P.B R SFE C TIVE; 
 
 OR THE 
 
 ART OF DRAWING 
 WHAT ONE SEES 
 
 COLLINS 
 
EDUCATIONAL DEPARTMENT 
 
 OF THE 
 
 0 BLAYDON DISTRICT 0 
 
 f Jnbustrial an6 Proui6ent Society ® 
 
 0 0 
 
 O LIMITED. 
 

 
 
THE ART 
 
 OF 
 
 DRAWING WHAT ONE SEES. 
 
LONDON : PRINTED BT 
 
 SPOTTISWOODE AND CO., NEW-STREET SQUARE 
 AND PARLIAMENT tsTREKT 
 
Digitized by the Internet Archive 
 in 2018 with funding from 
 Getty Research Institute 
 
 https://archive.org/details/perspectiveorartOOcoll_0 
 
Hori^tontal 
 
 eye, C 0. being made sufficiently short to fib on the paper, 
 led, the drawing will assume a natural appearance. 
 
 
PERSPECTIVE 
 
 OR 
 
 THE AET OF DEAWING WHAT ONE SEES 
 
 EXPLAINED AND ADAPTED 
 
 TO THE USE OF THOSE SKETCHING FROM NATURE. 
 
 BY 
 
 LIEUT. W. H. COLLINS, R.E. F.R.A.S. 
 
 Late Instructor in Surveying and Miiitary Drawing in tlie Royal Military Academy, Woolwich 
 
 LONDON: 
 
 LONGMANS, G Pv E E N, AND CO. 
 1872. 
 
 All rights reserved. 
 
' V/'.'V'V ► ^ 
 
 ■(.. . 
 
 
 r 
 
TO 
 
 E. N. 
 
 I DEDICATE THESE PAGES 
 
 IN REMEMBRANCE OP ATTEMPTS MADE TOGETHER 
 
 TO SKETCH FROM NATURE. 
 
PEEFACE. 
 
 So MANY DEAWiNGS, otherwise pleasing and 
 effective, are marred by defects in their ‘per¬ 
 spective,’ that I need make no apology for at¬ 
 tempting to explain, in a simple and concise 
 manner, the few rules which must be followed, 
 either instinctively or with intention, before a 
 drawing can be a true picture of what it is 
 designed to represent. 
 
 Knowing that one is naturally frightened from 
 a subject the entrance to which he sees barred by 
 formal treatises full of geometry and ‘ propositions,’ 
 I have endeavoured to write as simply as possible. 
 
PEEFACE. 
 
 viii 
 
 and to bring tbe subject witbin tbe comprebension 
 of tbe most ordinary intelligence. Tbe novice 
 may take heart in knowing that tbe necessary 
 rules are few, and tbeir application easy. 
 
 In tbe bope tbat I may bave at least partially 
 succeeded in rendering intelligible, if not in¬ 
 teresting, a subject generally most unattractive, 
 I offer tbis volume to those who feel in need of 
 help in tbeir efforts to sketch or colour. 
 
 W. H. Collins. 
 
 June 1872. 
 
CONTENTS. 
 
 PAGB 
 
 General considerations concerning drawings . . .1 
 
 Drawings for natural elfect (perspective) , . .10 
 
 „ for architects (orthographic) . . . .13 
 
 „ for advertisements (isometric) . . .16 
 
 ,, for maps of the earth (stereographic) , .17 
 
 Details of perspective . . . . . ,23 
 
 Vanishing points . . . . . .27 
 
 Distance of the eye . . . .31 
 
 Criticism . .... 35 
 
 Facts ascertainable from pictures . . . .39 
 
 How to find the vanishing points . . . .42 
 
 Necessary peculiarities of the perspective drawing . . 44 
 
 To draw a square . . . . . .47 
 
 To ascertain the character of an original figure from its picture 48 
 The correct dividing of a line . . . . .50 
 
 Nature of our perceptions on looking at a view. . . 53 
 
 Procedure in sketching an interior . . . .57 
 
X 
 
 CONTENTS. 
 
 Vanishing points 
 Distance of the eye 
 The pavement . 
 
 The table 
 The picture frames 
 The divisions on the panelling 
 Common mistakes 
 Hanging of pictures 
 Eeflections in water 
 Moonlight views 
 Complementary colours . 
 Colour of the sky 
 Colours of sunset 
 Subjective colours 
 Colours of mixed pigments 
 
 PAGE 
 . 61 
 
 . 64 
 
 . 66 
 
 . 68 
 
 . 69 
 
 . 73 
 
 . 75 
 
 . 77 
 
 . 78 
 
 . 79 
 
 . 83 
 
 . 85 
 
 . 86 
 
 . 89 
 
 . 91 
 
 1 
 
PEESPECTIVE DRAWING. 
 
 The writee of the following brief treatise on 
 Perspective Drawing ’ has fonnd through an 
 experience of some length that an amateur, in 
 seeking to provide himself with information con¬ 
 cerning drawing from jSTature, is at a difficulty in 
 doing so. He stands between two classes of writers— 
 artists and geometricians, neither of which exactly 
 supplies his want. The artist’s eye and sense of 
 beauty are pained by anything like a formal ‘ en¬ 
 gineering drawing,’ and his treatise gives a wide 
 berth to rigid and exact rules, which here, as in 
 other matters, fence round the processes of Nature. 
 The geometrician is skilled in drawing at his desk. 
 He is satisfied if his figures embody the proof of 
 his propositions. He concerns himself more with 
 the proof than with the drawing. It does not 
 matter in the least how ill the schoolboy draws a 
 
 B 
 
2 
 
 PEESPECTIVE DEAWING. 
 
 circle on liis slate; his demonstration is not 
 affected thereby, and the truth of any problem in 
 geometrical perspective is independent of the ap¬ 
 pearance of the figure. Thus the geometrician is 
 careless of effect, and careful only of his demon¬ 
 stration. He writes for the scholar and his 
 examination paper. It may be that he has never 
 tried to take a sketch from Nature, and does not 
 know how far his theories may be made to furnish 
 rules for his practice. 
 
 ^ Beauty,’ ‘ tone,’ and ^ feeling ’ of a picture are 
 the terms which the artist loves to use; and if 
 familiar with the terms and definitions of the 
 geometrician, he is loth to perplex his pupils’ 
 minds with them. He probably thinks that the 
 rules for what he calls foreshortening ’ are either 
 inapplicable or too abstruse to be succinctly ex¬ 
 plained. He is more disposed himself to leave all 
 human habitations with straight walls and parallel 
 lines, and sketch in solitude, among rocks, rivers, 
 and clouds, where he will find his most beautiful 
 effects, than to concern himself with ^ vanishing 
 points ’ and ‘ points of sight ’ around some formal 
 building. He may not know that perspective has 
 furnished rules which in most cases can be 
 brought to bear upon his drawing, and by which 
 
FEEE-HAND SKETCHING. 
 
 he may be tried with no uncertainty, and by which 
 he may be either acquitted or condemned. 
 
 The writer of this short treatise thinks that he 
 may supply the want which many of his friends 
 have felt. He has endeavoured to modify and adapt 
 some geometrical constructions so as to make 
 them suitable to the amateur, and he has treated 
 of some general points connected with drawing. 
 He has touched but very slightly on the subject, 
 still vague and indefinite, of colour and composition. 
 
 Any drawing in which the lines are ruled has 
 an unpleasing and formal effect. Though the 
 lines may in reality be straight, they look more 
 satisfactory when drawn with the hand than with 
 a ruler. In the former case each stroke the artist 
 makes will carry with it his ^ touch ’—his ‘ per¬ 
 sonal equation,’ to borrow a term from mathe¬ 
 matics, and will render the drawing essentially his 
 own, and consequently it will carry with it a value 
 far higher than if he had traced it with a ruler on 
 a pane of glass. But even when done with his 
 own unguided hand, the pleasing effect is due to 
 the above cause, not because a discretion has been 
 .allowed in the direction of the lines, or that their 
 position has been varied at his pleasure. They 
 must be placed where they appear to be. No 
 
4 
 
 PEESPECTIVE DEAWING. 
 
 variation is allowable in their position. The 
 general objection to the engineering drawing is 
 not because the lines are wrong, but because (when 
 they represent ^ perspective,’ which they mostly do 
 not) they are ruled, and because no effect of light 
 and shade is attempted. Dr. Brook Taylor, an 
 eminent authority on this subject, makes the fol¬ 
 lowing remark :—^ How many pictures are there to’ 
 be seen that are highly valuable in other respects, 
 and yet are entirely faulty in this point (perspective). 
 Indeed, this fault is so very general that I cannot 
 remember that I ever have seen a picture that has 
 been entirely without it; and, what is the more to 
 be lamented, the greatest masters have been the 
 most guilty of it.’ The writer so fully agrees with 
 this remark that he is emboldened in his attempt 
 to handle the subject in a popular way, and make 
 it intelligible to those who dislike geometry and 
 mathematics. 
 
 Only two grounds for an opinion can be offered 
 with confidence—the rational satisfaction of the 
 mind that the opinion is just, and a credential in 
 the form of results produced by acting on the 
 opinion. Artists who have treated of this subject 
 have written in the latter sense, and their opinions 
 have carried weight, se, in proportion as their 
 
NECESSITY FOR CORRECT DRAWING. 
 
 5 
 
 pictures have been pleasing. The former is tbe 
 ground of the conclusions offered in these pages. 
 Drawing, light and shade, and colour are the 
 three branches into which the art of painting 
 divides itself. The two last are based upon the 
 first, and however little of the satisfaction afforded 
 by the finished picture is generally ascribed to 
 the drawing, if this is not correct, the other 
 two, however varied, are powerless to remedy the 
 defect which underlies the whole. If, on the other 
 hand, the drawing is correct, the others become 
 optional, and in a great measure please or dis¬ 
 please, according to the taste of the observer. 
 
 There are a few words which must constantly 
 recur in this treatise, and it is necessary that a 
 distinct idea should attach to each of them. As 
 a description of anything is being given—say, of a 
 piece of machinery, the listener ought to be able to 
 build it in imagination ; for each new line of expla¬ 
 nation he will add a new piece to it, and finally his 
 physical conception of the machine will correspond 
 with the existing one. It is desirable that, wlien 
 planes and lines are talked of, the reader should 
 build such an image in his mind that he would 
 have no difficulty in actually constructing it out 
 of cardboard and lines of thread. Such distinct 
 
6 
 
 PERSPECTIVE DRAWING. 
 
 conceptions should accompany the terms that will 
 here be described as simply as possible. 
 
 A ^ line ’ will be what mathematicians call a 
 right ’ or a ^ straight line/ or, in other words, a 
 line that has no bend in it — such a line as 
 is produced by folding down a sheet of paper. The 
 creased edge is a straight line. 
 
 ‘ Parallel lines ’ are those lines which, lying in 
 the same plane, do not meet even if produced. 
 Lines drawn on a wall would be lines in the same 
 plane. And if, like the tiers of bricks, they did 
 not meet or approach each other, they would be 
 parallel. The two metal lines of a railway, when 
 straight, are parallel, for they lie on the same 
 plane, and are always the same distance apart. 
 It is not sufficient that the lines should not meet 
 to make them parallel. They should also be in 
 the same plane. For instance, a road running 
 underneath a railway would never meet the rail¬ 
 way ; but here they do not run side by side or lie 
 in the same plane, and, consequently, though they 
 would never meet, they are not parallel. 
 
 A plane is a perfectly flat surface, with no 
 hollow or bend in it. It must be like the surface 
 of a plate-glass window. A vertical, plane is one 
 that hangs like a sheet suspended from a line. 
 
TEEMS EXPLAINED. 
 
 7 
 
 A horizontal plane is one that corresponds with 
 the surface of a vessel filled with water at the 
 same place. 
 
 ^ Perpendicular to ’ or ^ at right angles to ’ mean 
 the same thing. The candlestick is perpen¬ 
 dicular to its base and to the table. In the 
 ordinary position of the table its surface is hori¬ 
 zontal, and the stem of the candlestick is vertical; 
 but if the table be tilted up, the candle will still 
 remain perpendicular to the table, though the 
 table ceases to be horizontal, or the candle to 
 stand vertical. A cord hanging with a weight to 
 the end of it is vertical; it ought not to be called 
 perpendicular. 
 
 A line is perpendicular to a plane if it meets it 
 directly, and inclines to no side—as the stem of a 
 candlestick meets the base which it stands upon, 
 but this perpendicularity will remain, even though 
 the candlestick be laid upon its side, or held in 
 the hand. It is desirable that this distinction 
 should be borne in mind, for the terms ^ per¬ 
 pendicular’ and ‘vertical’ are frequently con¬ 
 founded. 
 
 An ‘ original ’ line or figure is the actual line or 
 figure which we sketch. Its representation upon 
 the drawing is its ‘ projection.’ 
 
8 
 
 PEESPECTIVE DEAWING. 
 
 The drawing of a line upon the paper is called 
 ‘ plotting ’ the line. 
 
 The angle which two rays converging on the 
 eye contain between them is said to be subtended 
 at the eye. 
 
 The word ^ data ’ is frequently used when any 
 problem is considered. It means all that is given 
 to us, or that we know for certain. Every problem 
 consists in trying to arrive at something that we 
 do not know from what we do. All that we may 
 assume as known is our data. 
 
 A ^ perspective picture ’ of an object is an en¬ 
 largement of the picture thrown on the back of the 
 eye through the pupil, and interpreted by the brain. 
 The perception of the object or interpretation of 
 the little picture within the eye is sight; and the 
 image itself, or an enlargement of it, is the ^ per¬ 
 spective ’ view, or that which was or might have 
 been seen or perceived with ordinary undistorted 
 vision. 
 
 Every object in Nature which is illuminated 
 emits from it rays of light in all directions, in 
 straight lines. That portion of these rays which 
 come from any object to the eye is called a 
 pencil. The eye only becomes conscious of the 
 presence of the object through the effect of these 
 
LIGHT AND ITS EFFECT, 
 
 9 
 
 rays emitted by it impinging on the sensitive 
 nerve witbin tlie eye. They must be considered 
 as much realities as telegraphic wires; they must be 
 considered as a multitude of threads running from 
 all points of the object into the eye. Before the 
 existence of these rays was known, people looked 
 upon light as a sudden consciousness of the presence 
 of things in the direction towards which the 
 eye was turned. They looked upon the eye as an 
 opening through which the intelligence had access 
 to the outside world, and by spasmodic inspiration 
 became aware of the objects before it; but this is 
 not so. It is now known that a peculiar impulse 
 is transmitted to the eye in a straight line from 
 every point of an object. Each line of motion 
 along which this impulse travels is called a ‘ ray,’ 
 or, when considered in. reference to drawing, a 
 ‘ projector; ’ and all drawings formed according to 
 some defined principle by these ^projectors’ is 
 called a ^projection.’ Any set of rays converging 
 on a point is called a ‘ pencil.’ If any of these 
 rays should happen to enter the eye, the object 
 is seen in the direction from which they come. 
 Those issuing in one direction do not interfere 
 with or obscure those issuing in another. They 
 cross each other in what might appear to be the 
 
10 
 
 PEESPECTIVE DRAWINO. 
 
 wildest confusion, and yet without jostle or dis¬ 
 turbance. Each one of twenty persons in a room 
 can see as distinctly as if he were alone, and yet 
 the pencils converging on their eyes may have 
 crossed in every conceivable direction. 
 
 Let us consider a square house, this being one 
 of the simplest objects that could be drawn—as 
 emitting rays from it in all directions. 
 
 Pig. 1. 
 
 And let e be the position of an eye. As is 
 natural to suppose, only those rays which fall into 
 the eye can affect it, and these must of necessity 
 be limited to the pencil converging on it. Other 
 rays striking out in other directions might meet 
 other eyes, but except those lying within the 
 pencil converging on e, none would reach this 
 
DETAILED EXPLANATION. 
 
 11 
 
 point. It is with this pencil perspective drawing 
 is concerned. It is so called from being the 
 natural representation of the object as presented 
 to us by our sight {perspicio —I look at). ISTow, 
 imagine a plane called the ^ plane of the picture ’ 
 held athwart the pencil of rays, and suppose the 
 rays to stamp themselves upon it, as they pass, 
 and we should have a perspective view of the 
 house. E is the point of sight or vertex, p is the 
 plane of the picture, c, where the central ray of 
 the pencil meets the plane of the picture, is the 
 ‘ centre of the picture.’ This point c is called 
 the point of sight by some writers on perspective, 
 but it will here be called by its true name, the 
 centre of the picture. As this point lies on the 
 paper, and is not the point from which the sight 
 is taken, ^ point of sight ’ is obviously a mis¬ 
 nomer ; E, the central ray, is ^ the line of sight.’ 
 
 The pencil of rays should be cut perpendicularly 
 by the plane of the picture, or in such a way that 
 the cone formed should be what is called a right 
 cone, as in fig. 2, not as in fig. 3. 
 
 In this way, standing before a pane of glass and 
 shutting one eye, the distant view may be traced 
 with a pen and is a true perspective drawing, but 
 care should be taken that the view should be direct 
 
12 
 
 PERSPECTIVE DRAWING. 
 
 througli the glass, as in fig. 2, not oblique as in 
 fig. 3. 
 
 Fig. 3. 
 
 This plane of the picture will in the following 
 treatise be supposed to be always vertical and held 
 as here described direct across the line of sight. 
 
 ^ Perspective ’ embraces all positions of this plane, 
 oblique as well as not vertical, but the require¬ 
 ments of painting limit us to the above simple 
 positions, and consequently free us from much 
 complication. 
 
 It is not necessary that all drawings should look 
 natural or pleasing. It will be seen (fig. 1 ) that of 
 the myriad of rays issuing from the house but one 
 small portion has fallen upon the point E. It is 
 quite allowable and frequently desirable that other 
 rays or projectors should be considered, or that they 
 should be conceived to fall in some other manner 
 
ORTHOGEAPHIC DRAWING. 
 
 13 
 
 than simply on a point. It wonld thus appear 
 that there may he many other kinds of drawing 
 besides perspective—and this is so. The architect 
 who designs a house must convey his idea most 
 accurately to the bricklayer and mascn who will 
 build it, and for this purpose ^ perspective ’ would 
 not be suited. A general impression of the house 
 might be sufficient for the man who was going to 
 live there, and a perspective drawing representing 
 what he would see if it were built might satisfy 
 1 im, but such general information would not be 
 of the slightest use to the bricklayer or mason. 
 To meet this end another kind of projection has 
 been devised, called orthographic. It is much 
 simpler than perspective. It could never be seen 
 by the eye. 
 
 Rays which issue from the object parallel to 
 one another are to be considered in this kind of 
 drawing. We have now to select a column of rays 
 proceeding from the object, and no longer as 
 before a cone of rays. Let the object be a house. 
 
 Any set of parallel rays may be chosen ac¬ 
 cording to the view we wish to represent. These 
 rays are again supposed to be cut by a plane held 
 athwart them, and each ray is supposed to stamp 
 its own impress on the plane. We should thus 
 
14 
 
 PERSPECTIVE DRAWINO. 
 
 get a picture, but it would be as big as the house 
 itself. And consequently before it could be shown 
 on paper it would have to be reduced and drawn 
 by scale, say yV*^h or 
 
 quently in a railway station one sees pictures of 
 this kind. They are generally very formal and 
 very straight, no lines converge on them, and all 
 attempts at embellishment or effect are absent. 
 The figure represents such a picture. 
 
 Fig. 4. 
 
 P 
 
 It will be well to compare these two kinds of 
 drawings, that their differences maybe noticed. It 
 will be seen that in the perspective drawing the 
 size is much reduced, whereas in the ortho¬ 
 graphic it is the same size as the original. It 
 will also be noticed that no matter where the 
 plane of the picture cuts the rays in the latter case, 
 the projection is the same; while in the perspective 
 drawing it varies greatly with every change either 
 of the position of the eye or of the plane of the 
 picture. Another difference is that in the per- 
 
COMPARED WITH ORTHOGRAPHIC. 
 
 15 
 
 spective drawing tlie bounding lines of the house 
 converge, whereas in the other they are parallel 
 The two views are placed side by side. 
 
 Fig. 5. 
 
 It Tvould be useless to attach a scale to the 
 perspective drawing, for all the lines are not 
 diminished on the same proportion, and it would 
 be impossible to find from it by measurement the 
 length of a line in the house. It will be gathered 
 from this comparison that an orthographic pro¬ 
 jection is a much more easily made drawing, and 
 much more easily deciphered. 
 
 It is frequently thought more desirable to show 
 a great deal in one picture than to represent it 
 either as it might be seen or so as to enable a 
 builder or landscape gardener to undertake the 
 construction of the house or grounds. And for 
 such a case as this another projection has been 
 devised. A different set of rays would be selected 
 
16 
 
 PEESPECTIVE DEAWING. 
 
 from tliose chosen in either of the other cases. 
 Those coming from the corner of the house would 
 be dealt with, still keeping parallel to each other. 
 Like orthographic drawing, it would be an 
 imaginary picture, and could be seen nowhere, but, 
 as before explained, the rays issue from all parts of 
 the house, and it is quite allowable to choose which¬ 
 ever direction is convenient for the formation of a 
 picture. That only will appear natural which is 
 given by converging rays, but others may give a 
 
 Fig. 6. 
 
 great deal more information and consequently 
 may be preferred. 
 
 The owner of a manufactory who was anxious 
 to show the extent of the premises would select 
 this kind of drawing. 
 
 We frequent!}^ see such drawings in railway 
 
ISOMETRIC DRAWING. 
 
 17 
 
 stations, in which the outside and a great portion 
 of the premises of a factory are visible. They 
 appear to be standing on a slope, and are some¬ 
 thing of the nature of a bird’s-eye view. 
 
 If we wished to take a map of the earth, we 
 should have to resort to some other kind of 
 drawing. As can be imagined, the earth could 
 not be seen from any point outside it, being too 
 big. To see one-half of it one would have to go 
 infinitely far away, otherwise, as is evident from 
 the picture, he would not see a hemisphere. At 
 
 Fig, 7. 
 
 each successive point, a, b, c, &c., he would see more 
 as he receded, but would never, until he was in¬ 
 finitely far away, see the whole hemisphere, sup¬ 
 posing his sight to be strong enough. The rays 
 to his eyes would then cease to form a cone. They 
 would be parallel, and the drawing formed by 
 them would be orthographic. But to both of 
 
 c 
 
18 
 
 PEESPECTIVE DEAWING. 
 
 these kinds of drawing objections would attach. 
 It would be necessary for the perspective view to 
 fix the point of sights and its position would be 
 completely arbitrary; and in the orthographic 
 picture, as shown in the figure, those portions of 
 the earth near the edges would be much fore¬ 
 shortened and crowded together. 
 
 To meet these objections a projection called 
 stereographic has been invented. A photograph of 
 the surface of the earth taken from the inside, 
 supposing the earth to be a shell, would give such 
 a picture. It would have many advantages over 
 the other kinds. The pictures of the hemispheres 
 of the earth seen in the early pages of atlases are 
 of this kind. 
 
 This much has been said to show that ‘ perspec¬ 
 tive drawing ’ is one of many kinds; its character, 
 like that of the others, is fixed. Its rules are well 
 defined, so that it is taken out of the region of 
 generalities and ambiguities too generally indulged 
 in b}^ writers on drawing and painting. Of all the 
 kinds of drawing mentioned it is the most difficult. 
 The original purpose of a drawing—viz. to give 
 information concerning the object it represents— 
 has been to a great extent foregone in perspective 
 pictures. Effect and beauty have pushed this 
 
ITS LAWS ARE FIXED. 
 
 19 
 
 other purpose from the field, and consequently 
 true perspective, though the base and foundation, 
 is but a part of any drawing. It is to be regretted 
 that the rules for pleasing composition and effect 
 have not yet been efficiently explained. There can 
 be little doubt that if the artist could explain his 
 processes, his pupils would find it easier to follow 
 him, than when he represents his power to arrange 
 and please as some peculiar faculty incapable of 
 explanation, and only to be acquired by a life’s 
 practice. 
 
 It is thought by a beginner that correct drawing 
 is the result only of a correct eye, and that, like 
 the poet’s art, the peculiar faculty must be born 
 with one, and cannot be acquired; but it is as¬ 
 tonishing how bold one becomes in a fight when 
 well armed, and it is astonishing how soon the 
 novice is capable of bringing rigid rule to bear 
 upon the production of his own drawing, and upon 
 the criticism of his master’s. Master and he have 
 then become pupils of Nature, which as a teacher 
 has this advantage, that she never varies. 
 Questions, no matter where asked, will receive the 
 same reply. The same experiment will have the 
 same result, and, they who find out the rules of 
 perspective or of colour in England and in China 
 
20 
 
 PERSPECTIVE DRAWING. 
 
 will find that their explanations, when translated, 
 are the same. 
 
 Having had some experience in the instruction 
 of youth, the writer is of opinion that the most 
 frequent cause of failure in attempts both in 
 drawing and colouring is—-not knowing how. It is 
 not generally a failure of intelligence or capacity. 
 The bad drawing is to be traced to three defects—- 
 not knowing how, indifferent tools, and the absence 
 of muscular skill due to practice. The first two 
 can be overcome by the teacher, if he is master of 
 his subject; the latter can be acquired with the 
 requisite amount of practice. It would then be 
 found that our belief in the ' God-gifted faculty 
 w^ould be shaken, and, as we are not surprised at a 
 carpenter of dull intelligence making a good box, 
 v/e shall cease to be surprised at a stupid boy 
 making a fair drawing. Of course it is left to the 
 few to achieve eminence. Broadly speaking, the 
 amount of practice is the measure of the success. 
 The muscles must be schooled to recollect. The 
 fingers will i3lay a tune that they know, while no 
 mental efforts direct them. A difficult piece is 
 played by fingers which are already familiar with 
 the thousand small combinations which go to 
 build up the whole. So with a painting, muscular 
 
FUETHER DETAILS. 
 
 21 
 
 skill, and the practice of years, lies underneath 
 the oil colours and their pleasing effect. 
 
 Fortunately the number of aspirants to honour in 
 the arena of art are increasing, and there is a hope 
 that, when art is in the hands of a greater number 
 of educated men, we shall hear less of canting- 
 phraseology and more of the simple and rigid rules, 
 which some good men will glean from nature, by 
 the same inductive process which has been suc¬ 
 cessful in other matters. 
 
 We will now discuss the character of perspective 
 drawing more in detail. Eeferring to fig. 1, 
 we see the nature of the drawing. The im¬ 
 pression received in the eye is nothing more 
 than the image on the plane reduced in size. 
 
 It is obvious that the position of the eye may be 
 anywhere, as also the position of the plane of the 
 picture. An alteration in the position of the first 
 would give a new picture, for a new cone of rays 
 would impinge upon the eye; but an alteration of 
 the place, where the plane of the picture cut the 
 cone, provided it be held straight across it (i.e. 
 perpendicularly to central ray), would only cause a 
 difference in size of the picture. Holding a sheet 
 of glass before the eye, and moving it nearer and 
 farther from the eye, would only have the effect of 
 
PEESPECTIVE DEAWING. 
 
 22 
 
 diminisliing or increasing the size of a picture 
 traced upon the glass in either position. The 
 appearance would remain unaltered. As the 
 position of the eye and of the plane of the picture 
 may be anywhere, it follows that before a per¬ 
 spective picture can be drawn, or before the true 
 character of an object can be accurately ascer¬ 
 tained from its picture, these positions should 
 be known. It may be remarked that if the plane 
 be held obliquely, just as good a picture would be 
 seen through as it if it were held straight or perpen¬ 
 dicular. And yet this position has been forbidden. 
 The reason for that is this, that in looking at any 
 object the centre of the picture seen by us is on 
 the axis of the eye. In other words, the image 
 cast by the lens which lies over the pupil is 
 ecjually disposed round the axis or central line. In 
 the same way a picture taken by a camera has 
 for its centre the axial line of the camera. If a 
 view seen through glass held obliquely were traced 
 with a pen, and then looked at directly, it would 
 appear untrue. It would not be what the per¬ 
 spective view is meant to be—viz. that which 
 might have been perceived or seen. Only a 
 portion of the whole pencil entering the eye would 
 have been projected, and, in order that the picture 
 
POSITION OF THE PLANE OF PICTUEE. 
 
 23 
 
 should be a complete one, the plane of the picture 
 should have been extended equally far on the other 
 side of the axis. 
 
 Fig. 8, 
 
 All the dotted rays should have been allowed to 
 project themselves upon the glass. Another suf- 
 
 Fig. 9. 
 
 
 ficient reason would be that in looking at anything 
 one instinctively puts it directly before him, and 
 he directs the axis of the eye on each point. He 
 would stand directly before a picture in criticising 
 it, and would consequently condemn as distorted a 
 
24 
 
 PEESPECTIVE PEAWING. 
 
 picture taken obliquely as above described. It 
 follows from tliis that the point of sight should be 
 opposite the centre of the picture. It ought pro¬ 
 perly to be over the exact centre O 3 for the eye look¬ 
 ing in any one direction receives a circular image 
 equally trustworthy at equal distances, such as is 
 represented by the dotted circle ; but the direction 
 of ordinary vision being as a rule horizontal, there 
 is a field of greater interest above the selected centre 
 than below it, and artists generally place what is in 
 reality the centre of the picture about two-thirds 
 down the central line at b. In the photographic 
 picture, before the artist has shaped it to his 
 desire, the centre of the paper is the true optic 
 centre. 
 
 One of the differences noticed (fig. 5) between 
 the perspective and the orthographic projection 
 was that the lines of the house in the first con¬ 
 verged, whereas in the latter they did not. Now the 
 reason of this will be explained. Let there be two 
 objects of equal height, one more distant than the 
 other, and let the rays from each be traced to the 
 eye through the plane of the picture. 
 
 It is seen from the figure that the pencil from 
 the distant post A b is narrower than that from the 
 near one c d, and consequently would stamp the 
 
VAlS^ISHINa POINTS. 
 
 25 
 
 glass with a shorter image than the other. An 
 image appears to ns big or little according to the 
 
 Pig. 10. 
 
 angle under which it is seen. And the distant 
 figure is said, in the language of mathematics, to 
 ‘ subtend ’ a lesser angle than the near one, a e b 
 being less than c e d. If the tops of the two posts 
 were connected, they might represent a wall with 
 parallel edges, and the projection of the wall 
 would evidently be as in fig. 11, diminishing in 
 height as it recedes, until finally, if the wall should 
 
 Fig. 11. 
 
 be long enough, the two edges would vanish in a 
 point. If there should have been tiers of bricks 
 
26 
 
 PEESPECTIVE DEAWINa. 
 
 in the wall, these will follow the same rule, and 
 merge into what is called the vanishing point of 
 their parallel edges. AJl parallel lines have a vanish¬ 
 ing point. It was seen in the picture of the house 
 that the lines of the sides approached each other 
 as they receded from the eye; each set of parallel 
 lines was on its way to its vanishing point. Fre¬ 
 quently one sees a beam of light falling through a 
 break in the clouds, and it appears to expand like 
 a fan as it approaches the earth. This effect is 
 simply due to the aperture in the clouds, through 
 which the beam comes, being considerably farther 
 from the eye than where the beam falls oti the 
 ground. The width of the beam at each end is 
 the same, but, for the reasons explained in the 
 
 Pig. 12. 
 
 case of the wall, the edges converge towards each 
 other at the end farthest from the eye. 
 
 It nov/ becomes necessary to find out where this 
 
VANISHma POINTS. 
 
 27 
 
 vanishing point may be. All persons attempting 
 to sketch from nature v^ill admit that such lines 
 converge, but it is not everyone who can pnt the 
 point of his pencil on the spot in his drawing into 
 which they should run. 
 
 Suppose that one is standing in a square tunnel 
 and looking towards the end. He will see such a 
 view as this (fig. 13). As he changes his position 
 
 Fig. 13. 
 
 from side to side, he will notice that the point into 
 which the bounding lines of the tunnel run will 
 change also. They, in fact, will always fall into a 
 point where a line from his eye parallel to any 
 one of them will strike the background. Suppose 
 that all of the tunnel but one wall should be removed, 
 and we have the edges of that wall running into a 
 point on the drawing where a line from the eye 
 parallel to the wall would strike the background 
 of the view. It will presently be seen how ex¬ 
 tremely easy is the application of this principle in 
 
28 
 
 PEESPECTIVE DEAWINO. 
 
 practice. These vanishing points ascertained, the 
 rest of the building, supposing it to be one which we 
 are sketching, is plain sailing. 
 
 The plane of the picture has been hitherto 
 always represented as standing up vertically before 
 the eye, whereas in reality the sketching pad is 
 held in the lap. The pad is merely the paper on 
 which we copy the supposed tracing on the win¬ 
 dow-pane. Each time we look at the view this 
 tracing falls on the eye, and by retaining for a 
 few seconds in one’s memory what one has just 
 seen, he can transfer it to paper. 
 
 The perspective picture being the projection of 
 the object given by the rays converging on a point, 
 as already explained, it follows that the same view 
 of any object could not be seen from two different 
 points. Each point would have its own special 
 pencil of rays, and the pictures given by the inter¬ 
 sections of these pencils with a plane of the picture, 
 would of necessity be different. To do justice, 
 then, to the artist’s picture, the critic should pose 
 himself in reference to it, so that the line a b, 
 from his eye to the picture, should fall perpen¬ 
 dicularly on the point of sight. He would then 
 be in reference to the picture exactly as the artist 
 was in reference to the view which he painted; 
 
POINT OF OBSEEVATION FIXED. 
 
 29 
 
 and his distance from the picture should be the 
 true distance of the artist’s point of sight from 
 the plane of his picture. If, as we originally sup¬ 
 posed, the drawing had been traced on a piece 
 of transparent glass, while the head remained 
 steady and one eye was shut, and was afterwards 
 transferred to paper, and made into a picture, 
 the distance of the observer from the picture 
 should equal that of the eye in the first instance 
 from the glass. To receive in some cases a fair 
 impression from the drawing this becomes neces¬ 
 sary, and in others it is immaterial. If, for instance, 
 the view was one of a house, and the artist stood 
 very near it in sketching, it would take such a form 
 as is shown in fig. 14a, the lines of the two sides 
 
 Fig. Ha. 
 
 Fig. 14b. 
 
 and of the roof converging very rapidly upon their 
 vanishing points, whereas if the house was distant 
 it would appear as in fig. 14b, the same lines con¬ 
 verging far less rapidly. A picture of a house as 
 represented in fig. 14a, if looked at from too distant 
 
so 
 
 PEKSPECTIVE DEAWING. 
 
 a position, would appear unreal, while the figure 
 14b would not appear natural if the critic posed 
 himself too near it. The true position of the 
 observer is that which allows the conditions under 
 which the artist drew the picture to be reproduced 
 as nearly as possible. The eye is so sensitive, and 
 gives the brain such wonderfully exact impressions, 
 which it sometimes takes very delicate and precise 
 reasoning to trace, that it is but just to allow the 
 above restrictions to be observed in viewing a picture. 
 Each point of sight gives a distinct projection of 
 an object, and conversely each projection of a 
 house fixes the point from which it was viewed. 
 The eye becomes so skilled that from the look of an 
 object it will assign almost exactly the position 
 from which it was taken; and if, in looking at a 
 picture, we should do much violence to the feeling 
 of the eye by standing in a wrong position, the 
 picture will appear contorted. For instance, if we 
 view fig. 14a at a considerable distance, it appears 
 a false projection, and justly, for in this case the 
 point of sight is not more than a few inches from 
 the paper. Its exact position is easily ascertained. 
 The view of the interior given in the frontispiece 
 is a reduction of a sketch taken from one end of a 
 
SKETCH OE INTEEIOE. 
 
 81 
 
 hall. In the case of this sketch the plane of the 
 picture was about ten inches distant from the eye, 
 but in the reduced drawing it is only about five 
 inches—viz. the distance c o. The consequence is 
 that the picture viewed at the distance of ordinary 
 vision—viz. about ten inches—does not appear 
 quite correct. The upper lines in the far wall 
 appear to slope down too abruptly, and the lines 
 in the pavement to slope up too much, but if the 
 eye is held over the drawing at the true distance— 
 namely, c o (supposing this line to stand perpen¬ 
 dicularly from the paper)—the hall will assume 
 quite a natural appearance. Indeed, it must needs 
 do so, for the image is that which the real hall 
 produced upon the eye. It is not just, there¬ 
 fore, to view this sketch from a greater distance 
 than c 0. 
 
 It follows from the description of the vanishing 
 points given above that lines from the eye parallel 
 to the edges of the house— e v and e y ' (fig. 15) 
 parallel to ev and e v '—will run into the respective 
 vanishing points v and v', which can be distinctly 
 noted on the background of the picture which we 
 are drawing. When these points are ascertained 
 the lines of the house can easily be adjusted in 
 
32 
 
 PERSPECTIVE DRAWINa. 
 
 their places. The angle at e is obviously the same 
 as that at e. 
 
 If a drawing should contain the vanishing points 
 of only two lines making a known angle, we can, 
 
 Fig. 15. 
 
 o 
 
 by the converse of the above, find the position of 
 the point E or the distance of the eye from the 
 paper. We know that the eye is situated on the 
 per|)endicular from the point c. We know also 
 that the two vanishing points subtend the known 
 angle. If we suppose the line c o turned upwards, 
 so as to coincide with the paper, we have merely 
 to find a point e' on this line such that the angle 
 v' e' V is equal to the given one. The angle v' e' v 
 (fig, 15) is simply the angle v' e v turned up so as 
 lie on the paper. Fig, 16 shows such a case, in 
 which the points v and v' can be found. We 
 know that the sides of the house contain a right 
 
DISTANCE OF THE EYE. 
 
 33 
 
 angle. The point e', found by describing a semi¬ 
 circle on V v', and marking the intersection with 
 the perpendicular drawn from c gives us the 
 distance of the eye from the picture, viz. e' c. 
 
 Fig. 16. 
 
 The describing of the semicircle is merely a con¬ 
 trivance by which (due to the properties of the semi¬ 
 circle) the angle v' e' y is insured as a right angle. 
 
 Each house, then, that happens to be drawn in 
 a picture fixes the position of the eye of the 
 observer, and if the artist should introduce a 
 second house he is at once liable to error, which 
 may be easily detected, for it is obvious that each 
 house should give the same position for the eye. 
 If they should not do so the drawing will represent 
 an impossibility, and though the observer may 
 
 D 
 
34 
 
 PEESPECTIVE DEAWINa. 
 
 not know wky, or be able to interpret the dis¬ 
 pleasure of his eye, he will probably be displeased 
 with the picture. The behaviour of the parallel 
 furrows or ridges in a ploughed field as we pass 
 rapidly by them in a railway carriage exemplifies 
 very well the character of the vanishing point and 
 its dependence upon our position. The point in 
 the distance into which the lines seem to run 
 travels onward as we advance. Its movement is 
 most striking when we are in a position to look 
 down the ridges (to enfilade them). 
 
 It may be thought that such considerations as 
 those referred to here are inapplicable to perspec¬ 
 tive drawing such as usually undertaken by the 
 amateur, and refer more properly to the drawing 
 of the architect or builder. A straight and formal 
 house would seldom be chosen as the subject of a 
 picture, and the artist may be thought freed from 
 the foregoing restrictions if he should confine him¬ 
 self to waterfalls, mountains, and trees. But all 
 that has been said about the necessities of a house 
 or cube is true of other things. If we change our 
 position in reference to a house its figure changes 
 also. We can in this case determine the distance 
 and the direction of the house from the particular 
 shape it presents on the drawing. In the case of 
 
CKITICISM. 
 
 35 
 
 trees and rocks, their figure changes also for each 
 new position of the eye, but in their case we have 
 not the same power in criticising. Criticism can 
 only come in and approve or condemn where there 
 is some foothold of data to rest upon; but there 
 are verj^ few subjects that can be undertaken of 
 which something definite cannot be predicted. 
 When this is so, criticism can speak confidently. 
 For instance, it is certain that a piece of still 
 water is level, consequently all reflections in it 
 must obey certain laws. The face of a wall is 
 vertical. The roof of a house or cathedral will 
 slope evenly on both sides—the window sills will 
 be horizontal. A variety of such points can be 
 known with certainty in reference to most things 
 looked at. If an artist should draw a picture 
 containing such things, he is at once within the 
 reach of exact criticism; not the criticism of 
 feeling, taste, or opinion, but the criticism of law. 
 It might be possible to avoid all such things in 
 the choice of a subject, and evade reproof, and the 
 drawing might escape censure—not because it was 
 right, but because it represents what might have 
 been ; the trees may be represented too tall, and 
 the hillside may be drawn steeper than it is, but 
 still what is represented is not impossible. 
 
•36 
 
 PERSPECTIVE DRAWING-. 
 
 Books on perspective generally concern them¬ 
 selves with the purely geometrical character of 
 the projection, and the rules and constructions 
 given in them are for the most part inapplicable 
 to the purposes of the sketcher from ligature. 
 Before they can be applied, many lines must be 
 plotted in their original length, or in the case of 
 their being drawn as in the above illustrations, 
 which are purely explanatory, the whole of the 
 data must be plotted in miniature. It is essential 
 in nearly all geometrical constructions that the 
 distance of the eye from the plane of the picture 
 should be known. This distance in the case of 
 sketching from Nature cannot be considered as 
 part of our data. The reader who is familiar with 
 the problems and constructions of the ordinary 
 treatise on perspective will notice that in the 
 following descriptions of how to draw an interior 
 this distance is made to follow from the position 
 of a pair of vanishing points, which are found by 
 the simple methods here explained. In ordinary 
 cases of out-of-door sketching, the distance of the 
 picture is greater than the length of the drawing- 
 pad, and consequently though much assistance 
 may be derived from plotting this line upon the 
 paper, it may not be possible to do so. If the 
 
GEOMETEICAL PERSPECTIVE. 
 
 37 
 
 picture which it is designed to make contains any 
 intricacies of perspective, it is most desirable that 
 this distance should be actually drawn on the paper, 
 as explained in the example given of an interior. 
 If the drawing-pad is not large enough, a piece of 
 paper must be gummed to the margin of the drawing. 
 
 The character of the problem which in various 
 forms presents itself to the student of geometrical 
 perspective is this: The distance of the eye from 
 the plane of the picture is given, say two inches ; 
 the object to be represented, say a house, stands 
 at a distance of six inches on the other side 
 of the plane of the picture, and is represented 
 in miniature like a toy house. Its position 
 also with reference to the line of sight (see 
 fig. 1), i.e., whether placed straight or sideways, 
 is defined. It is desired to produce the picture of 
 the house formed on the plane of the picture by 
 the converging rays. The real case that presents 
 itself is this. Given a real house at an unknown 
 distance, placed in reference to the line of sight 
 in a position not defined, and the plane of the 
 picture at a distance from the eye which, though 
 it may be assumed, is arbitrary (it is usually 
 chosen at a distance of about a foot), it is de¬ 
 sired to produce the correct projection. It is seen 
 
88 
 
 PEESPECTIVE DEAAVIEG-. 
 
 that there are few points common to both cases. 
 It follows that the elaborate treatises on the 
 subject may almost leave untouched the points on 
 which the amateur artist might be directed with 
 advantage, or enclose them in so much that is 
 unnecessary that they cannot be easily reached. 
 A few very simple rules will be here laid down and 
 explained. When the reader is sufficiently familiar 
 with them to apply them to the testing of the 
 accuracy of other drawings, he will be surprised 
 to find how few pictures are correct. He will 
 seldom find the picture of an interior of a hall or 
 cathedral but which will represent what did not 
 exist. The typical case above referred to of the 
 miniature house, represented in fig. 1, has of 
 course its converse, viz., given the picture of the 
 house, its distance and the distance of the plane 
 of the picture, to produce the real object in 
 correct proportion. This is quite possible, and is 
 no more difficult than to draw the picture when 
 given the house, but it will be observed that the 
 converse of the proposition in the second case is 
 b}" no means so easy, and is frequently impossible. 
 It is this: given the picture of an object, such as a 
 picture in the ^ Illustrated London Hews,’ to find 
 out the true shape of the objects represented. Onr 
 
FACTS ASCERTAINABLE FROM PICTURES. 39 
 
 criticism may not be able to reach this point, but 
 it may be able to pronounce if the picture repre¬ 
 sents possibilities, or what we know from other 
 considerations must have been; for instance, does 
 it represent the picture frames as rectangles or as 
 diamonds ? Are the tiles laid symmetrically ? are 
 the columns round? Is the floor horizontal, or is 
 it tilted up like the platform of a stage ? These 
 things can generally be decided, and it requires no 
 argument to prove that it is desirable in making a 
 picture of what is before one, to make it to repre¬ 
 sent what one really sees. 
 
 From among the many rules and expositions of 
 perspective, a few may be gleaned which will give 
 material help to the amateur artist, and some may 
 be modifled so as to aflPord great confldence in the 
 execution of a drawing from Nature. It would be 
 quite possible to choose a subject for a picture 
 which,* as far as its perspective was concerned, 
 would baffle the criticism of the most exact, and it 
 is fortunate that some of the most picturesque 
 subjects approximate to this character. The more 
 dilapidated the ruin, the more charming is fre¬ 
 quently the effect; and the more rugged and 
 amorphous are the fragments of rock, the 
 prettier is the foreground. Still the wall is pro- 
 
40 
 
 PEKSPECTIVE DRAWINO. 
 
 bably vertical, the water is certainly horizontal, and 
 if it reflects an image it must do so according to a 
 certain law. An amateur who was obliged to 
 seek such a subject that his picture might evade 
 criticism would be in a sorry condition to under¬ 
 take a sketch, and his confidence in its execution 
 would be but slight. He would be unable to 
 attempt many of the most interesting subjects. 
 The interior or exterior of his own house would be 
 beyond his power. Sketches of places where he 
 lived, perhaps the most pleasing reminiscences he 
 could lay by, would be too difficult, or, if under¬ 
 taken, could only be exhibited with diffidence. 
 He has drawn a line for himself which he may not 
 pass, and excellence is beyond his reach. 
 
 The apparent size of an object depends upon the 
 angle under which it is seen. Things appear 
 larger when looked at through a telescope simply 
 because the angle under which they are seen is 
 increased. The angle which an object subtends 
 at the eye becomes smaller and smaller as the 
 object is removed, and exactly in the same pro¬ 
 portion as its distance is increased. A lamp-post 
 twice as far off as another would subtend half the 
 angle, and, if in the same direction, would be re¬ 
 presented in a perspective picture by a line exactly 
 
VANISHING POINTS. 
 
 41 
 
 half as long. This is the key note to perspective, 
 and from this follows the rule the adherence to 
 which is a first necessity of a drawing, viz.:— 
 
 The projections of all parallel lines converge to 
 a point called the vanishing point of those lines. 
 
 The lines of a railway, when not curved, would 
 appear to meet each other at some distant point, 
 which is the vanishing point for those lines. The 
 chief difficulty one has in sketching from Nature is 
 to find out where the vanishing points for sets of 
 parallel lines may be. Having found them, the 
 drawing will almost fall into its place. When we 
 come to describe the actual process of taking a 
 sketch, the way in which these vanishing points 
 may be found will be explained. Having found 
 them, we shall be concerned with the question of 
 foreshortening. Pictures and windows oblique to 
 our line of sight must of course appear narrower 
 than they really are, but the amount of this 
 narrowing or foreshortening is not so easily ascer¬ 
 tained. We will consider the vanishing point. 
 It may be thought strange that a picture could be 
 made of a line which was infinitely long, and yet 
 such is the base. The vanishing point of a line is 
 nothing more than that point on our drawing 
 where the picture of projection of the line would 
 
42 
 
 PERSPECTIVE DRAWING. 
 
 end, supposing it in reality to be infinitely long. 
 The line joining tlie chimney of a house and a 
 fixed star is practically infinitely long, and yet 
 such a line could be projected on the paper of a 
 sketch, and might not be more than a few inches 
 in length. If we suppose the star twice so far as 
 it is, this projection is not sensibly altered. The 
 line has a fixed termination in our drawing, and 
 the point where it terminates is its vanishing 
 point. The question is where is this point ? To 
 find it we must let the eye run along the line ; the 
 point where the line of sight strikes it becoming 
 more and more remote, the eye can only reach the 
 end when its line of sight is parallel to the 
 original line. The rule then takes this practical 
 form. Look parallel to any line, and where the line 
 of sight strikes the distant background, there is the 
 vanishing point. Although most parallel lines 
 which come under our notice are horizontal {i.e. 
 level) and consequently will have their vanishing 
 on a line level with the eye, as in the views already 
 given of houses, parallel lines which do not happen 
 to be horizontal, will also have their vanishing 
 point, thus the banisters of stairs, the edges 
 of roofs, beams of light from a cloud, &c., will 
 have vanishing points at different places on fhe 
 
APPARENT SIZE OF OBJECTS. 
 
 43 
 
 picture. Such cases are not common except in 
 sketches of interiors of buildings. 
 
 Fijr. 17. 
 
 We said that a lamp>post if twice as far off* as 
 another would be represented by a line half as 
 long, if in the same direction. This point must be 
 attended to. The second lamp-post will appear 
 half the size of the others, no matter where it is 
 situated, if it should be twice as far; but we must 
 recollect that we are now concerned with the 
 plane of our picture, and this will cut the two 
 pencils at different distances from the eye. The 
 distances of objects must be referred not to the 
 eye but to the plane of our picture. Thus boys 
 standing, one in the centre and one at each corner 
 of the picture, though the latter are much more 
 distant than the former in reality, must be repre¬ 
 sented the same height. We will take the case of 
 
44 
 
 PEESPECTIVE DEAWINa. 
 
 three posts of equal height. Although the posts at 
 the margin of the picture are nearly twice as far 
 
 Fig. 18. 
 
 off, and would if in the same direct line as the 
 centre one be represented as half the size, they 
 must be drawn the same height as the near one, 
 for it will be seen that the plane of the picture at 
 the points A and b is proportionately farther from 
 the eye, and cuts the pencil further off. This section 
 of the pencil is, in fact, of exactly the same height 
 as the section of the central one. 
 
 In the same way, if a column of the same width 
 the whole way up were to be sketched, though the 
 top might be much further off than the bottom, it 
 would be represented as of the same width. The 
 rays from the top would cut through the imaginary 
 plate of glass at exactly the same distance apart 
 at both ends of the columns. Fig. 19 explains such 
 
THE EYES OF POKTRAITS. 
 
 45 
 
 a case. See also the remarks concerning a pave¬ 
 ment, p. 65. 
 
 Fig. 19. 
 
 It is frequently thought curious, and instanced 
 as a proof of good drawing, that the eye of a por¬ 
 trait should appear to follow an observer through 
 the room. There is no test of good drawing in 
 this fact. If the eye should happen to look at one 
 in any position in a room it should do so in all. 
 When an ordinary eye in life is looked at, the 
 direction of the axis of the eye is determined with 
 
 Fig. 20a. Fig. 20b. 
 
 marvellous certainty. We are assisted to its de¬ 
 termination by our two eyes, and the combination 
 
46 
 
 PEESPECTIVE DEAWING. 
 
 of the two images, and also by the circular or 
 elliptical form of the iris and pupil. If these 
 should appear perfectly circular, as in fig. 20a, the 
 eye confronts one. If, on the other hand, they 
 should be elliptical, as in fig. 20b, the axis of the 
 eye passes to one side of the observer. One knows 
 in a moment if an eye looks at him, and he can 
 tell with almost equal certainty at what object it 
 is directed, or, in other words, we can assign its 
 true position to the axis of an eye from the pro¬ 
 jection of a circle on it. Now in the portrait 
 this position is fixed by the artist, and to the eye 
 of every observer it is the same; consequently, the 
 impression of direction should be the same to one 
 person as to another. It will be noticed that it is 
 only the eyes of full-face portraits which look at 
 one, unless the head and eyes should have different 
 directions, the latter being as in fig. 20 a. 
 
 Perspective, as far as pictorial art is concerned, 
 consists of two problems—to produce the pro¬ 
 jection of an object the character of which is 
 known; thus it may be required to draw a square 
 flag in a pavement, or rectangular picture frame, 
 or to represent correctly the top of a round table. 
 It is of such particulars that a drawing is made 
 up. The other is the converse of this, and affords 
 
TO DEAW A SQUARE. 
 
 47 
 
 us the power of criticising. Given the picture of an 
 object to produce its true character. If the shape 
 which we find the object to be, corresponds with 
 what from other considerations we know it must 
 be, the drawing will pass as correct; if not, it 
 stands condemned as incorrect. Dealt with in 
 geometrical fashion, the first problem is performed 
 in this way. 
 
 Let it be required to draw the picture of a square 
 fiag in a pavement, one line in the picture being 
 given. Let the given line be A b ; the distance of 
 the eye from the place of the picture must be 
 known. 
 
 Fig. 21. 
 
 Produce A B till it meets the horizontal line in 
 V, its vanishing point. Draw c o perpendicular to 
 v' V, and equal to distance of the eye. Draw o v 
 
48 
 
 PERSPECTIVE DRAWINa. 
 
 and 0 v' perpendicular to o v, v' is the vanishing 
 point of the sides of the square adjacent to a b. 
 Draw v' b, v' a. Bisect the angle v o v' in o y" and 
 draw v" a. The point of intersection d is the far 
 corner of the square. Draw d v. The projection of 
 the square is complete. Bor the clear understanding 
 of the construction, reference should be made to 
 fig. 15, p. 32 ; the triangle v o v' in the last figure 
 is nothing more than the triangle v E v' in fig. 
 15, turned upwards so as to correspond with the 
 plane of the paper. The angle at e, fig. 15, is the 
 same as that at o, and in the last construction, 
 having got one vanishing point v, the angle at 
 0 is made to equal the angle at a (viz. right angle), 
 and the second vanishing point v' is found. The 
 vanishing point of the diagonal is found by 
 drawing a line from o bisecting this right angle. 
 It will meet the horizontal line in the vanishing 
 point of the diagonal, v'h 
 
 The converse proposition is this. Given a 
 figure supposed to represent a square, does it do so ? 
 Let it be a b c d (fig. 21), and let the distance of 
 the eye from the paper be equal to o o, turned up 
 as in fig. 15, so as to lie on the paper. 
 
 Find the vanishing points v and v' by producing 
 the sides of the figure. On v v' describe a semi- 
 
CORRECT DIVIDING OF LINES. 
 
 49 
 
 circle. If the point where the line o c is 
 intersected correspond with o, the figure is 
 correct, if not it is incorrect. The points v and v' 
 being found, and it being known that they subtend 
 a right angle at the eye, the semicircle swept 
 on the line vv' at once gives us the point o, 
 determining the distance of the eye. Should it 
 correspond with the given distance, the drawing is 
 correct. A very simple case has been taken in the 
 preceding demonstration to illustrate the problem 
 of geometrical perspective. In both it will be 
 noticed that the distance of the eye was given; 
 but assuming the figure in the last to be correct, 
 the distance was found. In most pictures this 
 distance can be found and the remainder of the 
 drawing tested on the assumption that it is 
 correct. The following construction is frequently 
 necessary to the correct disposing of lines and 
 figures in a picture: It is desired to cut the line 
 A B in half—supposed to be horizontal. The por¬ 
 tions of the picture of the line will not be equal. 
 Let it be necessary to find the centre of a line 
 which we have chosen to represent the edge of a 
 table or a wall. 
 
 Let H R be the horizontal line, and let a b be the 
 line which we wish to bisect. For instance, this 
 
 E 
 
50 
 
 PEESPECTIVE DKAWING. 
 
 line A B miglit have been assumed as the length 
 of a table or mantelpiece of which we required the 
 centre. Take any point p at random on the line 
 H R immediately above A b. From a draw a line 
 
 Fig. 22. 
 
 A F ED 
 
 A D parallel to h r, or to the bottom of the paper. 
 Draw p B, and produce it until it cuts A d in e; 
 bisect A E in f, and join p f ; where tliis line cuts 
 A B —viz. o, is the centre. 
 
 If it were required to add a piece on to a line of 
 equal length to itself, this construction shows us 
 how it can be done. Let it be desired to produce 
 A 0 until the produced part be equal to it. We have 
 merely to draw p o and produce it to f, then to make 
 F E equal to af and join e p ; the point b thus found 
 is the extremity of the line. This is the most im¬ 
 portant problem. The reader should familiarise 
 himself with it by practice. It is useful in almost 
 every stage in a perspective drawing. It affords us 
 
NECESSAEY PROBLEMS. 
 
 51 
 
 the power of posing correctly the windows in the 
 side of any hnilding, or panels in a wainscoting, 
 or generally of dividing any horizontal line into 
 equal or assigned divisions. 
 
 We will now describe the actual procedure in 
 taking a sketch of an interior. A person who has 
 had much practice in sketching may be able to 
 draw objects very fairly near their true places. 
 But it is simply impossible that they can be 
 really correctly drawn without the assistance which 
 maybe derived from such problems as the foregoing. 
 Our sketch will be so chosen as to involve a good 
 deal of ^ Perspective.’ We will suppose it to be 
 the interior of a hall, hung with pictures and 
 banners, and with a tesselated pavement. (See 
 Frontispiece.) The process will be illustrative of 
 cases that may occur in less complication in any 
 ordinary sketch. 
 
 The first thing that will be done is to look round 
 the hall. At once we have an enormous contrast 
 between what we would wish to do and what is 
 possible. Our object is to make on paper such a 
 representation of the hall as shall convey to the 
 person looking at it the same idea that we have 
 received upon our minds from our glancing round 
 it. Our first feeling, knowing how restricted is 
 
52 
 
 PEKSPECTIVE DEAWIN&. 
 
 our power, is a misgiving lest we should attempt 
 the impossible. 
 
 We will just compare these two acts of looking 
 round the room, and looking at our picture when 
 finished. Looking at the hall, we move our head 
 about, and turn it from side to side. We thus 
 gain an idea of the distance of all things in it. 
 Our two eyes also, giving each a different picture, 
 as will be understood when we remember that a 
 distinct pencil of rays falls into each, will lead our 
 brain by its power of combining these pictures to 
 a just estimate of the various positions of objects. 
 The shutting of each eye alternately, while the 
 head remains steady, will prove by demonstration 
 that two distinct visions are seen for each steady 
 glance of the eyes ; but, apart from this, the motion 
 of the head is sufficient to produce a distinct idea 
 of distance. This will require some slight illus¬ 
 tration. Let one eye be shut, and a finger held 
 before the face ; let the head now be moved to and 
 fro sideways, slowly, and let the displacement of 
 the finger over the background of the view be 
 noticed. It will appear to change its position 
 many inches. Now look at some object a few feet 
 beyond the finger, and mark how far it travels over 
 the background while the head moves—probably 
 
PERCEPTION OF DISTANCE. 
 
 53 
 
 not more than an inch or two. Note successively 
 the displacement of objects, more and more 
 distant, over the field of the background, and it 
 will be seen that the change in place of near 
 objects is very great, while that of distant objects 
 is very slight. It is this comparative motion 
 which gives the brain the true idea of distance, and 
 in a slight change of position of the head the 
 artist has satisfied himself, perhaps unconsciously, 
 of how the various objects are situated. The 
 above is in its simplicity the theory of ^ Parallax,’ 
 by which the distance of the moon—which from 
 the earth is slight,—and the distance of the stars— 
 which is so great that the whole size of the earth 
 and its orbit are but as a grain of sand in com¬ 
 parison—have been ascertained. It appears, then, 
 that there is nothing abstruse in the idea; and 
 when the word parallax is interpreted, it merely 
 means ‘ comparative change.’ Travelling in a 
 railway carriage, we notice that we cannot look at 
 the sleepers on the line, or at the hedge beside 
 us—they move so rapidly. A tree some distance 
 off moves slowly back along the horizon, and a dis¬ 
 tant object seems hardly to move at all. If we said 
 to ourselves, ^ That tree which moves only half as 
 ^ fast backwards as this one, is twice as far,’ we should 
 
54 
 
 PEESPECTIVE DKAWING. 
 
 have done in a small way what the astronomer has 
 done with the stars. It is evident that shutting 
 alternately each eye is the same in effect as moving 
 one open eye backwards and forwards. Each eye in 
 the first case, and each position in the second, will 
 have a new view, and all objects will have made a 
 comparative change of position relative to the 
 background, which has given so great an amount 
 of information that we ought hardly to be surprised 
 if the best picture should be a failure. 
 
 We now come back to our sketch. The artist 
 takes his picture as if he had but one eye; and, as 
 we are now prepared to hear, one eye, if fixed, can 
 have no idea of distance, except what it draws 
 from its previous experience. This can be easily 
 tested by experiment. Try to put the finger of 
 one hand on the point of the pencil held in the 
 other, looking only with one eye, and keeping the 
 head steady. It must be rapidly done to be fairly 
 tried. It is as likely as not that the finger will 
 miss the point. We know from our definition of 
 the picture that it is the projection of the objects 
 formed by a pencil of rays. At once there is 
 an enormous difficulty thrown on the artist. He 
 is to represent in one sketch what he hopes will 
 produce the same idea as a view with both eyes 
 
THE IMPRESSION ON THE RETINA. 
 
 55 
 
 and a moving head, and, Tvhat is of equal import¬ 
 ance, with a head which, though it keeps its place, 
 turns round. From the definition of our picture, 
 by which we are bound and from which we cannot 
 extricate ourselves, we have one point of sight ; and 
 we have one central line of sight, round which the 
 picture should be equaUj posed, though it may 
 be, and generally is, extended twice as far above 
 as below for reasons given on page 24. Our picture 
 is taken as if we never raised our eye from where 
 our central line strikes the distant sky, or hills, 
 or bookcase, as the case may be. And yet in 
 sketching we must of necessity look round. In 
 taking a true perspective picture, we are sketching 
 what, properly speaking, we should not look at. 
 The imperfection of our eye in not seeing objects 
 clearly more than a few degrees to either side of 
 the central line, obliges us to look directly at 
 them; otherwise the outline is indistinct and 
 blurred. If this were not so, one might read a 
 whole page of a book without moving his eye from 
 some word in the centre. A mere trial of how far 
 from a word looked at one is able to distinguish 
 other words, will prove how very small a field of 
 view is in focus at once in the eye. Supposing the 
 objects not looked at to be distinct, it is their 
 
56 
 
 PEESPECTIVE DEAWING. 
 
 projection in this position of the eye that we 
 desire to produce. The back of the eye is slightly 
 concave or hollow, like the palm of the hand, and 
 consequently is not altogether similar to the plate 
 in a photographic camera. The objects only 
 directly in front, or on the axis of the eye, are in 
 true focus, while with the camera plate it is so ar¬ 
 ranged that a considerable field of view is in focus 
 at once. Our drawing must of necessity be upon a 
 plane surface, and resembles in every particular a 
 photographic picture. In such a picture the ob¬ 
 jects to either side of the centre are larger than 
 when looked at directly. This will be obvious on 
 reference to fig. 18, p. 44, and from this follows 
 what many persons must have noticed, viz. the 
 difficulty of attaching photographs together so as 
 to form a panoramic view. It is almost impos¬ 
 sible to adjust the edges of the pictures, for they 
 are found not to coincide. They would only fit 
 together when at equal angular distances from 
 the axis of the lens, or centres of the pictures. 
 The concavity of the back of the eye and the 
 indistinct character of all objects not directly 
 looked at tend to annul and render unnoticeable 
 the enlargement of objects to one side of the axis, 
 but where the image is received upon a plane 
 
CHOICE OF CENTRE OF PICTURE. 
 
 57 
 
 such enlargement is unquestionable. This matter 
 has been dwelt upon, as it is most desirable to 
 have a clear notion of what we see when looking 
 round at objects in reality and when looking at 
 their picture. In the first instance all the objects 
 seen in one sweep of the eye form a panorama 
 projected on the concave surface of a sphere or cy¬ 
 linder if the angle subtended by its width be smaU, 
 whereas in the other it is the projection on a plane. 
 It would be impossible to adopt a style of drawing 
 truly representing the first condition; we should 
 have to paint our picture on the interior of a bowl, 
 or hemisphere, and the view only could be seen 
 
 Fig. 23. 
 
 from one point of view at which each observer 
 would have to place his eye. The figure will 
 represent the two cases. 
 
 . To return again to our drawing, the first thing, 
 after having looked round us, is to choose the 
 
58 
 
 PERSPECTIVE DRAWING-. 
 
 centre of our picture. This should be on an 
 imaginary line drawn across the view at the height 
 of the eye. We are supposed to look straight 
 before us, our line of sight being level, or hori¬ 
 zontal. The choice of this centre altogether rests 
 with ourselves. We are going to reproduce on a 
 large scale one of the myriad projections which fell 
 on our eye as we turned the head, and we may 
 take which pleases us most. 
 
 A more agreeable and less formal picture is 
 given by taking our line of sight oblique to some 
 of the main original lines. If we prefer to take 
 a direct picture, so that the main lines of the 
 original shall be perpendicular to the plane of our 
 picture, our work will be simplified, but the draw¬ 
 ing will be stiff and less pleasing, and the follow¬ 
 ing must be borne in mind : The vanishing point 
 of all such lines perpendicular to the plane of the 
 picture is in the centre of the picture. Adopting 
 the rule previously given, it would be found to be 
 so, and lines parallel to the plane of our picture 
 would have no vanishing point at all, as would 
 also be determined by turning the head and looking 
 parallel to them. The line of sight in this case 
 would not meet the plane of the picture. The 
 drawing would present this effect. 
 
ESTIMATING POSITIONS. 
 
 59 
 
 We will choose the centre of the picture to one 
 
 side of this vanishing point, or, in other words, our 
 
 Fig. 24, 
 
 0 
 
 line of sight will be oblique to the main lines shown 
 in this sketch. 
 
 Having selected a centre of the picture o, a line 
 must be drawn through it as before. It will be 
 about two-thirds down the paper, and parallel with 
 the bottom margin. A line co must be drawn 
 through the centre of the horizontal line—at right 
 angles to it, or parallel to the side edge of the 
 paper. We must recollect distinctly what point 
 in the background is our centre, for it will coincide 
 with the intersection of these two lines. In our 
 sketch it is a point on the pillar seen through the 
 arch. The next step is to hazard the length of 
 some prominent original line near this centre. 
 Having assumed such a dimension, everything 
 connected with our picture is fixed ; nothing is 
 now arbitrary. We have, in doing this, assigned 
 
60 
 
 PEESPECTIVE DRAWINa. 
 
 the distance of the eye from the imaginary pane 
 of glass, the image on which we are supposed to be 
 copying. Now, every other line in the drawing 
 must bear its true proportion to this line. Let 
 this first line be the height of the arch; then, 
 on looking at the arch and refiecting, we say, ‘ Its 
 width is not nearly so much.’ We must hazard a 
 width and draw a rough arch. We must now 
 compare the proportions of our arch with those of 
 the original. If we are satisfied that they are cor¬ 
 rect, the drawing is half done, for on this founda¬ 
 tion we will build the greater part of it. Our 
 means of estimation and guidance, from this out, 
 for the position of things will be imaginary lines 
 drawn horizontally and vertically. The eye can 
 be trusted to run such lines from any point, and it 
 is by seeing if they cut above or below or beside 
 other points that we estimate the relative positions. 
 Some of the prominent objects near the arch must 
 now be filled in—for instance, the boundaries of 
 the waU facing us. The width and height of the 
 arch will lead us to the fixing the positions for 
 these boundary lines. The wall facing us has simply 
 been sketched in by the unassisted judgment. No 
 detail must be attempted until the framework in 
 which it is to lie has been satisfactorily drawn. 
 
VANISHING POINTS. 
 
 61 
 
 Now comes what is the kernel of our difficulty, 
 and what is a bugbear to beginners—our vanishing 
 points. What lines require them, and where are 
 they ? Without them we shall not know in what 
 direction to draw the main lines of the picture, 
 and with them all will be plain sailing. Every 
 set of parallel lines will have a vanishing point. 
 Fortunately we need not be perplexed with many, 
 for the greater portion of our lines, and those the 
 most important, are in one direction. These are 
 the main lines of the hall to our sides, the edges 
 of floor and ceiling to our right and left, the prin¬ 
 cipal divisions in the pavement, the upper and 
 lower edges of the picture-frames, the edges of the 
 hearthstone and mantelpiece—all of which will 
 run to one common point. We find where it is 
 by the rule previously given,—by looking parallel 
 to any one of them, and noting where the line of 
 sight strikes the background. In our picture (see 
 plate), it lies in the pillar supporting the right- 
 hand vase. As all the lines we now are consider¬ 
 ing are horizontal, the line from our eye parallel 
 to them must be horizontal also. It will impinge 
 upon some point in the horizontal line previously 
 drawn through the picture. It is well to note 
 that while it remained optional with us to select 
 
62 
 
 PERSPECTIVE PRAWING. 
 
 any point on tlie horizontal line as the centre of 
 our picture, the vanishing points of all lines are 
 fixed and remain so, however we may vary the plane 
 of our picture, provided'we keep our heads steady. 
 There ought to be no difficulty in looking parallel 
 to any line, but we may be assisted in doing so by 
 recollecting that the ray from our eye is to be chosen 
 so that the point where it strikes the background is 
 to be at the same distance from any of the lines as 
 our eye is. In our picture the vanishing point is 
 the same height from the floor as our eye, and also 
 the same distance from the side wall as our eye is. 
 If a division in the pavement should run under 
 our seat, we may be assisted by following it down 
 the hall to where, if produced, it would cut our 
 horizontal line. Let the vanishing point be 
 marked with a cross or star, so that there may be 
 no mistaking it. Into it all the lines referred to 
 must be made to run. It is seen that the drawing 
 at once takes form, and there is a satisfaction in 
 knowing that the framework so far is correct. . 
 The vertical edges of the wall confronting us have 
 been already drawn, having been placed where the 
 eye assigned them their position in relation to the 
 arch. It now becomes necessary to fix the upper 
 and lower edges of the wall, and for this purpose, 
 
FIXING THE DISTANCE OF EYE. 
 
 63 
 
 since we have chosen an oblique view, we will re¬ 
 quire the vanishing point for them, and all lines 
 parallel to them. If we acted upon our rule, and 
 looked parallel to them, or along one of the trans¬ 
 verse markings in the pavement, which would be 
 a safe guide, we should no doubt find the vanish¬ 
 ing point, but it is obvious that it would not be on 
 the drawing pad. It would cut the plane of the 
 picture at a considerable distance to the left. Our 
 determination of it by this process would be too 
 uncertain. In the former case the vanishing point 
 lay on our paper, and its position was easily laid 
 down among the articles to which we had assigned 
 positions, but here it lies on a part of the back¬ 
 ground not in our picture. For the present the 
 upper and lower lines of the wall facing us must 
 be assumed, care being taken to make the top line 
 slope downwards considerably to the left. They 
 will presently be corrected to their true places. 
 It was said that in assuming a distance for the 
 height of the arch we fixed the distance of our eye. 
 This is obvious when we consider that the pencil 
 of rays reaching our eye may be cut at any point 
 by the plane of our picture, but that at each point 
 its width and height will be different. If we had 
 traced a house upon a window-pane, we should 
 
64 
 
 PERSPECTIVE DRAWING. 
 
 find, on seeking to ascertain our point of sight, 
 that our tracing would only fit over the house 
 when we placed our eye at a distance from the 
 tracing which its size had fixed. It would be too 
 big if our eye were too near, and too small if our 
 eye were too far. 
 
 The distance of our eye, then, as we have said, 
 is fixed, and it becomes necessary to find what it 
 is. We must look upon the pavement at our feet, 
 and pick out a diagonal line in it. This line lies 
 exactly between the two lines whose vanishing 
 points we have been considering, one of which we 
 have found, and the other of which we could not 
 find. There are certain to be such lines among 
 the tiles; if there were not, we should have to 
 imagine one, and follow it with our sight until we 
 found its vanishing point. In our sketch this 
 vanishing point lies in the fireplace. It lies on 
 the horizontal line as does the other, and for the 
 same reasons. These two points subtend at the 
 eye an angle of 45°. There can be no doubt about 
 this, for rays from our eyes run to them exactly 
 above two lines in the pavement, which are known 
 to enclose 45°, inasmuch as the diagonal halves 
 the angle of the square which is 90°. Our eye is 
 also exactly before the point c, the centre of the 
 
FINDING DISTANCE OF THE EYE. 
 
 65 
 
 picture. Imagine threads from these two points 
 running into the eye. Now comes a construction 
 which must be carefully attended to. A piece of 
 paper containing a square angle must be folded 
 over so as to halve the angle, thereby producing 
 an angle of 45°, for the whole angle was 90°. 
 This piece of paper must be slid along the 
 
 Fig. 25. 
 o 
 
 line c 0 , as shown in the sketch, so as to rest 
 with its point 0 on this line, and a side touching 
 each point v and v'. Mark the point o thus 
 found. This triangle v o v' is the triangle formed 
 by the lines of thread to our eye turned over *so as 
 to lie flat upon the paper (see fig. 13). By its aid 
 
 F 
 
66 
 
 PERSPECTIVE DRAWING. 
 
 we have discovered that the distance of our eye is 
 0 c. We can now find any vanishing points with 
 certainty, provided we know what angles they sub¬ 
 tend at the eye. v and its fellow V' that we were 
 looking for subtend 90°. Draw o v",—which can 
 best be done by opening out the paper—and pro¬ 
 duce it. This line will intersect the horizontal line 
 in y". Unless w^e dtrsire to be very exact, we need 
 not draw more than a short portion of this line 
 (see sketch). Any lines occurring between oy" 
 and the horizontal line will slope downwards, 
 taking an intermediate position. If this point y" 
 is even roughly determined, we are in a position 
 to fill in the upper and lower boundary lines of the 
 wall facing us. 
 
 W^e will now do a little of the pavement. If 
 there is any uniform pattern spread over it, we 
 must divide the bottom margin of our picture into 
 ecjual spaces, representing, we will suppose, the 
 width of the ladders in the pavement confining 
 the pattern. The width must be hazarded. The 
 number must be counted between two objects 
 already fixed, if the eye cannot assign an ap¬ 
 proximate value without this aid. What is now 
 insisted on is the eq 2 iality of the divisions (see 
 pages 44 and 45). It is a case similar to that of 
 
THE PAVEMENT. 
 
 67 
 
 the three posts represented in fig. 18. The spaces 
 into which this line is divided do not appear under 
 equal angles when looked at successively, but the 
 pencils from them cut the plane of the picture 
 in points proportionately distant, and consequent!}" 
 the projections, or pictures, of these equal di¬ 
 visions will be equal. Each point given by the 
 division must be joined to v (see frontispiece). If 
 the pattern on the pavement should be squares, the 
 simplest way of getting them in will be by joining 
 these points to v" also, which point must be found. 
 If its distance should be considerable, a pin may 
 be placed through a loop on a piece of thread and 
 fixed at y "; a line can then be stretched succes¬ 
 sively to these points. It will be more convenient 
 to find the vanishing point V" of the other dia¬ 
 gonals, especially if the pattern be diamonds or 
 variegated. (We have already found v', situated 
 in the fireplace, the vanishing point for the 
 diagonals sloping to the left.) This is effected by 
 making the angle v'o v"' equal to 90°. This 
 can easily be done by adjusting the square angle 
 of the paper on the line y' o and drawing o y'". 
 The two vanishing points of the diagonals will 
 enable us, without any difficulty, to run up one 
 of the ladders on the pavement, drawing lines 
 
68 
 
 PEESPECTIVE DRAWING. 
 
 alternately to v' and y'" , Any variety of pattern 
 can be drawn, as shown in the sketch, with a little 
 ingenuity. 
 
 The top of the table is arrived at in this way 
 (fig. 26). Assume ab as its length. Through a 
 and B draw lines to the distant vanishing point 
 y". Find the centre of the table as explained 
 
 Pig. 26. 
 
 on p. 50. Join the centre so found to v', the 
 vanishing point of the diagonal, and produce to e. 
 The two corners n and e are thus found. Draw 
 lines through these corners n and e to c, and the 
 sides of a square table are determined. If the 
 
PICTUEE-FEAMES 
 
 69 
 
 table should be circular, the curved top must be 
 neatly fitted within this quadrilateral. 
 
 If the table should stand in the centre of the 
 hall, a vertical line through its centre should pass 
 through the centre of the floor. 
 
 The pictures on the wall will be within the 
 guides given by the vanishing point v. The 
 amount of foreshortening had best be estimated 
 by the eye. As there is rarely any definite 
 proportion between the length and breadth of a 
 
 Pig. 27. 
 
 picture-frame, this can be done without any 
 violation of a possibility. If the true character of 
 
70 
 
 PERSPECTIVE DRAAVING. 
 
 a frame be known, its true projection can be 
 drawn by the process described for laying down 
 the figure of a square—viz. by looking up to the 
 ceiling for the vanishing point V (fig. 27), of 
 one of the diagonals, and joining this point to b, 
 the corner of the picture, and producing this line 
 to where it cuts v a in the point n, which is thus 
 found to be one of the near corners of the frame. 
 The vanishing point v' will lie vertically over y. 
 Tlie point D having been found, the frame is easily 
 completed. The distance of point v^ may render 
 this process impracticable, in which case the 
 
 Fig. 28. 
 
 O 
 
 following may be adopted : On the side of the 
 picture a b, the length of which has been assumed, 
 
PICTURE-i’EAlVIES. 
 
 71 
 
 draw the frame in its true proportions, A b c d. 
 Draw V o' equal to y o, and join o' to the far 
 corners of the frame c and D ; where the lines 
 so drawn cut the lines va and yb— viz. d and 
 c—are the far corners of the picture. This con¬ 
 struction is more difficult to understand. The 
 principle upon Avhich it is based is this,—the 
 amateur need not trouble himself with it. 
 
 If two lines ab and CD parallel to each other be 
 drawn from the extremities of a line ad, and the 
 Fig. 29. 
 
 A B 
 
 C 
 
 points c and b be joined, cutting ad in a, then 
 if a B and c d be turned round to any new posi¬ 
 tions ab' and dc', still retaining their parallelism, 
 the line joining c' and b' will cut a d in the same 
 point a. (This is OYident to the geometrician.) 
 Each new pair of triangles lies in one plane ; they 
 are equiangular, and retain the original sides a b 
 and CD. ad will be constantly cut in the propor¬ 
 tion, aB : CD, ^.e. in the point a. 
 
 The ray from the eye to y (fig. 28) is parallel to 
 the upper edge of the picture-frame, for y is its 
 
72 
 
 PEESPECTIVE DEAWING. 
 
 vanisliing point. The line v B on the plane of 
 the picture connects the extremities of these two 
 parallel lines ; the visual ray from the eye to the 
 corner c of the frame joins the extremities of 
 these two parallel lines, and cuts the line yb in c. 
 Yo' and CA, still retaining their parallelism, are 
 laid flat upon the paper, and the point of inter¬ 
 section of VB is found at c—the point required. 
 The case is exactty similar to that given in 
 fig. 29. The bisection of the line is based on the 
 same principle. 
 
 It is frequently desirable to find out the lines 
 on a pavement which will represent the gradual 
 
 Fig. 30. 
 
 Y 
 
 crowding of equidistant lines as they are more and 
 more distant from the eye. Let two parallel lines 
 A B and c D be drawn to their vanishing point v, 
 let the diagonals to the figure be drawn, and let 
 A c and B D be drawn to their vanishing point, 
 thus completing the parallelogram. The inter- 
 
DIVISION IN THE PANELLING. 
 
 73 
 
 section of these diagonals will mark the point 
 which is equidistant; a line drawn through it to 
 the distant vanishing point will mark off little 
 parallelograms, and the same method of finding 
 their centres can be continued; but in this case it 
 cannot be said whether they are squares or not. 
 
 The only point which remains to be noticed in 
 our picture of an interior is the mode of dividing 
 any main line on the wall facing ns into the di¬ 
 visions which we see upon it. We have chosen 
 the centre of onr picture c, and the position of the 
 arch. We have roughly posed the vertical lines 
 bounding the wall. The distances of these lines 
 from either side of the arch are equal; the divi¬ 
 sions in the panelling are also equal. How are 
 the pictures of these points to be ascertained ? 
 This problem is generally explained (p. 50, fig. 22), 
 and was made use of in finding the centre of the 
 table. The particular case will now be dealt with. 
 The construction is different from that previously 
 given, as being, perhaps, more convenient. Let 
 us proceed to divide the horizontal line. We have 
 chosen the points a and c, and we wish to find 
 the point e, so that a o and c e may represent 
 equal lines. Draw ov'^ to the vanishing point of 
 the lines in this wall, draw ab parallel to it; 
 
74 
 
 PERSPECTIVE DRAWING. 
 
 draw o c cutting a b in d ; make d b equal to D a ; 
 and divide this line db in exactly the manner that 
 
 0 
 
 the original line is divided, and to the various 
 divisions draw lines from o ; where these produced 
 cut AE are the pictures of these points on the 
 drawing. The points ahcclef are thus found 
 in their true positions. The principle on which 
 this construction is based is that previously re¬ 
 ferred to. The line from the eye to v is parallel 
 to the line ae in the wall. These lines, from the 
 extremities of ao, are turned round so as to coin¬ 
 cide with the paper, retaining their parallelism. 
 
 If the main lines of a hall or interior are per- 
 
FALSE PICTUEES. 
 
 /D 
 
 pendicular to the plane of the picture, as is the 
 case when a direct view is taken, the vanishing 
 point of these lines will lie on the centre of the 
 picture; and the original lines parallel to the plane 
 of the picture, such as the transverse markings on 
 the pavement and the lines on the wall confronting 
 us, will be all parallel to the bottom margin of the 
 picture. They will have no vanishing point. If 
 the oblique view should be taken as that given in 
 the sketch (fig. 32), the vanishing point being to 
 one side of the centre, the transverse lines, being 
 now not parallel to the plane of the picture, will 
 have a vanishing point; and they must not be 
 allowed to appear parallel to the bottom edge of 
 the drawing-pad. Such an interior as that .drawn 
 
 Fig. 32. 
 
 is wrong for the reasons stated. The lines ah, cd, 
 &c. should not be parallel to the lower edge of the 
 
76 
 
 PERSPECTIVE DRAWING. 
 
 jframe. The mistake here shown is that most 
 frequently seen in drawings. 
 
 It has been said that a person desiring to look 
 at a picture should stand in reference to it as the 
 artist stood in reference to the original. This is 
 very desirable, though within certain limits not 
 necessary. Almost the same projection falls from 
 a picture upon the eye, no matter where situated. It 
 will, of course, be larger when the picture is near, 
 and smaller when remote, and will be slightly fore¬ 
 shortened when seen from one side; but, broadly 
 speaking, a picture will give the same projection to 
 a crowd of visitors looking at it, and the mental 
 impression which will follow will be the same. 
 Still the nearer one can pose himself on the di¬ 
 rection of the original line of sight, and at the true 
 distance, the better will be the effect. If a portrait 
 is taken of a man standing on a floor, a portion of 
 the floor is seen. If the figure should be raised 
 upon a dais, less and less of the floor is seen as the 
 platform on which it stands is elevated ; and when 
 the height of the eye, or horizontal line, is passed, 
 none of it is visible. A portrait of a man taken in 
 the first position, if hung up high upon a wall, will 
 have an unnatural effect, which simply arises from 
 the observer’s eye not being anywhere near the 
 
HANGING OF PICTURES. 
 
 77 
 
 true point of sight. The figure will appear to be 
 slipping off the floor, which will seem to stand at 
 Fig. 33. 
 
 
 an unnatural slope. Bending the picture for¬ 
 ward will in a measure counteract this unpleas¬ 
 ing effect, for it wiU tend to bring the line of sight 
 in such a position that the observer can place his 
 eye on it. 
 
 The figure shows what is here described. The 
 observer, being much below the line of sighi, sees 
 the floor as though it were tilted up, and the figure 
 as though it were slipping out of the frame. It 
 follows, from what has been said, that pictures 
 should be arranged in a gallery with some reference 
 
78 
 
 PERSPECTIVE PRAWINC. 
 
 to the ^ distance of the picture ’ and to the ^ line of 
 sio'ht.’ The width of an ordinary landscape view 
 taken upon a drawing-pad of about a foot or 
 eighteen inches long would subtend at the eye an 
 angle of about 90°, and the distance of the eye 
 would be about a foot. The width of a man taken 
 full size would subtend but a few degrees, and the 
 distance of the eye would be many feet. We see 
 at once how we violate the conditions referred to, 
 in hanging small pictures at a distance on the toj) 
 of a wall and hanging large ones near us at the 
 bottom. The latter, by retreating from them, can 
 no doubt be viewed from the proper distance ; but 
 the former, which should be held near the eye, so 
 as to subtend an angle of 90° or more, must be 
 viewed at a tenfold greater distance than should 
 be the case. These considerations seem to be lost 
 sije’ht of in all galleries. 
 
 It has been remarked that where still water 
 reflects an image, the reflection follow^s certain 
 laws; care must be taken that the finished sketch 
 shows no violation of such laws. The law of re¬ 
 flection is this: that any ray which speeds from an 
 illuminated body, if it meet with a sheet of water or 
 a piece of silvered glass, will be turned in its course, 
 so that it Avill leave the surface after impinging^ 
 
EEFLECTION OF THE MOON. 
 
 79 
 
 on it in a path similarly situated with regard to 
 the surface to the one it travelled before reaching 
 it. In the language of optics the angle of reflection 
 will be equal to the angle of incidence ; also the 
 plane in which this incident and reflected ray will 
 lie, will be perpendicular to the surface. So that, 
 in the case of water, the surface of which is hori¬ 
 zontal, the plane of reflection is vertical. From 
 this it follows that the reflection of any object in 
 still water will appear directly under the object 
 itself. The reflection of the moon in the sketch 
 
 Fig. 34. 
 
 must be made to appear exactly under the real 
 moon; but, more than this, its distance from the 
 plane of the water must be made equal on the 
 drawing to the height of the moon above it. o m 
 must equal om". 
 
 If the water should be slightly ruffled with the 
 wind, the moon, instead of being distinctly seen 
 
80 
 
 PERSPECTIVE DRAWINa. 
 
 in the water, will appear as a streak of light, 
 broadening from the horizon towards the feet. 
 This line of light is due to the ripples on the 
 water, each of them bending one of the rays that 
 fall on it in the direction of the eye. When the 
 water was still, though the whole of it received 
 rays from the moon, but one point was so situated 
 as to send the rays to our eye; but when ruffled 
 its surface is made up of little waves, each of which, 
 instead of emitting from it one ray only, will emit 
 a vertical fan of rays, one of which from each fan 
 will reach the eye. 
 
 To each observer of the moon there will be a 
 separate reflection, or line of sheen, so that no two 
 persons standing in a boat or on the shore will see 
 the same line of light on the water. 
 
 Whether the moon be in the centre of the pic¬ 
 ture or at one side, its reflection will be exactly 
 under it; and if the water ripples, its image in 
 each little wave will also be exactly under it. It 
 follows that in all cases the line of sheen (which 
 will join these points) must be made parallel with 
 one of the side edges of the drawing-pad. It may 
 be thought strange that this should be so, for it is 
 obvious to each person that the line of reflection 
 of the water will run to his feet, and he would be 
 
MOONLIGHT VIEWS. 
 
 81 
 
 disposed to represent it as in 1, fig. 35. But a 
 little thought will show that it must he represented 
 as 2, fig. 35. 
 
 Fig. 35. 
 
 1 
 
 The plane containing the reflected rays is ver¬ 
 tical, and the intersection of this plane with the 
 plane of the picture must he vertical. That this 
 is so can he easily demonstrated hy tracing on a 
 window-pane the line cast on the water hy the 
 moon. It will he found that, whether the moon is 
 in the centre of the picture or at one side, the line 
 of reflection in the water is at right angles to the 
 window sill, or base of the picture. 
 
 An old ruin on the edge of a lake by moonlight 
 is a favourite picture (fig. 36). The following con¬ 
 siderations will assist one in such a sketch : The' 
 moon is here shown at but a very short distance 
 above the castle. It will be remarked that in the 
 water there is no reflection. The reason for this 
 
 G 
 
82 
 
 PERSPECTIVE DRAWINa. 
 
 will appear on looking at fig. 37, representing a 
 section through the landscape. The moon being 
 
 Eig, 36. 
 
 at an enormous distance, the ray from it to the 
 eye is parallel to the ray from it to the water, 
 which would be reflected into the eye ; but this 
 latter ray is impeded by the opaque ruin, and 
 consequently cannot be reflected. It would be a 
 mistake easily detected to reproduce the moon in 
 both places under such circumstances. 
 
 A few remarks concerning colour will here be 
 added. White light, or the light of the sun, is 
 made up of all the colours of the rainbow 
 (literally) mixed together. The rainbow simply 
 exhibits the disintegration of a cone of rays at 
 the apex of which is the sun, and on the axis of 
 ’which is the observer. This can easily be as- 
 
COMPLEMENTARY COLOURS. 
 
 83 
 
 certained by observing the position of oneself as 
 regards the rainbow. It will appear to be a 
 
 Fig. 37. 
 
 E, the eye of ohserver. 
 
 c, the point in the water where the top of the castle is seen 
 reflected. 
 
 ji, the point where the reflection of the moon would appear if 
 the castle were removed. 
 
 portion of a circle swept round a line joining 
 oneself and the sun. As with the reflection of the 
 moon in the water, no two persons will see the 
 rainbow in the same position; for each it is a 
 circle, over the centre of which he stands himself. 
 When the rain-drops which cause the rainbow 
 have been dissipated, the light which was resolved 
 into many colours becomes whole again by the 
 intimate mixing of the colours. If when the 
 colours were spread out—or ‘ dispersed,’ blending 
 from deep red to indigo—we were to take one tint 
 away and allow the others to blend again without 
 
84 
 
 PEESPECTIVE DEAWIEG. 
 
 it, it is evident that the fusion of the remainder 
 would not be white. Whatever colour it happened 
 to be, would be justly called the complement of the 
 one taken away, for it is that which the withdrawn 
 colour would want to make it white. As eight- 
 pence would be the complement of fourpence, the 
 shilling being considered as the whole, or seven- 
 pence the complement of fivepence, so would any 
 colour be complementary to that which if mixed 
 with it would form white. Experiments to prove 
 that colours, if mixed in due proportion and of 
 the proper tints, will form white cannot be well 
 performed with ordinary paints; for these are 
 impure, and it is extremely difficult to choose the 
 correct tints. Nothing will prove this so well 
 by demonstration as the polariscope, by which 
 coloured lights can be made to blend ; but the 
 thing is obvious that if white light consists of the 
 blending, say, of six colours, any one or more 
 of these will together be complementary to the 
 remainder. As we should expect so we find, that 
 colours which are complementary present the 
 greatest contrast. That which completely neu¬ 
 tralises anything is obviously its greatest con¬ 
 trast. The yellow and purple of a pansie are 
 complementary, and consecmently the bi illiance of 
 
COLOUK OF THE SKY. 
 
 85 
 
 eacli is much enhanced by lying next its opposite. 
 The pink of the rose is also nearly complementary 
 to the bluish green of the leaves, and consequently 
 is more striking to the eye than v^hen held next 
 yellow or orange flowers. Artists avail themselves 
 of these contrasts to enhance effects, and avoid 
 them to produce harmony. If a portrait were 
 taken in a green chair, the face would not bear to 
 be coloured highly; but if in a red chair, the face 
 would bear a deeper red. 
 
 Very few remarks will be made on the subject of 
 colour. Artists have written much about it, but 
 the writer confesses that he has gathered but few 
 ideas from their works. Mr. Ruskin has written 
 six large volumes upon art, and yet appears to 
 pique himself upon his ignorance of many simple 
 points. It is strange if here, as in many other 
 subjects, the philosopher or chemist should in a 
 dry treatise, void of eloquence or rounded periods, 
 be found to offer in a few simple words the 
 explanation which has not been enclosed in the 
 meshwork of fine writing of the art critic. Talk¬ 
 ing of clouds and the colour of the atmosphere, 
 Mr. Ruskin observes: Ms it the watery vapour 
 or the air itself which is blue ? Are neither blue, 
 but only white, producing blue when seen over 
 
PEKSPECTIVE DEAWING. 
 
 SG 
 
 dark spaces ? If either blue or white, why, when 
 crimson in their commanded dress, are the most 
 distant clouds crimsonest? Clouds close to us 
 may be blue, but far off golden—a strange result if 
 air is blue. And again, if blue, why are the rays 
 that come through large spaces of it red ? And 
 that Alp, or anything else that catches far-away 
 light, why coloured red at dawn and sunset? No 
 one knows, I believe.’ 
 
 Very simple is the explanation of the colour of 
 the air and the tint of ^ that Alp at dawn and 
 sunset.’ Eound drops of water disintegrate the 
 
 Eig. 38. 
 
 sun’s light and produce a rainbow of many colours. 
 A globe of air would do the same, and this earth 
 in its outer covering resembles such a globe of 
 air. When the rays from the sun fall obliquely 
 on that portion of this envelope of air which forms 
 our sky, they are disintegrated in exactly the same 
 
COLOUR OF THE SKY. 
 
 87 
 
 way. The first colour in the morning will be that 
 of the ray most bent—viz. violet-grey—and the last 
 will be red. In the evening the first will be red 
 and the last will be violet-grey. In the morning 
 the mountain tops first catch those rays of the sun 
 Avhich are most bent or ‘ refracted,’ and these are 
 the violet; and the last caught are those least bent 
 —viz. the red. In the evening the reverse is the 
 case. The body of air through w^hich the rays 
 penetrate when the sun is on the horizon is con¬ 
 siderably greater than when it has risen, and, as 
 w^e should expect, its absorptive effect is in¬ 
 creased. The blue rays, which are those ordi¬ 
 narily reflected, are now absorbed, and the re¬ 
 maining light is a soft orange tint. 
 
 In India after the rains, when the air is charged 
 with moisture, the refraction is greater than in 
 these latitudes, and the various colours of the 
 rainbow are seen in the most gorgeous brilliancy 
 on the clouds at sunset and sunrise. The green 
 colour, which is seldom seen with us, is there 
 most distinct and beautiful. Mr. Ruskin, refer¬ 
 ring to a coloured solution of nettles, thinks that 
 ‘ perhaps some day, as the motion of the heavenly 
 bodies by the help of an apple,’ this question, ‘ by 
 the help of a nettle, maybe explained to mankind.’ 
 
88 
 
 PERSPECTJYE DRAWING. 
 
 It is very simply explained by tlie laws of refraction 
 and absorption of light. As regards the colour of 
 the air, this is due to its containing in it matter in 
 a state of extremely minute division. This matter 
 casts back upon the eye the tender blue rays falling 
 on it. The stronger waves of the red and other 
 lights break through the air, and not being reflected 
 do not evidence themselves. The slighter the depth 
 of air above one the darker the sky appears. On 
 the top of high mountains or in balloons it is almost 
 black. It is quite lawful to the artist—indeed, 
 necessary to him—to avail himself of any artifice 
 to produce on the mind of a person looking at his 
 picture the same effect that was received by 
 himself in looking at the original vievc. He must 
 make the distance bluish and hazy. This gives 
 to the eye, schooled by practice, the idea of 
 distance. He must take especial care that the 
 size of clouds and other things is reduced as they 
 recede from the eye. In colour also they must be 
 more and more faint. It is especially necessary 
 that the artist should avoid scattered lights. It is 
 this defect which mars the appearance of most 
 attempts of the beginner, without his knowing 
 why. In nature the lights are scattered, but a 
 drawing is not nature. By artifice it is designed 
 
SUBJECTIVE COLOURS. 
 
 89 
 
 to give the same mental impression; hut, as is 
 evident from the foregoing’, the conditions are so 
 extremely different in the two cases of looking at 
 a scene in nature and looking at its picture, that 
 any expedient is allowable which will increase the 
 natural effect of the latter. It is desirable that 
 there should be a focus of interest in each picture, 
 generally in or near the centre, and the main lines 
 in a drawing are advantageously arranged, so that 
 they guide the eye to this point. As in the hall 
 shown in the frontispiece the main lines run to a 
 point, so it is expedient in a landscape that the 
 main directions should lead to a centre. 
 
 A photographic landscape is seldom agreeable, 
 and yet it resembles the reality, in light and 
 shade, more closely than any picture taken by the 
 eye and hand can be expected to do. The reason is 
 that it errs in those respects just alluded to. Its 
 lights are gen:*rally scattered. There is no 
 grouping of the light and shade. There is also an 
 absence of composition, or what may be called the 
 tricks by which the eye may be assisted to a 
 pleasing and natural effect. It is well in landscape 
 painting that the masses of light and shade 
 should be balanced. If the drawing should be 
 very dark in one corner of the foreground, a dark 
 
90 
 
 PERSPECTIVE DRAWING. 
 
 cloud may be conveniently introduced into the 
 opposite corner in the sky; or if one corner should 
 be light, the opposite one should be light also. 
 
 The following point is worthy of remark: The 
 true colour of an object, which it would exhibit if 
 taken in the hand and examined, or inspected 
 from all points of view, is not always that which 
 it appears to have when it is one of many objects 
 seen together. This change of colour, due to 
 the contrast to which the eye is subjected, is very 
 slight, and might almost be discarded. Such tints 
 not really owned by the objects looked at are 
 called subjective. Any bright hue will tend to 
 make the colour on which it abuts of the com¬ 
 plementary tint; thus the shadows of green trees, 
 upon grass would appear slightly tinged with 
 red. But more important is the change of shade 
 of objects produced by contrast. An object appears 
 to become light or dark, according to the back¬ 
 ground on which it is projected. The amateurs 
 will be materially assisted by bearing this in 
 mind. A wooden paling which runs across a 
 background of dark trees and light grass will 
 change its depth of shade for each background. 
 It will be quite a light colour when passing the 
 trees, and quite dark while passing the grass. 
 
EFFECT OF MIXED PIGMENTS. 
 
 91 
 
 though in reality its colour is unaltered. This 
 fact can be easily observed by looking at the rail¬ 
 ings which enclose any ground containing trees 
 and grass. It would be a triumph of skill to paint 
 a white horse upon a white background, and the 
 avoidance of such necessities, though one of the 
 tricks of art, is really suggested by nature. 
 
 The amateur should recollect that water-colours 
 show their colours by their transparency. The 
 white light of the paper comes to the eye through 
 a thin layer of pigment, which bars a certain 
 portion of the light from passing. That portion of 
 the whole ray which is allowed to pass carries 
 with it its peculiar hue. The light from the 
 window or the sky plunges into the paper and 
 comes out again bereft of a certain portion. Why 
 the different pigments act as they do is another 
 matter which may be left to the consideration of 
 the chemist or philosopher, and with which the 
 artist need not concern himself. In oil-paints the 
 white-lead which forms the base of each colour 
 acts as the white paper with the water-colours, and 
 throws back to the eye the white light of day, 
 deficient of certain rays. It at once follows that 
 the water-colours must be lightly spread, or the 
 white light will not be able to pass through them, 
 
92 
 
 PERSPECTIVE DRAWINa. 
 
 in which case the paints ay ill be opaque and will 
 have only the dull colour which they exhibit in 
 their cakes, Avhich, as everyone knows, is not nearly 
 so beautiful as their colours when ‘ rubbed up ’ upon 
 a white palette. These considerations lead to the 
 folloAving suggestion: If bright greens should be 
 required in a drawing, it is better that the colour 
 should be procured as a green from the colourman 
 than made by the mixing of yelloAv and blue. Pro¬ 
 perly speaking, the yellow and the blue, Avhen 
 mixed, should give no colour at all but brown or 
 dirty grey, as the folloAving considerations will 
 show. The blue colour, when spread upon a piece 
 of paper, allows tlie white light to pass through it 
 bereft of all its rays except the blue. A layer of 
 yelloAV spread u^^on the paper Avould check all the 
 colours of the rainbow except the yellow; so that 
 if both layers were spread on the same spot, the 
 blue which escaped through the first would be 
 stopped at the second. If the order of layers was 
 changed, the yellow which escaped through the 
 first coat could not get through the second; so 
 that one would expect to see only a grey colour; 
 but the fact is that yellow—say gamboge—allows 
 some white light and some green and the whole of 
 the yellow to pass through it, and blue—say cobalt 
 
EFFECT OF MIXED PIGMENTS. 
 
 98 
 
 —allows somewliite light and some green and the 
 whole of the blue to pass through; so that where 
 the two layers are spread one over the other, or 
 are mixed, the wdiite light and the green fijid 
 their way clear through hoth, and consequently the 
 green is the colour which the eye perceives. 
 The writer is aware that no reflections of this 
 kind will lead to proficiency in drawing, but he 
 believes that no workman is the worse for 
 understanding the mechanics of his tools, and he 
 thinks that the amateur artist may at least be 
 interested, and perhaps benefited, by understanding 
 the conditions and surroundings of his craft. 
 
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