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No. 4. 
 
 PRICE, SO CENTS. 
 
 """ 
 
 K.t„«l ^Hin, U> A.t ., th. P»U.^.nt of Cn..... „ th. y.^ „„, thou-d Ight hundr*. .«d .ighty...gh, by T„, G»„ Pa,»T.». „„ p„.„.h,„ Co. o, Toronto, .t the Dap„t™„t c, AgricuHure. 
 
INTRODUCTORY REMARKS. 
 
 Object dbawinq may be appropriately called freehand 
 perspective, or memory drawing. Either one ot these three 
 names partially describes its character and the three together 
 indicate what it really consists of. It may appear to some that 
 the subject is not of any great importance, as compared with 
 freehand, geometry or perspective, these three being of such 
 practical utility to the artisan and artist, apart from their value 
 as educative mediums. But when it is considered that object 
 drawing embraces these three other subjects, and is the practical 
 appUcation of them, it must be treated as being equally, if not 
 more important than either of them. The power to reprMent 
 objects with facility is not the greatest benefit to be derived from 
 it by the majority of those studying it, in fact this should be 
 looked upon as a mere secondary consideration, even by those who 
 study it as forming part of an art, education. 
 
 In order to properly prosecute the study of object drawing it 
 is necessary to become familiar with the forms and construction 
 of common objects, and this, of court,e, presupposes that these 
 objects have been examined, not carelessly, but critically, until 
 tlie facts of their forms are indelibly impressed upon the memory. 
 The close observation of things is one of thi most useful habits 
 wliich a person can form, and the student is earnestly advised to 
 cultivate it. It is the tendency to lead to the cultivation of 
 observation which makes object drawing such an important sub- 
 ject, and in order to reap all the benefits to be derived from it, it 
 should be studied honestly and assiduously on the lines indicated 
 in this little book. 
 
 In object drawing no instruments other than pencils ana 
 rubber should be used. The pencils recommended for freehand, 
 viz., H and HB are suitable for object drawing and should be 
 kept well sharpened. ,. , , j 
 
 The outline of an object should be drawn as lightly and care- 
 fully as possible, and afterwards " lined in " with a firm, decided 
 stroke. For the first sketch the H pencil should be used, and the 
 HB pencil used for " lining in." v . -i. *i, *. 
 
 The student should strive earnestly to avoid the habit that 
 very many fall into of drawing their lines almost at random, 
 and it iiot correct, patching theTn with short strokes, making 
 their work look untidy in the extreme. The lines should not be 
 "painted" or "dotted "in but drawn without hesitation, firmly 
 and carefully. A good plan to adopt is to first decide in what 
 direction a line is to run and mark two points, judging their 
 position so that they will indicate not only the direction of the 
 line but its length also, and draw the line from point to point 
 without stopping, unless it is a very long one. In the case of a 
 curved line several points may be used, but they should not m 
 2 
 
 any case be placed less than half an inch apart. These points 
 should form part of the line when it is drawn and so unless 
 they are selected with great care they might better be omitted 
 altogether. 
 
 The geometric outline of every object should be drawn first, 
 no matter how expert the student is with hift pencil, and how 
 familiar he is with the mode of representing an object. Atten- 
 tion to this will save many disappointments and much annoyance. 
 It is not expected that the vanishing lines in an object shall 
 be drawn by means of a ruler, to a vanishing point selected and 
 marked on the paper. All vanishing points should have an 
 imaginary existence to the student but their position should be 
 selected with care, and the lines vanishing in them be drawn 
 freehand towards them as nearly^as possible, and not any longer 
 than is judged necessary. Mathematical accuracy in the freehand 
 drawing of an object should not be looked for. It should be 
 considered quite satisfactory if it represents with a certain 
 amount ih the facts of the form of the object, more 
 
 especially its proportions, for if they are right the details are 
 almost certain to be right too. 
 
 Sometimes, through not being perfectly familiar with the form 
 of an object, it may be difficult to decide just where or how to 
 commence a drawing of it. Unfortunately even the most com- 
 mon objects around us have not been examined by us as they should 
 be, and many will no doubt find this out. In such a case, the 
 best and in fact the only wise thing to do is to find the object 
 in question, examine it carefully, making notes of the form, size, 
 and relative position of its parts, if necessary to impress them on 
 the memory, and not till then to attempt to draw it, and to draw 
 it without referring again to the object itself, unless for the pur- 
 pose of criticizing the drawing and correcting errors. If the 
 working of the exercises is carried on in concert in a school it 
 would be well for the teacher to have the object required present 
 before the pupils if possible, give them an opportunity to examine 
 it and then analyse it before them, making constructive drawings 
 of its various parts on the blackboard. After this the pupils 
 might commence to draw. 
 
 In every case the drawings should be made as large as the 
 space allotted to them will aibw. 
 
 In the last two illustrations a little shading is used for the 
 purpose of adding interest to them, but the student should not 
 look upon this as an example for him to follow. He should con- 
 fine his whole attention to form, and lot light and shade alone 
 until he is expert in drawing correct outlines, and even then not 
 to meddle with it until he has had some instruction in represent- 
 ing shades of different tones by means of a pen or pencil. 
 
HIGH SCHOOL DRAWING COURSE. 
 
 OBJ 1 XT DRAWING. 
 
 _ Object Drawing, ns ilistinKuisliccl from ]\lrali!l drawing, 
 13 tho didwiiig of objects fioin iiKiiiiiiry, or fioni thci kTiowlpclKo 
 of tlifircoiistnidioa possessed )iy thts stud.Mit, ,ind when in llio 
 exorcisea n, drawinj; of a taF)lo or ii eliair is asUcd for, it is sup poyed, 
 not tliat lio has a taolo or a cliair befoio liiiii to eojiy, Init that iio 
 knows the sliapo of tho difl'orent parts of a table or a chair, and 
 how they are put togetlier, and is so familiar with tho manner of 
 n^presenting lines of different kinds in dillerent positions, that ho 
 can without hesitation draw the different parts of a table or chair 
 ill any position that may bo re<niired. 
 
 Tlio necessity of possessing this knowledge of tho shape and 
 construction of familiar objects does not present any serious 
 difficulty, as it recpiires only that tlio student shall use his eyes. 
 Object drawing is in reality the combination of three other 
 blanches of eliMiientary drawing treated of in this scries, viz.: 
 I'reehaiul, Geometry and Perspective Drawing, and i.< the end 
 towards which all instruction in elementary drawing should 
 be directed. Though somewhat similar, as regards its ivsults, to 
 model drawing it is as much in advance as model drawing is in 
 advance of drawing from flat copies, inasmuch as it is almost 
 purely a mental process. Model drawing is copying what is seen ; 
 object drawing is drawing what ia imagined. In the one the 
 eyes supply the neiressary information ; in the other it is supplied 
 by tho memory and imagination. 
 
 _ Tho_ principles of perspective govern the representation of 
 objects in object drawing as in model drawing, and thus no new 
 facts or rules have to be learned. 15ut these principles have to be 
 applied practically, and this is apt to iniz/lo the student unless he 
 IS thoughtful. He must bo prepared to apply them to the repre- 
 
 senfalion of objects placed in any and all positions. It may be 
 well, therefore, to simplify thcMn as ]w\rh as possible. 
 
 It is patent to (!Verybo(!y that objects ai)pe/ir to decrease in 
 si/o as they are removed away from the eye. Hence, starting with 
 this fact, if two parallel lines of ecpial length, one being more 
 distant than tho other, bo represented in persjiiyctive, the more 
 distant one will appear to be the shorter, and if lines U: drawn 
 joining their extremities, they will, if produced, meet. Thus it 
 IS seen that tho principle of converging lines is depi'iident upon 
 the fact thus stated, in fact, all or nearly all the principles of 
 perspective can bo traced back to it. 
 
 Tho great majority of objects, especially tliose made by man, 
 can bo analysed, or resolved into the elements which enter into 
 the composition of their forms. These elements may be con 
 sidered to be the simple geometric planes and solids, and it may 
 bo necessary at times to further resolve tho solids into planes and 
 the [ilanes into lines. As an illustr.ition, a barrel may be .said to 
 be based upon the cylinder, a pail upon the frustum of the erne, 
 a table upon the parallelopiped, a house upon a parallelepiped and 
 a triangular prism, or a parallelopiped and a pyramid, etc. 
 
 As a matter of fact it may bo said, that if a student possesses 
 the ability to represent properly any of the geometric planes and 
 solids 111 any position, he can draw any manufactured object that 
 can be mentioned. 
 
 The manner of representing geometric planes will be con- 
 sidered first. 
 
 Commencing with tho square : —It will need but a moment's 
 thought to convince any one that if a square bo in a plane which 
 is perpendicular to the picture plane and which contains tho 
 
fPiitro of visinn, it will lin rcpiosoiitc'l by alitif^; and tliat ns it 
 is riMiiovwl awiiy from lliis plaiH! it will iipiicu' to bccoiiu! widci-, 
 as shown in li;,'s. 1, 2, and 3. These illiistiations need iin oxplan- 
 ation. AftiM' tho lessons in iieispeftivo given in liook mnnlier 
 threo of this series, tlio student will understand tiiem. 
 
 Fig. 1. shows a Kcjuai'o in various )iositioi>s when its piano is 
 vortical and perjiendioular to the picture piano. 
 
 Pig. 2 shows a si|uaro in a number of positions when its plane 
 is horizontal, and Fig. 3 shows a square in sevend positions when 
 its piano is perpendicular to tho picture piano but at difTcrent 
 angles with tho ground plane. In all of these squares two .sides 
 aro reprosonti-d as being parallel to tho jiicture plino. 
 
 A very little observation and thnught will serve to impress 
 those facts of appearaneo upon tho mind so that when tho position 
 of a square is given it can bo drawn without any hesitation. 
 
 If, inste.id of a sipiare, an oblong 1"- retiuired, it can bodrawn 
 b- using a Square as a basis and lengthening two opjiosito .sides in 
 tiio s.imo diri^ction and joining their extremities Ijy a lino drawn 
 
 N K 
 
 V 
 
 ' / 
 
 1 
 
 '■-'^ 
 
 FIG. 1, 
 
 towards tho vanishing point of tho other sides. This is shown in 
 Fig. 4, where a b c d represents a sciuaro in diderent positions, 
 and a b c / an oblong. 
 
 Sometimes it m.iy bo required to draw an oblong the lengtli of 
 which is twice its width. In this ca.so draw a square, as abed 
 Fig. f), di-aw its diiigouals to lind tho centre, and through the 
 centre draw a lino towards tho vanishing point of either pair of 
 sides according to circumstances. Then tho oblongs b c f w\\\ 
 l)o the ono required. An oblong of any proportions ni.iy be 
 obtained l>y drawing a scjuare with its diagonals, drawing a liori- 
 zonlal lino tlirough tho centre, dividing this horizontal lino into 
 tho projier number of parts, iind drawing lines through tho points 
 of di\ision towiirds the vnnisiiing pnint nf t!ie t;ides out by tho 
 horizontalline. Thus if an oblong be rniuired its sides to bear 
 the ratio of 4 to 5, construct a .sipiare the sides of which will 
 represent 5, divide the horizontal line into five equal parts and 
 draw a lino through the fourth division as shown in Fig. 0, whioc 
 abed is the oblong re(iuiied. Fig. 6 shows also an oblong the 
 
 sides of which bear tho ratio of 3 to 7. In case tho long sides 
 of tho oblong aro re(iniied to bo parallel to the! picture plaim, i)ro- 
 ceed as before, and through tho point (.i)wliero tho lino corns 
 sjionding to l> c, Fig. C, intersects the diagonal of the scpiare, draw 
 a lino towards tho vanishing point of tho sides cut by b c. 
 
 \ 
 
 1 
 
 \ 
 
 1 
 
 
 \ 
 
 V 
 
 -.-.,.. - ..... — • -^ 
 
 
 
 
 
 
 / 
 
 \ 
 
 / 
 
 \ 
 
 \ 
 
 FIG. 2. 
 
 The square may bo used as tho basis of tho equilateral and 
 other triangles, and several of tho polygons, so that tho pupil will 
 do well to make himself perfectly familiar with tho wanner of 
 representing it. For tho present, howevei', it will bo necessary to 
 leave tho representation of tho square when none of its sides are 
 jiarallel to tho picture plane, as the student would not understand 
 it thoroughly until after tho perspective appearance of the circle 
 is under.stood. 
 
 The perspective appearance of the circle follows the same rule 
 as the appearance of the .siiuaro, that is, wdien in a plane perpen- 
 dicular to the picture plane and which contains tho centre of vision, 
 it is represented by a line, audits apparent width varies according 
 
 Ex 
 
 and p 
 opposii 
 the th 
 longest 
 sides u 
 
 ExK 
 
 two side 
 the othc 
 eacli sqi 
 
EXEKCISE 1.— Draw tliron squares, tlieir plaiies hein.' vertical 
 and perpendicular to tho picture plane. Show one a.s bein.' 
 opposite to the eye, another as bein^ to tli.! riirht of the first, and 
 the tlnrd us beiny to the left of the tirst. ' Mak(. the apparent 
 loiiKest^side of ea(.h about two and a half inches Ion- and two 
 sides of each parallel to the picture plane. 
 
 ExKHCi.SK 2.-Show tho appearance of acjuares in tho following 
 positions : — '^ 
 
 (1) Two sides perpendicular to picture plane, plane horizontal 
 on a level with the eye and to the left. 
 
 (2) Two sides paialh.l to picture piano, piano horizontal below 
 tho eye and to the right. 
 
 (3) Two sides parallel to picture plane, piano inclined upwards 
 towards the right, above tho eye and to tho left. 
 
 ( t) Two sides pel pcndi.ular to picture plane, piano inclined 
 Uownwaids towards the right, Ixdow the eye and to the left. 
 
 EXKRCISE 3.— Draw three squares, their planes being vertical, 
 two sides of each parallel to picture plane, one to tho left and' 
 the others to tiie right, eitlier above or below tho eye. (.'onvort 
 each square into an oblong. 
 
 oblo'l^'^s '•'- ^ -i.-Draw ill freehand perspective the following 
 
 fw/ilr?" 'u"T*';'' 'T««"'''« P'^''^"'"' to picture plane and 
 twice the length ot the short side.s, below the eye and to the 
 right. A1.SO show this oblong when its short sides are parallel to 
 the picture plan t^ plane is Jiorizontal, and it is above the eve 
 and to tho right. •' 
 
 (j2) PlaiH, vertic. ', to the left of the eye, short sides one-third 
 t he length ot the long sides and perpendicular to the picture 
 plane, tlic lower one of the short side* on a level with the eve 
 
 VA 
 
 I! 
 
 ■M 
 
to its (listaiiio from (lii:i ]il:iii(>. But one now fact in foniicctinii 
 wilIi till' linlci is, timt tlio transvcisn tw'v .if tlin clliiiso ri^inc- 
 siiiitiiiK It is itlii'ityn pcrpciuliculiir to tlin apparent diroction of (lin 
 axis of tho linlc, that is a liii(3 parsing tlu-oiij,'li tlioccntro jxt- 
 [XMuIiculir to its pliiic. Ilcnco wli(m tlio plane of a circlo is 
 111 lizontal, in wliirli pnsilioii tlii> axis is roprnsiMitcd by a vntiiiil 
 line, tlm traiiyvriKO axis of tlio ollipso roprosonting it is liorizontal. 
 
 This appears to ho a contradiction of tlio rosults olitalned in 
 some of tho prohleins and excrcisos in tlio book on Linear Per- 
 spootivo of this sorios, and to a certain extent it is. In illustration 
 Fig. 32, Book 3, tlio transverse axis of tho ellipso representing a 
 circle liaving its piano horizontal, is not horizontiil, and tho student 
 may with .some show of reason say that either the principles of 
 perspective as laid down and explained aro incorrect, or tlwt the 
 statement made in tho hvst paragrapli is false. 
 
 If the student refers back to tho book on Linear Perspective 
 and reads tho fourth paragraph of page 3, lie may perhaps bo 
 able to account for tho apparent discrepancy. When any one is 
 making a drawing of an object, his eye is fi.xed upon diii'oront 
 parts of it as his work proceed.s, and as tho direction of his gaze 
 is represented by the lino of direction, the line of direction is 
 being constantly changed, as is also tho picture plane which is 
 always perpeiulicular to the line of direction. From this it is 
 
 
 
 evident that tho only rays of light which render objects visible 
 for the puri)oses of drawing correspond to tho lino of direction. 
 .\ rule to bo deduced from this \a thai all vim<d rays muat pa»» 
 lhrim(/h (he picture plane at rhjhl awjlcn to it, lience a drawing of 
 an object will reipiiro the uso of perhajis a dozen or moro picture 
 planes, each oiio of which will contain the rcproseutation of some 
 particular part of the object. 
 
 m c 
 
 Strict attention to this fact, however, would complicate most 
 terribly a perspective problem, and for this reason it is assumed 
 that there is only one picture plane, that tha centre of vision is 
 llxed, and that any object lying within the field of vision can be 
 seen distinctly and be properly depicted upon tho picture phmo. 
 
 About the only way out of the difficulty is to consider the 
 picture plane to lie a curved surface, that is, the interior surface of 
 
 a sphere tlie centre of wliich is tlie spectator's eye, and the radius 
 of which is equal to the length of the line of direction. 
 
 In model or object drawing, in order to prevent distortion, the 
 object drawn is supposed to be always directly in front of the 
 spectator, and if it is not in this position, he is supposed to, if he 
 
ExRHrisK 5. -Show (Ih. appmraMc. ,.f tin- f, 
 (1) Slili'M as 2 to ;t, two shnitci- „i„.s panillol 
 
 pimio liorizonliil, iiliovn tlin t^yn to tlin ri.'lit. 
 
 (•J) Hides as I to (I, two slii.itcr oii,.s''p(.r 
 •■'■mn, piano vcrticiil, Iji'Id ■ 
 
 (M) Hides as 2 to 7, lo 
 111 tlio (lyi 
 to tlio riglit, 
 
 llowinj; ohloiiffs: 
 to picturo jiImic, 
 
 plan, piano vi.ti.-al, h.iow tlio ..y,, and't^ ii;:';^"''"' '" '''■^'"'■'^ 
 
 (.t) Hides as 2 to 7 lo,i„.r ones vcitical, piano indinod away 
 
 froiii tlio ,.yo towards tlio loft, contro on a loVul with the oyc- and 
 
 ExKlinsK f..- Show (ho dinVirnc^ in appcamnio between a 
 M|lian. and an ol.loiii; the sides of whieh n e as :\ to r> the 
 shorter ones l,ein« e,pial in l.Mi^th to the sides of the souaie.' The 
 panes of hoth are vei-tieal and two sides of oaeh a.v parallel to 
 tho pi.-ture plane. The squaio is to tlio left and the ohlonu t„ 
 he riKht of the r>e, its Ioi.k sides heinj; [.erpendieiilar to the imc- 
 turo piano, and both squaro and ohlong are lielow tho horizon 
 
 
iirlimlly (liii'M iinlr lucii hit lindy ivinl dniwiii;,' uintcriiils uri(il liis 
 liiiii <if (llii'i'lliiii |ia~ '■!( lliiuii;^li HoiiiM i'(iiis|iicuciu!i \>A\t (if till- 
 ii)>ji'> I, t<\ Kit il' lliU i'iiii>ii"4 llin lino of (liii'iliiiii to lio ollii'f tliiiii 
 )i(ii'i/iiiiliil, 1 1, St III, |ii'i liii|m, liocvidi'iit, to lliii Ktiiili'iit rroiii tills, 
 tliiifc tlii'i'i. [h ihiiIiIiiK iilniiit, (lie (Inittiiii,' of an (ilijrit tiikcii liy 
 ilHidf, to iiiijlciidi lU liniiliiiii with ri'^;.iid to niiytliirifj but the 
 |iiitnro |iliiiiii, tliii' lili'ii of tlio Kizo and ^lositiiin of olijrctH is 
 fornii'd l)y i'oiii|i)irlnK (Im'iii with ono anolhcr and «itli iTi-t;iin 
 tliinf,"! wliirli mil IWimI, im tlinBiil'fnciMif tlio wirtli ami llu) liovi/.oM, 
 or, i>i olliKi' WiihU, willi n hnri/outnl ]ilani\ 
 
 It in I'viilnnl. (hilt n ciiili' I'iiniiot lio jilatrd so that om' of its 
 diiiiiii'd'i'U in lint |iiU'iilli'l wilh (ho jiicturo iiI.iik^, mid lliat (lio 
 (Uainrli'i', vvhii h U |iiihillri tu Iho iiictuiu jilano, uiiU'i rs iiu cliaiigu 
 
 in;,' tlio diagonalH of tho Rquaro, ih a\mvo or bolow tho ti-an«vnrHO 
 axis of (ho ollipso accMiidinj,' ns tho fiiclo in ri'|ircHi'iitc'd as licinfj 
 lirloworahovo tho level of tlio eye, tho tiaiisvorsti axis of tlioolli|isu 
 being ill tho Li'iitro of tho oIlipKi', biscirtini,' tho conjiiKato axiH. 
 
 This, togi^thcr with tho relative foii'sliorti'iiin^ of tho diaiiiet(TS 
 of tho ciiile, is shown in Viff. H, wliieh ilUist rates tho ainie.iranee 
 of coneeiitric einles. Tho diaiiirter A II, of the lar;,'est eiirlo is 
 divided into ci^tht ei|iial |iarts, and other eiicles aro drawn with 
 tlio s.uiio centre, their eireiiiiifereneea passin;,' tlir(in;,dl tho Jioinls 
 of division, if theso cirele'i lio horizontal one diameter of each 
 will lio hnrizoiilal, and they will bo in the same line. ,Su|ilios(( 
 this line to bo C />, then (' /) will eotitain tho iipparent loiii,'est 
 di.viiiiter of tho cinles and A /> tlm shorleiit dianietors. Tho lino 
 
 -h-^. 
 
 cv i 
 
 ■V^ 
 
 FIG. 
 
 of diieiliori nnlhiiliitllloiHn l<'iij,'th by foresli-irtenin;;, but only 
 by riiisiia ii( JIm diotmien from the iiietnro jilano. TliiJl di.-uiieler, 
 howiner, 1h Iiiil. rri|i|'eRenteil by tho transverse axis of the, ellijiso 
 representing^ the I'll'i'lo, llefereiiee to Fig. 7 will make it plain 
 that tho iippiireiil. widest ]iait of a eirelo or a Bjihero is a little 
 neiir"r to tho eye (liiiM tho centre, and it is this apparent longest 
 lin»(^'/', ||'i«, 7l which is paralli'I to tho picture piano that is 
 rejiresenteil by the liiitisverse axis of the ellipse. It will be seen 
 that tho leliidui leiitjilis on the picture piano of A /i and CD 
 are a b ami e il, llnulianieter A H appearing the shorter. 
 
 The fact that (ho triiii'iverso axis of an ellipse does not corre- 
 spond to a di'iiiielei' iif the eirelo it represents, can be proved by 
 drawing a bi|iiiiiii containing a circle and representing both in 
 lierB|iectiui. Tliii petBpectivu centre of tho circle, found by draw- 
 
 A li will be divided into eight parts all uneiiual, while the 
 divisions of C D will be eipial. 
 
 Let H V represent the jiosition of tli<! eye of tho spectator, 
 P P till' iiicture plane, L I) tho litu? o? direction, .and yl Vi with 
 the divisions 1, 2, 3, 1, 5, (i and 7, the diameter, A /I, of tho largest 
 circle periicndicular to the picture plane. Tho rays of light pass- 
 ing from tho points 1, 2, 3, I, etc., in A /I to .S P, cut the picture 
 ).lano in tlio jioints 1, 2, .'1, -1, 5, 6, 7, /> which give tho perspective 
 positions of these points as compared with A, The divisions of 
 A /i decrease in si/.e as they approach b. Tho point 4 iiuliciitus 
 tho position of tho centre of the circles as compared with A and 
 6. As stated before, tho transverse axis of an ellipse bisects the 
 conjugate axis. Thus tho transverse axes of the four ellipses in 
 (juostion will 1)0 midway between A and b, 1 and 7, 2 and G, and 
 
ExKnfMSR S. -Show Ui<. iippfliimnrn „f a ciicl.i toii.liiri" tlic 
 
 picturo piano l)..l„w il y,., i(.s ,,|„„,. IwiiiK liDri/.ontiil. Mak.- 
 
 its iippuifiit longest (liiiinrtiT about tliiiu inclicH lonff. 
 
 ExKW.'iSK 9 — Two circles of tlm same nizo gtiuulinj^ upiiglit 
 with tlii'ir i.laiu'a pnrpondicular to tlio picturo plan.-, oiin touclicH 
 lli(! pii'luri^ piano, and tlii^ ifiitro of tlio otlirr i.i twiin tlm icnj^tli 
 
 <'f lliiiiliiinii'tiTaway fi tlm ccntro of tlio noarrr linlo, in a 
 
 linc! p..rp<'niliiular to the pi.tino jilano. liotli cird.'S aro to tlm 
 ri«lit with thi'ir ccntrivHoa ii 1i.m.| with thncyi'. Kiml ||i,.jr rcju 
 tivo sizeM ami jiositions, >;iippoHinj,' thrir ilianii-t.T!i to !«■ twoiuuhus 
 li.nL'. 
 
 ExKKCiHH 10.- -Draw in jicrspootivo a cirtio abovo tho oyo and 
 to tho left, its piano Immoj,' piirponditular to tin! pittui(^ piano and 
 inclnicd upwards towardn the rijjht. Mako tho tnuisverso axi.- 
 of tlm ollipsc at hiast three inches Ion),', and show by a point the 
 position of tlm L(Ultro of thi; circle. 
 
 ExKHClsB II.— A circle has its piano at an anKlo of 4r)' to 
 'Imlino of direction and vortical, its controls below tho oyo to 
 Im right. Whow its appearance, and in it draw two coiiccutric 
 ■ relo.s. 
 
 :! !i 
 
 i 
 
3 and 5 rosprotivoly. It will bo son, therefore, that the trans- 
 verse axes of the clitrerent ellipses wil' not bo in the sanio lino as 
 might be supposed, but are se)iiirate from one another, the axis of 
 tlie smallest ellipse auproaching nearest to the perspective centre 
 of the circles. 
 
 lA 
 
 \] 
 
 \j' 
 
 FIO. 9 
 
 Fig. shows a number of circles when their planes are vertical, 
 »nd Fij;. li) shows a number of circles when their planes are 
 horizontal, 
 
 
 J 
 
 <z: 
 
 __ ~> 
 
 ^, 
 
 .. ^ 
 
 
 •C- - 
 
 
 c 
 
 FIC 10. 
 
 In drawin)^ the ellipse it is well (o comn.onco with the trans 
 verse and conjupito axes at right angles to one another, and on 
 them set otr from the centre, half of the apparent length and widtli 
 of the ellipse. The curve can then be drawn through tin' four 
 
 10 
 
 points thus obtained, taking rare that the ends are neither too 
 sharp nor yet too much rounded. 
 
 .0 
 
 r 
 
 two 
 plan 
 
 fl'OIl 
 
 FIO. II. 
 
 Now that ho circle lias been dealt wi^h, the student is in a 
 position to understand the manner of representing the S(|Uare 
 when the sides form angles other than 90° with the picture plane. 
 
 E] 
 
 plane 
 sides I 
 and il 
 
 FIG. 12. 
 Supiwse a sipiare to be placed in front of the eye its 
 
 U 
 
itlior tno 
 
 Ex-ISHCISI.: 12— ShowtJ,,, piTspwtivo aj.iM.ai-.nM;.. of a square 
 
 piano and all fo„r suies of whiH. aro l.onzoiital. Its cenf o is in 
 iiont of spatr.tor and bolow tho eye. 
 
 KxKiicisK l.i. -Th.' sides of ail ol,l,m« an^ as l to fi tl.o 
 n,,,'.r oM(..s „.tniM« towar,|,s tim rigl.t at an auKlo of al.nn't HO' 
 to (ho h„o of direction, it is in front of and above tlio eye, its 
 plane being lioiizoutal. Show its appearance. 
 
 M 
 
 it IS in a 
 B S((uarp 
 re plane. 
 
 ExEunsK 11.. Rep„.,,.,a the oblong of Mx,.rcise 13 when its 
 plane us vertical and perpendicular to the picture plane, its orte 
 
 "i.d It 1. to tho left of the eye with its centre below the hori.on. 
 
 lAKurisK l;..-A.s,,ii,arois(.elow the eye and to tho ri«ht ■ 
 
 wa ds the right, and two sides form angles of about 35' wit 
 the picture plane. Whow its appearance. 
 
 eye its 
 
 li 
 
Jilano lioiizontal, two sides paritUol to t)in picture plane, and one 
 side in a vertical piano containing tlio lino of direction, as 
 A Jl C D \n Fi^-. 11. Iniajjine it now to be turned about tho point 
 A so that its sides shall occupy the dill'ercnt piisitions indicated by 
 the letters yl /y C and /). Tho side ^1 li is in the picture plane 
 in the first position, and is perpendicular to it in tho last jiosition, 
 while tho side A D which is )ierpendiiulnr to the picture piano in 
 tho first position is in it in tho last pusition. Tho sides A li and 
 A D l)eing rotated, each trace ii (piadrant, and these (|uadrants 
 fonn a semicircle, the rndius of which is cijuiil to the side of tho 
 square. 
 
 c 
 
 }.:,. 13, 
 
 If tins Kciiiicirrlo wi're re|ires('Htcd in pers|i(Tti\e it wonM 
 appear as shown in Fi;;. 11, and tlic! ends of two of the sides of 
 each Bipiare would b(! in its circunifercnce. In its circumference 
 select any point, as 4' or /)", noting whether it is aliov(! or below 
 the dia;;oiiiii <i c, and if it is below, as //, mark a point on tl"' 
 other side of the semicircle above tho diagonal, as d'. If the 
 point currrspoiiiiiiig to // ia in the dia;,'nii:il on the m\n sidi^, thi' 
 point corresponding to d' on the other siile must be in the diagonal 
 also. Having olitained two sides of the siiuare, the others can 
 easily bo found by lines diawn towards the proper vanishing 
 points. Fig. 12 shows a number of squares in cUll'erent positions 
 
 xa 
 
 ilrawn by means o. inis rule slightly modified, that U to NftV, tllfl 
 stjuaro is supposed to be enclosed in a circle. This cirelo Is (liuwn 
 first and its centre marked a littlo to one side of tliu traimvel'se 
 axis of the ellipse, according to the position of the elrelo, In 
 the curve of the ellipse select any point, as (i, and from i(. dl'ilW a 
 line through the perspective centre of the circlti. 'J'hiM llliii will 
 be one diagonal of the square required. Next noticn whethci' 
 this point, n, is nearer to tho transverse or coiijiigiilo n sin of the 
 ellipse. If nearer to tho transverse axis, thi^n maik a polMl, A, 
 nearer to the conjugate axis on the corresponding side, itiiil from 
 h draw a lino through tho perspective centre of tho eirejo to cut 
 the curve of tho ellipse in d. Join a h, b c, c it anil i/ ii, 
 
 In order to make uso of the S((uare as a ba>iis for tile repre- 
 sentation of the isosceles or equilateral triangle, the cii|i(-re ipf (he 
 
 \ 
 
 {) 
 
 L -\ 
 
 I 
 
 1 1 
 
 FIQ. 14. 
 
 sciuare must be found by means of tho diagonals and tlnoiiyli (he 
 centre a diameter drawn from the side correspondini; In the base 
 of th(! triangle. Of course it is necessary first to plino flioFiqniirn 
 in such a position that one of its sides corre,s|ionda to the dil eel inn 
 of tho bas(! of the triangle. On tho diameler iliinvn, iiiiirli ii. 
 l)oint insidi! the square, or beyond it on the diameli-r in'oiliiriil, 
 which will correspond to tho vertex of the triangle, and iojn (his 
 point to the extremities of tho base. It will bo well Hniiiellines 
 to draw l.'oth SqUiire aii>l triangle geometrically, n.-i in the easn of 
 the equilateral triangle, in order to find the position of the Vertex 
 with regard to the side of the sijuare. it will be foiiiid by 
 expcrin'ent that the altitude of tho eipiilateral tiiangle j ntbiait. 
 I of tho base, and iu drawing it the diameter of the Nijuaio may 
 
halfofthohei,htof th.wall. ll„p,.esent i,. t.f ^ o It .vdl ^0^;^^^^^^^^ . Spoctatc-s height is one- 
 
 Liic wau .1, rcuUiigular door and two circular windowa. Mako the drawing 
 
 about seven inches in length. 
 
 Exkuci.sk 1 (.-In the roof of ,i slicd inclined upwards to the 
 left at an angle of about 1,V with the ground, and the horizontal 
 erlgesof which form an angle of alwut 4.V with the picture plane 
 IS a circul.ir opening. The roof is square and to the left. Tlie 
 ryo of spectator is supposed to bo a little distance Ih'Iow the lower 
 edgo of th.! roof. Show th(> roof and opening 
 
 ExERCISR. ]«.— I'our posts are set upright in the ground so aa 
 to enclose an oblong, the shies of which are aa 5 to 8.°Tlie length 
 of the po.sts above ground is two-Hfths of the lengtli of the short 
 of To" .''"^ °''''"1S; Tl.e long sides of the oblong are at an allgL 
 One to th(. picture plane inclined ,away towards the right. 
 One corner o the oblong is opposite to the eye and the eye is one- 
 half the length of the posts above them. Show the position and 
 appearance of the posts. 
 
 -1 H 
 
 13 
 
 ii 
 
be divided into oi^ht parts, as explained in oonuoctioii with the 
 drawing of the oliionj;, and the seventli division joined to the 
 extremities of tlie base. In the case of the right-angled triangle, 
 ioin OIK. of the sides, produced if necessary, to the extremity of 
 the adjacent side. A scalene triangle will not often be required. 
 Fig. 13 shows the metliod of drawing triangles of difl'erent kinda 
 iu ditTereiit positions. 
 
 FIG. 15. 
 
 It is necessary to draw the polygons geometrically, enclosed in 
 squares, before proceeding to represent them persimctively, so that 
 the positions of their corners as compared with the corners and 
 sides of the square can be determined. In the ease of tlie 
 pentagon, Fig. 14, it is seen that two angles are in the base of 
 the square, one in each of the right and left hand sides, and one 
 in the vertical diameter a little distance from the upper e.xtremity. 
 
 14 
 
 In the perspective representation, unless it is obtained by the 
 rules of perspectiio worked out as explained in the book on 
 Linear Perspective of this course, it is not supposed to bo mathe- 
 matically correct, as the jioints must be delernuned by judgment 
 of the eye alone. Too exact rules for liiiding them would only 
 uiniecossarily hamper the situdent in his work. Illustration Fig. 
 14 shows how the pentagon would be represented, and where the 
 points corresponding to A BCD and A' would be placed when 
 the pentagon is in dilTerent positions. 
 
 In the case of the hexagon enclosed in a square it will be seen 
 that its centre coincides with the centre of the .square, and that 
 
 FIG. 16. 
 
 two of its angles, /''and C (Fig. 15), coincide with tlio extremities 
 of one of the diameters of the S(|Uare. If the hexagon be 
 enclosed iu a circle the circumference of which will touch each 
 of its angles, and each of the sides of the square, and if E and A 
 be joined to the centre, //, of the hexagoti and JH and A be nlso 
 joined, then K A will bisect /'// in A', and similarly 2). /i will 
 bisect lie in L, and FC will be divided into four equal parts, 
 and the points A' and L will be the centres of the oblongs a dejf 
 .ind b c ef respectively. 
 
 This geometric construction will make it easy to obtain the 
 perspective appearance of the hexagon iu any position. First 
 
ExERriSK 19.— Draw in porspcctive an oquiliitcrnl tri/uiglc, 
 one side of wliicli is parallel to the picture plane, its iiliuie being 
 honzontiil und below tlie eye and its vertical angle to the left. 
 
 ExKRcisB 20. -Show the siinie triangle when its plane is verti 
 ciil perpendicular to the picture jilane niul to (lie right of tiieeye; 
 one .side being perpendicular to the picture jilano and its vertical 
 angle being above the level of the eye. 
 
 ^ t 
 
 E.XKKCI.SK l!l.— An isosceles triangle the ba.se of wiiich is one- 
 fourth of the altitude lies on the ground with its base inclined 
 towards the left at nn arigle of -10' to tiic i)icturc plane. The 
 triangle is opposite to the (•y(\ Show its appearance. 
 
 E.VKRCLSE 22.— Show the appearance of a right-angled tri.inglc 
 its plane being horizontiil, above the level of and in front of the 
 eye ; its hypollienuse parallel to the iiicture iilane and its .sides as 
 3, t and .'). 
 
 ill 
 
 ift 
 
tlio square with its diagoiKilH and tlio diiimetcr i-om\siioiidiii;,- to 
 / 6', and the enclosed ciivlo must lie represented in the jirojier 
 position. Then, if two sides of tlie hexiif,'on iiro piiriUlel to thi; 
 pictui-o pliine, divido the di.-iineter /c into four e(|iiHl parts and 
 through the points of division draw lines towaids (he vanishin" 
 point of a d and h c to cut the curve of the ellipse in a W d' and 
 (• , and draw lines joining tlio six points thus obtained as shown 
 in iMg, IT). 
 
 \i two sides of the hexagon aro not parallel to the picture 
 plane, having drawn thes.ni.ire and circle in thc! proper position 
 as explained, draw (ho diameter eorri'sponding to m n. (Fig. 15.) 
 
 FIG. 17. 
 
 J«ext draw the diagonals of tho oblongs nhko iu»\ Inom to 
 find their centres, and tlirougli their centres draw lines towards 
 the vanislnng points of hk and Im to cut tho curve of tli.! 
 ellipse. _ Tho positions of the six angles of tho hexagon will thus 
 be oljtained, no matter in what position it may bo placed. Fig. 1 5 
 shows the hexagon in jiositioiia other than those referred to. 
 
 The octagon may be treated in two ways, as shown in Fig. 16. 
 It may bo enclosed in a sijiiar-c^, or two equal scpiaics, so placed 
 that tho diameters of each are in tho diagonals of tho other may 
 be enclosed in a circle. Tho portions of the sides of tho squares 
 lying between the points of intersection of their sid.'S form an 
 
 IG 
 
 octagon. Til using the lirst method (he po.sitiong of tho point-, 
 a, /(, e, d, (>tc., aro determined as in the case of tho pentagon, that 
 is by judgment of tho eye, lience tho result is, perhaps, not k.> 
 (■xaet as that obtained liy using the second method, by means of 
 which a somewhat exact result can be arrived at. Tho best way 
 of proceeding is to diaw in the proper position a K(iuar(s the 
 di.iineter of which will coi-respond to tho diameter of tlui octayon 
 reiiuired, and enclose it in a eiich;. Next draw the diaiiKUeis 
 of the square, producing them to touch the eur\e of the ellipse 
 and join tho points thus obtained. 
 
 It is not considered necessary to deal with i\\<: manner of 
 representing any of the other polygons, as they will very .seldom 
 
 f:c \i. 
 
 be needed, and if they are the student will, no doubt, Im- able to 
 modify some of the methods already expl.ained to suit any case 
 that may present it.self ; or ho may exercise his ingenuity and 
 originate a method of his own. 
 
 Tho ne.xt step will bo to uso the geometric planes mentioned 
 111 tho preceding p.iges, and convert them into geometric solids. 
 
 Coinmenemg with the .sipi.'ire ; wn may bp supposed to have a 
 combination of six s<iuares to form a cube, or of scpiares and 
 oblon.-a to form a parallelepiped, of .squares and tri.ingles to form 
 a prism, or of a square and triangles to form a pyramid. These 
 most coinmou combinations in which the square is present will 
 
ExF.uciSK 23. - Draw in frooliiinj porspprtlvo an isosceles tii- 
 iiM,','le, its altitude lieiiif; tUvrc. times tlie length of the l)ase, its 
 piano heiof,' perpeiidiiMilar to the pieture piano and inolined up- 
 wards towards the- left at an nULjle of alinut GO" to the ground. 
 Its base is in the ground plane; below the eye and to the left. 
 
 RxRucisK 24.— Slmw thn appearance of a right-angled trian'do 
 Iho .sides containing the right angle being a.s 2 to' 4, its piano 
 henig vertical and at an angln of about 4.")° to tho picture plane, 
 one corner of ba.^^o ojiposito to and below the eye. 
 
 E.\-F.RCI.SP. 2."i.— Draw in perspective a rogidar pent.agon, one side 
 of which is parallel to both picture piano and ground ))lann to the 
 right of ,and slightly above the eye. The plane of the pentagon 
 is liorizoiital, 
 
 ExERCLSE 26.— Show the appearance of f lie pentagon of last 
 problem when its plane is perpendicular to the pictuio pliino and 
 inclined upwards to the right at an angle of about 4y to the 
 ground plane, one of itn sides being parallel to the picture plane. 
 
 ! H 
 
 i H 
 
 17 
 
present no ililllcuHy to the student if lio lias nmile himself familiar 
 with the representation of tlie square in all positions, and he will 
 
 FIG 19 
 
 readily umlerstand the drawings in Fig. 17, whith represent four 
 tubes in diireri'nt positions. 
 
 IIG 20. 
 
 Illustration Fig 18 represents a square pyramid in four posi 
 tions.^ The only thing in connection with it that may appear 
 
 dilUoult is ti,i' posKion of the a.xls. U .'^liould ahvavs bo iicrpon- 
 (lirular to IIk? triuisvcrsc axis of the elliiwi! wliicli would represent 
 a circle containing tlie bn.se. 
 
 In Fig, I!) are shown a number of parallelopipeds. It nmv 
 perhaps, occur to tlie student that a cube and a parallelepiped 
 li.ivmg square ends, may be placfd in such positiims that the 
 aj.parent width of their sides will be the same, and lie may wonder 
 
 FIG. 21. 
 
 if there will ho any difleronco in their representations. The only 
 <li«erenoe will be du,. to the f,act that the far end of one is nearer 
 to the eye than the far end of the Cher, and will appear larger ■ 
 therefore the edges of the far end of the parallelopided must be 
 made smaller proportionally than the corresponding edges of the 
 cube, or, m other words, the retiring edges of the parallelepiped 
 
KxKHcisK 27.-A I.RxM.-on lira on tlio j^round with ono of ils 
 sue. parallel to the pictiiie plane, fts eentre is in front of spec- 
 tutor. Show Its appearanco. "^ 
 
 ;k, ,? r ' -^— ?';'"•' '" freehand perspeotivo a regular oet.ison, 
 vtB plane bemg vertical and at an angle of 45" to the picture plane 
 I«o sides ot octagon are parallel to the picture plane and its 
 centre is in the centre of vision. 
 
 Lm.i.< l.s... _.S .Show a regular hexagon, when its plane i. i„. 
 chned downwards iron, spectator, two .side.s being parallel to tin- 
 picture plane, Its centre being above the eye ,uM lo the rl d 
 
 E.XEKCISE 30._.Show an octagon when its plane is inclined 
 upwards from spectator at an angle of about 30' to the ground 
 One corner of octagon is resting on the ground in front of spec: 
 
 i» 
 
must convoryoinorpabriiiidyt hull llirmiMif tlin ml jr. Tlhisl rations 
 antul/i {l'\^. 11») inalin IIiIk clcir. l':Niii'rini'>:it will satisfy tli(i 
 Ktudi'iit tliat till) {greater tlio (lill'iToiU'O in liMi'^'tli lictwrcn tlici 
 rili,'i'H of tim ni'ar ami far riul of a parallrlDpipcd tlin grcati'i' will 
 1)1' its apparent liMi^'tli. (Sen /> and c, V\^. \'.i.) 
 
 A tiiaMi;ii!ar pi'isni in four jiusilinn.s in shown in I'ig. L'O. 
 
 In Kif;. 'Jl art! shown tho (lill'i'i'cnt j,'i''iiiii'ti'io forni-i in whi<'h 
 th(> rirrlo is jiri'sent. Thry aro tho sphere, cylinder and cone. 
 In di'awiiijf tho cylinder or conn it is lu'cessary to reiaeinlier what 
 has iMM'n said coiieernini; the relalivo positions of tho axis of a 
 I'irele and the transverse axis of tho ellipse whieli represents it, 
 and also that tho transverse axis of tlie ellipse does not contain 
 
 le is represenlc 
 
 ''7 
 
 FIG. 22 
 
 the centre of the cinle. The axis of the 
 the axis of the cylinder or cone. 
 
 The lu-iiuipal coniliinations of polyf,'ons are the pyramids and 
 Iirisnis. In l•'i^'. 2J aro shown a i>cntas,'onal pyrandd, a he\ai,'oiial 
 |)yraiiiid and prism, and an octagonal prism. Tin; manner of 
 ilrawiiif,' theiii is .-ipiiareiit. 
 
 "Wliat has heen done thus far is but a course of projiaratiou 
 for the real work of object drawing, which is the transf.jrmation 
 of tho g(!0iiietric planes and solids into tho forms of familiar ob- 
 jects. This c<>!\'-e of pn'parafion i,s a'i neressftry to the student 
 of drawing as tli.^ jiracti.e of scales is to tho student of the piano- 
 i\irt<.', anil he need iicit liopo for any great ammint of success in 
 his work if he does not thorouglily iiiid<M'stand the explanations 
 uiude in ooiiupction with the representatioas of lines and jilaues. 
 
 In tIm practical nppllrafiou of tho kuowledgo of this subject 
 that tho Ktuderit is now supposed to h.no gaim^d, ho may omit'the 
 construction lines shown in tho forcLroing ougravings according to 
 Ids faiinliarity with tho repn>senl:aion of tlio forms introluced. 
 They aro Only guide lines and may bo dispensed with as soon as 
 the student limls ho does not nei^l them. 
 
 One of tho most useful jioiiits to remember in tho dnwinr^nf 
 
 objects is tho inannerof tning the cylinder in tl 
 of inclined planes such as the lids of boxes, the 
 
 e ri'prcM nialioiis 
 covers of books, 
 
 nc. 23 
 
 doors, nte. Suppnso wo aro reipiirod to draw a box with it.q lid par- 
 tially raised. It will bo seen at onco that the li<l in turning upon 
 its hingi'S generates a portion of a cylinder, tho outer cormu's of tho 
 ends of tho lid being in tho circumiVi'ences of tho ends of tho cyl- 
 inder, thus tho box may bo said to bo composed of a cube or par- 
 allelopiped and a cylinder. Fig. i;,3 shows clearly how a box may 
 be drawn in outline and finished, and also hi w a drawing of a 
 door may bo llni.sl.cd. In all such olijccis it is necessary to show 
 tho edge which swings as converging in the sameipoint ns thoedge 
 in which aro tho hinges and also to allow for the thickness of the 
 material of which the box or other object is inade when drawiny 
 the inside edges. 
 
sinmin « ,„. t ... ;;nMu„l n, front of thn oy,. wi,|, f;,„r of it. ,.d „ s 
 oH,c,vl a,ul four uf U. face. «t uu ,u„lu of i;," t,. th, pi .u ^ 
 
 KXM., IHK .!.. M,„u- ,,,|„.nr,n,.., of ,a l«r.,ll,.|„pi,„.,I. its 
 
 ot Its oMor,;. f,.,.,.H i„ a liorjiiont.-il i,|;,„o ,„„| its M.rti.'al fa.vs 
 :.t ,m an.lo ot .|.V ,„ tho ,,i,..un. ,,1,.,,... Its („,, f,., . i. h,.|o»- 
 till, vyc ,iinl it.s loiiy cilgus riHiio towaril , tliu 1, fl. 
 
 Kxniicl.sK :!ri.— A .s,|,i,uo ],yi,umd is lyinu wit), o,i« of its tri- 
 an..,l,u- f,ava ju ,. h',rizo„tal ,,lan„ atul tl,o vertical ,,la u c , 
 tan,.„« Us ax.s rotjrn.g towards thn ri.ht at n,. a,„l,' of ,h„ t 
 . to tl,„ ,,„K,,„ pi .. j^i,^, ij^ ap,,..aranco who,, tl,o (op o.I.m, 
 of Its biuso IS below tl.o oyo and also wlic.i tlio lower ' 
 biiso IS oil a levfl with tho ryo. 
 
 IT eil;,'u of till 
 
 ExKWisi: .it Draw i„ f„.,.|.and ,M-rspoctivo a Bphero, its 
 re,, ro bemy „, the l„ie of ,li,vetion, and show the lino of oontaet 
 of tho surface of the sphe,-,, with a vertical plane passing throuL'h 
 Its cent,-o and ret,r,n,i; („wa,'ds the ri-lit at an an^-le of 55° to the 
 pictuiv plane. 
 
 u 
 
Ill Ki«, 'ii In nIkiwii hiiw a |iiirallnlnpi|)('il uvy \m coiivi'itccl 
 inio II liiii'Mitii, I''Ih. LTi rIimws h.iw ,v |wirall<'lo,,i[„.,l mwl tri.ui;,'nl;ir 
 |iiiaiii limy l.» niiniM (id int.i u Ik.usi.. Tlio pr.ik of tlio Kinall 
 «ii1jIh ill fiHiil, U riiiiiiil \,y HHciMtiiiiiiiifjflio iciitrn of tlio lidgn 
 Mini (III. I'lhl).. „( ||,„ f,ni,t, (if till! lioiisi>, iiiid drawiiiifa vciticiil 
 liii. til. Ill iliii |,iH,.|. |„,iiii („ ,.|,t n, lino £,.,„„ ^1,0 (,.,.|,troof tin- 
 
 t\B 24 
 
 n.lati<liM.wii rmvinM (III. vuiiUliin • !„,|,unf tl„> lioiuuntiil linrs 
 
 111 lll.( hllll.a „t till, iMMIfl... Tim Wuilh of tlio f,Ml.l<) is lll.llk.Ml oil' 
 
 on lliii liiitiol' ilin mv.s, ivnil lines diawn from tlio points whcro 
 It. h|j|lnf{ii I'liiiii III,. fnvi'M to the point of intpiBpotiou of tlio 
 ''"'y "f "'" * II M"''l" «itli tlioiimii, 1 f. ])ooi-s, Mindows, 
 
 oil',, llliiy l,r' h.lllrd III |.|.MIM11T, 
 
 no. 26 
 
 III KiK, yfl lliK iiiiitincr of dniwing what iii;i\- lie supposed t.. 
 lio a primillv" cliiilr, in hIiowh, us al^o Iho nianiier of drawing a 
 luiiiiiioi) piiMi inlilo, Tho I'oiistniction of the cornrra of tlw 
 fiaiiiowoik on whleh tlio top rests is drawn on a larger scalo to 
 enalihi (l|,. IiIiiiImiiI to understand nioro clearly tlia sniivli- draw- 
 ing \»hieli i>, III, ton Hiiiall a Hoalu to show tlio triio positi. "ii.l 
 
 iippeiiraueo of all Iho lines that \ioulfl lio visihlo wit h Ihn tabln 
 ill tlio position iiidieatud by tho drawiio,'. 
 
 riG. 26 
 
 A coniinoii step ladder is illustrated in Vijr, 27 
 (ion of tliu inaiiiier of drawing it is Jiecesriaiy. 
 
 No cxplana- 
 If tho student 
 
 understands its construction lin will find nodillicu' 
 in:;; it correctly. 
 
 t y in reproscnt- 
 
H ,MiK N-.timln,,. ..„. .,!■ itsfHcTs linrixontal, ,u„ its , xi. 
 
 .111:; itH ttXKs \..itn.al luxl its Iju.s,- l«.l„w tli.. I..n,0 , • ,|... ,!,■,. ' 
 
 .ietttils at pleasure. '"""' *''? «'«"' "'"' "P'-"<1 '«* an angle of al ,„t HO" with tl.t top of tlu- Ik^' A., 
 
 .u.J™"drwe7?:;:;:.,?;;^:" ^■•■'•' «- «'— '^-ow-s ti.. ...t top ... nght ,.., ..u. ..d t.. uotto, .w.. „„.. i,.,. 
 
Til tlio draw 
 UouMintric t'orni 
 tlint the .st;i\ rs 
 
 iiig of a 
 to use, i 
 apjicar ( 
 
 barrel tlio py] 
 IS is sci'ii ill 1 
 <> lici'oiii,' nan 
 
 iiulor 
 
 ''ij,'. 'J 
 
 DWVV 
 
 is tlip most convonipiit 
 
 1^. It will 1)(. IKlticiMJ 
 
 as tlicy ajiproaeh the 
 
 HG. V£. 
 
 sides, and that llipir curves 
 
 are nioro nearly parallel to tlio outline 
 
 of tlie sides wl.ile tl„. 1 e A •' P"™"" totliooutlin 
 
 01 uie Mil, s, « |„ie the lines of those staves in front of the pye uj 
 
 FIC, 29. 
 
 ^tiJ'i;:^'^^,::^;^';,,';--'-;'----! ..-.win. 
 
 ^^ P iiiPi. . unes are not thi; same as ||„.y would he if 
 
 thoy were cylindrical ; they are in reality portions of cones and 
 
 -1^""'"" V exa lin^r;^ -il'ir- i^XhllSr " '" ''''' 
 
 app..ran^ of the handle when V^r^lLi^:::\i'Z';^.:^^Z^ 
 aiic at dillerent inclinations to the plane of the ton of „%, T 
 and the right haml drawing when i^is at an n.loTtW tli .n^S 
 
 f;b. 30. 
 
 i3 where the lino across the top of the mil i,.t,.,.c„ * *■ . 
 verso a.xis of the ellipse renresontiM th f """T'*^*''« f-^n^- 
 tl.m„«h this point o ii te "" n ^r h ^u'-'^ H '"" ^'""" 
 'liroetion of the a.xis of the hand lo wi n , " 1 "'" W'i>-e"t 
 of the elHp.,e .vproseiitinl;; tl,: ii;'" '^°"""" *''" *-"-««« -- 
 A w.iteriiig can, as illustrated in ■RiV on ;„ , , „ 
 
 the co„,hin,Uion of Cylinders and c^liSi^f'wm S r!?^'" ° 
 l.ractico m drawing. If it is reniemhered h t tim s„w ^ n 
 
 and ho s,,outare in a plane pe,ne„di,.„l, r , tl , r.l " '" 
 
 liiglhela,-e handle, no dilli -ultv need I o f 1 ^ ™ntain- 
 
 -.-.■eet for,,, of the Object wh^ii; :;;:;',,::,*:::'''' "' "*•*""« "■" 
 
 .s J^:'a:''::u:i;:S:^ '-l ::-";';--centrieeirc,e« 
 struction must ],e .inders.id lU,,! ir:!!,;';:,:":,:^ ^''"' ''^ "- 
 
 Pc 
 
 pris 
 a be 
 
ExKROlSE 39. -Draw 
 
 Position anil details ut ploasurc. 
 
 ;i cliair clos(j to it, oUurvii 
 
 ig tho i.ioi)f r i.roi)ortions between tho two objects. 
 
 IvxKm I..K 10.-^T)raw .a ,,an.lleloi,i|„.,l sup|.,.r(ini; a t,.iaM.M,lar 
 l.nsm and use it a.s the ^enn.et.ie basis of a sehool house. Kh w 
 a bell-tower lu front, door, windows and other suitable details 
 
 E.\ 
 
 Wioiiasio (l.-Slmw a,,.,rti. fastahva.s, 
 
 the nght and at an anyl.3 with the pieture plane, 
 balustrade, balusters and newel j.ost to suit the t.uite 
 
 isc'encliii^' towards 
 J''inisli the 
 
 M 
 
In iMg 
 l);iK('(l 
 
 ipoii 
 
 aif s.iowi, a iiiiiii1)iT of olij.'c)^;, (1„! fcrmscif wliidi 
 
 til, 
 
 :V2 s' 
 
 l>pfi 
 
 lows ililW 
 
 tll( 
 
 oro iniiv 1)0 coiivcrti'd iiiti 
 
 foiuicl tluit tl 
 
 10 so;it (if a 
 
 |ilo strai;;lit. hacked cliiiii- illustratnd 
 Jt will bo 
 between 
 
 o one Willi a eiii-ved bao 
 
 •ciiiininii cli.-m- is nsua 
 
 'ly 
 
 ■ny 
 
 the top of 111,. ba,,d; and tlio bottom of tlio le-s." 'J'lio supports fo, 
 tlio bad; f.ii-m also til, ■ two back l,.p;s, and Jiesides lu'luf,' curved 
 an- fai-tliei- ap/ut at tlio top than at tlio bottom. Tlio uTifinisiicd 
 
 AN 
 
 'o 
 
 / r 
 
 
 V 
 FIG 31. 
 
 oiitliiio of a eoiimioii round wooden arni-eliair shown in Fi". 32 
 will \>r. a useful exereiso in drawing,' objei.'ts fashioned in a hitlio. 
 Tlio pjitteriis of th,' ditl'en'iit parts of the chair are given and 
 should bo imitated as nearly as possible. A portion of a 
 ley of a chair is drawn in geometric outlin,', and in perspec- 
 tive showing how slight a change is nwi'ssary. Tlio dilFerenco 
 is that in oiio tlio liiii's representing tlio divisions bi'twoon tho 
 members of thi' turning aro straight and in the otiicr curved 
 2G 
 
 <jnaED3niIi 
 
 f-'^ttrrit of //-■■w>A r.m -fv 
 
 FIG. 32 
 front support of the arm on each side sli,iiil,l I 
 than tho others. 
 
 le iiiiiije hirjfer 
 
E.\EUfiSK.42—Dniw 11 h.iricl .showing it staiuliiM' oil cud wilh I Kxrucisi.- 41 \t,.l ,. .. ,1 
 
 its top below the level of th« n-o. J^-^ f^TT ''''''"''' ''''^'"'-'^^^^^ 
 
 •* I I""' ^^■'"•■" '^'-^'o«- tl"^ eye with its luimlie in an upright position 
 
 KxKUcisK If.— Make a iliawini,' of a wlieelbanow wheel with 
 four .spukes, its axis liiiny horizontjj ami helow the eye. 
 
 E.XKitcisK l.'i.- Draw a wooden arm chair in adllTiTent position 
 to that shown in Fig. :i:i, filling in details ac^o, ding t.. the patterns 
 given. 
 
 "t ; 
 
 27 
 
 :|: 
 
Tho who,.ll,arrnNv,Ilnsfatr<l !„ Fig. 30 h an int.rostlncc ol.joct 
 ■ IH a f;oo,l suhj.M.t 1,„- pntctico. It should 1„. drawn in 
 
 w?J« ;^i" ;• ".^o,. to tho ,^-n,„,;d a„d dos,.,. to ono another 
 
 where the wlif..! ,« attadu-d than at tho othor on.l, honco thoy 
 
 LeannRS of tho whool aro fonnod of two pieces of hard wood, 
 
 m,e he,n.t:,st.,nod on tho en<l of ea.h hamllo and having a holJ 
 
 nilHl thro„,j,d. It for tho r.v,.pt,ion of tho iron pin in the .mkI rf 
 
 lio hnh. I,,, front hoard is wid.M- at tho top than at the 
 
 iM.ttOM,, and IS rounded .slightly at tho top, .and it .and th., Irgs 
 
 on 
 hail 
 
 Vl,.*r,^,yj ^ tf.trri' 
 
 FIG. 33 
 
 
 wi have difToront v.anisliin.cr points and thHr v.nnj.hin.' point- 
 will bo holow tho_ horizontal l.no. The .^idos aro movable, boin- 
 hold m position in front by a Imnd of iron fastoniHl to tho front 
 l.oaru and tho IlhuIIo, and at tho b.rk by .a wooden cleat whieli 
 fits into an inai .<ioeket fastened to the liandln near the le.r Tin' 
 
 are supportod by iron brace.s, the position., of which a.'e in- 
 cbc.atoc. llio perspectivo outline given will be useful o t. 
 student ns it show.s how a dr.awing of a wheelbarrow should 
 
l^XKiicisK If).— Draw a (•oiiinion wooden puil when .sliindiii" 
 on a lionzoMtal siirfaco with its top I.elow tho cyo. Show the 
 liaiKJh! in any position. 
 
 E.\i:i!cis|.; 17.— Draw a flowerpot in an iiivjrted iHisiilon, ita 
 axis bcm'' vertical. 
 
 as lu 
 
 K^''as 'i^JiiWe!''""' " "''"''"^'"•'°"'' "^'"« ^'"' l'<^'-«P«'^tive outline and details of construction given in Fig. M. Make the drawing 
 
 J 
 
Tim objncts illiistmfrri in Fi^s. 3^ aiul 3-. 
 
 and soi-vo to sliiiw a few <if tl 
 
 1' llllUlllKTlUlll! COMlbi 
 
 firi" (ill farnilidi- oti 
 
 nations of tin 
 
 >» lig. io, infoduco tho cono; tlio saucer, un'brclla, clock an!' 
 
 fornird by twoooi 
 (■ii<Hlar and 
 
 IPS aiida cvlind 
 
 b< 
 
 w; tli(< libs of tlH^ ninbiella 
 
 I , . I'l-i'sentrd l)y iiorlions of oliiiiM's Tl... 
 
 l-iip represented >. one spun in a l^^th'e, and, after iL^fouUini is 
 
 FIG 34, 
 
 Ixittle introdiirn tho snlipi.p . .,,-,] tl,-i i,v . ii.ii , , . 
 
 cvlinder N„tl,;n 7 ,1 ," , ? '^'"J"'' ''""'° •'^"" ^''•^^'k the 
 
 ■ ■luinj, any of theni. 'J lie student «ill find tlieni all easv if be 
 l-yyttentionto their geometric construction.; thus th "ioolt 
 
 FIO. 35. 
 
 dmwn, may bo treated in the same way as the turned work in 
 the eliairs shown i„ Fig. .32. It n,,,y be- represented either wi 
 o w, .out tbe poree a,n .bade. Tl,e illustrution shows the fo 
 ot tlio burn('r and chimney. 
 
EXEKCISE 4'.>. — |)|ri\v, ti 
 
 om memory, a ooiimioi, coal oil laiiin. 
 
 ExKItcisE r.O.— Draw ,1 ciii, and sa 
 
 \i 
 
 
 ,.n.,';"sn;,;^f:;,:-Sr';i;^-- «"»-' 
 
 f™^"";5 it;,::;'^;:; 2» —' -" '"■ ' 
 

 n u •, Ubl.,, paper, mk bottlo, la.np and pons will, if the a „n be 
 
 1 n""'' "'"'y.' ?'"' "t 0""' tl'^ro is a speculation as to th^ 
 probable cause of the interruption. Tl,e cause n.ay bo su'.^st h1 
 
 y thearranycnient of the objects. If the lan.p L -mt ii:;,!, 
 p pers iyn.« xn confusion on the table and iloo •, tl e ink S 
 
 pset an, the mk sp.lled, the writing stopped in the n i^dle of a 
 
 uiouoiit tli.it death la tiio interrupter w 1 bo su.'.'cstcd No ,■„., 
 .jo.n groupn.g should be atten.pted unless to cart ou tho^dea of 
 i^^m^i-^t^^^r'"' '" ''""" Wropriatr'Tho i,: 
 su^t In , i a ?"" """*' «"'"'"'"'"fc '""1 then try to group 
 
 su.tablo objects ui such a way as to express it, even to one who"^ 
 
 
 .....w;M,i.,„ „ .,„^ »„:;;;: ti'a ,i J, :;t„;::';,,?,:;;;trr 
 
 f:g 38. 
 
 not cognizant of tlie feehng underlying it. The .-roup in such n 
 
 havenotlnng to do with the artistic form of a con'posftion It 
 
 and what to avoul as regards form, as an uninteresti.,- object 
 .nay be viewed so as to appear wll, and vice versa. Tn%°rh a 
 i'bw'V. n."'''"T''",'"' ''?""''' "J^"" ^'"' "'^^^'"'" ^^■'■i'-'' its principal 
 guen for the guul.n.ce of the .student, especially as the nature f 
 <heeon,pos,t,onre,,uires a special arr.u.gen>enLf it li e .V 
 
„.r- ''-'"- ■' -- -.-' ■'• • -,-, « .„..,.„„ „„,„,, „.„., „„„„^„„^ ,„,_^,^,^ 
 
 T.,.!Jsr,^:,j;::,;\szHr ::;;:'.!;:,;;;■£:;!;;:;'»' - "" '"»" ■ -' «»--,;;:;„„::,;:,„,::, , ■;;: 
 
 1 sparle. 
 
 33 
 
;„.;,' 'iMvaiOM, ,u„l no,,., of tl,r,„Kl,„„l,| l,n„>,l„lv 
 
 ao,.rt,„„,l,nrt,o„isc.o,n,t,.,-,u..,.,l l.y a li,„. or s.t of 1 " "?,, 
 
 u.^f:;;t"\:.f';i:;f':i;:i,:'t-';:;::,:;^ 
 
 .atisfactory thau wl,.u throe or four oly.xls J ::;!L\i^"Z 
 
 .'.|i;i((' .■ivdiliililn lirrn. vet a I'r.w ir.i i i 
 
 .. Mn.l,. wl,„.|, will K..m. to ^:^■.l.!.(lH.stnW,.n./ ,"h .t ii 
 
 It>nHyImstat,.,i;„thMirst,,laon tl.at, an old oLjoct is .noro 
 pi.:tur, s,|„o tl,,„, a n.Nvono of tho sanm l;i,„l, l.„ it a r,u| v • 
 tcrico, liouM., aiiiMial or man. Nature if „llow,.,I <n ^. . ' ' 
 
 though an ol)|crt w losn fonn ii i,l,..,^l„„ „.,ii i • ' ' ■'•■^"'^- 
 
 .00,,,., a„,i i.i a,iv,.n tilr^wv;::;:^; .^ •;:;;,!; i::^ 
 
 oi,.! whos,. f,„„, is not 1,1, ,. .sin-. Natuiv's «• ,iV 7c ' , 
 
 '-. su.ai„,t H„..s an./ I„.„a,,''n.ai:s ^f ^.W ', "i^l:'' 
 ;'.n„..-s.a,„l «,.„..,.„ ly to nn.lo ,1,., work of „„.,, a, .1 I , s rh t 
 3Mto harmony w.th her own productions. Th,.-,, is no uc thing 
 
 
 Sn^^'cLlt!;.""'"'"'"'^ *^ ''-''« -'-" -- S!v,.s .,„ 
 T„s,„„ up the hints givr,,, wo havo appronriatenrs. s, s 
 
 no. 37. 
 
 as lack of harn.ony in X„( ,„,-, ,,,„l ,iij J.erforcrs ..rr^ni to I,o l.rourrht 
 to iM'ar upon outsid.) ol, ..cts to inako t!„.„, ■.,,„.,ll„ i """ght 
 
 to for,,, a„,l ,.olor. ]!,..;!„l|y la" JW, , ' ' S :":""""""^ "^ 
 .I-ay, and it will I,., i..st^uctivo 'to «,k :;; "s -.v'Sr^ 
 
 :^nho=-^--;-;-:-^^^ 
 
 I'|'rid.,a,lar. It n,ay ho that ono of tho ,.n,ls of tho ,u i,?, ^'n 
 
 of ■t'^pt Thl/r ■-r^.i-s' o^;h;;^:!,[:^i 1;"^ 
 
 corn..rs will l,e Hkoly to n,ako irn-Zular trans .,,.., ^ !['° 
 
 wall, if they arc n.adoof bnck or JJo.^.ffi ul^.^r':;^ ^^^ 
 

 FIG. 38. 
 
 shingles are broken, some of them are torn off tim r«nf • 
 with moss, tufta of m-,i.« „,.„ „, • . T' *"" '°°^^^ "ovei i 
 planter falls from tl e^wal s t he d Z"ff ll'^f "'" ^r^' -'■•""«'-' th„ 
 as ti„,e elapses, the ro^f and w,rr-^''"'" V"'"" '""«'''^' '""' 
 but a heap of rubbish to be nT ,t *^"*' "".^ '""' """""« '« '"f' 
 until it is'hidden frSm vi^w ^No or wS^ «""'""' ^""i"- 
 
 almost hv„h°r'f picturesque, surrounded 
 nit TL^ '''''° ?^ '^"""ice. A tattered and 
 patched garment is more picturesque than a 
 n«^ or a whole one. There is nithing p,!^ 
 
 IZ^^f "^^V'i''" "''«^"* '^'^^'-^ displaced 
 upon a ta,lor'a dummy, but the ragged liule 
 urch,„, old m experience, who looks longingly 
 u"'?- '^ P'St"'-'=«q"e- Instances might bo 
 mul ,phed of the eflect of age on ob Ictr 
 Contras a man old and poor, havingXhe 
 marks of age and poverty u^on himf with a 
 nmn young and well dressed ; an old ^on^^out 
 
 with one fresh from the shop. 
 
 Age seems to invest an obiect with ,-ot„„„„t -c . . 
 case with beauty and it with ^ I interest, if not in every 
 
 lines of a drawiiic in or,W t7 •'"'''' "^ *° ^°^ *■" ""«■■ the 
 
 ^ '"•"wiiig in order to change Us character. The student, 
 
 the proper linos i." thod aw nrnft^ ''"■*'.''*'™ °'" '«"«*»> »' 
 
 ThoSicconipany r m irat.V M "r"'"";'" «"'"'- "mployod. 
 the n.att,.r cleir if' ^ro " at' H a v In T ''r^ '' ,'""'? *" '"»'"' 
 «hows how breaking up t ol 1 «'';,« fn- '^'^TY ^i^- ^7 
 provo a drawing, an I Fi.-s 38 1 T 1 l'^ ''""'""' ^'" '"'- 
 
 hostillfurthorlmprovodlwhr .t; IT ^"^ " '''"^^'S "'"/ 
 
 direction of sonie o7ZtI^HH!:«"il; td^rt''"'- ^'""'^^^ 
 fHcts, and the addition of detai s ,, , m,?, ^"f"""^ ""■'"'" 
 
 mentioned, such as tho braces to tm«^ nece.ss,vry by the chang.-s 
 it not for these last the obTect wou d hv^ '" ^'^'^ f " "'''"'" 
 pearance. The supports bcinH if V, ^ ^--^ «"pl«'vsant ap. 
 look as if ateut to fill over a d'th.f . P^'-P""dioular make it 
 does it not fall? wSlt W^s ft t^'l^lni:™ "'''T-' ' " '^'''^ 
 
 -e^r;^!;:^^:^"::.^;;,-!;- ^>e-.o., an uneasiness, 
 the drawing in search of so^^^J^Z^"^ --'<'- .-hout 
 .^-hich cannot, p.-rhaps, be s„,vifh I T • "'t exist ,n it and 
 
 in something wanting Thii s , I ■ ',' " *"'''"'« '"'"t there 
 
 FIC. 39. ~~ "^ 
 
 produce a slight feeling of excitement Tt • 
 subjects to destroy repose fortleZ^- * "ecessary in some 
 or motion, as in agalC'ic hor 7"^ ?P'-'^««"'S excitement 
 of the excitement m- idea of moln ?' ^'"'f-' ^'''- ^'"^ «^'«"t 
 repose. "'°"°" "* P''oportionato to the lost- of 
 
THE HIGH SCHOOL 
 
 DRAWING COURSE. 
 
 TIIK FOLLOWINfi AHR THE HOOKS IN THIS COt'RSE : 
 
 I. I^^rcHauincl. 3.— Linear Porsix3ctive. 
 
 L^ Practical Geomotiy. 4.— Olvject Drawint^-. 
 
 5. — En d 1 1st I'i al Design. 
 
 Th.'... Ilnoks ,,rc fully illustr.itcul, and printed on heavy drawing paper. They are sold at 20 
 ' '11 n, at all bookstores. 
 
 cents 
 
 Hic Mechanical Draiviiig Course, 
 
 TIII.S (•OURSK WILL CONSIST OK Till': FOLLOWING BOOKS: 
 
 I.— Projection and Descriptive Geometry. 3.— Building Construction. 
 2.-^MacInne Drawing. 4.-Industrial Design. 
 
 5- — Advanced Perspective. 
 
 i" I'-.ll. of the above Courses, the trade will be supplied by Toronto Wholesale Dealer 
 
 in School Books. 
 
 lers 
 
 THE GRIP PRINTING Ap fUBLlSHItiG COJVIPANY, Publishers, 
 
 26 & 2S FRONT STREET WEST. TORONTO.