This is the first thing which the sketcher should consider. On paper one can only express points by placing them, as it were, geographically - north, south, east, and west - and if we can arrive at the latitude and longitude of the various points in the object we are drawing many of our difficulties vanish. In a drawing we deal with but two dimensions, height and width; this idea, if carefully considered, will be found to simplify the problem of expression.

In the drawing of a simple cube, for example (Fig. 1), to find the third point in relation to the two nearest to us, which lie in one vertical line, may justly be regarded as the "Pons Asinorum" of perspective (Fig. 2). Presume, as a means of ascertaining the position of the third point, that the vertical edge nearest to us (1 2) is, as it were, a foot rule: then the third point is so many inches above and so many inches to the right of the point 2.

Holding a pencil at full arm's length between the eye and the object, the lower edge coinciding with the point 3, a right-angled triangle will be observed composed of a portion of the vertical edge of the cube, the horizontal lower edge of the pencil, with the lower edge of the cube forming the hypotenuse of the triangle. If the third point can be accurately ascertained by observation and measurement, the remaining points can be deduced from this; for example, the point 4 in the illustration would be found below 3 and farther from 1 2; the point 5 less above 1 than 3 above 2; 6 slightly below 5; 7 between 1 and 6, and at a certain height above them. Above, below, right, and left are the positions which must be considered, observed and expressed.

Many teachers believe this measurement makes us mechanical, but surely any aid to accuracy is worthy of attention. Note how carefully the great teacher of modelling, Professor Lanteri, directs attention to the positions of points in modelling, and how earnestly he insists on measurement. There is little evidence of the mechanical in the work of himself or his pupils. Used as an aid to accurate observation, measurement will be found to be "a very useful servant," though the context of the proverb naturally applies. Illusions and delusions are frequent!}' dispelled by the measurement of the model.

Rules of perspective are equally vicious in their tendency, if allowed to have the ascendency over accuracy of vision. It is not too much to say that they should be dispensed with in the earlier stages.

* This and the following papers of the series have been developed, for publication in Arts and Crafts, from an address recently delivered by the author to the National Union of Manual Training Teachers.

The cube, though a stiff geometric model in itself, need not be regarded as the end of model drawing, yet it may not wisely be ignored as a type on which to base our knowledge of sketching. A rectangular box is an equally good model, but the same principle of the third point holds good (Fig. 3). Without a lid, the advantage of seeingthe back line 78 is a distinct gain, and the craftsman may extend his researches into the realms of furniture after he has mastered the cube; for tables, chests, chairs, cupboards, and the like require the same treatment, whilst architecture in its simpler forms may be drawn on similar lines (Figs. 4, 5, and 6). The proving of points may sometimes be of great service to the student; he can then be as sure of the accuracy of his drawing as the arithmetician is of his sum. Continuing the consideration of the lidless box (Fig. 3), if drawn to suitable scale the rectangle surrounding it may be added and the triangles A, B, C, D cut out; then the drawing, held between the eye and the object at proper focus, will, if correct, exactly fit the box visually (Fig. 7). The total width and height of the object will be decided; this, it is almost needless to say, is the most important proportion to observe whatever object we may be drawing. This method helps to convince the student of the visual accuracy or otherwise of his drawing and assists him in getting over that great difficulty in translating the "round" to the "flat," and helps him to draw what he sees in spite of what he knows; for nearly all teachers agree that therein lies the difficulty of object drawing. The method is, if a little more trouble, better than making a sketch at the side of the student's drawing, which he only copies without really seeing the object for himself. Some objects render themselves very suitable for this purpose, and the method may be used either in stencil or silhouette fashion, or both combined, giving interest and variety. Students when first shown these "cut-outs" are much helped. The drawing on a glass plane is helpful, too. Some teachers prefer to teach by angles, and use pieces of cardboard, wheels, protractors, umbrella ribs, miniature railway signals and other ingenious devices, but all having the same end - to fix and determine the direction of the line. The objection to angle treatment is that error increases with extension of the line, whilst with the point system the angle is made more correctly by knowing whence to where the line is to be drawn, for we must draw the line somewhere.

Another useful practice is to prove the drawing of a board on which rests a similar box (Fig. 8). Draw the box first. The two simplest points in the board to find are those which visually cut the edges of the box (a and b); where the further edges disappear behind it, their relative position may be readily ascertained by measurement. The next point (c) is found by measuring its distance below the line 6 4, the finding of the near corner a by its depth below the edge of the box and its distance to the left, by an imaginary vertical line; e- by an imaginary horizontal line and its distance to the right. We have now three points; if they are found to be in one straight line after having been obtained independently and without reference to each other, the accuracy of the line is unquestionable. The left edge may be obtained with four points, and the correctness made even more securely. Further proofs can now be found by holding the pencil and inclining it upwards or downwards only (neither inwards nor outwards) and observing where the line, it produced, would cut the opposite edge of the box, marking the point on your drawing without reference to the line already drawn, and testing; if the three points make one straight line you have again a proof of accuracy. In the example given this may be done both ways.

Object Drawing for Craftsmen. By Edward Renard, A.R.C.a. (Lond.).

Many teachers still insist on the board being drawn first. Try both ways, and decide for yourself which you find the more accurate and intelligent way of working.

The three-point system is not only useful in the drawing of common objects, but is used by the best teachers in drawing from the life, and will be found of the greatest service wherever accuracy is desired in all sketching from nature. The most advanced student will often be undeceived if he applies this simple test. Visual accuracy, a sense of sight proportion, may be much improved by an exercise which the late Lord Leighton is said to have employed, viz.: - to be able to draw a line three inches long either horizontally, vertically or inclined, then measuring it with a rule and gaining perfection by frequent practice. The pupil thus attains the power to set down correctly what he finds alter measuring the model. Edward Renard, A.R.C.A.

(To be continued.)