MODEL DRHiflZING
 
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 LOS AiN'GELES 
 UBRARY
 
 MODEL DRAWING 
 
 PKEPARED FOR THE USE OF THE STUDENTS 
 
 OF THE 
 
 Massachusetts normal Art School, 
 
 BOSTOK, MASS. 
 
 By ANSON K. CROSS. 
 
 
 
 
 BOSTOiT: 
 
 1890. 
 
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 COPTEIonTKD BT 
 
 ANSON K. CROSS. 
 1830,
 
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 INTRODUCTIOK 
 
 The value of a course in dra'wing when, the subject is 
 properly presented to the student can scarcely be over- 
 estimated, but it must be confessed that much of the 
 instruction given is such that its benefit is a matter of 
 doubt. At the beginning of his art education the student 
 should be taught to see correctly. When this has been 
 accomplished, and he is able to represent truly what is 
 before him as it appears, and not as he thinks he sees it, 
 then he is in a position to advance, and his imagination 
 may be cultivated. But as the first point to be gained is 
 ability to see truly,, it follows that we should from the 
 very start demand truth ; first truth of outline, next, truth 
 of light and shade, and then truth of color. We wish to 
 consider here simply truth of outline, but the student will 
 find that the study of appearances, and their representation 
 as fully as possible, even in so simple a medium as outline, 
 will have in great measure prepared the way for the more 
 difficult work in light and shade and color. The whole 
 question is simply one of seeing, and the student should 
 not trouble himself over technique, as he has enough to do 
 to represent nature truly. 
 
 It is often said that in nature there are no outlines. In a 
 way this is true, but it cannot be understood to mean that 
 
 (3)
 
 4 INTRODUCTION. 
 
 form is unnecessary or that it may be slighted. The stu- 
 dent cannot learn to paint or to make pictures in any me- 
 dium without drawing the forms of the objects. The 
 defining of the lights and shades and the various bits of 
 color which go to make the effect, is necessary to give 
 solidity and character to a picture, and it is useless to think 
 that anything can be accomplished with color or light and 
 shade until exact representations of form can be made. 
 
 Every object has definite form and size, and though it 
 may not be outlined it has boundaries. Although the rep- 
 resentation of objects in outline only is at best a conven- 
 tional and imperfect means of expression, so far often as 
 even form is concerned, the student can be taught to ob- 
 serve effects and may succeed in conveying a fair impres- 
 sion of the character of the object and of varieties of 
 surface and texture. 
 
 The student must work long and earnestly before 
 he can separate facts from appearances, as the knowledge 
 of the actual form prevents the mind from accepting 
 its appearance. The impression conveyed to the mind 
 of one not trained to accept the vision of the eye, is 
 the result of a combination of what the eye sees with what 
 is by far the greatest factor, what the mind knows con- 
 cerning the actual condition of the object. The student 
 must struggle continually not only against this influence 
 of his mind, but also against the effect which one line 
 exerts to change the apparent direction of others. This 
 effect is sometimes so strong that even the practised eye of 
 the artist is deceived, and we may safely say that the most
 
 INTRODUCTION. O 
 
 perfect eye, with the longest training (of sketching simply) 
 is not surety against mistakes. A knowledge of the per- 
 spective principles governing the appearance of form is 
 thus absolutely necessary to the draughtsman who would 
 be exact, and there is no reason why there should not be 
 exactness and artistic rendering at the same time.
 
 MODEL DRAWING. 
 
 FREEHAND DRAWING. 
 
 The most important points in freehand drawing are free- 
 dom, directness and accuracy. It is difficult to give direc- 
 tions which shall produce these results, as individuality- 
 will prevent all from working in a uniform way, and hand- 
 ling and technique are of little importance. Since the pro- 
 duction of correct drawings is the end desired, it is of no 
 consequence that such drawings are produced by different 
 persons in different ways, but it may be well to give a few 
 general directions, the most important being that the pencil 
 should be held lightly, and the first lines of the drawing 
 sketched in freely and very quickly. The paper should be 
 not less than eleven by fifteen inches, and the drawings 
 should be large. In beginning, it will be best to draw the 
 full size of the objects, as small drawings will produce a 
 cramped way of working. A long pencil will assist 
 the student to freedom of movement. It may be held 
 as a stick of charcoal between the thumb and first 
 two fingers, and as far from the point as possible. The 
 paper should be fastened to the board, witli its edges paral- 
 lel to those of the board. If the edge of the paper is not 
 quite straight, a horizontal line should be ruled near the 
 lower edge, so that directions may be referred to this line. 
 
 (6)
 
 SIXGLE OBJECTS. 7 
 
 Before attempting to represent any object, the student 
 should acquire the freedom of motion which is necessary 
 to good work, by drawing lines in all directions. Curved 
 lines will be produced by swinging the pencil from the 
 wrist, elbow or shoulder, and straight lines by a motion of 
 the entire arm. This movement should be practised until 
 lines can be drawn instantly across the paper in any direc- 
 tion. This free motion is most important for all sketching, 
 but in finishing or lining in a drawing whose proportions 
 have been thus sketched, more pressure will be required, 
 and the pencil may be held more firmly and nearer the 
 point. 
 
 The first subjects should be the geometric solids, with 
 the vase forms (such as are found in the models to be ob- 
 tained at Art Supply Stores), but common objects, as boxes, 
 etc., are equally good. We will explain the way in which 
 these should be studied, by making a sketch from a box 
 with its cover partly open (Fig. 1). First, nearly close the 
 eyes, and try to see the box not as a solid, but as a sil- 
 houette, the outline of the mass of the box, as seen against 
 the background, being what should first be carefully studied. 
 A little practise with the eyes nearly closed will enable one 
 to see the mass in this way. In order to see the direction 
 which the edges appear to have, lines may be drawn in the 
 air by moving the pencil point so that it passes in front of 
 the edges. Care should be taken not to move the pencil 
 away from the eye when this is done, that is in the actual 
 direction of the edges, but to keep the pencil point where 
 it would be if it were held upon a pane of glass placed
 
 8 SINGLE OBJECTS. 
 
 directly in front of the student. This test is the most 
 valuable of all, because it is the easiest and simplest to 
 apply. It is really the same as the one of the thread 
 explained on page 59, and nearly all other means of testing 
 will at last be discarded in favor of this first and simplest. 
 After careful study of the mass, its outline may be lightly 
 sketched, no measurements of any kind having been made. 
 The aim is to train the eye to exact seeing, and in order to 
 do this the student must learn to depend on his eye, and 
 put down its impression rather than the results of mechani- 
 cal tests of proportion. We must draw first, and afterwards 
 test hy measuring. When the outline of the mass has been 
 sketched then the inner lines may be drawn, and the result 
 carefully studied to see that it agrees with the appearance. 
 When it is as near as can be seen, it may be tested by 
 measuring the proportions, as explained on page 53. If the 
 sketch does not agree with these tests it must be changed. 
 All changes are to be made not by erasing, but by drawing 
 new lines, and the drawing must be carried on in this way 
 until the correct lines are determined. The first lines 
 must be very light, and as changes are made the strength 
 must be increased to distinguish them, until the correct line 
 is secured. The drawing now having been changed to agree 
 with the measurement of the whole height and width, and 
 tested by moving the pencil point to cover the edges, it will 
 be well to test it by means of vertical and horizontal lines 
 passing through all the angles of the box. Thus drop the 
 pencil point vertically from point 1, and see where it cuts 
 the lower edge, and carry the point horizontally from 2,
 
 SINGLE OBJECTS. 9 
 
 and note its intersection with the front edge. When these 
 tests have been made, the pencil point may be moved to 
 cover, and made to continue the edges A, B, C, etc., until 
 the points where they cut the opposite outline are noted. 
 These tests may also be applied by the pencil held hori- 
 zontal and vertical, and used as a straight edge to continue 
 lines. Such tests, if carefully made, should give a drawing 
 practically correct, and should be depended upon with the first 
 measurement of the whole height and width, which should 
 be very carefully taken. Any distances which are nearly 
 equal, as E, F, and F, G, may also be compared, but as a 
 rule very few measurements of proportion should be made, 
 as short measurements, or a short with -a long, cannot be 
 made with sufficient accuracy to be of any value. The 
 thread may be used instead of the pencil in making these 
 tests, as explained on page 59. The thread gives a fine 
 line, and its intersections with the various edges can be 
 seen exactly, so that until the eye can be very closely de- 
 pended upon the thread is preferable to the pencil. In all 
 of this work the changes must be made hy drawing new 
 lines and not hy erasing. This is most important, for the 
 erasing of lines and thus the keeping of but one line 
 throughout the various stages is most certain to produce a 
 hard and inaccurate drawing, and even although it may 
 finally be made to agree with all tests, it will still be lack- 
 ing in spirit. 
 
 It is very difficult for most students to draw lightly 
 enough to secure the correct result except in very black 
 lines, but it is better rather than to erase to throw the
 
 10 SIXGLE OBJECTS. 
 
 drawing away and start anew, until the correct lines can 
 be secured without too great heaviness. The reason for 
 this way of Avorking is, that we wish the student to depend 
 as much as possible on his eyes, and if he erases, and has 
 one line from the beginning, unnecessary time is given to 
 its drawing, and he will hesitate before erasing it. If light 
 lines are drawn and not erased, but others drawn as soon as 
 there is doubt about the first being rightly placed, the stu- 
 dent is much more free to change as each suggestion occurs, 
 and toward the last he has his choice (as the tests indicate 
 corrections) of the various lines already drawn. This is by 
 far the quickest and most accurate way, and besides it 
 prepares for quick and accurate sketching ; indeed the 
 student will not have to draw very long from the geometric 
 solids before he will be able to produce correct sketches 
 without drawing many unnecessary lines. 
 
 There is not much choice of pencils for this part of the 
 work, but it is well to use always as soft a one as the 
 nature of the work will permit. As no pressure should 
 be used, the lead barely making a mark on the surface of 
 the paper, and as all the lines except the correct ones must 
 be erased, there is no reason why the student who has diifi- 
 culty with the soft pencil should not use a hard one until 
 the drawing is ready to line in. 
 
 When the correct outline has been found, it is necessary 
 to finish the drawing. The paper must first be cleaned, all 
 the lines except the correct ones being erased. The easiest 
 way to reserve these lines will be to make them enough 
 stronger than the others, so that they will show faintly
 
 SINGLE OBJECTS. 11 
 
 when the latter have been removed. The drawing may 
 now be lined in with a soft pencil (and here the> pencil 
 must be held more firmly and nearer the point), the attempt 
 being not to produce a fine, even line, in imitation of a ruled 
 one, but rather a line of medium strength, which may be 
 easily drawn, and shall convey the idea of straight, un- 
 broken edges. For the present it is better for the lines to 
 be made of one strength, with no attempt at gradation, or 
 the frequent conventional lining in of the nearer edges in 
 heavier lines. This point will be considered later, but we 
 wish now to advise the student, if he is already familiar 
 with it, to forget it as quickly as possible, and to finish in 
 uniform lines or in the way explained on page 17. 
 
 The method of work presented in these notes is that 
 which should always be employed, and the student should 
 draw from various objects, in different positions, until he is 
 able to see them very nearly correct at first. The time 
 required for this will depend wholly upon the pupil, and 
 the care with which directions are followed.
 
 GROUPS. 
 
 After the practise from single objects, prisms, pyramids, 
 etc., two or three should be placed together, and here the 
 method is the same as for a single object. The usual way, 
 or that which the student would probably adopt, would be 
 to draw, first the prism A, fig. 4 ; next the vase B ; then 
 the cylinder C ; and last the frame D. The trouble with this 
 way of proceeding is that the objects are drawn one at a 
 time, and one added to the others, so that until the last is 
 drawn the proportion of the whole group, that is, the 
 greatest width in comparison with the greatest height, can- 
 not be seen. Indeed, this is often not even considered, the 
 student taking it for granted that since he has measured and 
 tested each object as he drew it, the single objects are cor- 
 rect, and therefore the group. But from what has been 
 said, it will be seen that each object is likely to be a little 
 out of proportion, indeed, we may say, is sure to be so. 
 This being the case the errors are multiplied, and if the 
 height and width are compared, the proportion will be 
 found to be far from correct. It is a principle commonly 
 acknowledged now, that in all teaching the whole should 
 be presented before its parts, so that it cannot be contra- 
 dicted that adding one object to another, until finally the 
 patch-work is complete, is a very uneducational way of 
 proceeding. Practically it is also a very unsatisfactory 
 one, as with each object the difficulties increase, and at last 
 it becomes impossible to place the drawings where they 
 
 (12)
 
 GROUPS. 13 
 
 belong. The only logical way is to draw the group all at 
 once, first considering it as a mass and blocking in its pro- 
 portions by straight lines passing from the principal points 
 (see Fig 5). When these lines have been drawn and con- 
 sidered, they may be tested by measuring the whole height 
 and width, and the directions tested by use of the thread 
 or pencil as explained. 
 
 The proportions of the whole being thus determined as 
 nearly as measurements can determine, the objects may 
 now be sketched in by eye, the most important lines being 
 drawn first ; that is, the lines whose positions and directions 
 are easiest seen. Such lines will be the longest lines, and 
 those which are brought out distinctly by shade, and lines 
 of one object which are nearly continuations of the lines 
 of some other object. It is evident that in this way the 
 drawings of the objects are proceeding at the same time, 
 and the shorter and less prominent lines being drawn last, 
 the group may be said to be drawn all at once. 
 
 While drawing, the student must think of the tests 
 applied by the thread, the horizontal and vertical lines, and 
 the continuing of lines ; and the drawing in the air, or pass- 
 ing of the pencil point over the edge to be represented, will 
 help greatly. The objects should be studied in this way, 
 and changed as often as found incorrect, until no further 
 changes can be made. It is now time to apply systemati- 
 cally the tests as explained in the drawing of the box, 
 
 Fig. 1. 
 
 The first test is to measure the height and width of each 
 single object of the group, and compare the same, and also
 
 14 GROUPS. 
 
 to compare with the dimensions of -the whole group. This 
 test is the most important, and the greatest care should be 
 taken with it. The best way will be, as soon as the propor- 
 tions have been determined, to draw horizontal and vertical 
 lines, forming a rectangle enclosing the drawing, and to 
 be ' careful that these lines are not removed. As we 
 have seen, slight inaccuracy can hardly be avoided, but 
 these dimensions are the longest measurements, and can 
 therefore be fixed more accurately than any others. This 
 being so, the best that can be done is to make the drawing 
 agree with these measurements ; and by this time the stu- 
 dent should be able to measure with the pencil or needle 
 as accurately as any drawings will require. This test Avill 
 generally change the drawing throughout, which should be 
 done not by erasing but by adding lines, and without other 
 measurements, until the eye can see no more changes. 
 Then the thread may be used for the tests of horizontal 
 and vertical lines first; and second, the continuing of all the 
 edges ; and third, for covering points in the group opposite 
 each other, and chosen at random, that the intersections 
 with the edges between may be noted. The thread used 
 thus will discover every discrepancy except the slight 
 deviations which only the accurate eye can detect. After 
 the training which is given by these drawings made en- 
 tirely by eye before any tests are applied, this accuracy 
 will soon be secured. When the correct lines have been 
 found, the others are to be erased as explained on page 10, 
 and the lining in is to be done. 
 
 But now the student will do well to think of effect, and
 
 GROUPS. 15 
 
 to see if more interest and expression cannot be given to 
 the drawing than is done by the even outline. The student 
 has, perhaps, been taught that the nearest objects are seen 
 most strongly, and that the strength diminishes with the 
 distance, and this is, of course, true in a general way. It 
 is the effect of gerial perspective, or the changing of color 
 by the intervening atmosphere. Thus, of a row of light 
 objects, the nearest will be the brightest, that is, the light- 
 est and most prominent, and of dark objects the same princi- 
 ple is true. The light object in the distance appears darker,* 
 and the dark one lighter, so that in a sketch taking in any 
 considerable distance this principle will be of assistance. 
 But it must be stated so as not to convey the idea that 
 there can be nothing in the distance which is stronger than 
 anything in the foreground, for we do not see objects more 
 or less distinctly according to their distance. Distance, in 
 fact, has practically nothing to do with it. We distinguish 
 objects as masses of color, light or dark, according to the 
 color against ivhich they are seen. This being so, it will 
 be seen that a light object in the background, as a white 
 house, seen against dark foliage, must be a much more 
 prominent feature of a landscape than a near object which 
 is seen against another of the same value. In general, when 
 there is little or no contrast of color between objects, then 
 are they difficult to see without regard to their distance. 
 
 Place a square of white cardboard centrally in front of a 
 larger square of the same, the latter coming in front of the 
 
 •Very light objects may change but little.
 
 16 GROUPS. 
 
 blackboard. The smaller can be seen very faintly, but in 
 comparison with the distinctness with which the larger is 
 seen against the blackboard the nearer plane is practically 
 invisible. This experiment proves that we see objects to 
 distinguish their form, through contrasts of color, and we 
 have to consider what can be done in outline simply to 
 render the effect of nature, for it is reasonable to expect 
 from every medium its full possibilities. Can no more be 
 done than to represent the outlines in an even line ? The 
 opinion seems to be general that more can be done. We 
 find that instructions are often given to shade the nearer 
 lines strong, the further ones light, and to grade the others 
 between them. Apply the rule to the representation of 
 the two planes of cardboard, and the nearer is lined in 
 heavily and the further lightly. This we find to be in 
 direct contradiction to the way we see the two objects, for 
 the nearer is barely seen against the further white, while the 
 more distant is distinct against the blackboard. In color we 
 certainly should not think of representing the nearer darker 
 than the further, or in any other Avay than as it appears, 
 and the same is true of light and shade. Why should we 
 not do the same with outline ? No reason to the contrary 
 can be given, for the difference in clearness with which the 
 various lines are seen is the result, not of distance, but of 
 contrast of light and shade. Of course we shall expect to 
 find the strongest line among the nearer ones, but further 
 than this we cannot go, and if we adopt the conventional 
 lining in often recommended, we are working by rule and
 
 GROUPS. 17 
 
 not by observation, and the result will be the production of 
 hard, mechanical drawings. 
 
 Character appears in the outlines. An object, as a cast, 
 having a smooth, hard surface, and an eren outline shows 
 these qualities in its outlines. They will be represented by 
 smooth and even lines. A cube with smooth faces has; 
 sharp'straight edges, which must be represented by straight 
 lines. A box made of rough boards will have broken 
 edges, and their character will be given by drawing the 
 irregular outline in which one surface cuts into the 
 other. A drawing from the figure can express the varia- 
 tions in the appearance of the outlines, some parts of which 
 are sharp, some parts blurred by light showing through, 
 or by a short growth of hair. The influence of light also 
 affects the appearance of the outlines, in some places making 
 them distinct, in other places indistinct. An even outline 
 for everything disregards all these variations of effect, so 
 also does any conventional variation of strength. If the 
 student is allowed to disregard effects in outline work, he 
 will have very great difficulty in seeing them in his later 
 work. There is no more labor involved in representing the 
 effects than in disregarding them, for one line is as easy to 
 make as another, observation only being required. The 
 student who can see can perform, and as long as any differ- 
 ences can be found between his drawing and nature he can 
 learn to correct the errors. 
 
 In pencil, as in the other mediums, we should do the best 
 we can to express what is before us, and the effect of the 
 drawing should be considered as well as the forms repre-
 
 18 ■ GROUPS. 
 
 sented. There is no reason wliy the student should not be 
 taught to observe the effect, and if once started correctly 
 he will advance rapidly, and will make drawings which, 
 since they are representations of nature, will have variety 
 of effect, will be true, and thus artistic. Xo rule can be 
 given other than to study and represent simply what is 
 seen, as far as possible as it appears. In outline, without 
 light and shade, it is impossible to draw always just what 
 is seen. For instance, some edges of the object may be so 
 lost in the shade as to be entirely invisible, but without 
 them the drawing would be incomplete and unsatisfactory. 
 A correct impression of the facts must he conveyed. No 
 important line, even though it be lost in shadow, can be 
 omitted, but otherwise the lines should be represented just 
 as they are seen. At first most students will have great 
 difficulty in finding that there is any difference in the way 
 in which the various edges appear. This is due to the fact 
 that but a single point can be clearly seen at any one time. 
 The eye passes rapidly over the whole extent of an object, 
 so that it is all carefully observed, but we are unconscious 
 of this motion. All parts of the object are seen distinctly, 
 and the variety in the effect is not realized, and all points 
 will continue to give the impression of equal strength in 
 the effect, until the ability to see the whole of an object at 
 once has been acquired. It is not possible, otherwise, to see 
 simply and broadly, to realize effects and masses, and the 
 student must practise until he can thus see before he thinks 
 of success in any medium, for all demand equally a study 
 of the comparative strength of detail.
 
 GROUPS. 19 
 
 The whole of an object of any size, or the effect of a 
 group, can only be seen when the vision is blurred so that 
 all parts are seen equally and necessarily indistinctly. 
 This effect conies from looking with the eyes in focus for a 
 shorter or longer distance, and is the same as that given 
 by looking through a lens of ten or twelve inch focus. 
 Opening the eyes and looking intently until the vision is 
 blurred, is better than nearly closing them, for this cuts 
 off most of the light and loses the color. In light and 
 shade this point would not do harm, but it is better to 
 study in light and shade so as not to be obliged to change 
 for the more advanced work. After a little practise the 
 student will be able to see the whole of the object without 
 special effort, and it must not be forgotten that this is the 
 only way in which effects can be seen. 
 
 Although no rule for lining in can be given, the effect 
 will always be found to conform to the principle that any 
 detail tvhich comes in either the mass of the light or the 
 mass of the shade is unimportant, that is, a light surface 
 against a surface also light is not prominent, and an edge 
 defining a surface which is in the shade against another 
 surface, also in shade, is seen faintly. The important fea- 
 tures, or the lines which are prominent, are those which 
 come between the light and shade.
 
 PERSPECTIVE PRINCIPLES. 
 
 Before beginning we will choose a term which shall mean 
 the position in which any line appears of its real length, 
 and any plane of its real shape. This will occur when the 
 line or the plane is perpendicular to the direction in which 
 it is seen, that is, is parallel to the picture plane. The 
 words parallel to the picture plane might cause confusion, 
 from the fact that in perspective the picture plane is gener- 
 ally vertical, and often takes in a wide field of view, while 
 in moael drawing the plane is perpendicular to the direc- 
 tion in which one looks, and is thus continually changing. 
 We wish a term which shall mean any position in which 
 any line or plane appears of its real shape, and will 
 select the phrase, " directly in front." Any line is directhj 
 in front when its ends are equally distant, and any rectan- 
 gular plane when its angles are equally distant from the eye. 
 
 Place a large cube horizontal, with its centre on a level 
 with the eye, the cube being a few feet distant. The front 
 face directly in front, with its four corners equally distant, 
 appears of its real shape (Fig. 6). Now turn the cube so 
 that its left side is seen very narrow (Fig. 7). It will be 
 noticed that the upper end of the vertical edge, B, at the 
 back appears beloAv, and the lower end appears above the 
 respective ends of the front vertical edge, A. In other 
 words, the further edge appears shorter than the front, and 
 the horizontal edges, D, E, connecting their extremities, 
 must appear to converge, and if continued would meet. From 
 
 (20)
 
 PERSPECTIVE PRINCIPLES. 21 
 
 this we see : First — That of two parallel and equal edges, the 
 nearer appears the longer, the relative lengths being in- 
 versely as the distances. See Fig. 8, in which B, being twice 
 the distance of A, appears one-half its length. Second — 
 That parallel retreating edges {all not directly in front) 
 appear to converge or vanish at a point called their vanishing 
 point. Third — That horizontal edges above the eye appear 
 in retreating to descend or vanish doivnward, while those 
 beloiv the eye in retreating appear to ascend or vanish iip- 
 ward. This is easily proved by the fact that the eye 
 must be dropped in looking from a nearer to a farther point 
 in the edge above the eye, and raised for the more distant 
 point in the line below the eye. Lift the eye to the level 
 of the top of the cube and it will appear a horizontal line, 
 thus showing that a horizontal line at the level of the eye 
 appears horizontal, and that a plane so situated is seen edge- 
 wise and appears a horizontal line, l^ow place the eye in 
 the first position, on a level with the centre of the cube. 
 The right hand vertical edge, C, is farther from the eye 
 than the central edge, A. It must therefore appear shorter, 
 and the horizontal edges, F and G, must converge as those 
 at the left. If both these sets of edges are continued they 
 will appear to meet at two vanishing points, and since the 
 edges are equally above and below the eye, the upper and 
 lower angles of convergence 1-2 and 3-4 must be equal on 
 each side of A, and the vanishing points be on a level with 
 the centre of the cube, that is, of the eye. Hence, we sse 
 that parallel horizontal edges appear to vanish at the level 
 of the eye. We will now draw upon the end of a room,
 
 22 PERSPECTIVE PRINCIPLES. 
 
 Fig. 9, lines which continue the apparent directions of the 
 horizontal edges at floor and ceiling, which are perpendi- 
 cular to the end. We find them to intersect at a point 
 which is directly opposite the eye. This point on the wall 
 being the picture of the infinitely distant point in which 
 the continued lines seem to meet, and the line from this 
 point to the eye being parallel to the lines A, B, C, D, we 
 see that the vanishing poiiit of any set of parallel lines is 
 in a line parallel to them passing through the eye. To draw 
 these lines on the wall two students must work together, 
 but the directions can be determined with a straight edge, 
 and the students may work individually by drawing the 
 interior of any room. This experiment is the best way to 
 show that to find the vanishirig ^Joint of lines we must look 
 in their direction. 
 
 All parallel edges which have one end nearer the eye than 
 the other must appjear to converge, and the convergence must 
 he in the direction of their farther ends. According to this 
 statement, when the cube is above or below the eye its 
 vertical edges must vanish. The edges do appear to vanish, 
 but they are not so represented. In a model dratoing, verti- 
 cal edges are represented hy vertical lines. 
 
 Place a small cube so that its top and front faces are seen, 
 and its right side is seen as a vertical line (Fig. 10). The 
 edges, A, A, A, are so nearly directly in front that they may 
 be represented by parallel horizontal lines. Line B of the 
 drawing will be found to be longer than line C, and yet C 
 is nearer the eye. We see that the first statement illus- 
 trated by Fig. 8 must be qualified. A study of Fig. 11 will
 
 PERSPECTIVE PRINCIPLES. 23 
 
 show that of two parallel and equal lines unequally distant 
 from the eye, the nearer A-B appears the shorter when its 
 angle with the plane of the picture is greater than forty-five 
 degrees^ and that of two lines, B-D and A-C, the nearer B- 
 D appears the longer when the angle of the lines with the pic- 
 ture is less than forty-five degrees. This statement may not 
 be exact for lines whose angle is very nearly forty-five 
 degrees, but when there is a noticeable difference it is cor- 
 rect. The figure also shows that of two equal lines, A-B and 
 B-D, perpendicular to each other and having one end com- 
 mon, the one which makes the greatest angle with the pic- 
 ture appears the shorter. That which is nearest parallel 
 appears the longer. 
 
 Fig. 12 shows that two lines perpendicidar to each other, 
 at equal angles with the picture and having their ends 
 equally distant, appear of equal length. The statement 
 often found that of parallel and equal lines the more dis- 
 tant appears the shorter, has accomplished perhaps as much 
 harm as good, for it is only correct for lines directly in front 
 and for vertical lines. 
 
 In Fig. 13 line A-B represents the ground, and points 
 1, 2, 3, etc., equi-distant points situated in a line lying on 
 the ground. The lines drawn from these points to the eye 
 represent the rays in which the points are seen, and the 
 intersections of the rays with the picture plane show that 
 the equal distances appear unequal, the nearest appearing 
 the longest, the furthest the shortest, and the intermediate 
 distances proportional between these lengths, and this is 
 always true of equal spaces on any retreating line.
 
 24 PERSPECTIVE PRINCIPLES. 
 
 It will be seen that there are three sets of parallel edges in 
 the cube, and that they all appear to'vanish, unless directly 
 in front, and are so represented unless they are vertical, or 
 situated as in Figs. 10 and 14. They vanish in the direction 
 of their farther ends, and these points are angles of the 
 invisible faces of the solid. If both ends of a line answer 
 this condition, the line must be considered as directly in 
 front, even if the eye is not exactly opposite its centre. 
 In general, parallel straight lines which extend on both sides 
 of the spectator must be represented by parallel straight 
 lines. If the eye should be opposite one end as in Tig. 10, 
 and the edges are short, they will be best represented by 
 parallel horizontal lines. If the edges are long and near 
 the spectator, it may sometimes be better to distort the 
 nearer and smaller part of the object in favor of the farther 
 and larger part, by drawing the more distant end smaller 
 than the nearer Fig. 14. This, however, will seldom hap- 
 pen, and unless special permission to the contrary is given, 
 the edges are to be treated as if directly in front until a side 
 face is seen. 
 
 In nature there is no so-called parallel or one-point per- 
 spective, that is, parallel perspective is not true to appear- 
 ances. It therefore should be avoided, and the difficulties 
 which have just been considered will be best settled by 
 moving so that the edge is directly in front, or so that a 
 side face is seen and there are two vanishing points. When, 
 however, this cannot be done, and parallel straight lines 
 extend on both sides of the spectator, the student must 
 represent them by straight lines, and in the case of hori-
 
 PERSPECTIVE PRINCIPLES. 25 
 
 / 
 
 zontal edges by horizontal lines. Long parallel straight 
 lines in nature appear curved. This is shown in the shadows 
 of clouds at sunset, which sometimes may be seen extend- 
 ing across the sky, and converging in the east and west. 
 In many drawings from nature of streets, etc., by our best 
 illustrators, the curvature is so marked that it is most 
 noticeable. The representation of straight by curved lines 
 should not be allowed the student, and, as shown on page 
 72, straight lines may be substituted for the curved, chang- 
 ing the drawing but little when there are two vanishing 
 points. When the end of a room is shown certainly no one 
 would wish to represent the curvature, for the drawing should 
 give the impression of nature, and this can only be done by 
 straight lines. 
 
 '■0-' 
 
 THE CUBE. 
 
 These principles are illustrated by the cube (of four-foot 
 edge, scale ^ in. = 1 ft.) drawn in various positions : 
 
 First. The cube with four edges vertical, its under sur- 
 face being on the level of the eye, one surface only visible, 
 and the eye being opposite the centre of edge A-B. The 
 under surface must appear a horizontal line. The front 
 surface, although its upper angles are further from the eye 
 than the lower, will, unless the eye is very near the object, 
 appear practically of its real shape (Fig. 15). 
 
 Second. Lower the cube until its top is four feet below 
 the level of the eye (Fig. 16). The receding edges of the 
 top will vanish in a point on the level of the eye, and in a 
 line drawn through the eye parallel to the edges. This
 
 26 PERSPECTIVE PRINCIPLES. 
 
 places the point above the centre of the cube. The front 
 face being below the eye will be foreshortened (as shown 
 by Fig. 17), so that it will not appear of its real shape. 
 The edge, E-F, being further from the eye than A-B, will 
 appear shorter, just as C-D does. It will appear the length 
 of 1-2, and the vertical edges, by connecting points A-1 and 
 B-2, will be represented by inclined lines. The representa- 
 tion of vertical by inclined lines is not satisfactory, and the 
 model drawing must have vertical lines. If the lines are 
 drawn vertical from A and B, the front face will seem too 
 wide ; if from 1 and 2, it will be too narrow. The proper 
 effect will be given by verticals midway between, or if they 
 are drawn from A and B, the line 1-2 must be dropped to 
 give the correct impression. It will be seen that the model 
 drawing is not the exact drawing upon the inclined picture 
 plane, but this drawing corrected by substituting vertical 
 for inclined lines. When edges are situated on each side 
 of the eye, as are A-C and B-D, they must always appear to 
 vanish at a point which is directly opposite the eye, for the 
 vanishing point of a line is in a parallel to the line passing 
 through the eye. 
 
 Third. Place the cube with its vertical faces at forty- 
 five degrees to the picture plane, its top being on a level 
 with the eye (Fig. 18). The top is seen edgewise. The 
 sides, since at equal angles, will appear of equal width. 
 The edges, A and B, must vanish upward at equal angles, 
 the angle depending wholly on the distance of the eye. If 
 short, the convergence will be rapid, and the angle of con- 
 vergence will decrease as the distance increases.
 
 PERSPECTIVE PRINCIPLES. 27 
 
 Fourth. The cube, with its lower surface on the level of 
 the eye, and its vertical faces at angles of thirty degrees to 
 left and sixty degrees to right (Fig. 19). The left face, 
 being nearest parallel to the picture plane, appears the 
 Avider. The edges, A and B, vanish downward at angles 
 Avhich depend on the distance of the eye, but that of A must 
 always be less than that of B. 
 
 Fifth. The cube, with its top four feet below the eye, 
 and its sides at forty -five degrees (Fig. 20). The sides must 
 appear of equal width, and the angles of the lines on each 
 side be equal. There are four parallel edges extending to 
 the right, and four to the left. Parallel lines appear to 
 converge at a point, and for horizontal lines this point is at 
 the level of the eye. The two vanishing points will then 
 be on the level of the eye, and must be equi-distant from 
 the drawing. This distance depends on the distance of the 
 eye, increasing equally with it. (For an angle of forty-five 
 degrees the distance of the vanishing point is equal to that 
 of the eye.) In this position of the square, which is the 
 base of the cube, it will be seen that one diagonal of the 
 base is parallel to the picture plane, and appears a horizontal 
 line. The other diagonal appears a vertical line, and 
 the further angle of the square is directly over the nearer 
 one. 
 
 Sixth. The cube above the eye, with its horizontal edges 
 extending to left, at sixty degrees, and to right at thirty 
 degrees (Fig. 21). Both sets of lines will vanish at points 
 in the horizon, the vanishing point at the left being the 
 nearest to the drawing, for the line at the greatest angle
 
 28 PERSPECTIVE PRINCIPLES. 
 
 must appear the shortest. The diagonals of the horizontal 
 surface will also vanish. Of the diagonal 1-2, 2 is the 
 nearest point, and the line must vanish to the left. Point 
 3 is the nearest end of 3-4, and this line vanishes to the 
 right. 
 
 Seventh. The cube, resting on an edge on the ground, 
 four of its faces being at forty-five degrees to the ground, 
 being seen from above, and having three faces visible 
 (Fig. 22). Let line 1-2 be the edge on the ground. For four 
 faces to be at forty-five degrees to the ground, it is neces- 
 sary that the diagonals of the two faces which are vertical, 
 shall be vertical and horizontal. Vertical lines from 1 and 
 2 must be the vertical diagonals. The horizontal diagonals, 
 34 and 5-6, must bisect the vertical and vanish in the hori- 
 zon. The edges parallel to 1-2 vanish at the left, at the 
 level of the eye. From point 3 an edge extends downward, 
 and another upward. The lines which are parallel must 
 vanish respectively up and down to the right. 
 
 These principles will enable one not only to correct or 
 test drawings made from the object, but what is more im- 
 portant, to design or draw without the objects. Thus, let 
 line A, Fig 23, be the nearest edge of a cube, situated 
 below the eye, with its faces at such angles that the width 
 on each side extends to B and C. Drawing a horizontal 
 through the end of A we know that the edge extending 
 to the right must make a greater angle than that going to 
 the left. Such practice will enable one to draw quite 
 correctly without the objects.
 
 TERSPECTIVE PRINCIPLES. 29 
 
 THE SQUARE PYRAMID. 
 
 When the pyramid stands on its base, its axis being ver- 
 tical, is drawn by erecting a vertical at the intersection of 
 the diagonals of the square. When two sides of the base 
 are directly in front (Eig. 24), one side only of the pyra- 
 mid will be seen if its axis is long, or if it is above the eye. 
 If its axis is short or wholly below the eye, two side faces 
 may be seen, and will appear equally (Fig. 25). When two 
 faces are seen all the edges of the base must vanish. When 
 two faces are seen alike, the edges of the base are at equal 
 angles with the picture plane. The slant edges at front 
 and back appear to coincide, and one diagonal of the base 
 is horizontal (Fig. 26). 
 
 When two faces of the base are seen unequally (Fig. 27), 
 the axis of the pyramid will be perpendicular to a line 
 which is parallel to the picture plane. A plan view of the 
 square and the P. PI, will show the position of the line a-b 
 with reference to points 1 and 2 of the square. This line 
 must pass behind point 2 (which point is nearer the eye than 
 point 1), and in front of point 1. When the pyramid is 
 vertical line a-b will be horizontal. When the pyramid is 
 oblique (Fig. 28) the line may be a test, but not sufficiently 
 accurate to be of value except when drawing without the 
 object. 
 
 THE TRIANGLE AND PRISM. 
 
 When this figure is equilateral or isosceles, and rests on 
 a base, the altitude is vertical, and intersects the centre of 
 the base (Fig. 29).
 
 30 PERSPECTIVE PRINCIPLES. 
 
 The prism with equilateral ends, resting on a face on the 
 ground. 
 
 First (Fig. 30). When neither end is seen, the long 
 edges are directly in front, and must be represented by 
 parallel lines. When one end is seen, and two sides equally 
 (Fig. 31), the edge A of the end is directly in front. When 
 an end and a side are seen (Fig. 32), the end will be tested 
 by a vertical through point 1. This should come at point 4. 
 the centre of the base 2-3, but 4 does not bisect the line 2-3, 
 as the nearer half must perspectively appear longer than 
 the further half. The edges must vanish in the direction 
 of their farther ends. This direction is at once apparent, 
 except in the case of 1-2, whose direction will be deter- 
 mined by seeing which point, 1 or 2, is nearest to the line 
 3-7. The point which is nearest is the nearest end of the 
 line 1-2. Suppose the prism placed so that the edges of 
 the face on the ground are at equal angles with the picture 
 plane. They will vanish equally, and the line 2-3 will be 
 equal to one-half of 2-6, the nearer half perspectively ap- 
 pearing a little longer than the further half. 
 
 THE EEGULAR HEXAGOX AXD SOLIDS. 
 
 In the hexagon there are four sets of parallel lines. A, B, C, 
 and D. The diagonal 0-4 is divided into four equal parts 
 by the diameters D, D, and the diagonals B-C. A model 
 drawing of the figure may be tested by seeing that the 
 parallel edges vanish in the direction of their further ends, 
 and that the diameters divide the diagonal into four per- 
 spectivelij equal parts.
 
 PERSPECTIVE PRIXCIPLES. 31 
 
 In Fig. 33 the hexagon is shown directly in front. In 
 Fig. 34 it is shown after it has been revolved back about 
 the angle 0. Figs. 35 and 36 are the same, the hexagon 
 being revolved about the side A. In Figs. 34 and 36 the 
 lines a-a may be drawn, thus enclosing the hexagon by a 
 rectangle. The intersection of the diagonals of any rec- 
 tangle gives its centre!. By drawing them in these figures 
 and lines b, the angles of Fig. 34 are determined. In Fig. 
 33, to get points 1 and 3, it is only necessary to divide by 
 diagonals each half. 
 
 To draw the hexagon on a given line, a-b, as diameter 
 (Fig. 37). Draw the sides A and B, then the further dia- 
 meter c-d. Draw the diagonals, and make the distance 4-5 
 less than 3-4, and 1-2 greater than 2-3. 
 
 To draw a hexagon on a given side, A-B (Fig. 38). Draw 
 the diameters from A and B, and draw the further side, 
 C-D. Draw the diagonals A-D and B-C, and the diagonal 
 through 3. If A-B and C-D are directly in front, 1, 2, 3, 4 
 and 5 will be equi-distant points. If not directly in front, 
 the points will be perspectively equi-distant. 
 
 In the prism and pyramid, Figs. 39, 40, 41 and 42, no 
 more than three of their side faces and an end can be seen 
 at any time. If two only are seen, the diameters of the 
 base are directly in front. When three are seen, and the 
 outer ones appear of equal width, the ends of the middle 
 face are directly in front. When the outer faces are seen 
 unequally, the narrower, A (Fig. 39), must be the more 
 distant, and this shows the direction in which the edges, 
 a-b and c-d, of the middle face vanish. The vanishing of
 
 32 PERSPECTIVE PRINCIPLES. 
 
 the parallel edges must make the invisible end wider than 
 the visible, as in the cylinder (page- 35). The tests for the 
 pyramid are the same as for the prism and the square 
 pyramid. When three faces are seen and the outer ones 
 equally, the axis is perpendicular to the longest diagonal. 
 When two are seen equally, it is perpendicular to the diam- 
 eter. When two or three are seen unequally it is perpen- 
 dicular to a line between the diameter and the diagonal. The 
 faces visible will show whether this line is nearest parallel 
 to the diagonal or to the diameter. In Fig. 40 the question 
 may arise, " Shall the nearer half, a-c, of the diameter, a-b, 
 be a little longer than the further part, c-b ? " It will be seen 
 that doing away with the convergence of the vertical lines 
 makes the equal distances a-c and c-b equal in the drawing. 
 
 THE CIRCLE. 
 
 The circle appears of its real shape when directly in 
 front. It appears as a straight line when the eye is in its 
 plane, and in other positions in which its entire circumfer- 
 ence is seen, it appears as an ellipse. 
 
 Fig. 43 represents a square, two sides being directly in 
 front. A circle inscribed in the square will be represented 
 by an ellipse, which is tangent to the sides of the square, at 
 the ends of the diameters of the square, in points 1, 2, 3 
 and 4. The centre of the square must perspectively come 
 nearer the further side, C-D, and it is at once seen that the 
 centre of the circle is not the centre of the ellipse, that is, that 
 the long axis of the ellipse is not a diameter of the circle. 
 This is shown again by Figs. 44 and 45.
 
 PEBSPECTIVE PRIXCIPLES. 33 
 
 Fig. 45 is a plan view, showing the circle, the eye, and 
 the cone of rays from the eye to the circle, -represented by 
 its outer rays, a-a. Fig. 44 is a side view, showing the 
 ground, B-D, the circle, C-C, the eye, and the cone of rays, 
 b-b. The picture plane, at right angles to the central ray, 
 A, shows the width of the ellipse at 1-2. The central ray 
 intersects the ground at c, and this must be the position of 
 the chord 34 of the circle (seen in plan view), which ap- 
 pears the long axis of the ellipse. Points 3 and 4 are not 
 the tangent points of lines a-a. 
 
 All lines whose ends are unequally distant must vanish. 
 It follows that in any circle there can be but one diameter 
 which does not vanish. This must be the one which is 
 perpendicular to the line of sight, and thus directly in 
 front. A horizontal line directly in front appears horizon- 
 tal, and thus a horizontal circle must appear as a Itorizontal 
 line, or as a horizontal ellqise ; for though the diameter 
 directly in front is not the long axis of the ellipse, it is par- 
 allel to the chord of the circle which is the long axis of the 
 ellipse. The line of any circle which is the long axis of its ap- 
 pearance is thus a chord of the circle which is directly in front. 
 
 When on the level of the eye the horizontal circle ap- 
 pears a horizontal line, and when below or above the eye, 
 an ellipse, whose width increases with the distance of the 
 circle from the level of the eye (Fig. 46). 
 
 The short axis of an ellipse is perpendicular to its long. 
 It represents a diameter of the circle which is perpendi- 
 cular to the chord which appears the long axis. This dia- 
 meter will be found to appear to coincide with a line per-
 
 34 PERSPECTIVE PRINCIPLES. 
 
 penclicular to the plane of the circle erected at the centre 
 of the circle. Hence, if two lines are perpendicular to each 
 other, one is directly in front, and the other intersects the 
 centre of the first, the right angles thus made will appear 
 right angles until the second line is seen as a point. 
 
 The circle when vertical, at an angle with the picture, 
 and its centre on the level of the eye, will appear a vertical 
 ellipse. When the vertical circle is below the eye, the two 
 equi-distant points in its circumference, which are the ends 
 of the long axis of the ellipse, must be, the upper point 
 behind the highest point in the circle, and the lower point 
 in front of the lowest point. The chord (that is the long 
 axis of the ellipse) connecting these points must be an 
 inclined line. When the circle is above the eye, the ends 
 of the diameter of the ellipse will be in front of the highest 
 and behind the lowest points in the circle, and the axis of 
 the ellipse will incline in a direction opposite from that 
 which it has when below the eye. 
 
 The axis of the ellijjse which represents a vertical circle 
 on any level except that of the eye, must he an inclined line 
 (Fig. 47). In this figure we have a circle A, vertical, and 
 on the level of the eye, and circles B and C of the same 
 size, directly over and below A, and in the same plane. It 
 will be seen that the ellipses of B and C are tangent to 
 verticals tangent to A, but that their short axes are shorter 
 than that of A. To determine the inclination of the axis 
 look for the two equi-distant points which are its ends, or 
 look for the direction which a perpendicular to the circle at 
 its centre would have, for the long axis is perpendicular to
 
 PERSPECTIVE PRINCIPLES. 35 
 
 this direction. The latter Avay (which is the better) con- 
 siders the circle the base of a cylinder whose direction 
 determines the direction of its end. 
 
 THE CYLINDER. 
 
 Less than half the curved surface of the cylinder can be 
 seen at any one time. 
 
 Fig. 48. When an end only is seen, it must appear of its 
 real shape. When neither end is visible (A), the cylinder 
 must be directly in front, both ends appearing narrow el- 
 lipses. When one end appears a straight line (B), the other 
 must appear a narrow ellipse. 
 
 The long axis of an ellipse appears perpendicular to a 
 line which is perpendicular to the circle at its centre. This 
 line in the cylinder is its axis, and in drawing the cylinder 
 and cone the long axis of the ellipse of the base must always 
 be at right angles to the axis of the solid. 
 
 When the surface of one base of the cylinder is visible, 
 that of the other must be invisible. The visible end being 
 nearest the eye, the invisible must appear shorter, and the 
 elements connecting them must converge as any parallel 
 straight lines. The question of the comparative width of 
 the visible and invisible ends has caused much trouble. A 
 study of Figs. 11 and 12 will show this width to be depend- 
 ent upon the position of the cylinder. When it is at a less 
 angle than forty-five degrees with the picture, the invisible 
 base will be the wdder, but when it is at a greater angle 
 than forty-five degrees, the invisible base will be the nar- 
 rower. This, however, is not exact for angles very near
 
 36 PERSPECTIVE PRINCIPLES. 
 
 forty-five degrees, and refers to positions in which the 
 object is at a sufficient distance to permit its entire repre- 
 sentation. For unusual conditions, as a very long object 
 very near the spectator, or for a number of objects placed 
 in a straight line and extending for some distance, it can- 
 not apply, as the distortion caused by the use of any one 
 picture plane would be very great. Such conditions, how- 
 ever, are not normal, and it is best not to attempt to draw 
 an object which is so near as to create a visual angle of 
 over thirty degrees. The invisible base is always at a 
 less angle to the plane which gives its real appearance; 
 that is, it is at a greater angle to the ray from the eye to 
 its centre than the nearer end (Fig, 49), and, though nar- 
 rower than the visible end when the cylinder is at a greater 
 angle than forty-five degrees, is also shorter, and is always 
 proportionally voider than the visible end. This is the only 
 rule that can be given, the difference depending upon the 
 distance of the eye, and decreasing as this distance increases. 
 When this distance is short it is quite marked. 
 
 Figs. 50, 51, 52, 53, 54 and 55 show the cylinder in 
 various positions, and all illustrate this principle. In these 
 drawings, the length of the cylinder is supposed to be twice 
 its diameter. In Fig. 50 the cylinder is horizontal, on the 
 level of the eye, and extends to left at forty-five degrees to 
 the picture plane. The short axis of the visible end must 
 be perspectively one-half of the element a-b. In Fig. 51 
 the cylinder is at an angle with the ground, and still at 
 forty-five degrees to the picture plane, the appearance being 
 the same as Fig. 50. Figs. 53 and 54 show two cylinders,
 
 rEKSPECTIVE PRINCIPLES. 37 
 
 one being exactly over the other. In Fig. 52 the cylinder 
 is below the eye, and extends directly back. The tendency 
 will be to represent the ends by circles, but they can only 
 so appear when no part of the curved surface is visible. 
 
 THE CONE. 
 
 The cone appears a circle when its axis is seen as a 
 point ; a triangle when its base is seen as a line. In other 
 positions both the circle and the curved surface will be 
 visible, the circle appearing an ellipse. The curved surface 
 will be represented by the two contour elements, which 
 must be tangent to the ellipse (Fig. 56). The entire curved 
 surface will be visible when the axis is toward the eye. 
 When the cone extends in the opposite direction none of 
 the curved surface will be seen. Between these positions 
 any part may be visible. The base of the cone being at 
 right angles to its axis, as in the cylinder, it must appear 
 as an ellipse whose long axis is perpendicular to the axis of 
 the cone. In Fig. 56 more than half the curved surface of 
 the cone is visible ; in Fig. 57 less than half ; and in Fig. 
 58 nearly all is seen. 
 
 To draw the cylinder, cone, or similar object, the method 
 illustrated by the box should be followed, the mass being 
 blocked in first. In the case of all symmetrical objects 
 having an axis, this imaginary line should not be drawn 
 first as is often recommended, but after the proportion and 
 position has been secured, the drawing may be tested by a 
 centre line before lining it in. On no account should this 
 line be drawn first.
 
 38 PERSPECTIVE PRINCIPLES. 
 
 COKCENTRIC CIRCLES. 
 
 Eig. 59. Concentric circles must appear ellipses whose 
 directions are the same, but since the centre of the circle 
 doeg not appear the centre of the ellipse, the long axis of 
 the larger ellipse, line A-B, comes in front of the long axis, 
 G-H, of the smaller ellipse. The smaller circle is half the 
 diameter of the larger, and a diameter, C-D, of the larger 
 circle is divided into four equal parts by the inner circle. 
 Although the diameters of the ellipses do not coincide, they 
 are generally so little apart that the equal divisions of the 
 diameter of the circle are nearly enough represented by 
 equal spaces on the long axis of the larger ellipse. The 
 equal distances on the diameter, E-F, appear perspectively 
 equal (Fig. 13), so that practically we may say that if the 
 distance, H-B, is one-fourth of the axis, A-B, the short 
 axis, E-E, will have the distances E 1 and F 3 perspective 
 fourths of the entire length, E-F. Thus, in Fig. 60 the 
 distance, 0-1, is one-sixth of the long axis, 0-6, and the dis- 
 tance, a-b, is perspectively one-sixth of the short axis, a-g. 
 This will enable us to test the drawing of the ring (Fig. 61), 
 in which we must further see that the thickness (which is 
 given by the lines 1-2, 3-4 and 5-6, all being equal in the 
 object) shall in the drawing be so perspectively, the nearest 
 1-2 being the longest, and the farthest 5-6 being the short- 
 est. This figure illustrates the fact that in most drawings 
 from nature there will be but a very little distance between 
 the axes of the ellipses representing concentric circles. In 
 this drawing we see that the retreating parallel circles do
 
 PERSPECTIVE PRINCIPLES. 39 
 
 not appear to come together as they recede until the further 
 half of the circle is reached. Thus we see that curved, 
 parallel retreating lines may appear to converge or diverge. 
 
 FRUSTUM OF PYRAMID AND CONE. 
 
 When any pyramid is cut by a plane parallel to its base, 
 the section is similar, and its edges are parallel to those of 
 the base. "When drawing this form this fact must be kept 
 in mind ; and also that the slant edges continued must 
 meet in the axis of the solid. The legs of stools, chairs 
 and tables present this form. The draAvings of such ob- 
 jects should be tested by continuing the legs to see that 
 they meet at a point over the centre of the base (Fig. 62). 
 
 The frustum of the cone (Fig. 63) is a form found in 
 many common objects. Frequently there are rings about 
 the cone (Fig. 64). As already shown, the visible curved 
 surface of the cone may range from the entire surface to 
 none. When there are circles or rings about its surface, 
 they will show in the same proportion as the surface con- 
 taining them. Thus, when the cone inclines toward the 
 eye, more than half the ellipses representing the rings will 
 be seen, and Avhen the cone inclines from the eye a small 
 part will be visible (Fig. ^i)). In this figure it will be 
 noticed that, if the middle ellipse at the front comes mid- 
 way between the top and the bottom, behind its posi- 
 tion will be the same (perspectively). This, and the fact 
 that the width of the ellipse must increase proportionally 
 until the further circle is reached, will enable such lines to 
 be drawn correctly.
 
 40 PERSPECTIVE PRIXCIPLES. 
 
 In Fig. 66 the width, of the band A seems greatest at the 
 sides because there it is foreshortened less than in front. 
 The width of the bands, A-A, will be greater or less at the 
 sides according to the angle of the cone, and the direction 
 in which it is seen. When the cone has its larger base 
 visible (Fig. 65), the nearer part of the band will appear 
 widest at its nearest point. 
 
 The drawing of the dish (Fig. 67) shows that the nearest 
 part, since it inclines away, may appear narrower than 
 the side of the dish at the back. However, it is impos- 
 sible to state a rule for all the above shapes regarding 
 appearance. 
 
 In the double cone (Fig. 68) the smaller circle A is com- 
 mon to both surfaces. Since one of the cones must incline 
 away from the eye, less than half of the ellipse can be 
 visible. The contour elements of each cone must be tan- 
 gent to the ellipse, and those of the farther cone will inter- 
 sect or pass behind those of the nearer cone. 
 
 The torus is a plinth with a circular top and bottom, 
 connected by a surface whose section is a semicircle. This 
 form is very common in furniture. It may be represented 
 correctly by drawing first the plinth of which the plane 
 surfaces are the ends. If a semicircle be drawn from the 
 ends of the long axes of the two ellipses, and a line be 
 drawn tangent to the semicircle and to the ellipses above 
 and below, this line will be the outline of the torus (Fig. 69). 
 When the ellipses are wide, and the drawing large, the 
 outline will come a little outside that of the plinth at front 
 and back.
 
 PERSPECTIVE PRINCIPLES. 41 
 
 THE RING OF CIRCULAR SECTION. 
 
 (Fig. 70). This object will be represented by two concen- 
 tric circles when it is directly in front, but when fore- 
 shortened its outlines will not be ellipses. This is due to 
 the fact that the rays come tangent below in front ; and 
 behind, above the centre of the ring, and the line on the 
 rin^ which is on the contour is not a circle. When much 
 foreshortened the further inner outline will pass behind and 
 intersect the line which represents the nearer part. This 
 drawing may be tested by the centre line of the object, 
 which is a circle and appears an ellipse. Draw this ellipse, 
 and suppose a sphere to pass around the circle. The centre 
 of the sphere being in the circle, its surface must describe 
 the surface of the ring. The sphere will be represented by 
 circles whose centres are in the ellipse, the one behind 
 being slightly smaller than the nearer. The ring must be 
 represented by lines drawn tangent to these circles. 
 
 FRAMES. 
 
 Any objects of the geometric forms, constructed of pieces 
 of uniform size, may be tested by means of the diagonals of 
 the figure, for polygons whose sides are parallel and whose 
 centres coincide have the same diagonals. Thus, in the 
 frame, Fig. 71, if the line A be drawn, its intersection with 
 the diagonals must give the extremities of lines B and C. 
 In the cubical frame, by continuing the line A to the edge 
 1-2, a point in the line E is secured. 
 
 In the triangular frame the perpendicular from each
 
 42 PERSPECTIVE PRINCIPLES. 
 
 angle to the opposite side gives the angles of the inner 
 figure, and any side, as A, being drawn, the lines B and C 
 will extend from 1 and 2, parallel perspectively to the sides 
 of the outer figure. 
 
 In hexagonal and other frames the same principle will 
 apply. 
 
 Fig. 74 presents forms frequent in furniture. The upper 
 form A consists of a ring outside a cylinder, and is really 
 the form found in the torus, explained on page 40. The 
 lower form C is a v-shaped groove cut into the cylinder. 
 This is the double cone explained on page 40. The inner 
 form B is a semicircular groove. This will be represented 
 by two ellipses, showing the circular edges, and when the 
 ellipses are wide and the groove is narrow nothing but the 
 ellipses can be seen, as at D. If the ellipses are narrow, ' 
 and the groove is wide, the curved surface will be repre- 
 sented by a curved line (as shown in the figure), which ends 
 above the diameter of the ellipse. A similar line is found 
 in vase forms when the stem joins the base (Fig. 75). 
 
 VASE FORMS. 
 
 In Fig. 76 we have in elevation a common form, in which 
 there are three circles represented by straight lines. Fig. 
 77 is a model drawing of the same form in which the circles 
 are represented by ellipses. A common mistake is shown 
 at the right side, where the outline of the body is drawn to 
 the end of the long axis of the ellipse. The line is cor- 
 rectly placed at the left. It must come tangent to the 
 ellipse at the back, and thus pass above the end of the long
 
 PERSPECTIVE PRINCIPLES. 43 
 
 axis. Another point wliich is frequently iinnoticed is, that 
 when the handle of a vase seems to extend from its outline, 
 it intersects the vase in a line inside the outline (Fig. 78), 
 and the more the handle extends toward the eye the fuller 
 the line of its intersection with the vase. 
 
 Fiir. 79 is a side view of a vase. The exact dimensions 
 of the model drawing (Fig. 80) may be obtained by sup- 
 posing the eye at a certain distance, and drawing the visual 
 rays to intersect the picture plane, which is placed at right 
 angles to them (see side elevation). The top of the vase 
 being against the picture plane, the long axis of the top 
 ellipse will be very nearly the full diameter of the top. 
 The circles below being behind the picture plane, a little 
 must be allowed for the effect of perspective, as well as for 
 the fact that the long axis of the ellipse is not a diameter 
 of the circle. In this vase there are three plinths, A, B 
 and C, whose circles will appear ellipses. The curve of the 
 neck will intersect the under ellipse of the top, and will 
 end below as in Fig. 75. The curve of the body of the 
 vase must come tangent behind to the lower ellipse of the 
 middle band, as explained in Fig. 77. 
 
 Fig. 81 shows the lower part of a vase. It consists of 
 the spherical body and a cylinder with a round edge as 
 base. The round edge is a thin torus, and should be drawn 
 as illustrated by Fig. 74. The cylinder intersects the body 
 in a circle, which appears an ellipse. If the ellipse is nar- 
 row, part of it will be visible, but the outline of the body 
 must come tangent to it, and cover the ends of the axis of 
 the ellipse (Fig. 82). If the ellipse is wide the curve may
 
 44 PERSPECTIVE PRINCIPLES. 
 
 come tangent in front, as in Fig. 83, and if the ellipse is 
 wider it will be invisible behind the outline of the body 
 (Tig. 84). 
 
 Fig. 85 gives a side view of the top and bottom of another 
 vase. The top consists of two cone forms, with a cylindri- 
 cal band between them. There are five circles, and to re- 
 present the top, four ellipses and the ends of the fifth must 
 be drawn. The body and the base are connected by a cylin- 
 der. The body will be represented by lines tangent to the 
 upper ellipse at the front, as in Fig. 82. The curve of the 
 base will be tangent to the lower ellipse behind, as in Fig. 
 77. The lower edge is the frustum of a cone, and in this 
 form the straight lines tangent to the ellipses must not be 
 forgotten, as is apt to be the case, especially when the 
 ellipses representing the two bases intersect, as at the top 
 when the straight line can hardly be seen, and when knowl- 
 edge only will produce an exact drawing. 
 
 The principles which have been explained will enable one 
 to see as it is impossible to see without them, and to draw 
 without the objects, to draw from memory, and to design 
 geometric forms of any size and in any position. They will 
 be of so much use to the practical draughtsman that he can- 
 not afford to be without them, even were it very difficult to 
 obtain this knowledge. The principles are, however, so 
 simple that there is no excuse for violations of the few 
 essential ones; but such violations are found very frequently 
 not only in the work of the amateur, but also in that of the 
 professional draughtsman. 
 
 The student who has a knowledge of working drawings
 
 PERSPECTIVE PRIKCIPLES. 45 
 
 may test his ability to draw from a description of the form 
 and its position, by taking any sheets of projection show- 
 ing objects one after another, supposing them to be seen 
 from a certain point, and making model drawings which 
 shall represent them. Thus, Fig. 87 is a working drawing 
 showing several objects, and their relations to each other, 
 and the planes of the drawing, and Fig. 88 is a model 
 drawing of the same. 
 
 We will suppose the objects to be seen from the left and 
 from above so that three faces of the cube are visible. 
 
 The cube is the first object, and any drawing which shows 
 the top, front and left sides answers the requirement. When 
 the cube is correct the G. L. which is parallel to the edges 
 extending to the right should be drawn. 
 
 The cone is the next object. Its base is a circle of the 
 same diameter as the base of the cube. The best way to 
 place the ellipse which is the appearance of this circle is to 
 draw a square whose sides are parallel to the base of the 
 cube. The ellipse must come tangent to the square at its 
 diameters. The distance between the cone and the cube is 
 equal to half the side of the cube. This distance 1-2, will 
 be found by drawing the diagonals of the right front face 
 of the cube, and set off on line A-B from 2 to 3 gives the 
 nearest angle of the square. Its sides extending to the 
 right are continuations of and are perspectively equal to 
 those of the first square ; and the sides extending to the 
 left are parallel to those of the first. It should be remem- 
 bered that these lines continue and vanish at right and left 
 in a horizontal at the level of the eye, and all parallel lines
 
 46 PERSPECTIVE PRINCIPLES. 
 
 should be continued as far as the drawing will allow, so that 
 they may be given the proper convergence. The student 
 should not attempt to have the vanishing points come on 
 the paper. The diameters of the base being drawn, give the 
 tangent points of the circle and square, and through them 
 the ellipse must pass. The circle is horizontal, and the 
 axis of the ellipse must be a horizontal line. The distance 
 between the centre of the ellipse and the centre of the 
 square is so slight as to be hardly noticeable. The long 
 axis of the ellipse must be, however, in front of the centre 
 of the square ; and in a larger drawing where the ellipse is 
 wide, if the axis should be drawn through the centre, the 
 error would be very noticeable. The axis passes through the 
 centre of the square, and must be represented by a vertical 
 line. Its length is readily determined by reference to the 
 vertical edges of the cube, which are half as long as the 
 axis. 
 
 The cylinder is next to be considered. The front circle 
 is in the plane of the front face of the cube, and it will be 
 best drawn by means of the square which circumscribes it. 
 The sides of the square are parallel and equal to those of 
 the front right face of the cube. Of course the distance 
 5-6 must be less than 3-4, as 3-4 is less than 1-2, and 4-5 is 
 less than 2-3 (See Fig. 13). The diagonals of the square 
 give its centre, and through this point the axis of the cyl 
 inder must pass. The vertical and horizontal diameters 
 give four points in the ellipse, whose long axis is a little in 
 front of the centre of the square, and at right angles to the 
 axis of the cylinder. In the same way the further end may
 
 PERSPECTIVE PRINCIPLES. 47 
 
 be drawn. The length of the cylinder being twice the side 
 of the cube, the distance 7-8 is perspectively equal to 5-7. 
 
 The hexagonal prism is the last object. It is vertical 
 with one face in the plane of the line A-B. A diagonal of 
 its base is parallel to A-B. Its length may be placed on 
 A-B from 9 to 10, perspectively equal to 5-6, the distance 6-9 
 being perspectively equal to 4-5. Points 11, 12 and 13 
 dividing 9-10 into four perspectively equal parts, being 
 placed, the diameters of the hexagon will extend from 
 4 and 13 to the left vanishing point. The side 14-15 having 
 been drawn, the diagonals 11-15 and 13-14 give the centre. 
 Through this point the diagonal parallel to 11-13 passes, 
 and the lines from 9-10 give in it the two remaining angles 
 of the base 16 and 17. The left vertical face is the narrower. 
 This shows that 16 is nearer than 13 and the diameter 16- 
 13 inclines upward slightly from 16. 
 
 These drawings will call for lines at definite angles with 
 the ground and the vertical plane. Such angles may be 
 determined by means of the cube, and for this reason it will 
 be well to draw this object first, even when it is not called for 
 (Fig. 89). The edges of the cube being perpendicular to 
 the two planes, the diagonals of its faces are at forty-five 
 degrees. If smaller angles are desired they can be obtained 
 by subdividing the angles of forty-five degrees. In making 
 this division it must be noticed that equal angles never aj)- 
 pear equal when occupying different positions with regard to 
 the picture plane. Pig. 90 shows that equal angles appear un- 
 equal and larger the more the lines of the angles are foreshort- 
 ened, so that to divide any angle, tna part whicn is most nearly
 
 48 PERSPECTIVE PRINCIPLES. 
 
 directed toward the eye, must be represented by the greater 
 angle, and as equal angles approach the position of directly 
 in front they will appear smaller. Such practice will more 
 quickly than anything else sIioav the student whether he 
 really understands the principles, or has been merely memo- 
 rizing them. The latter, which unfortunately is the only 
 way many students study, will be found entirely useless, 
 and those who have been working thus, must start again 
 with the determination to see with their own eyes, and 
 accept nothing which they have not verified by careful 
 study.
 
 INTERIORS AND GENERAL WORK. 
 
 All drawings, whatever the subject, should be carried on 
 in the same way, first by blocking in the mass of the whole, 
 and then the masses of the various parts, the detail coming 
 last. In drawing from objects having curved lines, the 
 student should be careful not to be content with the general 
 effect of the line, but should in finishing see that he does 
 not lose the character, which is given by the slight changes 
 in direction which occur in many lines. Thus, in drawings 
 from the cast, lines which at first glance seem of uniform 
 curvature, will be found to be composed of many short 
 lines, having different directions, and often straight or 
 nearly so. The student will get the character only by look- 
 ing for these short, straight lines ; but this method of draw- 
 ing curves must not lead him to put straight lines where 
 none can be seen, as, for instance, in an ellipse. 
 
 After the groups of geometric solids, common objects, 
 boxes, furniture, etc., should be taken. These may be ar- 
 ranged in groups ; and here the student may study to make 
 a pleasing arrangement. This work leads directly to the 
 drawing of interiors. Xo principles other than those ex- 
 plained with the geometric solids are involved. The only 
 question or difficulty likely to arise will come from the 
 larger space to be represented. As this space is not defi- 
 nitely outlined, the whole cannot be blocked in as in a 
 group of models. The best way will be to draw the central 
 group or the most prominent mass of the subject first, and 
 
 (49)
 
 60 INTERIORS AND GENERAL "WORK. 
 
 then add the surrounding parts. It -will be well to take for 
 comparison some long and important line of the central 
 mass. If care is exercised in determining the proportions 
 of the rest, with this line as unit, the smaller subdivisions 
 of each space will come without trouble. 
 
 In this work, as in all, the aim should be to represent 
 as nearly as possible the appearance of everything. The 
 subject being larger, and the straight lines longer, their 
 apparent curvature is often sufficient to be most noticeable, 
 and as we do not wish to represent straight lines by curved, 
 it is evident that we cannot draw everything just as we see 
 it. See pages 24 and 71. It will be well to avoid the repre- 
 sentation of a wall which extends far on both sides of the 
 spectator, as this will make the drawing very different from 
 the appearance. If one wall only is to be represented it is 
 better to draw from one end of the room, and thus cause the 
 lines to vanish. When two walls are shown they will both 
 vanish. When three are to be represented the middle one 
 must have no vanishing. Fig. 91 shows that were it to 
 vanish the whole of the left wall (and of course the further 
 edge. A, must appear shorter than the nearer, B) would be 
 outside of both vanishing points of the drawing, and the 
 distortion of all to the left of the left vanishing point would 
 be most marked. In general, when any horizontal lines 
 extend on both sides of the spectator, they should be repre- 
 sented by horizontal lines. 
 
 In interiors it is sometimes necessary to draw as the room 
 would appear from a supposed position far enough away to 
 show more than can be seen from any attainable position.
 
 INTERIORS AND' GENERAL WORK. 51 
 
 Such drawings will call for a thorough knowledge of all the 
 principles. 
 
 In interiors and in street scenes there is not only the 
 question of horizontal foreshortening to be considered, but 
 also vertical. It is impossible to make a sketch which shall 
 include an extended range of vision, and shall give the 
 exact appearance of each part and also of the whole. We 
 get.^the real dimensions of the appearance of any object on 
 a plane which is perpendicular to the rays to the object. 
 Carry this principle out, and the surface which gives the 
 exact appearance of an extended range is that of a sphere 
 which cannot be developed. This then is the reason why 
 we cannot always draw just what we see. 
 
 The space which can be included in a model drawing, and 
 which may be represented ou a plane without noticeable 
 distortion, should not include an angle at the eye of over 
 twenty-eight degrees. If this is much exceeded, the ques- 
 tions of the curvature of parallel lines both for horizontal 
 and vertical distances will arise, but as most drawings re- 
 quire a larger angle the question must be considered. 
 
 The mind, knowing lines to be straight, will hesitate to 
 accept their representation by curved lines, or knowing 
 them to be vertical, will not accept readily their representa- 
 tion by inclined lines. The draAving should give the im- 
 pression of nature as far as possible, even when the eye is 
 not at the proper distance. The impression of vertical 
 lines is given by vertical lines, and of straight lines by 
 straight lines. For this reason it seems best that the stu- 
 dent should represent what he sees as nearly as possible,
 
 52 INTERIORS AND GENERAL WORK. 
 
 but in accordance with the perspective principle that straight 
 lines shall be represented by straight lines. This will cause 
 him to represent straight edges, which extend on both sides 
 by parallel horizontal lines, and to substitute for the curved 
 lines found in buildings, at angles with the picture, straight 
 lines extending to two vanishing points. This will change 
 the drawing very little, as shown on page 72. 
 
 In drawings of street scenes the lines are long and broken, 
 and the curvature may not be noticed if each part is drawn 
 as it appears. In these subjects also, one does not know 
 what the conditions are (the edges might be curved in 
 nature), and so there is not the contradiction between the 
 knowledge of the facts and their appearances. If the artisc 
 chooses to represent straight by curved lines he has nature 
 as authority, and the example of noted predecessors, and 
 no one would wish to say that his drawing was not good, 
 or that it would be improved by plane perspective. Whether 
 or no, the foreshortening of horizontal and vertical distances 
 shall always be given, is a question which can be answered 
 only as it arises, and decided according to the conditions of 
 the subject and the aim of the drawing. It is a question 
 for the artist rather than the student, who should, until he 
 has attained by long practice ability to judge proportions 
 correctly, never be permitted to draw other than those 
 he sees.
 
 TESTS. 
 
 In beginning, the student should understand that the 
 drawings are of no value in themselves, but are of use only 
 as they train the eye to see correctly. The eye can be 
 taught, or rather the mind can be made to accept the image 
 of the eye only by depending upon it, and if the student 
 begins by measuring and testing he will never be able to 
 draw otherwise. This is undesirable for many reasons, the 
 most important being that no measurements or tests can be 
 applied which will take the place of correct perception, or 
 begin to equal it in exactness. It is thus most important 
 that the student from the beginning depend entirely for his 
 first drawing upon his perception of its appearance. 
 
 The readiest way of determining the proportions of an 
 object is by the use of a pencil, or other straight, slender 
 rod, held at arm's length, and made to cover the lines to be 
 compared. Thus the top of the pencil may be made to 
 cover the top of the object, and the thumb-nail held against 
 the pencil to cover the bottom of the object. If the pencil 
 is then turned into a horizontal position, the height of the 
 group may be compared with its width. If the measure- 
 ment covering the height extends over one-half the width, 
 the object appears twice as wide as high. In this way the 
 proportions of any object or group may be determined. It 
 is important that the student should see that such use of 
 the pencil is simply to obtain the proportion of height to 
 width, and not to determine the actual size of the drawing. 
 
 (53)
 
 54 TESTS. 
 
 In fact this use of the pencil should not be allowed, for the 
 eye and hand will be in different positions when taking the 
 various measurements, and if they are transferred to the 
 paper, as is the wish of many beginners, the drawings re- 
 sulting will be entirely out of proportion. The slightest 
 change in the distance of the pencil from the eye in com- 
 paring proportions will occasion great inaccuracy. The 
 only way to be at all correct is to hold the pencil as far 
 from the eye as possible, the arm being perfectly straight, 
 and the pencil being turned by twisting the entire arm. 
 The pencil must be at right angles to the direction in which 
 we look for the measurement. Xearly all students have 
 the idea that this means parallel to the side of the room or 
 the bench upon which the object is resting. This, however, 
 is wholly false, for the position of the object with reference 
 to its surroundings is of no consequence, and must not be 
 considered. If the student has a cube to represent he must 
 look at it, and the plane which gives its real appearance 
 must be perpendicular to the direction in which he looks, 
 and the pencil must always be held thus when taking meas- 
 urements. A good way is to find some position in the 
 fingers in which the pencil will be perpendicular to the 
 arm, and the arm being outstretched will bring the pencil 
 into practically the correct position (Fig. 92). Those who 
 cannot do this readily, and who do not hold the pencil 
 rightly, will find that a pin stuck into the pencil at right 
 angles to it, in such a position that it may be seen while 
 taking the measurements, will correctly place the pencil. 
 When the pencil is held so that only the head of the pin
 
 TESTS. 55 
 
 can be seen, it must be perpendicular to the direction in 
 which the student looks (Fig. 93). But a much better 
 device may be made by bending a piece of soft wire (a hair- 
 pin), about a large knitting needle, as shown in Fig. 94, 
 so that one end will project at right angles to the needle, 
 and the other, after passing around the needle several times, 
 shall extend back, and project a little distance perpendicu- 
 lar to the first end. The long end, at right angles to the 
 needle, will place the needle correctly. The wire should 
 press the needle just enough to keep it in position. It may 
 be moved by the finger or thumb, and the measurement 
 taken by sighting by the short end. This slide will be 
 found of very great assistance, and as it is important that 
 measurements should be exact, it is desired that every stu- 
 dent be provided with this measuring rod. It will also be 
 found a great help when, as is generally the case, one meas- 
 urement is not an easily determined part of the other. In 
 measuring, the smaller measurement should be taken first, 
 and then compared with the larger. If the former is one- 
 half or one-third of the latter it will be easily determined ; 
 but if the first goes once and a fractional part, as one-fifth 
 or one-sixth, this part is not easy to determine, and if the 
 two measurements can be secured in such a way that they 
 may be compared at length, the proportions may be more 
 surely determined. This may be done by taking the smaller 
 measurement by the sliding wire, and the larger by the 
 thumb, and in this way the two can be compared at leisure. 
 Much care must be taken that the distance of the reedle 
 from the eye shall be the same for all lines compared with
 
 56 TESTS. 
 
 each other. The distance is so apt to vary that unless each 
 comparison be made several times -with the same result, 
 there is little chance of the measurement being correct. It 
 is useless to think that tests not carefully taken are worth 
 the time given them, and it is much better to take the one 
 proportion of height and width carefully than to spend the 
 time necessary to do this on half a dozen measurements, 
 which are sure to contradict and do more harm than 
 good. 
 
 It is impossible to compare accurately a short distance 
 with a long. If the height is equal to or one-half the width, 
 care will so determine it, but with every change of the hand 
 in moving a short distance over a long inaccuracy is pro- 
 duced, so it is well to avoid all such comparisons. The 
 inaccuracy arises from inability to hold the pencil at exactly 
 the right place, also from the change in distance of the pen- 
 cil, which every movement away from the first position occa- 
 sions. This movement may be seen to occur by tying a thread 
 to the pencil, and measuring the distance of the pencil from 
 the eye, by holding the thread with a finger of the left hand 
 against the brow. If the arm is dropped for the measure- 
 ment of a near object, and the string is tight, it will slacken 
 when the arm is raised, and in the same way it will change 
 for horizontal movement. The only way then in which 
 really exact measurements can be taken, will be by the use 
 of such a measuring thread for the pencil, but we wish to 
 simplify the subject as much as possible, and if reasonable 
 care is exercised the variation of the distance of the needle 
 may be made so slight as to be unimportant, at least in the
 
 TESTS. 57 
 
 first part of our work, wliich will consist iu the drawing of 
 small objects, singly or in groups. 
 
 Whenever possible all comparisons should be made by 
 swinging the pencil from a vertical into a horizontal posi- 
 tion by a motion of the whole arm from the shoulder, and 
 avoiding a change of position of the pencil, by sicinging it 
 about one end of the first measurement. Thus, if the height 
 and width of a table is desired, instead of measuring the 
 width along the top, and then dropping the hand to take 
 the vertical measurement (which will be done by almost all 
 students, or what amounts to this, the measurement of the 
 height and the lifting of the hand for comparison with 
 width), make the measurement by taking the width along 
 the top, and swing the pencil down about the thumb, thus 
 not changing the distance of the hand. The easier way 
 will be to take the measurement at the bottom, and swing 
 the pencil up about the thumb (see Fig. 95). This way of 
 measuring will be easily acquired, and will assist very 
 greatly to correctness. 
 
 A short distance may of course be compared with a long 
 with a degree of accuracy which varies with the student, 
 but such measurements are not recommended, and are not 
 necessary, as other tests will bring better results. Another 
 way by which distances may be compared is by marking 
 upon the edge of a straight-edge or bit of cardboard with a 
 pencil, and then comparing at leisure. The use of the pin 
 or the needle with a sliding wire may be necessary at first 
 for most students, but after practise these helps will not be 
 required, and the pencil will be held correctly without diffi-
 
 58 TESTS. 
 
 culty. If the back end of the pencil is used to measure by, 
 the pencil will be placed correctly when the end is seen as 
 a straight line, thus more simply producing the same result 
 as the sliding wire on the needle.* 
 
 The above are the direct tests for proportions, and if 
 carefully taken should give the correct mass of the drawing, 
 but for the smaller proportions, and for the directions of 
 lines, there are other tests Avhich are more important. The 
 lines with which it is most natural to compare directions 
 are vertical and horizontal lines. A horizontal line, whose 
 ends are equally distant, appears horizontal, and is repre- 
 sented by a horizontal line, while a vertical line appears 
 vertical, and is represented by a line in the drawing which 
 is perpendicular to the horizontal. If a straight-edge be 
 held horizontal with its ends equally distant from the eye, 
 it will represent a horizontal line in the drawing, and by 
 looking over the ruler thus held, the directions of lines of 
 the object may be compared with the horizontal. A piece 
 of fine thread with a Aveight attached will serve as a plumb- 
 line, and by holding it in front of the object its lines may 
 be compared with the vertical. The thread is often better 
 than the rule for the horizontal line. Care must be taken 
 to hold the thread perpendicular to the line of sight. This 
 position is easiest obtained by directly facing the group 
 and extending the arms equally, so that both ends of the 
 
 *When sketching from nature, if horizontal edges extend on both sides of the 
 spectator and it is desired to make a perspective instead of a model drawing, its 
 dimensions may be compared by holding the pencil parallel to the plane on 
 ■which the drawing is supposed to be made.
 
 TESTS. 59 
 
 thread are the same distance from the eye. But more care 
 must be exercised to get the thread horizontal. This can 
 only be done by looking at the thread alone, until it is 
 levelled, when the student may look behind. If this is not 
 done, the lines behind will be most likely to make the thread 
 seem horizontal Avhen it is not. If there are horizontal 
 edges behind, which are parallel to the picture, they will 
 appear horizontal, and will place the thread correctly, but 
 if the lines are not directly in front they will not appear 
 horizontal, and so will cause the thread to be out of level. 
 
 It may seem that unnecessary space has been given to 
 these directions, but it has been found almost impossible 
 to make many students understand the matter, and hold the 
 thread correctly, even with repeated explanations and illus- 
 trations. Some, after months of study, are found holding 
 the pencil or thread at an angle of from ten to twenty 
 degrees away from the correct position. Hence it is not 
 thought that any explanation can be too careful. But the 
 problem is so simple that any student who wishes to suc- 
 ceed should have no difficulty after giving careful attention 
 to directions. Of this the student may be sure, that he will 
 never learn to draw until he is able to discover his mistakes, 
 and as the thread is a most important test it should be cor- 
 rectly applied. 
 
 Any object, as the cube (Fig. 96), having been drawn, it 
 may be tested by the thread as follows : Hold the thread 
 horizontal to cover 5, and note its intersection with 1-6 and 
 6-7. Now hold the plumb-line so as to cover point 3, and 
 notice where it intersects 5-6. Then hold it to cover 6-7,
 
 60 TESTS. 
 
 and find its intersection with 2-3. Then hold the thread 
 to cover 1 and 5, also 2 and 4, and .compare the direction 
 of the thread with the horizontal. Next cover 2-7, and see 
 where this line continued cuts 5-6, then 4-7 to intersect 2-1. 
 Now cover in succession any two opposite points, as 1-3, 
 and 3-6, and 4-1, etc., and place the intersections on the 
 inner edges. 
 
 Such use of the thread is simply a more exact method of 
 discovering angles than drawing the lines in the air with 
 the pencil point, the first method explained. When the eye 
 is trained, the first, which is of course the simplest, will be 
 all that is needed. But most students will find the use of 
 the thread preferable, as it gives a fine line which can be 
 made to exactly cover the edges of the object. Its inter- 
 section also with the edges can be seen much more readily 
 than that of a line formed by the side of the pencil, whose 
 size hides considerable of the object. If these tests with 
 the thread are applied, they cannot fail to discover every 
 error of importance. 
 
 Another and last test may be made by holding two pen- 
 cils, or better two rulers, together, at right angles to the 
 line of sight, and separating them until one covers 2-3, and 
 the other covers 5-6. If great care is taken the directions 
 of these lines with reference to each other may be seen, and 
 the drawing tested by continuing these lines in the drawing. 
 
 We have dwelt thus carefully upon each test to be applied 
 in the hope that the student may realize their importance, 
 for he will learn to draw correctly only through his own 
 efforts, gaining with each discovery of error. He can never
 
 TESTS. 61 
 
 become a draughtsman as long as he depends upon a teacher 
 for corrections. Let him carry his drawing so far that a 
 thorough application of all the tests explained will show 
 no error, then, as it is simply a question of exactness to be 
 determined by the eye, if the trained eye of the teacher 
 discovers mistakes so slight that the student cannot rightly 
 be expected to determine them for himself, these may be 
 pointed out. As the chief benefit results from what the 
 student sees and does himself, he will be much better off 
 without a teacher than with one who does his work for him. 
 There are many who say that measurements and tests 
 are mechanical, and that to learn to draw the student should 
 draw by eye simply. It is true that measurements and 
 tests, as unfortunately too many students are taught to use 
 them, cannot fail to produce hard and mechanical drawings, 
 and retard progress. Still, it seems better for the student 
 when he can see no further to be shown by tests where his 
 eyesight has failed, rather than to carry drawings only as 
 far as he can by eye alone, and then put them away, and 
 begin others which can be carried but little if any farther. 
 Therefore the student is advised to apply the tests ex- 
 plained, after he has carried his drawings as far as he can 
 see, and not to put any drawings away which the tests show 
 to be inexact. This training, it is believed, will most 
 quickly produce ability to draw correctly at sight.
 
 THE PLANE OF THE DRAWING. 
 
 The mind through the sense of sight perceives form, the 
 rays of light from any object entering the eye, and being 
 focussed on the retina, and forming an image of the object 
 as in the camera, except that in the latter the image is 
 formed on a plane surface, while that in the eye is formed 
 on a spherical surface. As but a single point can be seen 
 clearly at any time, the image of the eye is practically the 
 same as that of the camera. The problem for the artist is 
 to make his drawing so that it shall convey the same idea 
 of form, size and position as the objects which it represents. 
 It is evident that this must occur when the drawing pro- 
 duces the same image in the eye as the objects, and to do 
 this the drawing must be similar to the image. 
 
 The rays from any object to the eye form a conical body. 
 If this cone of rays be intersected by any plane the inter- 
 section must be a picture of the object, which if the object 
 be taken away will still create its image in the eye. If 
 this plane of the picture be at right angles to the cone, the 
 section (the picture) will be a true picture of the object, 
 that is, be similar to the image of the eye. In Fig. 97 a 
 circle. A, is placed vertical and in front of the eye. In the 
 drawing it is represented by line A. The cone formed by 
 the rays of sight is represented by lines b-b, and a vertical 
 plane cutting through the cone of rays by line P. If the 
 student will take any cone and hold it horizontal, it will 
 perfectly illustrate the figure, the base of the cone being 
 
 (02)
 
 THE PLANE OF THE DRAWING. 63 
 
 the circle A, and the eye being at the apex. "With the cone 
 the student will at once see that a vertical plane between 
 the eye and the base of the cone will intersect it in a circle, 
 and this circle is the picture of the base, A. 
 
 If now the plane of the picture be inclined to the axis of 
 the cone (Fig. 98), the intersection with the cone will still 
 be a picture of the circle, but in shape it differs from that 
 in Fig. 97, which is a circle. This oblique intersection is 
 seen to be an ellipse, but it is important to notice that it 
 does not appear so to the eye at the apex of the cone, but 
 appears a circle exactly covering the base of the cone. It 
 will be seen that it makes no difference how the plane of 
 the picture, P, is placed, or Avhat the proportions of the 
 ellipse resulting. The ellipse always must appear to the 
 eye a circle, in fact the circle of the base, A. But when the 
 eye is removed from the apex of the cone the ellipse will 
 appear an ellipse, and will not then be a picture of the 
 circle. The circle of Fig. 97 and the ellipse of Fig. 98 are pic- 
 tures of the circle A, and both create in the eye, when at the 
 apex, a circular image of the circle, but the former only is 
 similar to the object A. 
 
 In looking at pictures we naturally hold them in front of 
 us, and at right angles to our line of vision, as in the position 
 of the plane, P, of Fig. 97. If plane P, of Fig. 98, is thus 
 held, the ellipse upon it will be seen as an ellipse, that is, will 
 create an ellipse as image in the eye. This cannot create 
 the idea of a circle. We see that the first picture is much 
 preferable to the second, for it is a circle, and wherever the 
 eye is placed will create a circle in the eye. (It is of course
 
 64 THE PLANE OF THE DRAWING. 
 
 understood that it is always looked at perpendicularly.) The 
 first picture Ave will distinguish from the second, and from 
 all others which might be made, by calling it a true picture, 
 meaning, that it is similar to the image created in the eye 
 by the object. It is seen that there can be but one position 
 of the plane which will give a true picture, and this must 
 be at right angles to the direction in which the object is 
 seen. The plane, of course, cannot be perpendicular to all 
 the rays, and by this is meant the central ray. A true 
 picture of any object may be obtained by drawing upon a 
 sheet of glass with a brush and color, or a pencil of soap, 
 or on a wire screen with chalk, the glass or screen being 
 placed at right angles to a line from the centre of the object 
 to the eye, and the eye and screen being fixed and lines 
 drawn to cover all the edges which are seen. It is desired 
 that every student make drawings in this Avay, a small pane 
 of glass and a pencil of soap being the best materials. The 
 drawings should be made with the glass at right angles to 
 the rays, and also when held obliquely, so that the drawings 
 may be compared, and the student realize that the glass 
 must be perpendicular to the direction in which he looks, 
 for the drawing to give the real appearance of the object. 
 
 It will appear that a drawing on any plane or surface can 
 create the correct impression only Avhen the eye is in the 
 position which it had when the drawing was made. All 
 drawings, then, are best seen from some one point or distance. 
 This distance the trained eye will naturally select. How- 
 ever, as draAvings and pictures will be viewed by untrained 
 eyes, and as the proper point may not always be accessible,
 
 THE PLANE OF THE DRAWING. 65 
 
 it is very important that all be avoided which will cause 
 marked distortion when the picture is not seen from the 
 proper point. If the picture is a true picture, the distortion 
 produced when it is viewed from a longer or shorter dis- 
 tance than the proper one will appear not in the shape of 
 its parts, but only in the relative sizes of the objects repre- 
 sented. Thus, the distortion of a true picture is always 
 less than that of a drawing. on a plane which is oblique to 
 the rays, and so the true picture is by far the best drawing 
 that can be made for general use.
 
 REPRESENTATION. 
 
 A Paper comparing Perspective and Model Drawing, 
 
 READ AT THE AnNUAL MeETING OF THE INDUSTRIAL 
 
 Art Teachers' Association, January 5, 1889.
 
 REPRESENTATION. 
 
 This term includes all drawings, constructive and decorative works, 
 being as fully representations as perspective views, the geometric views 
 conveying ideas of facts and actual dimensions, the pictorial of facts 
 and apparent dimensions. We will consider simply the representation 
 of appearances, and our subject is really " Pictorial Drawing." 
 
 The aim of such drawing undoubtedly should be to awaken in the 
 mind of the beholder the same impression as to form, size and position 
 as the objects themselves would create when viewed from the artist's 
 position. Drawings to be appreciated require certain education or 
 qualities, but pictures and illustrative drawings are so numerous that 
 this education is unconsciously acquired, and, by the average intellect, 
 photographs and pictures are readily understood. 
 
 Photographs and drawings such as isometric are often very different 
 from the image which would be produced upon the eye by the objects, 
 and yet they are accepted without difficulty, the mind having a con- 
 ception of the form and giving to the drawing the most reasonable 
 interpretation; so that a quite conventional or incorrect drawing, so 
 far as appearances are concerned, may be almost as readily read and 
 accepted as one more nearly agreeing with the appearance. This does 
 not affect our decision as to the aim of the artist ; it does, however, 
 assist him in his work, which otherwise would sometimes be nearly, if 
 not quite, impossible. 
 
 A drawing which produces upon the eye the same image as the 
 object must be one whose proportions agree with the appearance, the 
 angles between the visual rays to the drawing being relatively the 
 same as between the rays to the object. If the horizontal or vertical 
 angles should be greater to the drawing than to the object, the drawing 
 
 (69)
 
 70 KEPRESENTATION. 
 
 ■would be correspondingly too wide or too high. In the light of this 
 statement let us consider a plane perspective drawing, a drawing upon 
 a vertical plane in which the eye being fixed, each line of the drawing 
 covers the edge of the object which it represents. Fig. 1 is a pers. 
 drawing representing vertical and horizontal prisms. Fig. 2, which is a 
 side elevation, shows that the visual rays to the vertical prism intersect 
 the P. PI. obliquely, and that the measure of the angle between them 
 will be not in the P. PI., but in the plane L M, perpendicular to the 
 rays,* and thus the perspective drawing A is too high, the correct height 
 being the distance 1-2 and the difference seen by comparing A with B. 
 Suppose the perspective drawing A upon the vertical plane and the 
 shorter B upon plane L M, the spectator's eye being fixed at S. P., both 
 must appear alike, and convey the same impression as the object, but 
 as ordinarily viewed from a point not S. P., the first must create a 
 wrong impression of the proportions of the prism. In the same man- 
 ner Fig. 3 proves that the perspective drawing D of the horizontal 
 prism is too wide, E being the real appearance. From these drawings 
 we see that a plane perspective drawing is as the object really appears 
 only when the object is directly in front, the representation of objects 
 in all other positions being distorted, vertically, when the object is 
 above or below C. V., horizontally, when at the side, and obliquely, 
 that is both ways, for all other positions. Of course when the eye is 
 at S. P. the distortion is not noticed, but as this is rarely, perhaps 
 never the case, it follows that a perspective drawing generally cannot 
 give a correct impression of the sizes of the objects. 
 
 By Fig. 2 we find that a drawing of the prism to agree with the ap- 
 pearance must be made upon plane L M at right angles to the rays ; 
 this is a perspective drawing upon a plane oblique to the ground, and 
 as parallel retreating lines appear to converge we find that the vertical 
 edges of the prism which are oblique to the P. PI. are represented by 
 converging lines. Vertical lines must appear to vanish as any other 
 retreating lines, but in order that these lines in the drawing may not 
 seem to represent edges actually inclining, the eye, as it should be for 
 
 * The central visual ray.
 
 REPRESENTATION. 71 
 
 any perpective, must be at S. P. ; from any other position the drawing 
 will tend to give the impression of inclined lines in nature, which is as 
 serious a matter as the distortion vertically of the perspective drawing 
 upon the vertical plane, and the drawing is thus no better than the first. 
 Our aim is to obtain a drawing which may be viewed naturally, whose 
 proportions shall agree with the appearance and which shall give a 
 correct impression of the facts. This we shall accomplish if we change 
 the drawing B by substituting vertical for the inclined lines represent- 
 ing the vertical edges. Thus corrected we will call it a " model draw- 
 ing," which term we use in the sense of the best drawing — the 
 drawing which to the ordinary observer shall convey the same idea of 
 form, size and position as the objects themselves, not necessarily a 
 drawing of the geometric forms, but of any subject whatever. If we 
 attempt to make such a drawing from an extended range of objects we 
 shall find that the P. PI., in order to be at right angles to the rays to 
 all, will become the surface of a sphere ; this is undevelopable and 
 although a drawing might be made which would give the exact appear- 
 ance of every object, it is evident that it could not give the relative 
 positions, and would be no more a picture than a canvas covered at 
 random with smaller sketches. It follows then, that a drawing which 
 shall comprise a wide field of view and give the appearance and the 
 relations of everything drawn is an impossibility. 
 
 What can be done to produce a drawing whose proportions shall 
 agree with the appearance and which shall give correct information of 
 the relations of objects within a reasonable limit ? There is often less 
 of height than of width to be represented, and the system known as 
 curvilinear perspective results. In this the P. PI. is vertical and cylin- 
 drical, S, P. being in the axis. This surface is developable, and a 
 drawing upon it will have its horizontal distances correct, though the 
 vertical must be distorted as in Fig. 1. Fig. 4 is a plan view showing S. 
 P., the curved picture plane and three cubes. The P. PI. being curved, 
 the angles of the cubes with it increase with the distances, and in the 
 drawing F their lines converge the quicker the further we get from the 
 cube in front, and thus we find straight lines represented by curved.
 
 72 REPRESENTATION. 
 
 This drawing will give the impression of curved lines in nature and is 
 not a satisfactory solution of the problem, the perspective drawing G 
 upon plane P being much more acceptable in its representation of 
 parallel straight lines by straight lines converging to one vanishing 
 point. Now if we change the drawing with curved lines by substituting 
 straight lines tending to one V. P., we shall have a drawing H whose 
 horizontal distances are correct and which gives a true idea of the 
 facts, and if as shown by Fig. 2 we make the correction for the heights, 
 the drawing II will agree in proportion with the appearance and will 
 convey correct information of the facts, and this " model drawing " 
 answers the conditions. We see that it is neither a plane nor a 
 cylindrical perspective, but a combination of the good qualities of each, 
 further improved by having the vertical dimensions agree with the 
 appearance. It may be considered a plane perspective whose widths and 
 heights have been corrected to agree with appearances. This drawing 
 comes very near to perfect agreement with appearances, the image 
 created by it upon the eye being practically the same as that caused by 
 Nature herself, and we must accept it as the best possible to obtain. 
 
 What is the practice of our illustrating artists ? We find that they 
 do not measure the lengths and angles of all lines, and constructing a 
 diagram work out their drawings by perspective rule, but that they 
 generally work almost entirely by appearances, and often refuse to 
 admit that perspective can be of assistance to a person who can see 
 and who wishes to record his feelings. As the artist endeavors to 
 represent real appearances, the sketches illustrating perspective dis- 
 tortions must explain why his opinion is thus. Upon examination, 
 the drawings from some of our best illustrators will be found to be so 
 exact as regards relative proportion and direction of lines, that the 
 curvature resulting from representing each part of a straight line as it 
 appears, will be plainly seen, and the drawings thus are good examples 
 of curvilinear perspective, except that they are as correct vertically as 
 horizontally, and if straight lines should be substituted for the curved 
 they would be exactly what we have decided to be the best representa- 
 tion of both the facts and the appearances.
 
 REPRESENTATION. 73 
 
 What is the best ti'aiaing to enable one to draw freely and correctly ? 
 The artist will often say, " continued practice," and consider scientific 
 study of little or no value. The teacher, will say, " present the facts 
 of form with the principles of perspective," and each will argue strongly 
 that his method is the most satisfactory. "We must judge by results, 
 and if we find that the best drawings are made by the artists, then 
 their opinions are entitled to consideration. It may be said that the 
 artist understands how to draw and the teacher to instruct, and that we 
 should not expect to compare the teacher's drawing with the artist's. 
 Still until the teacher can present work equalling or excelling that of 
 the artist and not the result of the artist's method of work, an im- 
 partial judge must decide that any criticisms of the artist have founda 
 tion. 
 
 Representation is defined as the art of delineating objects as they 
 appear to the eye. The eye sees all objects as surfaces, the mind can 
 only infer that they have thickness, and thus to represent the appear- 
 ance it is onl}' necessary to determine the direction which the edges 
 appear to have. For this the artist says, " practice," the teacher, 
 " facts of form and perspective principles," both agree, then, that the 
 eye unpractised and unassisted is not to be depended upon. Two 
 elements, physical and intellectual enter into all drawing, the first, the 
 exercise of the eye and hand, the second, the habit of observing with 
 exactness and memorizing observations, so that the mind may com- 
 pare and reason, the latter obviously of the greater importance : the 
 child of six years who, seeing a drawing carried on, said, " that 
 drawing was thinking and then drawing aromid the think," having 
 most clearly defined the subject. 
 
 The work in our schools is based upon a study of the facts of form 
 and of perspective principles. A knowledge of the facts is the first 
 obtained by the student, who certainly has a very practical idea before 
 a study of theory or of api^earance may be made. There can be no 
 question but that this knowledge is a hindrance when he attempts to 
 represent the appearance ; thus how many, if any, ever represent a 
 foreshortened horizontal surface by too little, or even little enough of
 
 74 KEPRESENTATION. 
 
 vertical distance ; and who ever realized without a special effort that 
 the long axis of the ellipse representing a vertical circle above or 
 below the eye is not a vertical but an inclined line (see Fig. 5), and 
 the tendency must always be that the image of the eye be overthrown 
 by the conception of the mind. Does the study of perspective counter- 
 act the effect of this knowledge of the facts, and are its principles 
 presented in a way to assist correctness of observation? We have 
 seen that a perspective drawing gives the real appearance only when 
 the object is directly in front ; the illustrations have been in angular 
 perspective, but the study is introduced by parallel perspective. Fig. 
 G, K is a parallel perspective drawing of a cube. In this the edges 
 parallel to the P. PI. are represented by horizontal lines, but the cube 
 being at the left, three faces are visible, and it is evident that these lines 
 can not appear horizontal ; the real appearance is shown by P, and 
 the distortion of the parallel perspective drawing is more serious than 
 that of the angular perspective drawing. 
 
 Instrumental perspective introduced by numerous drawings in 
 parallel perspective must create a wrong idea of the appearance of 
 form. This is generally uncorrected by any statement of the instructor, 
 and the knowledge of pers2)ective attained at the cost of an entire 7nis- 
 conception of appearances can he of little value in free-hand drawing. 
 Instrumental perspective is the latter part of our public school 
 course. Is the preceding work such that the student may acquire the 
 power of careful observation which is not given by the study of the 
 facts of form or of perspective 1 We find that as in perspective later, 
 the first work is from objects in which but one set of horizontal lines 
 vanish, the directions being to draw a horizontal line representing the 
 level of the eye (the horizon), determine the proportions by pencil 
 measurement, and see that the retreating edges meet at a point in the 
 horizon. So many illustrations of this nature are to be found, that one 
 wonders where the favored schools may be which have plinths, prisms, 
 etc., for every student, for this is almost a necessity where neither end 
 of the object is to be seen, and if not thus placed the drawings made 
 must be copies of the illustrations and not from the object. Next
 
 REPRESENTATION. 75 
 
 comes the use of two vanishing points, as before the horizon is first to 
 be drawn, and the retreating edges are to meet at points in this line, 
 their angles being determined by strips of paper held, one horizontal 
 and the other to cover the edges. It is easy for the student to follow 
 these directions so that perspectively the drawing is correct ; but is it 
 easy to determine how far below the horizon the drawing shall be 
 placed, or where between the vanishing points 1 Directions (measure- 
 ments) may be given, but if so he is not making the drawing ; and if 
 he measures the angles of the retreating edges and continuing them to 
 cut the horizon thus locates the points, how may he be sure of the 
 angles ? Certainly not by the use of the paper strips. This must be 
 admitted by any candid observer who has seen students measuring 
 proportions and angles with the pencil or paper held parallel to retreat- 
 ing edges, and in all positions except correctly at right angles to the 
 line of sight. From the beginning of this free-hand work, perspective 
 principles are explained and all the illustrations and explanations give 
 the student the impression that the drawing is made upon a vertical 
 plane, and this the student comes to think of as parallel to the wall of 
 the room or to the edge of the table supporting the group ; an inevit- 
 able conclusion by which the plane for almost all is from 20° to 45° 
 away from the position which will give the correct appearance ; and it 
 seems that perspective is made an instrument whereby a certain number 
 of drawings may be produced, which the students accept as the appear- 
 ance of the objects from which they are supposed to be drawing, the 
 teachers evidently thinking that so long as perspective principles are 
 illustrated the discrepancy between the perspective drawings and the 
 actual appearance is of no consequence. In the work from groups 
 following there is a difference of opinion as to the steps. Some say 
 draw the upper object first, others, the lower or principal one. This is 
 an interesting question in view of the statement so strongly made by 
 educators that a subject must be considered as a whole before its parts 
 are taken up, and yet we are told that we must determine the width 
 and length of each object before beginning to draw, and there is no 
 certainty as to whether we shall draw first, the upper, lower, or yrinci-
 
 76 REPRESENTATION. 
 
 pal object. If the statement that a subject must first be treated as a 
 whole is true in one case, it must be for all, and especially for art, and 
 •without further dicussion the absurdity of these questions is made 
 evident. But we will now follow a student in his study of the group 
 of models illustrated by Fig. 7. Following the directions given, the 
 student draws the vase first, determining its width and height and get- 
 ting the outlines symmetrical about the vertical centre line ; this done 
 he takes the prism, then the cylinder and last the frame, treating each 
 in the same manner as the vase. What is the result ? — He completes 
 his drawing before he can tell whether its entire width is correct for its 
 height, and often without even considering the question, and working 
 as he does, is led to think of the appearance of each object by itself, 
 and not in its relation to the whole. The proportions of each object 
 having been determined before drawing there is nothing to be done 
 but to make the drawing to these measurements. He does not under- 
 stand that measurements at best can only assist not perform the work 
 of the eye, and that as he depends upon them they are more likely to 
 give incorrect than correct results ; but he makes the drawing, thinking 
 that since each object is made of its determined proportions that when 
 the last is complete, the group must be correct, and though perhaps a 
 suspicion that it is not, flashes upon him as he surveys the finished 
 drawing, he refuses upon reflection to entertain the idea, for has he 
 not made sure of each object as he drew it, and the thought of erasing 
 his finely finished lines convinces him that if his di-awing does seem a 
 little queer it is correct, and that he cannot see rightly. This drawing, 
 a whole obtained by considering and adding to one another its various 
 parts, entirely out of proportion, awkward and mechanical, is put away 
 as a work of art, and we find that the free-hand work is free-hand 
 perspective and not model drawing, that the power of observation has 
 not been trained or depended upon, that perspective rules come first 
 and cause a subordination of appearances to mechanical and uneduca- 
 tional means, and as a result the student even after graduating has no 
 facility in drawing, and if put before a new subject is entirely at a loss 
 4s to how to proceed. Is it to be wondered at, if in continuing this
 
 REPRESENTATION. 77 
 
 •work and being brought to practically consider these questions, and to 
 discover that he has been working in ignorance he decides that per- 
 spective is a snare to be carefully avoided ? 
 
 Having seen that perspective dravrings are distortions and having 
 followed the changes in tlie positions of the plane, and the corrections 
 by which a model drawing is produced, is it possible to explain them 
 to the student and to make model, instead of perspective drawings ? I 
 answer to the first part of this question, most decidedly no, but that 
 this is not necessary or at first desirable, and that it is possible to teach 
 mod'el drawing loithout this special theoretical consideration of the plane 
 of the drawing or of perspective principles, and that practically the 
 differences resulting from a change in the position of the plane can 
 be shown as follows: Give the student a frame covered with wire 
 gauze, and have him mark upon it the appearance of the object, the 
 frame being held vertical or in any position oblique to the visual rays, 
 and then at right angles to the same. On comparing the drawings, the 
 student will readily see that only the latter gives the real appearance, 
 and as a result of this experiment will understand that the pencil, 
 where measurements are taken, must be perpendicular to the direction 
 in which he looks, and that when held horizontal in this position, it 
 will be represented by a horizontal line, as will also any line of the ob- 
 ject which it then appears to cover. Having realized this most im- 
 portant point, which the present teaching never does, our aim should 
 be that the student acquire as quickly as possible the ability to see 
 correctly, and not at first abstractions and theories, but facts of ap- 
 pearances. This power of correct observation must be the result of a 
 continued perception, through his own efforts, of the imperfections of 
 previous observations. It follows, then, that we must furnish practical 
 means for correction and be sure that their proper use is understood. 
 The pencil and a thread with weight attached are all that is required 
 and may be used as follows, see Fig. 9. The outline of the appear- 
 ance should first be sketched by eye, and then tested by the pencil, its 
 entire height with the width, then all visible lines lightly sketched and 
 the test made by holding the pencil or thread horizontal, and thus
 
 78 REPRESENTATION. 
 
 taking horizontal lines through the angles of the object and noting 
 where these lines cut the front and opposite side, and comparing with 
 the drawing. It is almost impossible for many students to hold the 
 pencil correctly at right angles to their line of sight, but this difficulty 
 may be avoided by driving a large needle exactly at right angles into 
 the centre of the pencil ; when only its end is seen the pencil is in the 
 proper position. By the plumb-line vertical lines may be taken through 
 the angles of the objects, and the points where they cut the opposite 
 side noted as of the horizontal lines. These tests are simple and will 
 discover all mistakes, but to insure correctness the thread may be held 
 to cover and continue all edges of the object so that their intersections 
 with the opposite side may be noted, the direction of diagonals and 
 of any lines whatever connecting points on opposite sides be deter- 
 mined, and their intersections with intermediate lines, and last two 
 straight edges held to cover any two parallel lines will show the appar- 
 ent angles between them. These tests will surely point out any differ- 
 ences between the drawing and the appearance and are all that should 
 be employed until, the student having acquired control of the means 
 and being able to make fairly good drawings, occasion may be taken, 
 as the nature of the drawing presents, to call attention to perspective 
 principles which are illustrated in the finished sketches, but it will be 
 better to delay such explanation than to incur the risk that the stu- 
 dents may utilize the principles to avoid the careful observation 
 necessary to give correct judgment and freedom in drawings. Draw- 
 ings made in this way may not at first be as successful perspectively 
 as if drawn by rule and the vanishing points, but they will be much 
 more educational and will enable the student to see correctly, that is 
 to accept the image of his eye as the real appearance. It will be seen 
 that the use of the thread in this way lays especial importance upon 
 the actual construction (the facts), as an aid to its representation 
 (thus continuing all edges and diagonals and noting intersections, is 
 simply making use of the actual construction to test its representation), 
 but in all cases the drawing should be made by the eye before any tests 
 are applied. The eye should be depended upon and thus trained to
 
 REPRESENTATION. 70 
 
 correct observation before abstract principles are presented, I should 
 rather saj^ let the principles present themselves, or be deduced from 
 the drawings, as may easily be done, for instance — when a drawing 
 representing several parallel horizontal lines whose V. P. comes on 
 the paper has been completed, the student may be shown that these 
 lines continued intersect, and that the point is on a level with his eye. 
 In this way by practically discovering perspective truths they will be 
 understood in such a way as to be of value. 
 
 Fig. 9 shows this method applied to the group before considered. 
 The proportions of the whole group being first sketched by light lines 
 joining the principal points, the entire width and height then deter- 
 mined as carefully as possible, and the objects then drawn all at once, 
 by seizing the important lines of each and considering them with refer- 
 ence to the group as a whole, the cord being frequently used as ex- 
 plained to determine the correctness of recorded observations. The 
 pencil, which must be long, being held freely and the lines drawn with 
 a quick movement, and when found to be incorrect others drawn be- 
 side them, until, the proper position having been verified by careful use 
 of the thread, all other lines are erased at one time. Working in this 
 way the student not having the false idea that it is possible to deter- 
 mine exact proportions and slight differences before drawing, will de- 
 pend more upon sight, will expect to change his first lines, and will do 
 so as each test indicates. He will soon find that each line tests many 
 others, that he can see more readily than measure the fine effects nec- 
 essary to exactness, and that a group is not more difficult than a single 
 object. It will not be necessary for the vanishing points to come on 
 the paper that he may be sure of his drawing, or that he crawl over a 
 floor twenty feet square used as a drawing board to test a half impe- 
 rial paper. In this connection I wish to suggest that if instead of lin- 
 ing in with lines of one strength, or conventionally, the nearer edges 
 being represented by the stronger lines, the students are made to study, 
 and represent the edges as they appear, some brought out by shade or 
 shadow strongly, others in the light or shade, and perhaps barely visi- 
 ble, lightly, they will be started in the direction in which only they can
 
 80 REPRESENTATION. 
 
 advance and make artistic sketches from nature, and the observation 
 involved will be of the greatest value when light and shade is taken 
 up. This dependence upon sight trained by these tests is the only way 
 to prepare for practical work from nature, and the student, whatever 
 his training, who acquires facility, must come to depend upon it largely, 
 and any one who attempts to formulate rules to govern the production 
 of art works will soon find his task beyond him. 
 
 It may be said that this dependence upon individual observation is 
 not possible for public school work as each student would require at- 
 tention which it would be impossible for him to receive. Although 
 this objection has force, still there is no doubt that the proper use of 
 the thread and pencil could be insisted upon by the teachers and se- 
 cured ; this attained, the efforts of the students would be in the right 
 direction, and if not perfect, would be more valuable than any attempt 
 to work by rules which in most cases can be simply memorized, not 
 understood. 
 
 Having seen that the study of the facts of form and perspective 
 causes a neglect of appearances, and the working in an impractical way, 
 shall we decide that perspective and science are useless? Because per- 
 spective drawings to give the correct impression require to be seen from 
 S. P., and because perspective principles have been misused, are not 
 sufficient reasons for not teaching the subject. As shown in the first 
 illustrations, drawings must conform to perspective principles to be ac- 
 ceptable and some drawings must be parallel perspective.* A knowl- 
 
 *See Fig. 10 which represents the two nearer cubes shown in Fig. 4, and a third 
 cube at the riglit of the spectator and in line with the others. We have seen that 
 representing straight lines as they appear (curved) is not acceptable and we must 
 determine the direction of a straight line which shall represent the horizontal 
 edges nearest parallel to the spectator. It is evident that a horizontal line will 
 equalize the distortion and give the most satisfactory result, and whenever ob- 
 jects are in line with one another and on each side of the spectator this drawing 
 must generally be made. 1 Bay generally because the judgment and good sense 
 of the artist should be depended upon and in drawings from large subjects out 
 of doors where the lines are broken the curvature of the lines may not be noticed 
 and may sometimes give the best result, as much in Fig. 10 as in Fig. 4. In Fig.
 
 RETKESENTATIOX. 81 
 
 edge of perspective must then assist the draughtsman, and as a study 
 to be taken up after tlie students have acquired ability to represent 
 appearances fairly well, and with the distinct understanding that per- 
 spective drawings do not do this, I think that perspective should 
 be taught, just when, depending upon circumstances, although it seems 
 that in all but the higher grades the time might be given with better 
 advantage to model drawing. 
 
 We have stated that many illustrations are so correct in representing 
 the exact appearance of nature that the apparent curvature of straight 
 lines may be seen. On the contrary many more drawings, while in the 
 main correct as to proportions, are so full of discrepancies that hardly 
 three of a system of parallel lines can be found to intersect at the same 
 point, and often these points for horizontal lines will be above or below 
 the horizon, and geomi'tric forms are distorted. Errors such as these, 
 of greater or less importance, are to be found in the work of even the 
 best illustrators and noted artists, the most perfect eye with the long- 
 est training not being surety against carelessness or the influence 
 
 10 the question will arise shall we make a perspective drawing throughout or 
 shall the foreshortening of horizontal distance at tlic right and left, and of verti- 
 cal distance above and below the centre be given. This again is a question which 
 the artist must decide as each case arises. But for the woilv in the public schools 
 it is not necessary that the question bo considered — lot straight lines be repre- 
 sented by straight lines, straight lines extending on each side by horizontal lines 
 and insist upon ihe pencil being always at right angles to the visual rays when 
 measurements are taken, and unless an unusually bright student draws from a 
 cube directly in front so that he sees only the top and front (faces, the question 
 will never occur as the foreshortening of the vertical face is so little ordinarily 
 that in any figure except the square it will be hardly noticed. 
 
 It will be seen that parallel perspective introduces many more puzzling ques- 
 tions than angular, and if objects are to be drawn with only two faces visible it 
 would be well not to take the cube, as the student should, from the first and all 
 the time, be made to determine the angular dimensions of the apisearancc of 
 objects, which can only be done with the pencil held at right angles to the rays 
 to the parts as they are drawn, and when he completes his course he should bo 
 able to harmonize these dimensions with perspective appearances which are nec- 
 essary to most drawings.
 
 82 REl'KKSKNTATIOX. 
 
 which one line has to change the apparent direction of another. We 
 remember the criticism of a picture which showed tlie full moon and 
 setting sun in one sky. This is no more serious a contradiction than 
 many which are apparently unnoticed, such as shadows or sunlight in 
 the shade, and the shadows in part of a picture advancing, indi- 
 cating the sun in front of the spectator, while in another part they re- 
 treat and show the sun behind. These mistakes may pass unnoticed 
 because of an uneducated or lenient public, still there can be no ques- 
 tion but that the drawings would be better true. Perspective is the 
 remedy for such mistakes, and an extensive scientilic knowledge is not 
 required ; no more is really necessary than an observance of the princi- 
 ples as they are illustrated in- the simplest sketches which may be made 
 from nature, though there can be no question but that the broader the 
 knowledge the better, and that a course in plane and solid geometry, 
 especially intersections, perspective, shadows, reflections, etc., will 
 benefit any draughtsman. He may not apply or make use instrument- 
 ally of his knowledge, but unconsciously as he works its influence, 
 will produce drawings, which, while giving the proportion and the feel- 
 ing will not transgress laws of nature or of perspective, but in design- 
 ing it will have its greatest value, since when nature cannot be studied 
 knowledge must be depended upon. 
 
 We must conclude then, that the best method of instruction is that 
 which adds to a practical way of working from the object, a knowledge 
 of the facts of form and of perspective principles, which may supple- 
 ment the power of sight to produce correct drawings. 
 
 In closing I quote a sentence from a work of the 18th century by 
 Gerard DeLaircsse : " I conclude then, that pictures exhibiting nature 
 contrary to what she ought to be are liable to censure, and that we 
 ought to seek the truth by reasoning, and then waiving old customs 
 and prejudice to believe our own eyes." 
 
 ANSON K. CROSS. 
 
 Boston, December, 1888.
 
 NOTE. 
 
 The illustrations, which have been reduced from the hasty sketches prepared 
 for blackboard use, are from the notes for the perspective lectures which have 
 been given the last four years in class B of the Massachusetts Normal Art School.
 
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