair paper for the vertical section1 the points in which the section line intersects the contours should be measured on the scale of the map from a zero point in that line1 and the measurements plotted upon the datum line4 ,perpendiculars should then be drawn through these plotted points1 and on these perpendiculars the reduced altitudes of their respective contour points should be plotted4 ,a line drawn through these surface plotted points will be the surface line4 ,when the horizontal scales of the map and the section are the same1 the contour plane lines may be drawn on the paper for the section parallel to the section line on the map1 and perpendiculars raised to intersect them from the points on the map in which the section line intersects the contours1 in the manner previously described4 ,the points of intersection with the parallel lines will be the surface contour points in the vertical section4 ,for practical purposes1 the parallel lines and the perpendiculars are only temporarily drawn in pencil until the surface trace shall have been obtained and drawn in ink1 with the datum line4 ,,section ,,iv4--,,civil ,,engineers' ,,and ,,surveyors' ,,plans4 ,in the preceding ,sections the manner of laying down plans has been fully described and the principles involved in the operations minutely explained4 ,it now only remains1 therefore1 to direct attention to certain matters relating to the preparation of plans1 which are necessitated by the circumstances of particular cases4 ,civil engineers' plans usually consist1 if we except harbour surveys1 of a representation1 to a rather large scale1 of long and narrow tracts of country through which it is proposed to construct a means of communication1 such as a railway1 a road1 or a canal4 ,they do not differ essentially from other plans1 the survey being taken in the ordinary way1 and the plan laid down according to one or other of the methods described in the preceding ,section4 ,the width of railway surveys varies from five to twenty chains1 at the option of the engineer4 ,an important matter demanding careful attention is to survey1 plot1 and number all fields and other enclosures1 houses and other buildings situate within the limits of deviation1 that is1 the boundaries of the space beyond which it is not proposed to deviate the line of railway4 ,the object of numbering every separate enclosure1 road1 building1 or other object on the plan1 is that they may be the more readily described in a book prepared for that purpose and called the ,reference ,book4 ,parish and county boundaries are shown by dotted lines1 as explained in a former ,section4 ,frequently it is necessary1 in consequence of the smallness of the scale adopted for the plan1 to give enlarged drawings of certain portions4 ,in these cases1 whenever practicable1 the enlarged plan should be placed directly under or over the small plan to which it refers1 as such an arrangement is not only more pleasing to the eye1 but is far more convenient for reference than one in which there is no relation of position between the two plans4 ,the proposed railway should be represented by a full and heavy line1 and the limits of deviation shown by strong dotted lines4 ,the names of the different parishes through which the line passes should be conspicuously written1 and the name of the county placed at the top of each sheet2 the sheets also should be distinctly numbered4 ,it is not usual to distinguish different kinds of fences on plans of engineering projects1 as on estate plans to a large scale2 on the former it is sufficient to distinguish between fenced and unfenced lines of division of land1 marking the former by plain1 and the latter by dotted lines4 ,it is almost needless to remark that a scale of distances should accompany every plan4 ,the section should be drawn to the same horizontal scale as the plan1 and the exaggeration of the vertical scale should be such as to show distinctly the irregularities of the surface4 ,the horizontal datum line of the section should have marked on it a scale of distances corresponding with those marked along the centre line of the plan1 in order that corresponding points on the plan and the section may be readily found1 and great care should be taken that horizontal distances on the plan and on the section exactly agree4 ,cross sections are longitudinal sections of existing lines of communication which the proposed work will cross2 they may cross the centre line of the proposed work either at right angles or obliquely4 ,cross sections may also be required where the ground slopes sideways2 in general they should be ranged accurately at right angles to the centre line1 and they should be plotted without exaggeration1 that is1 their vertical and horizontal scales should be the same as the vertical scale of the longitudinal section4 ,all cross sections should be plotted as seen by looking forward towards them along the centre line4 ,to distinguish the nature of the soils passed through1 sections are frequently coloured1 as shown in ,plate #ba4 ,the information given by this means concerning the character of the strata is of very great value to the engineer or to the contractor1 inasmuch as it enables them to predicate with some degree of certainty the amount of labour that will be required in executing the proposed work4 ,it is1 therefore1 highly important that the draughtsman correctly represent the character of the strata4 ,the conventional modes of representing these features are shown on ,plate #bj1 which should be carefully studied and copied4 ,it is necessary that the engineering draughtsman should be acquainted with the 8,standing ,orders0 of ,parliament relating to the preparation of plans and sections1 in order that he may fulfil the conditions therein laid down4 ,and as most of the important details involved by the exigencies of practice in the preparation of such plans and sections are prescribed by these ,standing ,orders1 we will give so much of them as relates directly to the matters under consideration2 by so doing1 the details will be clearly and fully described1 and the requirements of the law concerning them authoritatively made known4 ,nature of the ,documents required4--8,in cases of bills relating to engineering works1 a plan and also a duplicate thereof1 together with a book of reference thereto1 and a section and also a duplicate thereof1 as hereinafter described1 shall be deposited for public inspection at the office of the clerk of the peace for every county1 riding or division in ,england or ,ireland1 or in the office of the principal sheriff clerk of every county in ,scotland1 and where any county in ,scotland is divided into districts or divisions1 then also in the office of the principal sheriff clerk in or for each district or division in or through which the work is proposed to be made1 maintained1 varied1 extended or enlarged1 or in which such lands or houses are situate1 on or before the #cjth day of ,november immediately preceding the application for the bill40 8,in the case of railway bills1 the ordnance map1 on the scale of one inch to a mile1 or where there is no ordnance map1 a published map1 to a scale of not less than half an inch to a mile1 or in ,ireland1 to a scale of not less than a quarter of an inch to a mile1 with the line of railway delineated thereon1 so as to show its general course and direction1 shall1 on or before the #cjth day of ,november1 be deposited at the office of the clerk of the peace1 or sheriff clerk1 together with the plans1 sections1 and book of reference40 8,in cases where the work shall be situate on tidal lands within the ordinary spring tides1 a copy of the plans and sections shall1 on or before the #cjth day of ,november1 be deposited at the office of the ,harbour ,department1 ,board of ,trade1 marked #8,tidal ,waters1' and on such copy all tidal waters shall be coloured blue1 and if the plans include any bridge across tidal waters the dimensions as regards span and headway of the nearest bridge1 if any1 above and below the proposed new bridge1 shall be marked thereon1 and in all such cases such plans and sections shall be accompanied by a published map or ordnance sheet of the country1 over which the works are proposed to extend1 or are to be carried1 with their position and extent1 or route accurately laid down thereon40 8,in the case of railway bills1 a copy of all plans1 sections1 and books of reference1 and the aforementioned published map with the line of railway delineated thereon so as to show its general course and direction1 is required to be deposited at the office of the ,board of ,trade1 and at the ,private ,bill ,office of the ,houses of ,parliament2 and in cases where any portion of the work is situate within the limits of the ,metropolis1 a copy of so much of the plans and sections as relates to such portion of the work is required to be deposited at the office of the ,metropolitan ,board of ,works4 ,also a copy of so much of the plans and sections as relates to each parish in or through which the work is intended to be made1 or in which any lands or houses intended to be taken are situate1 together with a copy of so much of the book of reference as relates to such parish1 is required to be deposited with the parish clerk of each such parish in ,england1 with the school-master of each such parish in ,scotland1 and with the clerk of the union within which such parish is included in ,ireland40 ,plans4--8,every plan required to be deposited shall be drawn to a scale of not less than four inches to a mile1 and shall describe the line or situation of the whole of the work 7no alternative line or work being in any case permitted71 and the lands in or through which it is to be made1 maintained1 varied1 extended or enlarged1 or through which every communication to or from the work shall be made2 and where it is the intention of the parties to apply for powers to make any lateral deviation from the line of the proposed work1 the limits of such deviation shall be defined upon the plan1 and all lands included within such limits shall be marked thereon2 and unless the whole of such plan shall be upon a scale of not less than a quarter of an inch to every one hundred feet1 an enlarged plan shall be added of any buildings1 yard1 courtyard or land within the curtilage of any building1 or of any ground cultivated as a garden1 either in the line of the proposed work or included within the limits of the said deviation1 upon a scale of not less than a quarter of an inch to every one hundred feet40 8,in all cases where it is proposed to make1 vary1 extend or enlarge any cut1 canal1 reservoir1 aqueduct or navigation1 the plan shall describe the brooks and streams to be directly diverted into such intended cut1 canal1 reservoir1 aqueduct or navigation1 or into any variation1 extension or enlargement thereof respectively1 for supplying the same with water40 8,in all cases where it is proposed to make1 vary1 extend or enlarge any railway1 the plan shall exhibit thereon the distances in miles and furlongs from one of the termini2 and a memorandum of the radius of every curve not exceeding one mile in length shall be noted on the plan in furlongs and chains2 and where tunnelling as a substitute for open cutting is intended1 such tunnelling shall be marked by a dotted line on the plan40 8,if it is intended to divert1 widen or narrow any turnpike road1 public carriage road1 navigable river1 canal or railway1 the course of such diversion1 and the extent of such widening or narrowing shall be marked upon the plan40 8,when a railway is intended to form a junction with an existing or authorized line of railway1 the course of such existing or authorized line of railway shall be shown on the deposited plan for a distance of eight hundred yards on either side of the proposed junction1 on a scale of not less than four inches to a mile40 ,book of ,reference4--8,the book of reference to every such plan shall contain the names of the owners or reputed owners1 lessees or reputed lessees1 and occupiers of all lands and houses in the line of the proposed work1 or within the limits of deviation as defined upon the plan1 and shall describe such lands and houses respectively40 ,sections4--8,the section shall be drawn to the same horizontal scale as the plan1 and to a vertical scale of not less than one inch to every one hundred feet1 and shall show the surface of the ground marked on the plan1 the intended level of the proposed work1 the height of every embankment and the depth of every cutting1 and a datum horizontal line1 which shall be the same throughout the whole length of the work1 or any branch thereof respectively1 and shall be referred to some fixed point 7stated in writing on the section71 near some portion of such work1 and in the case of a canal1 cut1 navigation1 turnpike or other carriage road or railway1 near either of the termini40 8,in cases of bills for improving the navigation of any river1 there shall be a section which shall specify the levels of both banks of such river2 and where any alteration is intended to be made therein1 it shall describe the same by feet and inches1 or decimal parts of a foot40 8,in every section of a railway1 the line of the railway marked thereon shall correspond with the upper surface of the rails40 8,distances on the datum line shall be marked in miles and furlongs1 to correspond with those on the plan2 a vertical measure from the datum line to the line of the railway shall be marked in feet and inches1 or decimal parts of a foot1 at each change of the gradient or inclination2 and the proportion or rate of inclination between each such change shall also be marked40 8,wherever the line of the railway is intended to cross any turnpike road1 public carriage road1 navigable river1 canal or railway1 the height of the railway over or depth under the surface thereof1 and the height and span of every arch of all bridges and viaducts by which the railway will be carried over the same1 shall be marked in figures at every crossing thereof2 and where the roadway will be carried across any such turnpike road1 public carriage road or railway1 on the level thereof1 such crossing shall be so described on the section2 and it shall also be stated if such level will be unaltered40 8,if any alterations be intended in the water level of any canal1 or in the level or rate of inclination of any turnpike road1 public carriage road or railway1 which will be crossed by the line of railway1 then the same shall be stated on the said section1 and each alteration shall be numbered2 and cross sections in reference to the said numbers1 on a horizontal scale of not less than one inch to every three hundred and thirty feet1 and on a vertical scale of not less than one inch to every forty feet1 shall be added1 which shall show the present surface of such canal1 road or railway1 and the intended surface thereof when altered2 and the greatest of the present and intended rates of inclination of such road or railway shall also be marked in figures thereon2 and where any public carriage road is crossed on the level1 a cross section of such road shall also be added2 and all such cross sections shall extend for two hundred yards on each side of the centre line of the railway40 8,wherever the extreme height of any embankment1 or the extreme depth of any cutting1 shall exceed five feet1 the extreme height over or depth under the surface of the ground shall be marked in figures upon the section2 and if any bridge or viaduct of more than three arches shall intervene in any embankment1 or if any tunnel shall intervene in any cutting1 the extreme height or depth shall be marked in figures on each of the parts into which such embankment or cutting shall be divided by such bridge1 viaduct or tunnel40 8,where tunnelling1 as a substitute for open cutting1 or a viaduct as a substitute for solid embankment1 is intended1 the same shall be marked on the section40 8,when a railway is intended to form a junction with an existing or authorized line of railway1 the gradient of such existing or authorized line of railway shall be shown on the deposited section1 and in connection therewith1 and on the same scale as the general section1 for a distance of eight hundred yards on either side of the point of junction40 ,besides the information thus written on the plan1 it is useful to the engineer1 though not prescribed1 to have the levels of important points either written or shown by means of contour lines1 especially when the plan is to be used in selecting a line of railway4 ,the results of trial pits and borings may also be written on the plan1 and the estimated cost of each part of the work placed opposite to its position on the paper4 ,working ,sections4--,for working sections the horizontal scale adopted is usually three or four chains to the inch1 and the vertical scale #cj or #dj feet to the inch4 ,a working section should show the level of the ground1 the level of the proposed work1 and the height of embankment or depth of cutting at every point of the ground where the level has been taken1 these quantities being found by calculation1 not by measurement on the paper4 ,the position and levels of all 8bench marks0 should also be clearly indicated4 ,at every crossing of road1 river or stream of any kind1 should be inserted some remark respecting the work to be constructed1 with a reference to the number of the working drawing prepared4 ,the latter may be a special drawing1 as for a bridge1 or a general drawing1 as for a level crossing and gates4 ,the results of boring should also be shown on the working section4 ,as soon as the works of construction have been determined upon1 notes should be inserted from the working drawings1 or other sources1 of the angles of skew at which the line crosses roads or streams1 the spans of arches on the square and on the skew1 the rise of the arch1 the depth of the arch stones1 and of the puddle1 if any be used1 and1 if the works be on an inclined plane1 the rise or fall from centre to centre of the piers4 ,similar memoranda should also be made of girder bridges1 culverts1 and other works occurring along the line4 ,to all working drawings the acting engineer always affixes his signature4 ,besides an acquaintance with the 8,standing ,orders10 the engineering and surveyor's draughtsman should possess a knowledge of the ,regulations of the ,local ,government ,board1 for these have to be complied with in the preparation of plans relative to main sewerage1 drainage1 and water-supply4 ,these ,regulations are as follows4 ,boundary ,maps4--,in cases in which a special district is proposed to be formed for the adoption of the ,local ,government ,act1 a map must be submitted1 accompanied by a written description of the proposed boundary1 designated by letters from point to point1 commencing from a fully and clearly defined point on the north side of the map marked by the letter ,a and a written description1 then proceeding eastward by natural or other well-defined features1 until the description closes upon the point started from4 ,the name of the proposed district must be printed on the map1 with the area in acres4 ,the population and the number of houses1 with the rate of increase as ascertained at the two last decennial periods upon which the census was taken1 must be given1 and a duplicate or tracing of the map furnished4 ,maps for ,division into ,wards4--,a map of the entire district must1 in this case1 be submitted1 with the main boundary distinctly defined1 and the name of the district clearly printed thereon4 ,the proposed division into wards must be by lines1 clearly defined on the map of the district2 brooks1 roads1 footwalks1 streets1 fences1 or other easily recognizable lines of division may be adopted4 ,such lines must be defined on the map by a margin of colour4 ,the proposed boundary-lines must be described in the same manner as in the boundary map1 and the name or number of the ward1 with the relative areas1 population1 and rateable value must be given4 ,a duplicate map or a tracing must be deposited at the ,local ,government ,act ,office for future reference4 ,plans of ,proposed ,works4--,it is in all cases necessary1 upon application being made by ,local ,boards for the ,secretary of ,state's sanction to a loan for the execution of works1 that plans1 sections1 detailed estimates1 and specifications be submitted with the application1 accompanied with the information relative to area1 population1 number of houses1 and rateable value of the district required for boundary maps4 ,tracings of such plans and sections1 and copies of the estimates and specifications must be sent in for filing at the ,local ,government ,act ,office4 ,general ,plan4--,a general plan exhibiting the area which will be affected by the proposed works must be laid down to a scale of not less than two feet to a mile4 ,it should have figured upon it the levels of the centres of all the streets and roads at their intersections and angles1 and at every change of inclination2 also1 where a district is near the sea1 it should show the high and the low tide level of the sea1 and where there is a river1 the summer and the flood-water levels should be recorded4 ,permanent bench marks having reference to the surface levels should be cut on public buildings1 or other permanent and suitable objects1 throughout the district1 and clearly marked on the plan4 ,sections should accompany this plan1 upon which the levels of the cellars should be shown4 ,such a plan may be used for showing the lines of main-sewers and drains1 lines of water-pipes1 and gas-mains4 ,the lines of main-sewers and drains should have the cross-sectional dimensions and the gradients distinctly marked upon them4 ,the dimensions of water and gas pipes should also be shown in figures or in writing4 ,detailed ,plan4--,a detailed plan for the purposes of house-drainage1 paving1 the sale and purchase of property1 or other purposes of a like character1 must be constructed to a scale of not less than ten feet to a mile4 ,upon this plan must be exhibited all houses and other buildings1 bench marks1 the levels of streets and roads1 of cellars1 of the sea at high and low tide level1 and the summer and the flood level of rivers4 ,three feet by two feet will be a convenient size for the sheets of this plan1 and by representing the marginal lines of the sheets upon the general plan1 and numbering the sheets to correspond1 the general plan will become a very useful index4 ,as it may occasionally be desired to carry out works piecemeal1 with a view to save the time which would be occupied in the preparation of a complete plan from actual survey1 it is sufficient in the first instance to furnish a general plan of streets and roads only1 with the surface levels and those of the deepest cellars1 and the proposed scheme of works shown thereon1 after which the works can proceed in sections4 ,but with each separate application for sanction to a loan1 a correct plan and section or sections should be submitted1 accompanied by detailed estimates and specifications4 ,it must1 however1 be understood that the complete plan of the entire district must be proceeded with1 so that1 when the works are finished1 the ,local ,board and the office of the ,local ,government ,act may possess a proper record4 ,mining ,plans4--,the plotting of mining surveys is performed in the same manner as the surface traverse surveys already described4 ,before proceeding to lay down the plan1 it is well to divide the paper into squares of #aj chains side1 or #aj acres area1 by two sets of lines crossing each other at right angles1 one of which sets should represent meridians4 ,this operation should be performed with scrupulous care2 and to ensure accuracy1 beam compasses should be used to lay off the divisions4 ,the lines should be finely drawn in colour to distinguish them from other lines to be put upon the drawing4 ,care must be taken to get the plan fairly upon the paper1 so that the conformation of the outline or boundary to the edges of the paper may have a pleasing effect to the eye2 and the direction of the meridians must be determined according to this condition4 ,by having the plan thus divided into squares of #aj acres each1 the quantity of ground worked out may be approximatively estimated at any time by inspection1 and the total quantity may be readily computed in the same manner4 ,besides dividing the plan itself in this way1 it will be found extremely useful to have a sheet of tracing paper1 or better1 tracing cloth1 divided into squares of #cafbbh links side1 or #a acre area1 in black lines2 each of such squares being subdivided into #d by lines in colour1 to show quarters of an acre4 ,to find the area of any portion of exhausted or of unworked ground1 it is only necessary to lay this divided sheet over such portion and to count the squares and quarters included in it4 ,by reason of the variations of the magnetic meridian1 the date of a survey should always be written on the plan2 and as the plan of underground workings is laid down piecemeal as the workings progress1 often extending over a period of many years1 care must be taken to reduce all bearings to the original meridian4 ,unless these matters are strictly observed1 serious errors may result4 ,when two or more veins of mineral are being worked one above the other1 and are placed upon the same plan1 they are distinguished by means of colour4 ,it matters not what colours are employed for the several separate workings so long as they are distinct from each other4 ,also the mode of applying the colour1 whether with the brush or with the pen1 is entirely a question of taste4 ,it may1 however1 be observed that as mining plans are constantly being added to1 it is very difficult to avoid a patchy appearance when the colour is laid on with the brush4 ,plate #cc shows the manner in which mining plans are got up4 ,estate and ,town ,plans4--,plans of estates and towns1 including as they do only a limited area and requiring great distinctness of detail1 are laid down to a large scale2 for the form and character of the detail are1 on such plans1 of equal importance with its position4 ,with such a scale as is required in these cases1 it is possible1 not only to clearly distinguish natural and artificial features1 but to introduce means of producing pictorial effect into their representation4 ,the nature of these means may be seen in the examples of plans appended to this work4 ,the manner of showing the various kinds of fences has been already described4 ,trees are usually shown in elevation for the sake of artistic effect2 but care must be taken to give them such dimensions as will accord with the scale of the drawing4 ,houses and other buildings are shown in plan of the correct form1 and washed for distinction in light red for dwelling-houses1 dark grey for outhouses1 and light grey for public buildings4 ,dark grey is also used for all wooden and iron buildings to distinguish them from those constructed of the ordinary materials1 brick and stone4 ,but besides such distinctions1 others are needed to indicate the character of natural features and artificial constructions4 ,these are obtained either by showing the object roughly in elevation1 or by some purely conventional means4 ,the signs of this character that are likely to be frequently required on estate plans are shown on ,plate #ae4 ,the manner of representing water1 which has been described in a preceding ,section1 will be found illustrated in detail on ,plate #aa4 ,plates #aj and #ad show various kinds of trees2 in this form they may be introduced very effectively into plans of estates4 ,the several stages which a plan passes through in the office are shown on ,plate #b4 ,if the plan is to be coloured1 the colouring must be done before the lettering is put on4 ,plate #c shows a plan lightly coloured1 as used by surveyors1 solicitors1 and others2 and ,plate #ag shows a finished plan in colour4 ,the methods of laying on the colours and the principles involved in the operations have been fully described and explained in a former ,section4 ,in ,plate #ac is given a town plan showing a proposed street improvement4 ,such a plan must be laid down to a large scale1 and the details in and near the part affected must be drawn in clearly and accurately4 ,the uncoloured portion represents the plan as prepared for lithographing4 ,when pink colour is used to show the proposed street1 the buildings should be coloured in black by a light wash of ,indian ink4 ,yellow or any other bright tint may be used for the proposed street1 the object being merely to distinguish it clearly4 ,existing streets should be coloured in yellow ochre1 except when that colour is used for the proposed street1 in which case burnt sienna may be used4 ,the ,plates relating to this ,section are ,nos4 #b1 #c1 #aj1 #aa1 #ac1 #ad1 #ae1 #ag1 #ai1 #bj1 #ba1 and #cc4 ,,section ,v4--,,map ,,drawing4 ,the principles and practice of map drawing1 being in the main identical with those of ordinary plan drawing1 have been generally explained and described in the preceding ,sections4 ,in the present ,section1 therefore1 we have only to direct attention to such details as belong especially to the former class of topographical representations4 ,these details relate chiefly to the selecting of objects and features on the surface of the ground whose character entitles them to special notice1 and therefore to distinct delineation2 to the practical methods of sketching such objects and features in the field1 and to the means and the manner of reproducing them on the finished map4 ,the first and the last of these questions have been treated by ,mr4 ,james in his ,handbook of ,topography1 and the second by ,lieut4 ,r4 ,s4 ,smith of the ,united ,states' ,army1 in so concise and yet so complete a manner that we have not hesitated to avail ourselves of their labours rather than attempt to offer any instructions of our own4 ,the following is1 therefore1 worthy of respectful attention4 ,single ,stroke ,streams4--,in inking in streams1 begin at the source and draw downwards towards yourself1 increasing the pressure on the pen as you descend4 ,the use of the steel pen in drawing single stroke streams is very objectionable4 ,even soft steel pens are apt to cut the surface of the paper1 and in sharp bends it is quite impossible to ensure an even width of line with the best yet made2 by re-inking1 much time is lost1 and frequently a rough jagged line is the result4 ,the common quill pen finely pointed will work well on any sort of paper4 ,double ,line ,streams and ,rivers4--,in maps of a small scale from #h to #cb miles to the inch1 it is usual to darken the north-western bank1 supposing the light to fall from the ,n4,w4 corner of the map2 but on maps of a large scale it is usual to attend strictly to the height of the banks1 and the draughtsman should carefully represent the exact nature of each bank on his field-sketch or plane-table sheet4 ,colouring ,streams or ,rivers4--,single stroke streams may be inked in with either a dark line of ,prussian blue1 or a light line in ,indian ink may first be drawn and a streak of ,prussian blue or cobalt run neatly along it4 ,cobalt is much used both in single and double stroke streams--it is certainly the prettiest and most lasting blue we have1 and the preference should be given it1 as it imparts a high finish to ,,ms4 maps4 ,in maps which contain much hilly ground1 the streams should be drawn in with light ink and a very fine pen at first1 and be re-drawn with dark ink or dark blue after the shading of the hills4 ,large rivers on all maps published in ,england are now coloured with a flat-wash of cobalt or ,prussian blue4 ,some draughtsmen prefer shading rivers according to bends1 and keeping the shade as falling from the ,n4,w41 but this system cannot be carried out on maps of a large scale1 where the height of the bank is correctly represented4 ,islands and ,sand-banks1 ,sandy and ,pebbly ,beds of ,rivers4--,islands which are only visible at low water1 on well-coloured maps1 are usually first washed over with a light shade of burnt or raw sienna1 or a mixture of raw sienna and light red2 the last-mentioned colour does not easily mix with water1 and should not be used if any other can be substituted4 ,after the tint is dry1 dot finely with light ,indian ink or dark burnt sienna4 ,sand-banks are coloured in the same way4 ,sandy beds may be similarly treated1 omitting the dotting if pressed for time4 ,pebbly beds should first be tinted with a mixture of burnt or raw sienna1 then dip into a dark shade of burnt sienna any coarse camel-hair brush1 and splitting the brush by drawing it between the forefinger and thumb1 dot in the tinted portions4 ,care must be taken to avoid having too much colour in the brush1 or the dots will run into each other and make ugly daubs4 ,another very easy and successful method of dotting in sand or pebbly beds is with a tooth-brush4 ,first1 on tracing or any other thin paper1 trace out exactly the limit of the tinted portion requiring dotting1 cut out these portions from the trace and place it correctly over the original1 dip a tooth-brush lightly into a saucer of colour of the required depth of tint1 and holding it in the left hand over the uncovered portions1 with the forefinger of the right hand or the blade of a pen-knife1 gently splutter the colour from the brush2 when it is necessary to cover a large space with dots1 this will be found the simplest and most speedy way of doing it4 ,roads and ,pathways4--,the main or trunk roads in any country should be very distinctly represented by double and perfectly parallel ink lines1 coloured between the lines with lake or carmine4 ,district roads metalled1 or those made between chief towns1 should be shown by a single line coloured with lake or carmine4 ,unmetalled roads and paths by only a single line in burnt sienna4 ,the same system should be carried out in roads in a mountainous country1 and the draughtsman should give1 either on the map or in the column of remarks1 such information regarding roads as is likely to be useful to travellers or military authorities4 ,mountain ,passes4--,on large scale maps these should be distinctly marked1 and the windings of the road correctly shown4 ,along the ,pass1 write the name in small lettering1 and state whether it is practicable for horses1 or fit only for men on foot4 ,on maps of a small scale1 it will be sufficient to show the pass by a zigzag line across the hollow1 with a note as above4 ,fords and ,ferries1 ,toll-gates4--,fords should be carefully noted and the name and depth of water during the rainy and dry seasons given1 if possible4 ,the number of boats at every ferry should be correctly ascertained1 and noted on the map4 ,toll-gates may be shown on roads with a light line drawn across the road1 and the words 8,toll-gate0 be clearly written on the side of the road4 ,encamping ,grounds1 ,mile ,stones1 ,wells1 ,springs and ,tanks1 should be correctly shown and named on all maps4 ,telegraph ,lines and ,stations must be shown on all maps drawn to a scale of four miles to an inch and upwards1 by the usual symbol4 ,on maps of a small scale1 show by dots or a thin line of yellow1 giving a reference under the title4 ,the ,stations are of the first importance1 and should be represented by the symbol4 ,railways1 ,stations1 and ,termini4--,railways are represented by a strong black line1 with or without thin lines drawn at right angles to the main line4 ,they should of course be very carefully and accurately laid down1 as they form the chief feature in any country4 ,stations are shown by well-defined circles1 and the name given in plain lettering4 ,termini are best shown by blocks representing the size of the buildings according to the scale of the map4 ,except on maps of a very large scale1 jungle should not be shown over hilly ground4 ,representing such objects as trees1 jungle or brushwood1 over plains or flat lands1 on all ordinary scale maps1 is very necessary1 and the exact limits of the jungle or waste should be surveyed and correctly given by a dotted line1 but over hilly ground it would be impossible to do so without impairing the beauty and hiding the features of the hill drawing4 ,if it is actually necessary to make it known that the hills have jungle on them1 let a foot-note to the effect be inserted amongst the remarks or under the title of the map4 ,under the head of remarks or notes1 it is always very necessary to state the kind of jungle which exists in the surveyed tracts1 for the information of speculators and timber merchants1 and for the guidance of the lithographer or engraver4 ,notes on maps1 whether statistical or geographical1 can never be too full2 they are useful in supplying at once information which could be obtained only from reading reports1 and frequently they render topographical details intelligible where there might otherwise be doubt or misconception4 ,they can be recorded in any spare corner or blank space on the map4 ,size of ,cities1 ,towns and ,villages1 and the different ways of representing them4--,it is of the utmost importance that all maps of a large scale should show the size accurately of cities1 towns and villages4 ,if the scale admits of it1 the several blocks or groups of houses with the roads between them should be correctly drawn4 ,sketching1 ,shading1 and ,copying ,hills4--,in sketching hills1 always begin by fixing--#ast4 ,the drainage2 #bnd4 ,those features which are most prominent1 such as peaks1 rocks1 ledges of rock running with the strata of the hills1 trees remarkable for some peculiarity in shape or size so as to be recognized from various positions1 and any other objects likely to help the eye in filling in the details2 and lastly1 sketch the details1 beginning always with the ground nearest yourself4 ,endeavour to portray your ground faithfully--#ast4 ,by preserving the direction and bend of streams as in nature2 #bnd4 ,by giving the run of the ridges correctly2 #crd4 ,by fixing the peaks1 ledges of rock1 precipitous falls and flats carefully2 #dth4 ,by showing the saddles or depressions between peaks1 which can only be done by giving the peaks on either side sufficient relief in shading2 #eth4 ,by attending strictly to the true breadth of valleys2 #fth4 ,by suppressing all hollows with a suitable depth of tint2 #gth4 ,by careful representation of the banks of streams in the valleys2 and lastly1 by finishing shades and touches1 in which is comprehended the retouching with brush or pen work the entire piece1 strengthening the shade of the higher ridges and peaks to show their relative heights1 and suppressing the white tint along the ridges4 ,many excellent draughtsmen are in the habit of leaving the ridge of mountain ranges quite white2 this is evidently a mistake1 for1 unless the ridge of any range of hills is of one uniform height from end to end1 it cannot correctly be left white4 ,thus a wrong impression is conveyed of the surface of the ridge1 the white streaks look harsh and are displeasing to the eye1 and a stiff and unartistic look is given to the finish of the drawing4 ,the means of communication1 whether by roads or minor tracks1 are important1 both for civil and military purposes1 and should be carefully inserted in the map4 ,this can generally be done with facility in a hilly country1 as the fixed marks will be visible in sufficient number along the road1 so that the latter may be drawn in at once by plane-table operations along the line of communication to be surveyed4 ,in flat countries1 or where the view is circumscribed1 it may be necessary to resort to measurements and plotting2 but should any case occur where the fixed points of reference are far apart1 the traverse system must be resorted to1 and the road should be plotted from computed co-ordinates4 ,field ,sketching4--,field sketches are made with the lead pencil1 and may be drawn upon every page of the compass-book1 or upon the alternate pages1 at the option of the topographer4 ,in the former case1 the bearings and distances are recorded upon the drawing2 in the latter1 the record occupies the left-hand page1 and the sketch the opposite one4 ,the page for sketching should be ruled in squares1 with blue or red ink1 forming thus an indeterminate scale1 the length of the sides of the squares being assumed at pleasure1 according to the nature of the ground4 ,both the record and the sketch are read from the bottom of the page upward4 ,suppose the stations of the survey to be #ajj feet apart2 then1 assuming the side of the square to be #ajj feet1 commence the sketch at the bottom of the page--in the centre1 if the survey promises to be tolerably straight2 if otherwise1 at some point to the right or left of the centre1 the reason for which will be explained directly4 ,let the bearing from the first station1 the starting point or zero1 be ,n4 #aj ,e4 ,draw a line from the bottom of the page upward2 the side of the square being assumed #ajj feet1 number the stations upon the squares as far as the line is run1 say #cbe feet1 and write the compass angle down along this line4 ,let the bearing from the second station1 or ,no4 #a1 be ,n4 #a ,w42 draw a line1 making1 as nearly as can be judged by the eye1 the proper angle with the last bearing1 and proceed as before4 ,when the page is exhausted1 commence with a vertical line at the bottom of the next one1 marking upon it the remainder of the old bearing1 and making1 by the eye1 a new series of approximate protractions as before4 ,if it can be foreseen1 as in most cases it can1 that the line of survey will be very crooked1 bending1 for example1 from left to right1 then commence the bearing at the bottom of the page accordingly1 beginning at a point on the extreme right1 and running it diagonally to the left1 so as to make due allowance for the great deflection anticipated in the next bearing4 ,such cases may be foreseen in running around an inclosure1 or in following a curving stream or ridge4 ,the advantages of the system of squares in sketch books completely overbalance the one disadvantage1 which is1 that the diagonal bearings will not make exact distances upon the squares1 while the vertical and horizontal ones will4 ,it will be remembered that the surveying book is designed to be exact only in its record and the general features of the ground1 and that a slight change of scale is not material1 as it can be made exact when the survey is protracted upon the map4 ,by these approximate protractions1 any page of the book of survey conveys a very just notion of the bearings and distances1 and of the relative positions of the general features of the ground4 ,the first station being at the bottom of the page1 note down1 in the space between it and the second one1 all the features of the ground passed over by the line of survey2 as to whether it is cultivated1 forest1 marsh1 c42 whether it is crossed by streams1 ditches1 c41 and their width2 if it rises or falls2 about what degree of slope1 c4 ,on both sides of the line introduce1 according to the scale1 and their distances1 as judged by the eye1 all topographical objects within sight1 such as buildings1 roads1 streams1 hills1 c41 c41 drawing them to the scale if possible1 and if they cannot be got upon the page1 describing briefly their nature and position4 ,in sketching hills endeavour to project as many horizontal curves as possible1 which should be lightly put in1 and then the shading lines may be drawn over them4 ,the degree of slope should be frequently written down in numbers upon the sketch4 ,the names of localities1 streams1 hills1 farms1 c41 should also be entered4 ,thus far we have supposed a measured line upon the ground1 to which the situation and dimensions of objects might be referred4 ,it is much more difficult to embody the relative positions and dimensions1 where all is left to the eye4 ,here a cultivated judgment is of the greatest value4 ,practice alone can make a good sketcher under such circumstances4 ,rules must1 from the nature of the case1 be few and general4 ,in the first place1 all objects within the field of vision are presented to the eye in perspective1 whereas the sketch is to be a plan4 ,the apparent diminution of dimensions in distant objects must therefore be corrected on the plan4 ,for example1 the windings of a crooked stream1 or a road1 in perspective1 are much exaggerated in retiring into the distance2 they must therefore be straightened out in the sketch more and more1 as they are more removed4 #bnd4 ,in looking at variously placed hills from a somewhat elevated station1 the eye will in some cases look directly1 or perpendicularly1 at the face of some slopes1 while in others1 the surface of the slope1 if prolonged1 will pass through the eye1 and will not be seen in its true dimensions1 though its inclination may be judged4 ,in sketching the shapes of hills1 bodies of water1 masses of forest1 c41 these facts must be taken into consideration1 and to ensure skill1 eye sketches of a small portion of ground having well-marked features must be frequently made1 and compared with measurements of the same features4 ,in sketching a single hill1 the best station is at the summit4 ,first endeavour to represent the lowest horizontal curve of its surface2 then a medial one2 then the form of the level space at the summit1 or the highest horizontal curve4 ,others may then be introduced between these1 until the ground is sufficiently expressed4 ,the angles of inclination should be frequently noted down in numbers2 all accidents of ground1 such as ravines1 rocks1 c41 should be carefully placed1 and all other objects1 such as houses1 fences1 trees1 c41 should be put down in their proper relative positions and dimensions4 ,having thus prepared a skeleton of horizontal curves1 numbered as to inclination and heights1 the sketch will always serve a useful purpose without any lines of greatest descent4 ,after sufficient practice in this method1 the eye will become so cultivated as to enable the draughtsman to express the form of ground by lines of descent at once1 the mind conceiving the position of the horizontal curves1 and thus supplying the necessary data for the shading lines1 the relative thickness and length of which for the different slopes is a matter very easy of acquirement4 ,but this should not be attempted until the method by horizontal sections is thoroughly mastered4 ,it is easy thus to make a sketch of a single hill1 but when there are many1 and the general face of the country is sloping also1 the difficulties of representing the connection of the different hills at their bases are considerable4 ,in such cases the direction and lengths of the valleys1 or water-courses if there are any1 must first be noted1 bearing in mind the illusions of perspective in both its effects1 previously mentioned4 ,then establish the positions of the different summits1 marking down their relative heights1 after which put in the other objects to be represented1 such as roads1 trees1 buildings1 c41 referring their positions to each other1 and correcting them where they are found to disagree4 ,horizontal curves present the readiest means to the beginner in sketching declivities4 ,when1 after some practice1 the form of a body suggests1 as it always will1 its horizontal sections1 then it will be time to resort at once to the lines of greatest descent4 ,the greatest difficulties to be overcome in the practice of eye-sketching are1 #ast1 that of converting a perspective view into a plan1 in all its true proportions2 and #bnd1 in forming a just conception of the intersections of different slopes at their bases4 ,hence the rule1 to project first upon the sketch1 all the lowest lines1 or water-courses1 and then the highest parts or summits4 ,then the middle lines and objects may be placed1 and the sketch filled up by referring all others to those three groups which may be regarded as determined4 ,the lead pencil for field drawing should be moderately hard1 and the general tone of the drawing should be rather light4 ,the shading of slopes ought not to overpower by its depth the distinctness of other objects1 and the pencil should be so used and of such a quality as not to be easily defaced by rubbing4 ,we have already described some of the duties of the 8examiner0 in verifying and supplying detail in the field4 ,the following fuller exposition of those duties and the methods of performing them is taken from an excellent little treatise on ,land ,surveying1 by ,john ,a4 ,smith1 ,c4,e4 ,examination of ,maps in the ,field4--,for the purpose of the examination1 the 8examiner0 should be furnished with an elegant and accurate trace1 ink copy1 of the plotted detail of the district1 and he should be provided with a suitable sketch case1 lined with prepared ass skin1 pencil1 linear scale1 chain1 c41 and labourers4 ,the trace copy1 in one sheet1 should be in extent not more than can be conveniently secured in the sketch case4 ,it is desirable that the marginal detail on the trace copy shall be common to the adjoining sheets for examination4 ,if the district be extensive1 and if there be no more than one examiner engaged on the examination1 adjoining sheets should not be given to the same examiner1 that the character of the examiner's work may be ascertained by independent examinations of the same marginal detail4 ,in the examination of the detail representation on a map the 8examiner0 should be mainly guided by a few leading considerations2 these are3-- #a4 ,the position of a straight line1 or detail1 on the map will be correct when its actual and plotted position on the ground and map makes equal angles with another known line and intersects it in a known point1 the position of which line and point on the ground has been previously ascertained to be correctly represented on the map4 #b4 ,the line1 or detail1 will be correctly laid down--given in magnitude and position--when its position and length on the ground and map are ascertained to correspond accurately4 ,from #a and #b it will be seen-- a4 ,that the point of intersection of two given straight lines on the ground1 and the corresponding point on the map1 will be a given point on the map1 if the corresponding lines on the map be ascertained to be correctly laid down in position4 ,and1 b4 ,that any two points being given or correctly determined1 the straight line terminating in them will be a given line4 ,further1 c4 ,that a straight line traced or drawn through given points1 is given in position4 ,it should be kept in view that lines may be more accurately traced1 and to a greater distance1 with the naked eye1 when the party tracing is rather above than below the level of the field on which the trace shall be made4 ,it may be also seen that a point on the map which is the common point of intersection of three straight lines drawn through well-defined points in the detail will be a given point1 if lines traced through the corresponding detail points on the ground be found to have a common point of intersection4 ,and further1 that the correct determination of two such points on the map determines1 as already stated1 the position of a straight line through these points4 ,the determination1 in the above manner1 of three such common points of intersection correctly determines the representation of a given triangle4 ,in the examination the sides of the triangle determined by intersections1 as above1 should be measured on the ground1 to ascertain and verify the accuracy of the determinations of the angular points on the trace or map4 ,the production of detail lines1 and lines traced through plotted points1 should be taken up in the chain measurements of the sides of this triangle4 ,through these verified points straight lines should be traced1 and drawn in pencil1 to well-defined points in the detail1 such as the buttals of fences1 the corners of houses and walls1 gate piers1 c4 ,on these lines the intersected and neighbouring detail should be examined by chain and scale measurements4 ,in the measurement of the lines the internal and adjacent external detail should be very carefully examined1 and corrected on the map where found in error4 ,the examination of the detail should be carried forward by the production and intersection of given lines1 and also by chain measurements from given points1 to verify the position of the detail or other points on the map4 ,this examination should be continued to the limits of the trace sheet4 ,in remote parts of the trace and district1 lines of verification should be drawn1 traced on the ground and measured with the chain to verify the scale measurements by the examination4 ,these lines should be long1 and in situations affording few facilities for the accurate determination on the map of the position of the plotted detail by other modes of examination4 ,the straight line passing through the extremities1 or other well-defined points in curved detail1 should be regarded as a detail line1 and the position of the intermediate curved detail verified by ordinates or tangents4 ,buildings and adjacent detail should be carefully examined by productions1 c41 because of the greater difficulties these details usually present to the surveyor and plotter1 and the consequent liability to small errors in the position of some of the plotted points1 which affect the direction of lines determined on them4 ,among the ,plates appended to this work will be found several examples of map drawing suitable for reference4 ,plate #af shows the signs used on ordinary maps and charts4 ,plates #bi and #cj contain signs used chiefly upon ,indian and colonial maps2 and ,plates #ca and #cb give the signs employed upon military maps1 with a section and a plan of fortifications4 ,these signs should be neatly drawn and their dimensions suited to the scale of the map1 the same remark applying to these as to trees in elevation4 ,plate #a is a plan showing the principal characters of work used in mapping4 ,this plan has been very carefully compiled and drawn to render it suitable as a plan of reference4 ,plate #ab illustrates the construction and colouring of hills according to the several methods described in the preceding ,sections4 ,other examples1 with rocky cliffs1 will be found on ,plate #ad4 ,plate #ah contains a piece of the ,ordnance map drawn to a scale of one inch to the mile1 and furnishes an example of finished work4 ,upon the same ,plate will be found a piece of chart showing soundings1 intended as a reference for hydrographers and others engaged in marine surveys4 ,and ,plate #bh shows the manner in which geological maps are prepared4 ,the whole of these examples will be found worthy of careful study as specimens of the draughtsman's art4 ,the ,plates relating to this ,section are ,nos4 #a1 #aj1 #ab1 #ad1 #ah1 #bh1 #bi1 #cj1 #ca1 and #cb4 ,,section ,,vi4--,,mechanical ,,and ,,architectural ,,drawings4 ,it is not within the scope of the present work to explain and to illustrate the principles according to which mechanical drawings are executed4 ,these must be studied in special treatises on ,projection4 ,the several methods of giving expression and embellishment to this class of drawings have1 however1 been fully described1 and the principles upon which these methods are founded carefully explained4 ,it now remains for us to add a few general remarks and some detailed instructions on the practical application of these principles and methods4 ,before commencing the delineation of any machine1 the draughtsman should make himself thoroughly acquainted with its character2 that is1 he should ascertain the nature of the work it is designed to perform1 the means by which it performs that work1 and the manner of its construction4 ,this preliminary study is necessary to enable him to obtain a good general idea of the more important parts1 which he will have to give prominence to in the drawing1 and to understand the nature of the various connections between the numerous pieces of which the machine is composed4 ,the dimensions of the several parts must be carefully taken1 and when drawing from actual machinery1 rough sketches should be made to serve as a guide in getting out the complete drawing4 ,the dimensions should be clearly marked upon such sketches4 ,as a general rule1 it is best to begin with the ground line and position of main driving shafts1 from which dimensions may be taken in every direction4 ,the manner of writing the dimensions1 whether upon the rough sketch or upon the complete drawing1 should always be thus #b #f for lateral1 and thus #e for vertical dimensions4 ,to enable the draughtsman to take these with accuracy1 he should be provided with a pair of callipers for measuring the diameters of shafts1 a plumb-line for obtaining lateral distances when the objects are not in the same horizontal plane1 and a two-foot rule4 ,the chief point to be attended to in commencing the drawing of a machine is to obtain the correct positions of the centre lines of its principal component parts1 especial regard being had to the centres of motion4 ,these centre lines have been explained in a former ,section4 ,having laid down these lines accurately in their relative positions1 separate sketches may be made on a large scale of each part of the machine1 and the details of each part constructed upon each corresponding centre line in succession1 until the whole machine is built up4 ,the centre lines should be drawn in red1 and the dimensions should be laid off on each side of them4 ,it will frequently be necessary to take a careful section1 to obtain sufficient information from which to draw the plan and the elevation4 ,with respect to the written dimensions on a drawing1 it may be remarked that they cannot be too full or too numerous4 ,indeed1 without complete written dimensions a drawing is almost useless2 for though a scale may and should in all cases be attached1 great labour would be required to make use of the drawing by means of the scale only4 ,every dimension which an engineer is likely to require to know should1 therefore1 be plainly written4 ,nor is it sufficient to give a dimension once only1 as on the plan1 for example1 and to omit it on the elevation or on the section4 ,it should never be necessary to refer to another drawing to find a dimension4 ,the lettering should be clearly executed1 and the direction of the lettering should be the same as that of the figuring1 an example of which has been given2 that is1 it should read from the front or from the right-hand side of the drawing4 ,if a drawing is to be coloured1 the lettering1 and all dark lines1 such as shade lines1 must be left till after the colour has been applied4 ,on all coloured drawings the draughtsman should endeavour to obtain a bright1 clear tint by repeating the washes a sufficient number of times4 ,in preparing a flat-wash the tint should be mixed up slightly darker than is required1 and the solid colouring matter allowed to settle before using4 ,the solution1 being poured off without disturbing the sediment1 will give a perfectly clear and pure tint4 ,tints for colouring perspective drawings should always be prepared in this manner4 ,the methods of laying on flat-washes and of shading by colours have been described in former ,sections4 ,the following additional remarks on colour shading are taken from ,worthen's #8,cyclopdia of ,drawing4' ,a means of adding considerably to the definiteness of a coloured mechanical drawing1 and of promoting1 in a remarkable degree1 its effective appearance1 is obtained by leaving a very narrow margin of light on the edges of all surfaces1 no matter what may be the angles they form with the surfaces that join them4 ,this should be done invariably2 we do not even except those edges which happen to have shadows falling upon them4 ,in such cases1 however1 this margin1 instead of being left quite white1 should be slightly subdued4 ,the difficulty of achieving this effect of imparting a clear1 regular1 unbroken appearance to these lines of light seems very formidable1 and1 indeed1 almost insuperable4 ,the hand of the colourist may be as steady and confident as a hand can be1 and yet fail to guide the brush1 at an almost inappreciable distance from a straight or a circular line1 with that precision and sharpness so requisite for the production of this beautiful effect4 ,we shall1 however1 explain a novel and an effective method of arriving at this most desirable result4 ,suppose the object about to receive the colour to be the elevation of a long flat rod or lever1 on the edge of which a line of light is to be left4 ,fill the drawing pen1 as full as it will conveniently hold1 with tint1 and draw a broad line just within1 but not touching1 the edge of the lever exposed to the light4 ,as it is essential to the successful accomplishment of the operation that this line of colour should not dry1 even partially1 before the tint on the whole side of the lever has been laid on1 it will be well to draw the pen a second time very lightly along the line1 so as to deposit as much tint as possible4 ,immediately this has been done1 the brush1 filled with the same tint1 should be passed along so as to join the inner edge of this line of colour and the whole surface of the lever to be filled in4 ,by this means a distinct and regular line of light is obtained without sacrifice of time4 ,a still more expeditious way of colouring such surfaces is to draw a second line of colour along and in contact with the opposite edge of the lever or other object1 and to fill in the intermediate space between the two wet lines with the brush4 ,in this way a clear1 uniform outline to the tint is obtained4 ,the blades of the drawing pen must not be sharp1 and care must be taken not to press heavily upon it1 as otherwise the blades will leave their course visible--an unsightly betrayal of mechanical means to obtain such regularity in the colouring4 ,flat circular surfaces may be treated in the same way1 by using the pen compass instead of the drawing pen4 ,when such surfaces are large it will be judicious to colour them in halves or in quadrantal spaces1 but great care must be taken to join the parts neatly4 ,the lines of junction may be obliterated by slightly washing them1 or by laying a very light tint over the whole surface1 taking care in crossing the lines of junction to rub them lightly with the brush4 ,the line of light upon cylindrical objects may be beautifully produced by the same means4 ,to indicate this line with perfect regularity is highly important1 for if strict uniformity be not maintained throughout its length1 the object will appear crooked or distorted4 ,having marked in pencil the position of the light1 and filled the drawing pen with a just perceptible tint1 draw a line of colour on one side of the line of light4 ,then1 with the brush filled with the same tint1 fill up the space unoccupied by the shade tint1 within which the very light colour in the brush will disappear4 ,the portion of the surface on the other side of the line of light being treated in the same way1 the desired effect1 of a stream of light1 clear and mathematically regular1 will be obtained4 ,the effectiveness and expeditiousness of this method will be most noticeable on long circular rods of small diameter1 where a want of accuracy is more immediately perceptible4 ,the extreme depth of shade1 as well as the line of light1 may1 on such rods1 be marked by filling the pen with dark shade tint1 and drawing it exactly over the line representing the deepest part of the shade4 ,on either side1 and joining this strip of dark colour1 another1 composed of lighter tint1 is to be drawn4 ,others successively lighter should follow1 until1 on one side1 the line of the rod is joined1 and1 on the other1 the lightest part of the rod is nearly reached4 ,the line of light is then to be shown1 and the faint tint used at this part of the operation spread with the brush lightly over the whole of that portion of the rod situate on either side of this line1 thus blending into smooth rotundity the graduated strips of tint drawn with the pen4 ,for the correct representation of a building1 plans1 sections1 and elevations are required4 ,the plan is usually a horizontal section of the building close above the ground floor4 ,the position and the dimensions of the walls and the rooms of a house are shown by this means4 ,as the walls are shown in section in the plan1 sections of the various walls must1 of course1 be supplied before the plan can be drawn4 ,it is usual to colour the section of the walls in a ground plan2 but not unfrequently a dark wash of ,indian ink is preferred to colour4 ,the number of sections required will depend upon the regularity of the building2 but generally it will be found that two half-sections are sufficient4 ,these two half-sections are usually placed side by side1 separated by a single line4 ,the lines on which they are constructed must be drawn distinctly on the plan1 and lettered4 ,the section is then described as 8,section0 or 8,half-section0 on ,a ,b1 c4 ,usually the line of section is broken in plan1 and the section is then said to be on ,a ,b1 ,c ,d1 one half being on ,a ,b and the other half on ,c ,d4 ,separate sections to larger scales are required for the details of construction1 such as joints of rafters1 mouldings to windows1 and other parts needing distinct representation4 ,elevations generally represent the whole of one side of the building1 and every side that differs from the rest must have its own elevation4 ,such elevations are termed ,front1 ,back1 and ,end ,elevations1 or ,north1 ,south1 ,east1 and ,west ,elevations4 ,in order to show the foundations1 a section of the ground is sometimes given with an elevation2 in such a case the level of the ground should be shown by a distinct line4 ,sometimes the portions of the structure below the ground are shown by dotted lines4 ,such portions should not be coloured4 ,in getting out the drawings the plan should first be drawn1 then the sections1 and finally the elevations4 ,the colouring of elevations will afford the student an opportunity of applying the knowledge he may have acquired from a former ,section of this work1 and of displaying his artistic taste4 ,in the accompanying ,plates will be found examples of colouring mechanical and architectural drawings4 ,these should be studied in conjunction with the ,section on colouring in the first part of this work4 ,plate #bb shows a piece of marine engine carefully coloured to indicate the material of which the several parts are made1 and ,plate #bc contains a piece of permanent way1 consisting of wrought-iron rail and bolt1 cast-iron chair and wooden sleeper and block1 and an elevation of a skew bridge1 accurately coloured and shaded in accordance with the principles already explained4 ,it is not within the scope of this work to treat the subject of projection1 whether orthographic1 isometrical1 or perspective2 but we have given examples of each of these for the purpose of illustrating the remarks and instructions on colouring given in the ,section referred to above4 ,thus ,plate #bd is a perspective drawing1 such as are frequently made by architects1 requiring a high degree of skill and taste on the part of the colourist4 ,and ,plate #bg contains two isometrical views of a building4 ,these examples are intended to serve as models of finished colouring4 ,the ,plates relating to this ,section are ,nos4 #bb1 #bc1 #bd1 and #bg4 ,,section ,,vii4--,,copying ,,and ,,reducing4 ,duplicates of drawings are very frequently required2 so frequently1 indeed1 and in such numbers1 that their production constitutes a large portion of the work executed in every drawing office4 ,generally1 these duplicates are required to the same scale as the original drawing2 but often it becomes necessary to reduce or to enlarge the scale to render the drawing suitable to the purpose for which it is intended4 ,the various means and methods by which such duplicates are produced are1 therefore1 important matters to the draughtsman1 and especially to the young draughtsman1 whose labours in the drawing office will for a long time be confined almost exclusively to their employment4 ,these means and methods will now be described4 ,drawing from ,copy4--,drawing from copy is rarely resorted to for the purpose of obtaining duplicates1 the process being too slow for practical requirements4 ,but it constitutes the principal means1 after the study of projection1 by which pupils in the office are initiated into the art of producing drawings4 ,a few hints concerning the best modes of proceeding in these operations will1 therefore1 be serviceable1 both to the instructor and the instructed4 ,first draw a horizontal and a vertical line through the middle1 each way1 of the sheet upon which the copy is to be made2 draw also similar lines upon the copy4 ,as these lines divide the paper equally1 they may1 for the sake of distinction1 be called 8divisional lines40 ,if the centre lines are not shown on the copy1 these must next be drawn in lightly with the pencil1 great care being taken to place them correctly4 ,the position of these centre lines relatively to the divisional lines may then be transferred by means of the dividers from the copy to the fair sheet1 upon which they must be drawn finely but distinctly4 ,sometimes it will be necessary to draw other lines upon the copy1 and to transfer them in like manner to the fair sheet4 ,the details may then be drawn in upon these centre lines1 by transferring to them the measurements taken from the centre lines of the copy4 ,in taking measurements from a centre line through an object that has both sides alike1 the dividers should be turned over to ascertain whether the distance on the other side of the centre line is the same1 so as to prove the accuracy of the drawing with respect to the centre line4 ,all measurements must be taken in the exact direction of the distance to be measured1 and be transferred in the same direction1 or an obviously incorrect distance will be the result4 ,in making the mark1 the point of the dividers should not be pushed into the paper1 a just visible mark being all that is required2 care must also be taken1 when using the compasses1 not to press the leg into the paper1 as the holes thus made render circles and arcs inaccurate1 are unsightly at all times1 and completely destroy the unbroken appearance of a tint on a coloured drawing by retaining the colour4 ,when drawing in circular details with the pencil1 it will be well to place a small hand-drawn circle around the centre for reference when inking in2 also1 when a curve is struck from several centres1 a temporary pencil line to represent the radii should be drawn from the centres to their respective arcs4 ,when two or more views of the same objects are given1 they should be worked upon simultaneously2 because1 having once drawn in the centre lines1 one measurement may be applied to the corresponding part in each view1 and so time and trouble saved4 ,in copying maps and plans by this method of drawing from copy1 both the copy and the fair sheets are divided up into small squares1 by drawing a number of other lines parallel to the divisional lines described above4 ,the intersection of detail with these lines may then be readily and correctly transferred from the copy to the fair sheet4 ,copying by ,tracing4--,tracing furnishes the most expeditious means of multiplying drawings4 ,when a tracing is required in outline only1 the usual way is to fasten the sheet of tracing paper with ordinary drawing pins over the drawing to be traced2 the sheet of tracing paper should be sufficiently large to allow the pins to be clear of the drawing4 ,if the sheet is not large enough for this1 strips of thin paper1 with one edge gummed to the tracing paper and the other to the board1 may be used4 ,when this method is not practicable1 the pin holes may be effaced to some extent by turning the drawing upside down1 and pressing back the edges of the holes with the flat end of a pencil1 after the tracing has been removed4 ,if the tracing is to be coloured1 it must be stretched on the board1 or it will never lie flat after being moistened2 and if the colouring is to be applied before the tracing is removed from the drawing1 it is essential that the tracing paper be larger than the drawing1 so that it may be cut off without injury to the latter4 ,when there is not sufficient time to stretch the tracing paper1 the tendency to buckle up when drying may be greatly lessened by placing weights around any part immediately after the colouring has been laid on4 ,if the tracing is to be mounted1 the colouring should be applied after mounting4 ,when tracing cloth is used1 a much better appearance will be produced by applying the colour to the back of the tracing4 ,in performing the stretching process1 the sponge must not be applied directly to the tracing paper1 but to a piece of clean white paper laid over it2 sufficient moisture will pass through to the tracing paper in a few seconds4 ,sometimes1 when the sheet is small1 merely breathing upon it will be found sufficiently effective4 ,as tracing paper is thus greatly affected by the breath1 it has been recommended to entirely finish both circles and lines within a small area at a time1 when copying a drawing1 as if all the circles were put in first1 as on a drawing1 many of them might be out of position before the lines could be drawn4 ,this recommendation is1 however1 of doubtful value4 ,when tracing from another tracing1 a piece of white paper should be placed beneath the copy to render the lines distinct4 ,a tracing may be made upon ordinary drawing paper by means of the glass drawing board4 ,this consists of a sheet of plate glass let into a wooden frame about #c inches wide flush with the face1 the inner edges of the frame being rebated for this purpose4 ,this copying board is placed on a table in front of a window1 and supported at an angle of about #be1 so as to get a strong light beneath1 which light may be increased by placing a sheet of white paper upon the table to reflect upwards4 ,the original drawing being pinned down to this board with a sheet of drawing paper or parchment over it1 the finest lines will be plainly visible1 and the drawing may be traced in the same manner as upon tracing paper4 ,to alter the light1 the angle of the board may be changed4 ,this method1 which is coming extensively into use1 is a very convenient one for copying plans and maps4 ,copying by ,transfer4--,copying by transfer has superseded the method already described as 8drawing from copy40 ,transfer paper1 as employed for this purpose1 may be made in the following manner4 ,take half an imperial sheet of very thin paper1 such as tissue paper1 and having stretched it upon a board1 rub some common blacklead powder well into it4 ,then1 having removed the dust and superfluous blacklead1 well rub the sheet with a cotton rag to prevent its soiling the paper when used for transferring a drawing4 ,a sheet of transferring paper prepared in this way will last for years4 ,red transfer paper1 which is principally used by lithographers1 is prepared in the same manner with red ochre4 ,to transfer a drawing1 the sheet of transfer paper is laid with its prepared face upon the paper which is to receive the drawing1 and over this is placed a tracing of the drawing to be copied1 carefully pinned down4 ,the straight lines of the tracing may then be transferred to the drawing paper below by going over them with a style or other pointed instrument that will not cut the tracing4 ,for the regular curves and circles1 it will be sufficient to mark the centres by a small cross1 thus1 1 and the radii by short lines4 ,other curves may be transferred by means of the ,french curve4 ,by this means a copy of the original drawing is obtained in black or red lines1 which may be afterwards inked in4 ,though three distinct operations are required in this process1 making the tracing1 transferring1 and inking in1 a drawing can be much more rapidly copied by means of it1 than by measuring off with the dividers1 as in drawing from copy4 ,reducing and ,enlarging4--,it is evident that in drawing from copy1 the drawing may be reduced or enlarged at pleasure1 since it is only necessary to take half or twice the dimensions as required4 ,usually proportional compasses are employed for this purpose4 ,when reducing by scales1 it is obviously not essential to use the same scale as that to which the original is made2 the dimensions on one scale may be readily transferred to any other1 and the student will do well to make himself familiar with the operation4 ,for reducing or enlarging plans1 several means are employed3 one of these is known as the method of squares1 and is illustrated on ,plate #bf4 ,in the preceding remarks on drawing from copy1 it was shown how in copying to the same scale1 both the copy and the fair sheet were divided into squares of equal size1 and how the intersections of the detail with the lines forming these squares on the copy were transferred by measurement to corresponding points on the fair sheet4 ,it is obvious1 therefore1 that if the squares on the latter be larger or smaller than those on the former1 as the intersections will be transferred to the same relative positions on the fair sheet as they occupy on the copy1 the plan1 or other drawing1 will be enlarged or reduced accordingly4 ,this is the principle upon which drawings are reduced by this method4 ,proportional compasses are required in the operations4 ,drawings may also be rapidly reduced or enlarged by means of instruments called the ,pantograph and the ,eidograph4 ,both of these instruments are shown on ,plate #bf4 ,the following very complete description of the pantograph and the eidograph is given in an excellent work on #8,mathematical ,drawing ,instruments1' by ,w4 ,f4 ,stouley1 of ,holborn1 ,london4 8,the pantograph1 as represented on the plate1 consists of four rules of stout brass1 which are jointed together in pairs1 one pair of rules being about double the length of the other4 ,the free ends of the shorter pair are again jointed to the longer in about the centre4 ,it is important that the distance of the joints on each of the short rules should exactly correspond with the distance of the joints on the opposite longer rules1 so that the inscribed space should be a true parallelogram4 ,to enable the instrument to work freely and correctly1 all the joints should be perfectly vertical1 and with double axes4 ,under the joints casters are placed to support the instrument1 and to allow it to move lightly over the paper4 ,one of the long rules has a socket fixed near the end1 which carries a tracing point when the instrument is used for reducing4 ,the other long rule1 and one of the shorter rules1 have each a sliding head fitted upon it1 which is similar to one of the heads of a pair of beam compasses4 ,each head has a screw to clamp it in any part of the rule1 and carries a perpendicular socket1 which is placed over the edge of the rule in a true line with the joints4 ,each socket is adapted to hold either a pencil holder1 tracing point1 or fulcrum pin1 as may be required4 ,the rules upon which the heads slide are divided with a scale of proportions3 #a--b1 #aa--ab1 #i--aj1 c41 which indicate as one is to two1 as eleven are to twelve1 as nine are to ten1 c4 8,a loaded brass weight1 which firmly supports a pin that fits exactly into either of the sockets1 forms the fulcrum upon which the whole instrument moves when in use4 8,the pencil holder is constructed with a small cup at the top1 which may be loaded with coin or shot to cause the pencil to mark with the required distinctness4 8,arrangement is made to raise the pencil holder off the drawing4 ,this is effected by a groove down one side of the pencil holder1 in which a cord is fixed1 passing from the pencil along the rules1 turning the angles over small pulleys1 and reaching the tracing point1 where it may be readily pulled by the hand to raise the pencil4 ,this will be found especially convenient when the pencil is required to pass over any part of the copy not intended to be reproduced4 8,the pantograph is set to reduce drawings in two ways1 termed technically the erect manner and the reverse manner4 ,it will be necessary to give full details of each manner1 particularly in relation to the scales engraved upon the instrument1 which are not very intelligible2 indeed comparatively few professional men are sufficiently acquainted with them to avail themselves of their full value4 8,by the erect manner of setting the pantograph1 the reduced copy will appear erect2 that is1 the same way as in the original4 ,the general position of the parts of the instrument set in this manner is shown in the plate1 where it will be seen that the fulcrum pin is placed in the socket of the sliding head upon the outside long rule1 and the pencil holder in the socket upon the short central rule4 ,by this method of setting the instrument1 it will reduce in any of the given proportions not exceeding half-size1 technically from #a--b4 ,the scales engraved upon the rules that accord with the erect manner of setting are those which have #a for the first proportion2 as #a--b1 #a--c1 #a--d1 c4 ,the other scales may be used1 but will not accord with the reading1 except through arithmetical deductions1 the results of which may be given more clearly by the following complete ,table than by rules with exceptions4 ,,table ,,of ,,reductions ,,by ,,the ,,pantograph ,,in ,,the ,,erect ,,manner1 ,,the ,,fulcrum ,,being ,,placed ,,in ,,the ,,socket ,,upon ,,the ,,outside ,,rule1 ,,and ,,the ,,pencil ,,upon ,,the ,,central ,,rule4 ---------------------------------- ,reading given upon,reduces in the the ,scales4 ,proportion of ---------------------------------- #a--b #a to #b #a--c #a #c #a--d #a #d #a--e #a #e #a--f #a #f #a--g #a #g #a--h #a #h #a--i #a #i #a--aj #a #aj #a--aa #a #aa #b--c #b #e #c--d #c #g #d--e #d #i #e--f #e #aa #f--g #f #ac #g--h #g #ae #h--i #h #ag #i--aj #i #ai #aj--aa #aj #ba #aa--ab #aa #bc ---------------------------------- 8,in the above ,table the readings which are given with the proportions are given to show clearly which proportions agree with the erect scales2 many of those that do not agree with the reading are very useful1 as #b--c1 which is often required to reduce a drawing from a scale of #bj to one of #ej4 8,in the reverse manner of setting the pantograph1 the reduced copy appears reversed1 or upside down1 to the original4 ,the fulcrum pin is placed in the socket upon the short central rule1 and the pencil holder is placed in the socket upon the outside rule4 ,this is generally the most convenient way of using the pantograph for large drawings1 as the original and copy come edge to edge1 and need not overlap each other1 which is often compulsory in the erect manner2 the range of scale is also much greater1 as the proportions include the unit proportions of the erect scale1 and continue in ratios up to full size4 8,the following ,table will give the readings of the instrument which accord with the reverse setting1 and those which may be used to this setting1 obtained by calculation4 ,,table ,,of ,,reductions ,,by ,,the ,,pantograph ,,in ,,the ,,reverse ,,manner1 ,,the ,,fulcrum ,,being ,,placed ,,in ,,the ,,socket ,,on ,,the ,,central ,,rule1 ,,and ,,the ,,pencil ,,in ,,the ,,socket ,,upon ,,the ,,outside ,,rule4 ------------------------------------ ,reading given upon ,reduces in the the ,scales4 ,proportion of ------------------------------------ #a--b #a to #a full size #a--c #a #b #a--d #a #c #a--e #a #d #a--f #a #e #a--g #a #f #a--h #a #g #a--i #a #h #a--aj #a #i #a--aa #a #aj #b--c #b #c #c--d #c #d #d--e #d #e #e--f #e #f #f--g #f #g #g--h #g #h #h--i #h #i #i--aj #i #aj #aj--aa #aj #aa #aa--ab #aa #ab ------------------------------------ 8,the above ,table and the previous one give the proportions for reductions1 the tracing point being in every instance considered upon the outside rule4 ,if it were required to produce an enlarged copy1 which the pantograph will do but very imperfectly1 the pencil and tracer would have to change places2 the proportions of course would read the same4 8,in using the pantograph some care is required in setting the fulcrum weight in the best position to allow easy action of the instrument over the space required4 ,it should always be roughly tried over the boundary before commencing the copy4 8,the ordinary pantograph will in no instance work over a large drawing at one operation1 but it may be shifted about as required1 using care1 and testing the copy after the fulcrum is moved1 to see that the tracer and pencil correspond in those parts already produced1 that the pantograph will reach in its shifted position4 ,the fulcrum weight being generally made with needle points to attach it to the drawing will be found very difficult to shift so short a distance as is frequently required4 ,this may be easily remedied by attaching with gum a piece of indiarubber over each of the sharp points1 when it is required to be used for large drawings4 ,the rubber will hold the paper sufficiently if the pantograph work freely in the joints and casters1 as it should do4 8,in copying the buildings which frequently occur in plans of estates1 c41 a straight slip of transparent horn will be found very convenient to guide the tracing point4 ,some draughtsmen have the horn cut with an internal angle1 by which one side and one end of a building may be traced without shifting the horn4 8,architects and mechanical engineers seldom use the pantograph2 however1 it may perhaps be sometimes used with advantage for tracing in the most difficult and tedious parts of a drawing with a precision impossible by hand4 ,this applies particularly to such parts as are frequently repeated1 as capitals1 trusses1 bosses1 tracery1 c41 upon drawings to very small scales4 ,in these instances it is only necessary to make a detail sketch1 say six times the size required1 and to place the fulcrum weight in such position that the pencil will pass over the parts required to be filled in1 the tracer at the same time resting on a corresponding part of the detail sketch1 which may be placed in position under the tracing point1 and be held sufficiently by two lead weights4 ,for a second ornament on the same drawing1 the detail may be shifted without moving the fulcrum4 8,to follow the outline of any object of the ornamental class1 or for the reduction of mechanical drawings to a size suitable for wood or other engravings1 the strip of horn will be found particularly useful2 indeed1 to obtain any degree of precision1 it will be better1 generally1 to let the tracer follow a guiding edge placed over the original for that purpose4 ,french curves are particularly useful1 although perhaps only a small piece may be available at once4 ,the tracer may rest on the surface until another part of the curve is found to correspond with the continuation of the line4 8,in some old pantographs a guide is fixed to the tracing point4 ,the guide is a kind of handle similar to a drawing pencil1 the point of which is hinged to the point of the tracer4 ,this gives a convenient and firm hold of the point1 and appears to the author a useful appendage4 8,pantographs have been made in many shapes unnecessary to describe1 as they are all of one principle--that of a parallelogram jointed at the four corners2 the principal difference being in the position of the points and fulcrum in relation to the parallelogram4 ,one thing is essential in every construction1--that is1 that the fulcrum1 tracer1 and pencil should always be in a true line when the instrument is set for use4 ,the parallelogram may be in any position on the instrument1 to the fancy of the maker4 8,the ,eidograph was invented by ,professor ,willis in #ahba4 ,it is a most ingenious and exact instrument1 for many purposes superior to the pantograph1 within the range of its working powers1 which1 however1 may be considered to be limited to reducing or copying off1 between the full size of the original and one-third of the size2 for greater reductions1 the balance of the various parts is thrown so far out that it appears clumsy to use1 and is really inferior to the pantograph4 ,the great merit of the eidograph is1 that within its range it reduces conveniently and exactly in all proportions2 for instance1 we may reduce in the proportion of #i to #be as readily as #a to #b4 ,it is also in every way superior to the pantograph in freedom of action1 there being no sensible friction on the single fulcrum of support1 and in its movement it covers a greater surface of reduction4 8,it is somewhat curious that an instrument of such great merit should be little known in the profession1 where its uses would be so constantly convenient4 ,this may partly be attributed to the very few published descriptions which are to be found in works treating on mathematical instruments4 ,it is not intended1 however1 to infer that there are not many eidographs in use1 but that the writer presumes they are comparatively little known1 from his personal acquaintance with professional men1 and from the number of large pantographs that are made and sold to perform work that could be done so much more exactly and conveniently by the eidograph4 ,this remark will not apply to the small pantograph1 which is less expensive than a small eidograph1 and answers perfectly for the reduction of small plans--as1 for instance1 those frequently attached to leases and conveyances4 8,the details of the construction of the eidograph are as follows3--,the point of support is a heavy1 solid1 leaden weight1 which is entirely covered with brass2 from the under side of the weight three or four needle points project1 to keep it in firm contact with the drawing4 ,upon the upper side of the weight a pin1 termed a fulcrum1 is erected1 upon which the whole instrument moves4 ,a socket is ground accurately to fit the fulcrum1 and attached to a sliding box1 which fits and slides upon the centre beam of the instrument4 ,the sliding box may be clamped to any part of the beam by a clamping screw attached4 ,under the ends of the beam are placed a pair of pulley wheels1 which should be of exactly equal diameter2 the centre pins of these revolve in deep socket fittings upon the ends of the beam4 ,the action of the two wheels is so connected as to give them exact and simultaneous motion4 ,this is effected by means of two steel bands1 which are attached to the wheels4 ,the bands have screw adjustment to shorten or lengthen them1 or to bring them to any degree of tension4 ,upon the under side of each of the pulley wheels is fixed a box1 through which one of the arms of the instrument slides1 and is clamped where required4 ,at the end of one of the arms a socket is fixed to carry a tracing point1 at the end of the other arm a similar socket is fixed for a pencil4 ,the pencil socket may be raised by a lever attached to a cord1 which passes over the centres of the instrument to the tracing point4 ,the two arms and beam are generally made of square brass tubes1 and are divided exactly alike into #bjj equal parts1 which are figured so as to read #ajj each way from the centre1 or by the vernier cut in the boxes through which the arms and beam slide they may be read to #ajjj4 8,there is a loose leaden weight which fits upon any part of the centre beam1 packed in the box with the instrument4 ,the weight is used to keep the instrument in pleasant balance when it is set to proportions which would otherwise tend to overbalance the fulcrum weight4 8,in the above details it will be particularly observed that the pulley wheels must be of exactly equal diameters4 ,it is upon this that chiefly depends the accuracy of the instrument1 the periphery of these wheels being the equivalent to the parallelogram1 which has been already described as the essential feature of the pantograph4 ,the adjustment of the wheels to size1 by turning in the lathe1 is1 perhaps1 the reason the results of the eidograph are more exact than those of the pantograph1 which has no equivalent compensation for the always possible inaccuracy of workmanship4 8,from the details just given1 the general principle of the eidograph may be easily comprehended4 ,thus1 the wheels at each end of the beam being of equal size1 the steel bands connecting them being adjustable1 so as to bring the wheels into any required relative position1 it follows1 that if the arms fixed to the wheels be brought into exact parallelism1 they will remain parallel through all the evolutions or movements of the wheels upon their centres2 consequently1 if the ends of the arms be set at similar distances from the centres of the wheels1 any motion or figure traced by the end of one arm will be communicated to the end of the other1 provided the fulcrum of support be placed also at a similar distance from the centre of one of the wheels4 8,to adjust1 or ascertain if the eidograph is in adjustment1 is very simple1 from the reason that when the arms are parallel the adjustment is perfect for all proportions4 ,the manner of ascertaining this is as follows3 place all the verniers at zero1 which will bring them to the exact centres of the arms and the beam1 place the arms at about right angles with the beam1 then mark simultaneously with the tracer and pencil point1 turn the instrument round upon its fulcrum1 so that the pencil point be brought into the mark made by the tracer2 then1 if the tracer fall into the mark made by the pencil the instrument is in adjustment4 ,if it should not fall into the same mark1 the difference should be bisected1 and the adjusting screws on the bands should be moved until the tracer fall exactly into the bisection1 which will be perfect adjustment4 8,when the eidograph is in adjustment1 if the three verniers be set to the same reading on any part of their scale1 the pencil point1 fulcrum1 and tracer will be in a true line4 ,if it should not be so1 it will show the dividing of the instrument to be inaccurate4 ,thus we have a simple way of testing the eidograph in every important particular4 8,the divisions upon the eidograph do not positively indicate the reductions required to be performed by the instrument1 but merely give a scale1 which1 with the assistance of the vernier1 divides the beam and arms into #ajjj parts4 ,to obtain the quantity to which the verniers are to be set1 it is necessary either to apply to a table of proportions relative to divisions1 or to simple arithmetic1 as will be shown4 ,a printed table is very generally placed inside the lid of the box in which the instrument is packed1 which contains part of the following proportions3 ,,table ,,for ,,reducing ,,or ,,enlarging ,,proportions4 --------------------- ,proportions4,divisions on ,bars4 --------------------- ,as #a is to #b #ccccc #a #c #ej #a #d #fj #a #e #fffff #a #f #gadbh #a #g #ge #a #h #ggggg #a #i #hj #a #aj #hahah #b #c #bj #b #e #dbheg #c #d #adbhe #c #e #be #d #e #aaaaa #e #f #iji --------------------- 8,the table here given answers for the general purposes of reducing1 such as the bringing of a plan from one chain scale to another1 the quantities of which are found by the following rule3 8,to find the quantity equal to any given proportion for the setting of the eidograph4--,subtract one sum of the proportion from the other1 and multiply this difference by #ajj for a dividend2 add the two sums of the proportion together for a divisor3 the quotient from the working of this will give the number to which the arms and beam are to be set4 8,for instance1 let it be required to reduce a drawing in the proportion of #c to #e4 #e - #c #b #ajj --- #e #c #h7 #bjj 7#be 8,the centre beam is to be set to #be on the side nearest the pencil point1 the pencil arm is also set to the #be nearest the pencil point1 and the tracer arm is set to the #be farthest from the trace4 ,if it were required to enlarge in the same proportion1 each side would have to be set at the opposite #be4 8,to clearly illustrate the subject1 it may be well to give another example4 ,let it be required to reduce an ordnance plan of five feet to the mile to a scale of three chains to the inch4 ,first1 we must have like terms1 therefore to reduce both proportions to feet to the inch will1 in this instance1 be the most simple way2 thus3 #e feet to the mile #hh feet to the inch4 #c chains to the inch #aih #aih - #hh #aaj #ajj ----- #aih #hh #bhf7 #aajjj 7#chdfa 8,if the slides of the instrument be set to #chdf1 it will be1 practically1 sufficiently near40 ,photography is also frequently resorted to for the purpose of reducing and enlarging drawings4 ,the results are satisfactory within certain limits of size2 for it is obvious that when the drawing is large1 the parallel lines will converge in the photograph1 for reasons which will be understood from the laws of perspective4 ,for enlarging small and intricate drawings1 photography is very useful4 ,in preparing drawings for reduction by this process1 all lines and shadows should be put in in ,indian ink only4 ,for optical reasons1 colour cannot be reproduced by photography1 and as certain colours produce an effect which might not be anticipated by the inexperienced1 it will be well to warn such against these effects1 to prevent disappointment at the results obtained4 ,thus blue1 for instance1 shows very indistinctly1 and yellow surfaces in coloured drawings come out very dark4 ,drawings for ,lithographers and ,engravers4--,the drawings required by the lithographic draughtsman are simply outline drawings or tracings1 with the shaded drawing for reference when such is required4 ,the shaded drawing should be traced when in outline only with a fine-pointed pencil1 not too hard4 ,the engraver prefers such a tracing to the drawing itself1 unless he can have the latter before it is shaded4 ,he will1 however1 require the shaded drawing as a guide in copying in the shadows4 ,as the drawing always gets soiled under such circumstances1 unless protected1 it is prudent to place it upon a board of the exact size1 with a glass over it to fit1 the glass being kept in its place by a strip of paper pasted round the edge4 ,the drawing will not be required at all if only an outline engraving is to be made4 ,in that case1 the lines that are to be shade lines must be indicated on the pencil tracing2 a dot in red ink on each of such lines will be sufficient4 ,a scale should always be put upon lithographs and engravings1 instead of merely stating that it is drawn to some particular scale1 because the paper just before receiving the impression is damped1 and consequently expands4 ,for this reason1 no engraving is of the same size as the original drawing2 and as the degree of moisture varies1 no two engravings from the same plate ever are exactly equal in size4 ,hence the necessity for drawing the scale is obvious4 ,the ,plate relating to this ,section is ,no4 #bf4 ,,trigonometrical ,,formul4 ,to compute the ,sides of ,triangles4--,let ,a ,b ,c be the angles of a plane triangle1 and a b c the sides opposite4 ,then1 for right-angled triangles1 we have b a sin4 ,b b c tan4 ,b or b c cot4 ,c c a cos4 ,b c b cot4 ,b c b tan4 ,c and for oblique-angled triangles we have a sin4 ,b b ----------1 sin4 ,a a sin4 ,c c ----------4 sin4 ,a ,to compute the ,areas of ,triangles4--,when two sides and the included angle are known1 a and b representing the two sides and the included angle1 a b sin4 ,a --------------4 #b ,to find by logarithms the area in acres and decimals of an acre1 ,log4 ,a log4 a log4 b log4 sin4 - #aecjajc4 ,when two angles and the included side are known1 and being the angles and a the included side1 a sin4 sin4 ,a ------------------4 #b sin4 7 7 ,to find by logarithms the area in acres and decimals of an acre1 ,log4 ,a #b log4 a log4 sin4 log4 sin4 - log4 sin4 7 7 - #aecjajc4 ,when the three sides are known1 a b c being the three sides and s their half sum1 ,a 7s7s - a77s - b77s - c774 ,to find by logarithms the area in acres and decimals of an acre1 ,log4 ,a log4 s log4 7s - a7 log4 7s - b7 log4 7s - c7 ---------------------------------------- ------------------------- - #e4 #b ,,inclined ,,measure4 ,,table ,,showing ,,the ,,reduction ,,in ,,links ,,and ,,decimals ,,of ,a ,,link ,,to ,,be ,,made ,,per ,,chain ,,for ,,every ,,half ,,degree ,,of ,,inclination ,,from #c ,,to #cj4 7#ajj versed sine of the inclination47 ---------------- ,angle4,reduction4 ---------------- #c #j #jae #c #cj #jai #d #j #jbd #d #cj #jca #e #j #jch #e #cj #jdf #f #j #jee #f #cj #jfd #g #j #jge #g #cj #jhf #h #j #jig #h #cj #aaj #i #j #abc #i #cj #acg #aj #j #aec #aj #cj #afg #aa #j #ahd #aa #cj #bja #ab #j #bai #ab #cj #bcg #ac #j #bef #ac #cj #bgf #ad #j #big #ad #cj #cai #ae #j #cda #ae #cj #cfd #af #j #chg #af #cj #dab #ag #j #dcg #ag #cj #dfc #ah #j #dhi #ah #cj #eag #ai #j #ede #ai #cj #egd #bj #j #fjc #bj #cj #fcc #ba #j #ffd #ba #cj #fif #bb #j #gbh #bb #cj #gfa #bc #j #gie #bc #cj #hbi #bd #j #hfe #bd #cj #ija #be #j #icg #be #cj #igd #bf #j #ajac #bf #cj #ajea #bg #j #ajij #bg #cj #aacj #bh #j #aaga #bh #cj #abaa #bi #j #abec #bi #cj #abif #cj #j #acdj ---------------- ,,curvature ,,and ,,refraction4 ,,table ,,of ,,corrections ,,in ,,feet ,,and ,,decimals ,,of ,a ,,foot4 ---------------------------------------- ----- ,distance ,curvature4,refraction4,correction for ,in ,miles4 ,curvature and ,refraction4 ---------------------------------------- ----- #jd #ja #jc #ag #jb #ae #cg #je #cb #a #fg #ji #eh #a #aej #ba #abi #b #bfg #ch #bbi #b #dag #fj #ceg #c #fjj #hf #ead #c #hag #aag #gjj #d #ajfg #aeb #iae #d #acee #aic #aafb #e #affg #bch #adbi #e #bjah #bhh #agcj #f #bdja #cdc #bjeh #f #bhah #djc #bdae #g #cbfh #dfg #bhja #g #cgeb #ecf #cbaf #h #dbfi #faj #cfei #h #dhai #fhh #daca #i #edjb #ggb #dfcj #i #fjbj #hfj #eafj #aj #ffgj #iec #egag ---------------------------------------- ----- ,,index4 ,a4 ,angle1 to bisect1 #af ----1 to construct1 equal to a given angle1 #ag ----1 to draw a line making a given1 #ae ---- of light in mechanical drawings1 #dh ---- ---- in topographical drawings1 #ed ,arch1 ,gothic1 equilateral1 to draw1 #bc ----1 ---- lancet1 to draw1 #bd ----1 ---- obtuse1 to draw1 #bd ----1 ---- ogee1 to draw1 #be ----1 ---- ,tudor1 to draw1 #bd ----1 ,moorish horse-shoe1 to draw1 #bd ----1 semi-elliptical1 to construct1 #bc ,architectural drawings1 #aba ,arcs1 centres of1 to be marked1 #aj ,areas to triangles1 to compute1 #adb ,b4 ,bisecting an angle1 #af ,blacklead paper1 #h ,book of reference1 #ig1 #aja ,books for field sketching1 #aae ,borders and corners1 #fi ,borings1 #ajd ,bottle indiarubber1 #i ,boundary maps1 #ajd ,bows1 #b ----1 spring1 #b ,broken lines1 #cj ,brushes for tinting1 #da ,buildings--plans1 sections1 and elevations1 position of1 on drawing1 #abe ,c4 ,carbonic paper1 #h ,cartridge paper1 #f ,centre lines1 #aj ---- ----1 care to be taken in placing correctly1 #aj ,centre of circle1 to find the1 #ah ,centres of arcs to be marked1 #aj ,cinquefoil1 ,gothic1 to draw1 #bf ,circle1 to describe1 through three given points1 #ag ----1 to draw a tangent to1 #ag ----1 to draw radii of1 the centre being inaccessible1 #ah ----1 to find the centre of1 #ah ,circles1 concentric drawing1 #aj ,cities1 to represent size of1 #aab ,civil engineers' plans1 #if ,cleaning drawing pen1 #c ,cleaning off drawings1 #i ,cleanliness1 importance of1 #i ----1 precautions to be taken to ensure1 #i ,cloth1 tracing1 #g ----1 ----1 ,sager's vellum1 #g ----1 ----1 sizes of1 #g ,colour for buildings1 #dg ---- for cultivated land1 #dg ---- for fences1 #dg ---- for grass-land1 #de ---- for gravel1 #df ---- for marsh1 #de ---- for mud1 #df ---- for roads1 #dg ---- for sand1 #df ---- for streets1 #dg ---- for water1 #de ---- for woodland1 #df ---- for uncultivated land1 #dg ,colouring cylindrical objects1 #abd ---- drawings1 #aa1 #abb ---- rivers and streams1 #aaj ,colours1 #ci ----1 conventional1 ,table of1 #dd ---- for sections1 #dd ,compasses1 #b ----1 manner of using1 #b ----1 pencil leg of1 #b ----1 points of1 #b ----1 removing movable leg1 #b ,competition drawings1 paper for1 #f ,concentric circles1 drawing1 #aj ,construction of scales1 #aa ,continuous cartridge paper1 #f ---- tracing paper1 #g ,contour lines1 #cg ,contours1 to plot1 #ij ,conventional colours1 ,table of1 #dd ,copying by tracing1 #abh ---- by transfer1 #abi ---- drawings1 #aa1 #abf ---- from tracing1 #aa ,corners and borders1 #fi ,cross sections1 #ih1 #ajb ,cultivated land1 to represent1 #cb ,curvature and refraction1 ,table for correction of1 #adc ,curved lines1 #bi ---- ----1 to draw1 #bi ,cutting off drawings1 #g1 #aa1 #ab ,cylinders1 various methods of shading1 #fd ,cylindrical objects1 to colour1 #abd ---- surfaces1 shade lines1 #ej ---- ----1 shading lines1 #ea ,cyma recta1 to draw1 #be ---- reversa1 to draw1 #be ,d4 ,dented drawing-board1 to remedy1 #ad ,detail plotting1 #hi ,dimensions of drawing table1 #b ---- to be written on drawings1 #abb ,distances1 scales of1 #gj ,dividing a line into equal parts1 #aj ,dotted lines1 #ca ,dotting pen1 #ca ----1 regular1 to produce1 #aaa ,drawing1 copying and reducing1 #abf ----1 inking in to commence from top of1 #aj ----1 stretching paper for1 #f ,drawing concentric circles1 #aj ---- from copy1 #abg ---- lines1 #aj ,drawing board1 dented1 to remedy1 #ad ---- office1 essentials of1 #a ---- ----1 gaslights1 #b ---- ----1 position of windows1 #a ---- ----1 skylights unsuitable1 #a ---- paper1 sectional1 #h ---- ----1 to join sheets of1 #ab ---- papers1 #e ---- ----1 sizes of1 #e ---- pen1 #c ---- ----1 cleaning1 #c ---- ----1 more than one required1 #c ---- ----1 setting1 #c ---- ----1 supplying with ink1 #c ---- table1 dimensions of1 #b ---- ----1 position of1 #b ,drawings1 cleaning off1 #i ----1 competition1 paper for1 #f ----1 colouring1 #aa ----1 cutting off1 #g1 #aa1 #ab ----1 ink for1 #h ----1 margin to be left1 #aa ----1 mechanical and architectural1 #aba ----1 parchment for1 #h ----1 to colour1 #abb ----1 to preserve rolled1 #ab ----1 to reduce or enlarge1 #acj ----1 to remove grease spots from1 #aj ----1 to varnish1 #ad ---- for lithographers and engravers1 #ada ---- for specifications for letters patent1 #h ,dusters1 #b ,e4 ,eidograph1 #acf ----1 method of setting1 #aci ----1 table for setting1 #aci ----1 to adjust1 #ach ,elevation of trees1 #cf ,ellipse1 to draw1 #ba ,elliptical arch1 to construct a semi-1 #bc ,encamping grounds1 #aab ,engravers1 drawings for1 #ada ,enlarging by instruments1 #aca ---- by scales1 #acj ---- by squares1 #acj ,equal parts1 to divide a line into1 #ae ,equidistant and parallel lines1 to draw1 #bh ,equilateral arch1 to draw1 #bc ---- triangle1 to construct1 on a given base1 #af ,erasure of ink lines1 #aa ---- of pencil marks1 #i ,error-sheets1 #ia ----1 examples of1 #ib ,errors1 #ia ,essentials of drawing office1 #a ,estate plans1 #ajg ,examination of maps and plans1 #aag ,f4 ,ferries1 #aaa ,field-book1 example of1 #hj ,field sketching1 #aad ,fir-graining1 #cb ,flat-tints1 #dj ,formul1 trigonometrical1 #adb ,g4 ,gaslights in drawing office1 #b ,glass-paper to erase ink lines1 #aa ,glue for mounting paper1 #f ,gothic cinquefoil1 to draw1 #bf ---- equilateral arch1 to draw1 #bc ---- lancet arch1 to draw1 #bd ---- obtuse arch1 to draw1 #bd ---- ogee arch1 to draw1 #be ---- quatrefoil1 to draw1 #bf ---- trefoil1 to draw1 #be ---- ,tudor arch1 to draw1 #bd ,gradients1 to lay down1 #ie ,graining1 fir1 #cb ----1 oak1 #cb ----1 wood1 #cb ,grass-land1 to represent1 #cd ,gravel1 to represent1 #ce ,grease spot1 to remove from drawing1 #aj ,h4 ,hexagon1 to describe a regular1 #ba ,hills1 representation of1 #ch ----1 sand1 to represent1 #cf ----1 shading1 horizontal system1 #ec ----1 ----1 vertical system1 #eg ----1 sketching1 shading1 and copying1 #aac ,horizontal zones1 #ch ,horse-shoe arch1 to draw1 #bd ,i4 ,importance of cleanliness1 #i ,inclined measure1 ,table for correction of1 #adc ,indian ink1 #h ---- ----1 preparation of1 for drawing1 #i ---- ----1 quality of1 #i ,indiarubber1 native or bottle1 #i ----1 vulcanized1 #i ,ink for drawings1 #h ----1 ,indian1 #h ----1 preparation of1 #i ----1 quality of1 #i ---- lines1 erasure of1 #aa ---- ----1 to avoid smearing1 #aj ---- slab or saucer1 position of1 when in use1 #aj ,inking in to commence at top of the drawing1 #aj ,instruments1 #b ----1 quality of1 #b ,islands1 #aaj ,j4 ,joining sheets of paper1 #ab1 #ac ,jungle1 #aab ,l4 ,lakes1 outline of1 #cj ,lancet arch1 to draw1 #bd ,land1 cultivated1 to represent1 #cb ----1 uncultivated1 to represent1 #cg ,lead-pencil marks1 erasure of1 #i ,lettering1 #ff1 #abb ----1 position of1 on plans and maps1 #fi ,letters1 arrangement of1 in titles1 c41 #fh ----1 kinds to employ1 #fg ----1 mechanical construction of1 #ff ----1 size of1 #fg ,level-book1 example of1 #id ,line1 dividing into equal parts1 #aj ----1 regular pentagon on a given1 #bj ----1 to bisect a given straight1 #ae ----1 to construct a square on a given1 #ai ----1 to divide a1 into equal parts1 #ae ----1 to draw a1 making a given angle1 #ae ----1 to erect a perpendicular to1 #ae ,lines1 drawing1 #aj ----1 broken1 #cj ----1 centre1 #aj1 #abb ----1 combinations of1 #ca ----1 curved1 to draw1 #bi ----1 curved and straight1 #bg ----1 contour1 #cg ----1 dotted1 #ca ----1 ink1 to avoid smearing1 #aj ----1 parallel and equidistant1 to draw1 #bh ----1 reference1 #gh ----1 section1 #bi ----1 ----1 to draw1 #bh ----1 shade1 application of1 #dh ----1 shading1 #ej ----1 ----1 in topographical drawings1 #eb ----1 straight1 difficulties in ruling1 #bg ----1 ----1 to draw1 #bg ----1 wavy1 #cc ---- of greatest descent1 #eg ---- of uneven thickness1 #cj ,lithographers1 drawings for1 #ada ,local ,government ,board1 regulations of1 #ajd ,m4 ,machine-made paper1 #f ,machinery1 rough sketches of1 #aba ,manner of using compasses1 #b ,map drawing1 #aji ,maps1 boundary1 #ajd ----1 field1 examination of1 #aah ----1 signs used in1 #abj ---- for division into wards1 #ajd ,margin to drawings1 width of1 #aa ,marshy ground1 to represent1 #ce ,mechanical drawings1 #aba ,mile stones1 #aab ,mining plans1 #ajf ,moorish horse-shoe arch1 to draw1 #bd ,more than one drawing pen required1 #c ,mountain passes1 #aaa ,mounting paper1 glue for1 #f ---- ---- on stretchers1 #ac ---- tracings1 #abi ,mud in rivers1 to represent1 #cf ,n4 ,native indiarubber1 #i ,needle to erase ink lines1 #aa ,north points1 #fi ,northings and southings1 #hg ,o4 ,oak-graining1 #cb ,obtuse arch1 to draw1 #bd ,ogee arch1 to draw1 #be ,orchards1 to represent1 #cf ,outline of lakes1 #cj ---- of ponds1 #cj ---- of rivers1 #cj ,oval1 to construct1 the width being given1 #ah ,p4 ,pantograph1 #aca ----1 methods of setting1 #acb ----1 tables for setting1 #acc1 #acd ----1 to use1 #acd ,paper1 blacklead1 #h ----1 carbonic1 #h ----1 cartridge1 #f ----1 continuous cartridge1 #f ----1 drawing1 #e ----1 ----1 to join1 #ab ----1 ----1 sizes of1 #e ----1 glue for mounting1 #f ----1 machine-made1 #f ----1 sectional1 #h ----1 stretching for drawing1 #f ----1 tracing1 #g ----1 ----1 continuous1 #g ----1 ----1 preparation of1 #g ----1 ----1 sizes of1 #g ----1 ----1 to join1 #ac ----1 transfer1 #h ----1 ----1 preparation of1 #abi ----1 to join sheets of1 #ab ----1 to mount on stretchers1 #ac ---- for competition drawings1 #f ---- for large plans1 #f ,parabola1 to draw1 base and height being given1 #ba ,parallel and equidistant lines1 to draw1 #bh ,parchment for drawings1 #h ,parliamentary plans and sections1 #ajj ---- standing orders1 #ih ,paste1 #ad ,patent1 drawings for specifications1 #h ,pathways1 #aaa ,pen1 dotting or wheel1 #ca ,pencil marks1 erasure of1 #i ---- leg of compasses1 #b ,pencils1 #d ----1 pointing1 #d ---- for field sketching1 #aae ,pentagon1 to describe1 on a given line1 #bj ,perpendicular1 to erect a1 #ae ,plan of trees1 #cf ,plans1 civil engineers' and surveyors'1 #if ----1 estate and town1 #ajg ----1 large1 paper for1 #f ----1 mining1 #ajf ----1 railway1 #ig ----1 parliamentary1 #ajj ,plotting1 #gg ---- angular surveys1 #ha ---- contours1 #ij ---- detail1 #hi ---- sounded points in submerged districts1 #ij ---- traverse reference lines1 #hd ---- vertical sections1 #ib ,pointing pencils1 #d ,points of compasses1 #b ,ponds1 outline of1 #cj ,position of drawing table1 #b ---- of ink slab or saucer when in use1 #aj ---- of windows in drawing office1 #a ,precautions to be taken to ensure cleanliness1 #i ,preparation of colours for tinting1 #dj ---- of ink for drawing1 #i ---- of stretchers1 #ac ---- of tracing paper1 #g ---- of transfer paper1 #abi ,preserving drawings1 rolled1 #ab ,q4 ,quality of ,indian ink1 #i ---- of instruments1 #b ,quatrefoil1 ,gothic1 to draw1 #bf ,r4 ,radii of circle1 to draw1 the centre being inaccessible1 #ah ,railway plans1 #ig ---- sections1 #ajb ---- stations and termini1 #aab ,railways1 #aab ,rectangle1 to construct1 similar to a given rectangle1 #bj ,rectangular co-ordinates1 to plot by1 #hg ,reducing and enlarging drawings1 #abf1 #acj ---- by instruments1 #aca ---- by scales1 #acj ---- by squares1 #acj ,reference1 book of1 #ig1 #aja ---- lines and points1 #gh ---- lines1 secondary1 #gi ,refraction and curvature1 ,table for correction of1 #adc ,regulations of ,local ,government ,board1 #ajd ,removing movable leg of compasses1 #b ,rivers1 beds of1 #aaj ----1 mud in1 to represent1 #cf ----1 outline of1 #cj ---- and streams1 colouring1 #aaj ---- ----1 inking in1 #aji ,roads1 #aaa ,rolled drawings1 to preserve1 #ab ,roman cyma recta and cyma reversa1 to draw1 #be ,roofs1 to draw1 #cj ,rough sketches of machinery1 #aba ,ruling straight lines1 difficulties in1 #bg ,running water1 to represent1 #cc ,s4 ,sager's vellum tracing cloth1 #g ,sand1 to represent1 #ce ---- banks1 #aaj ---- hills1 to represent1 #cf ,scales1 #gj ----1 choice of1 #gb ----1 construction of1 #aa1 #gj1 #ge1 #gf ----1 diagonal1 #ge ----1 vernier1 #ge ----1 ,tables of1 #gc1 #gd ---- of construction1 #gd ---- of distances1 #gj ---- of shade1 ,english1 #ei ---- ----1 ,lehmann's1 #eg ---- ----1 standard1 #ec ---- ----1 ,united ,states'1 #ei ,sectional drawing paper1 #h ,section lines1 #bi ---- of water1 to represent1 #cj ,sections1 colours for1 #dd ----1 cross1 #ih1 #ajb ----1 parliamentary1 #aja ----1 railway1 #ajb ----1 to plot1 from contour map1 #if ----1 working1 #id1 #ajc ---- of wood1 #cb ----1 vertical1 to plot1 #ib ,semi-elliptical arch1 to construct1 #bc ,setting drawing pen1 #c ,shade lines1 application of1 #dh ---- ----1 cylindrical surfaces1 #ej ,shading1 #dh ---- cylinders1 various methods1 #fd ---- hills1 horizontal system1 #ec ---- ----1 vertical system1 #eg ---- ----1 rounding curves1 #ee ---- lines1 #ej ---- ----1 cylindrical surfaces1 #ea ---- ---- in topographical drawings1 #eb ---- in colours1 #fc ---- ----1 cylindrical surfaces1 #fd ---- ----1 hill slopes1 #fc ,sides of triangles1 to compute1 #adb ,sizes of drawing papers1 #e ---- of tracing cloth1 #g ---- of tracing paper1 #g ,sketches1 rough1 of machinery1 #aba ,sketching1 field1 #aad ,skylights unsuitable for drawing office1 #a ,sounded points1 to plot1 #ij ,specifications for letters patent1 drawings for1 #h ,spring bows1 #b ,springs1 #aab ,square1 to construct1 equal to 1 1 c41 of a given square1 #ai ----1 to construct1 in any proportion to a given square1 #bj ----1 to construct1 on a given line1 #ai ----1 to construct1 which shall be a multiple of a given square1 #ai ,standing orders of ,parliament1 #ih ---- water1 to represent1 #bi ,stations1 railway1 #aab ----1 telegraph1 #aab ,straight-edge1 thickness of1 #e ,straight line1 to bisect a1 #ae ---- lines1 difficulties in ruling1 #bg ---- ----1 to draw1 #bg ---- and curved lines1 #bg ,stretchers1 mounting paper on1 #ac ----1 preparation of1 #ac ,stretching paper for drawing1 #f ---- ----1 glue for1 #f ,supplying drawing pen with ink1 #c ,surveyors' plans1 #if ,swamps1 to represent1 #ce ,t4 ,table1 drawing1 position of1 #a ----1 ----1 size of1 #a ,table for correction of curvature and refraction1 #adc ---- for correction of inclined measure1 #adc ---- for setting eidograph1 #aci ---- of conventional colours1 #dd ,tables for setting pantograph1 #acc1 #acd ,tangent1 to draw1 to a circle1 #ag ,telegraph lines and stations1 #aab ,thickness of straight-edge1 #e ,tinting1 #ci ,tints1 art of applying1 #dj1 #da1 #dc ----1 brushes for applying1 #da ----1 double or alternate1 #db ----1 flat1 #dj ----1 preparation of1 #dj ,toll-gates1 #aaa ,topographical drawings1 shading lines in1 #eb ,to remove grease spots from drawings1 #aj ,town plans1 #ajg ,towns1 to represent size of1 #aab ,tracing1 copying from1 #aa ----1 to copy by1 #abh ---- cloth1 #g ---- ----1 ,sager's vellum1 #g ---- ----1 sizes of1 #g ----- paper1 #g ---- ----1 continuous1 #g ---- ----1 preparation of1 #g ---- ----1 sizes of1 #g ---- ----1 to join sheets of1 #ac ,tracings1 to mount1 #abi ,transfer paper1 #h ---- ----1 preparation of1 #abi ,transferring1 to copy by1 #abi ,traverse plotting by rectangular co-ordinates1 #hg ---- reference lines1 to plot1 #hd ,trees in plan1 #cf ---- in elevation1 #cf ----1 to represent1 #cf ,trefoil1 ,gothic1 to draw1 #be ,triangle1 equilateral1 to construct1 #af ----1 to construct1 the length of base and angles at base being given1 #ag ----1 to construct1 the lengths of the sides being given1 #af ,triangles1 primary and secondary1 #gh ----1 to compute the areas of1 #adb ----1 to compute the sides of1 #adb ,trigonometrical formul1 #adb ,tudor arch1 to draw1 #bd ,u4 ,uncultivated land1 to represent1 #cg ,v4 ,varnishing drawings1 #ad ,vellum tracing cloth1 ,sager's1 #g ,vertical sections1 to plot1 #ib ,villages1 to represent size of1 #aab ,vulcanized indiarubber1 #i ,w4 ,washes1 art of applying1 #dj1 #da1 #dc ----1 brushes for1 #da ----1 double or alternate1 #db ,water1 running1 to represent1 #cc ----1 standing1 to represent1 #bi1 #cc ---- in section1 to represent1 #cj ,wavy lines1 #cc ,wells1 #aab ,whatman's drawing papers1 #f ,wheel pen1 #ca ,width of margin to drawings1 #aa ,windows1 position of1 in drawing office1 #a ,wood-graining1 #cb ,wood sections1 #cb ,woodland1 to represent1 #cf ,working sections1 #ajc ,z4 ,zones1 horizontal1 #ch ,,the ,,end4 ,,london3 ,,printed ,,by ,,william ,,clowes ,,and ,,sons1 ,,stamford ,,street ,,and ,,charing ,,cross4 ,,plates4 ,illustration3 ,,plate #b4 ,,plan ,,sent ,,to ,,be ,,copied ,,plan ,,traced ,,by ,,junior ,,hand ,,plan ,,shewing ,,writing ,,gauged ,,plan ,,finished ,b4 ,alexander1 ,lith4 ,e ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #c4 ,,plan ,,of ,,estate ,,at ,,haslington1 ,,bucks4 #ahgd4 ,b4 ,alexander1 ,lith4 ,e ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #d4 ,,roman ,,capitals ,,italic ,,capitals ,angle #fj degrees ,,round ,,hand ,angle #ec degrees ,,mechanical ,,construction ,,of ,,letters c4 #h ,lines #f ,lines #d ,lines #c ,lines #b ,lines ,b4 ,alexander1 ,lith4 ,e ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #e4 ,,open ,,stone ,,letters ,do4 ,do4 ,,with ,,ornament ,,ornamental ,,letters4 ,,egyptian ,,with ,,ornament ,,roman ,,with ,,ornament ,do4 ,,small ,,with ,,ornament ,,old ,,english ,,with ,,ornament ,do4 ,,small ,,with ,,ornament ,,figures ,,with ,,ornament ,b4 ,alexander1 ,lith4 ,e ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #f4 ,,alphabets4 ,,old ,,english ,capitals4 ,do4 ,do4 ,small4 ,,german ,,text ,capitals4 ,do4 ,do4 ,small4 ,,gothic ,capitals4 ,do4 ,small4 ,,church ,,text ,capitals4 ,do4 ,do4 ,small4 ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #g4 ,,plan ,,of ,,an ,,estate ,,called ,,the ,,lower ,,cedars ,,near ,,the ,,town ,,of ,,birmingham #ahgd4 ,,plan ,,of ,,property ,situate in the ,parish of ,,hammersmith1 ,,middlesex4 ,plan of a ,valuable ,freehold ,estate known as ,,frognal ,,near ,,hampstead ,,heath4 ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #h4 ,,plan ,,of ,,land ,,to ,,be ,,laid ,,out ,,in ,,building ,,plots ,,belonging ,,to ,,the ,,late ,,sir ,,joseph ,,paxton1 ,,in ,,leases ,,of #ii ,,years1 ,,subject ,,to ,,the ,,annexed ,,condition4 ,scale of ,chains4 ,scale #f ,chains to an ,inch ,scale of ,feet4 ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #i4 ,scale of ,chains4 ,scale of ,feet4 ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #aj4 ,,ordinary ,,beech4 ,,wood4 ,,firs4 ,,light ,,brushwood4 ,,firs ,,other ,,trees4 ,,cocoa ,,palm ,,trees ,for ,colonial ,plans4 ,,swamp4 ,,marsh4 ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #aa4 ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #ab4 ,,construction ,,of ,,hills4 ,,finished ,,hills4 ,,contour ,,hills4 ,,finished ,,hills ,,in ,,color4 ,,contour ,,hills ,,in ,,color4 ,,hills ,,in ,,chalk4 ,,broken ,,hilly ,,country4 ,,hills ,,in ,,color4 ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #ac4 ,,plan ,,shewing ,,proposed ,,new ,,street4 ,half ,black for ,lithography ,half ,color for ,paper4 ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #ad4 ,,ash ,,beech ,,birch ,,cedar ,,cypress ,,elm ,,fir ,,mountain ,,ash ,,oak ,,plantation ,,forest ,,pine ,,poplar ,,sycamore ,,thorn ,,weeping ,,willow ,,yew ,,mountains ,,rocky ,,cliff ,do4 ,,in ,,color ,do4 ,,in ,,color ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #ae4 ,,signs ,,used ,,in ,,plans4 ,fence ,farm ,buildings ,fence with ,bank ,churches ,fence with ,hedge ,windmills ,footpath ,water ,mills ,bridle ,paths ,lime ,kiln ,occupation ,road ,sunk ,road ,public ,road ,raised ,road ,wall ,quarry ,parish ,boundary ,inn ,hamlet ,boundary ,sand ,pits ,county ,boundary ,rocks ,parish ,county ,boundary ,mud ,railway ,gas ,works ,tramway ,glass ,works ,stream ,iron ,works ,brook ,column ,ditch ,old ,castle ,mineral ,waters ,covered ,passage ,canal ,saw ,mill ,river ,stone ,windmill ,ponds ,wooden ,windmill ,lake ,cotton factory ,wooden ,fence ,woollen ,factory ,post and ,rail or thus ,well ,chains ,post ,dry ,well ,hurdle ,fence ,salt ,works ,gates ,field ,wall ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #af4 ,,signs ,,used ,,in ,,maps ,,and ,,charts4 ,fortress ,rocks always covered ,citadel ,reef of ,rocks ,fortified ,castle ,sand never covered ,walled ,town ,sand sometimes covered ,open ,town ,shoals always covered ,country ,town ,mud ,bank ,beach dry at ,low ,water ,little ,town ,rocky ,ledges which cover and uncover ,city ,sandy ,beach dry at ,low ,water ,episcopal ,city ,lighthouses 7position of7 ,borough or ,corporation ,can ,buoys ,light ,ship ,nun ,buoys ,light ,house ,mooring ,buoy ,anchorage for ,ships ,buoys with ,beacons ,do for ,coasters ,coral ,reefs ,wreck ,kelp ,stopping ,places ,fish ,weir ,head of ,navigation ,swampy ,land ,floating ,light ,vessel ,rocks ,harbour ,rocks dry at ,low ,water ,telegraph ,viaduct ,signal ,house ,tunnel ,buoys ,railway ,bridge ,channel ,marks ,bridge over ,stream ,no ,current ,pontoon ,bridge ,direction of ,current ,bridge 7,brick or ,stone7 ,rocks sometimes covered ,foot ,bridge ,rocks never covered ,towns ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #ag4 ,plan ,,of ,,melton ,,hall ,,estate ,situate in the ,,county ,,of ,,lincoln1 #ahgd4 ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #ah4 ,,piece ,,of ,,ordnance ,,map4 ,,piece ,,of ,,chart ,,shewing ,,soundings1 c4 ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #ai4 ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #bj4 ,,sand ,,gravel4 ,,red ,,sandstone4 ,,clay ,,gravel4 ,,limestone4 ,,bog4 ,,clay ,,slate4 ,,millstone4 ,,granite4 ,,sandstone ,,coal4 ,,spoil ,,bank4 ,,pure ,,gravel4 ,,clay ,,calcareous4 ,,peat ,,clay4 ,,sandstone4 ,,shell ,,marl4 ,,limestone ,,with ,,bog ,,with ,,timber4 ,,sandstone ,,with ,,gypsum4 ,,mineral ,,veins4 ,,mud4 ,,sandstone ,,coarse ,,clay ,,slate ,,with ,,mineral ,,fine4 ,,veins4 ,,combination ,,of ,,the ,,above4 ,spoil ,bank ,clay ,clay ,calcareous ,limestone ,sand ,yellow ,clay ,bog ,gravel ,rock ,red ,sandstone ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #ba4 ,,parliamentary ,,railway ,,section4 ,,ditto1 ,,shewing ,,geological ,,strata4 ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #bb4 ,,piece ,,of ,,marine ,,engine ,,of ,h4 ,m4 ,s4 ,s4 8,,research04 ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #bc4 ,,skew ,,bridge4 ,,permanent ,,way4 ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #bd4 ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #be4 ,ornamental ,writing4 ,london ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #bf4 ,,methods ,,of ,,reducing ,,or ,,enlarging4 ,,by ,,squares ,,by ,,eidograph ,,by ,,english ,,pentagraph ,,by ,,french ,,pentagraph and by ,photography4 ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #bg4 ,,isometrical ,,view ,,of ,,building4 ,,exterior4 ,,interior4 ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #bh4 ,depositary ,rocks4 #a-ah ,igneous ,rocks4 a-b ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #bi4 ,,signs ,,used ,,in ,,indian ,,colonial ,,plans4 ,telegraph ,hills with ,peaks ,trunk ,road 7,metalled7 ,do4 in ,contour ,district ,do4 ,scarped ,face of ,hill ,do4 ,unmetalled ,ravine ,ford ,garden ,nullah or ,khall ,paun ,garden ,bund or ,embankment ,village ,old ,bank of ,river ,ferry ,hedges with ,trees ,flying ,bridge ,river with ,islands ,haut or ,bazar ,river with ,sand ,bank ,mud ,fort ,stone ,sluice ,gate ,pucka ,fort ,lake or ,tank ,deserted ,village ,salt ,pans ,principal ,survey ,stations ,cultivated ,ground ,secondary ,do4 ,burial ,ground ,flag for ,surveying ,sand ,hills ,ridge of ,hills ,high ,ground ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #cj4 ,,signs ,,used ,,in ,,indian ,,colonial ,,plans4 ,salt ,golah ,jhow ,jungle ,salt ,chowkey ,jheel ,silk ,factory ,tamarind ,trees ,indigo ,factory ,bamboo ,jungle ,sugar ,factory ,salt ,waste ,post ,office ,salt ,waste with ,jungle ,dak ,bungalow ,mangoe ,tope ,police or ,thana ,stan4 ,cocoa ,nut ,trees ,magistrate's ,kutcherry ,betel ,nut ,trees ,stone or ,pucka ,houses ,trees generally ,mahomedan ,mosque ,date ,trees ,hindoo ,temple ,palm or ,tar ,trees ,telegraph ,tower ,mangrove ,signal ,staff ,brides ,boundary ,pillar ,rail ,road ,wooden ,boundary ,post ,pucka ,well ,kucha ,well ,forest ,jungles ,low ,jungles ,grass ,jungles ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #ca4 ,,military ,,signs ,,and ,,fortifications4 ,tte du ,pont ,passable for ,troops ,vedettes ,infantry ,engaged ,military ,pits ,cavalry ,encamped ,mines ,village ,inundated ,infantry ,encamped ,sand ,bags ,village ,burnt ,intrenchment ,caltrop or ,crows ,feet ,cannon ,trenches ,cavalry ,engaged ,park ,palisades ,barrier ,mortar ,shells ,block ,house ,field ,piece and ,limber ,ammunition ,waggon and ,limber ,,section ,,of ,,glacis1 ,,ditch1 ,,rampart1 ,c4 ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #cb4 ,,military ,,signs ,,and ,,fortifications4 ,infantry ,column ,impassible for ,artillery ,cavalry ,line ,abatis ,chevaux de frise ,redoubt ,mortar ,battery ,cavalry ,column ,impassible for ,cavalry ,guns on ,march ,gained ,gun ,battery ,field of ,battle ,lost ,impassible for ,infantry ,sentinel ,baggage ,waggons ,infantry ,line ,fortified ,castles ,guns in ,position ,closed ,palisades ,redan or ,fleche ,rifle ,pits ,,gabions ,,fascines ,,plan ,,of ,,bastioned ,,fort ,,with ,,lunettes4 ,b4 ,alexander1 ,lith4 ,e ,f4 ,n4 ,spon4 ,london ,new ,york4 ,illustration3 ,,plate #cc4 ,,portion ,,of ,,mining ,,plan ,,shewing ,,pillar ,,workings4 ,,as ,,shewn ,,by ,,hand ,,on ,,paper4 ,,as ,,shewn ,,by ,,engraving ,,or ,,lithography4 ,b4 ,alexander1 ,lith4 ,e4 ,f4 ,n4 ,spon4 ,london ,new ,york4 ,transcriber's ,notes ,inconsistencies in spelling1 hyphenation1 lay-out1 the use of quote marks1 diacriticals and accents1 etc4 have been retained4 ,depending on the hard- and software used to read this document1 some elements may not display as intended4 ,the browser version of this document 7available from www4gutenberg4org7 gives best results1 and contains larger versions of several illustrations4 ,the minor differences between the ,table of ,contents and the headings in the text have not been standardised4 ,several plates have been printed with poor colour overlays1 this has not been remedied4 ,some double-page plates have been re-combined1 but the area between the pages may not be exactly as printed in the original work4 ,page #acf1 ,professor ,willis3 should be ,professor 7,william7 ,wallace2 ,professor 7,robert7 ,willis invented other drawing tools4 ,plate #bf1 pentagraph 7#b73 as printed in the source document4 ,changes made3 ,some missing punctuation has been added silently1 some minor typographical errors have been corrected silently4 ,some tables1 calculations1 formulas1 etc4 have been re-arranged for better readability4 ,page #ae3 apply a straight-edge ,f changed to apply a straight-edge ,d ,page #ge1 ,fig4 #ge3 ,lehman's ,scale changed to ,lehmann's ,scale ,page #hc3 the third reference line ,c ,d changed to the third reference line ,c ,a ,page #acb3 the erect manner and the reverse manner changed to the erect manner and the reverse manner4 ,heading ,,plates added after ,index4