There is, however, another point to be noticed in this bridge of Turner's. Not only does it slope away unequally at its sides, but it slopes in a gradual though very subtle curve. And if you substitute a straight line for this curve (drawing one with a rule from the base of the tower on each side to the ends of the bridge, in Fig. 34., and effacing the curve,) you will instantly see that the design has suffered grievously. You may ascertain, by experiment, that all beautiful objects whatsoever are thus terminated by delicately curved lines, except where the straight line is indispensable to their use or stability; and that when a complete system of straight lines, throughout the form, is necessary to that stability, as in crystals, the beauty, if any exists, is in colour and transparency, not in form. Cut out the shape of any crystal you like, in white wax or wood, and put it beside a white lily, and you will feel the force.Of the curvature in its purity, irrespective of added colour, or other interfering elements of beauty

4 The Law Of Curvature Perspective Elements 42

Fig. 34.

4 The Law Of Curvature Perspective Elements 43

Fig. 35.

Well, as curves are more beautiful than straight lines, it is necessary to a good composition that its continuities of object, mass, or colour should be, if possible, in curves, rather than straight lines or angular ones. Perhaps one of the simplest and prettiest examples of a graceful continuity of this kind is in the line traced at any moment by the corks of a net as it is being drawn:nearly every person is more or less attracted by the beauty of the dotted line. Now it is almost always possible, not only to secure such a continuity in the arrangement or boundaries of objects which, like these bridge arches or the corks of the net, are actually connected with each other, but - and this is a still more noble and interesting kind of continuity - among features which appear at first entirely separate. Thus the towers of Ehrenbreitstein, on the left, in Fig. 32., appear at first independent of each other; but when I give their profile, on a larger scale, Fig. 35., the reader may easily perceive that there is a subtle cadence and harmony among them. The reason of this is, that they are all bounded by one grand curve, traced by the dotted line; out of the seven towers, four precisely touch this curve, the others only falling back from it here and there to keep the eye from discovering it too easily.

And it is not only always possible to obtain continuities of this kind: it is, in drawing large forest or mountain forms, essential to truth. The towers of Ehrenbreitstein might or might not in reality fall into such a curve, but assuredly the basalt rock on which they stand did; for all mountain forms not cloven into absolute precipice, nor covered by straight slopes of shales, are more or less governed by these great curves, it being one of the aims of Nature in all her work to produce them. The reader must already know this, if he has been able to sketch at all among mountains; if not, let him merely draw for himself, carefully, the outlines of any low hills accessible to him, where they are tolerably steep, or of the woods which grow on them. The steeper shore of the Thames at Maidenhead, or any of the downs at Brighton or Dover, or, even nearer, about Croydon (as Addington Hills), are easily accessible to a Londoner; and he will soon find not only how constant, but how graceful the curvature is. Graceful curvature is distinguished from ungraceful by two characters: first, its moderation, that is to say, its close approach to straightness in some part of its course1; and, secondly, by its variation, that is to say, its never remaining equal in degree at different parts of its course.

This variation is itself twofold in all good curves.

A. There is, first, a steady change through the whole line, from less to more curvature, or more to less, so that no part of the line is a segment of a circle, or can be drawn by compasses in any way whatever. Thus, in Fig. 36., a is a bad curve, because it is part of a circle, and is therefore monotonous throughout; but b is a good curve, because it continually changes its direction as it proceeds.

4 The Law Of Curvature Perspective Elements 44

Fig. 36.

The first difference between good and bad drawing of tree boughs consists in observance of this fact. Thus, when I put leaves on the line b, as in Fig. 37., you can immediately feel the springiness of character dependent on the changetulness of the curve. You may put leaves on the other line for yourself, but you will find you cannot make a right tree-spray of it. For all tree boughs, large or small, as well as all noble natural lines whatsoever, agree in this character; and it is a point of primal necessity that your eye should

4 The Law Of Curvature Perspective Elements 45< p>Fig. 37.

4 The Law Of Curvature Perspective Elements 46

Fig. 38.

4 The Law Of Curvature Perspective Elements 47

Fig. 39.

4 The Law Of Curvature Perspective Elements 48

Fig. 40.

I cannot waste space here by reprinting what I have said in other books: but the reader ought, if possible, to refer to the notices of this part of our subject in Modern Painters, vol. iv. chap. xvii.; and Stones of Venice, vol. iii. chap. i. § 8.always seize and your hand trace it. Here are two more portions of good curves, with leaves put on them at the extremities instead of the flanks, Fig. 38.; and two showing the arrangement of masses of foliage seen a little farther off, Fig. 39., which you may in like manner amuse yourself by turning into segments of circles, - you will see with what result. I hope however you have beside you, by this time, many good studies of tree boughs carefully made, in which you may study variations of curvature in their most complicated and lovely forms.1

B. Not only does every good curve vary in general tendency, but it is modulated, as it proceeds, by myriads of subordinate curves. Thus the outlines of a tree trunk are never as at a, Fig. 40., but as at b. So also in waves, clouds, and all other nobly formed masses. Thus another essential difference between good and bad drawing, or good and bad sculpture, depends on the quantity and refinement of minor curvatures carried, by good work, into the great lines. Strictly speaking, however, this is not variation in large curves, but composition of large curves out of small ones; it is an increase in the quantity of the beautiful element, but not a change in its nature.