§ 12. How produced in natural forms.

and their differences of beauty depend on the different proportions borne to each other by those infinitely small right lines of which they may be conceived as composed.

When these lines are equal and contain equal angles, there can be no connection nor unity of sequence in them. The resulting curve, the circle, is therefore the least beautiful of all curves.

When the lines bear to each other some certain proportion; or when, the lines remaining equal, the angles vary; or when by any means whatsoever, and in whatever complicated modes, such differences as shall imply connection are established between the infinitely small segments, the resulting curves become beautiful. The simplest of the beautiful curves are the conic, and the various spirals; but it is difficult to trace any ground of superiority or inferiority among the infinite numbers of the higher curves. I believe that almost all are beautiful in their own nature, and that their comparative beauty depends on the constant quantities involved in their equations. Of this point I shall speak hereafter at greater length.

The universal forces of nature, and the individual energies of the matter submitted to them, are so appointed and balanced, that they are continually bringing out curves of this kind in all visible forms, and that circular lines become nearly impossible under any circumstances. The acceleration, for instance, of velocity, in streams that descend from hill-sides, gradually increases their power of erosion, and in the same degree the rate of curvature in the descent of the slope, until at a certain degree of steepness this descent meets, and is concealed by, the straight line of the detritus. The junction of this right line with the plain is again modified by the farther bounding of the larger blocks, and by the successively diminishing scale of landslips caused by the erosion at the bottom. So that the whole contour of the hill is one of curvature; first, gradually increasing in rapidity to the maximum steepness of which the particular rock is capable, and then decreasing in a decreasing ratio, until it arrives at the plain level. This type of form, modified of course more or less by the original boldness of the mountain, and dependent on its age, its constituent rock, and the circumstances of its exposure, is yet in its general formula applicable to all. So the

curves of all things in motion, and of all organic forms, most rude and simple in the shell spirals, and most complicated in the muscular lines of the higher animals.

This influence of Apparent Proportion, a proportion, be it observed, which has no reference to ultimate ends, but which is itself, seemingly, the end of operation to many of the forces of nature, is therefore at the root of all our delight in any beautiful form whatsoever. For no form can be beautiful which is not composed of curves whose unity is secured by relations of this kind.

Not only however in curvature, but in all associations of lines § 13. Apparent whatsoever, it is desirable that there should be reciprocal relation, Proportion in and the eye is unhappy without perception of it. It is utterly vain to endeavour to reduce this proportion to finite rules, for it is as various as musical melody, and the laws to which it is subject are of the same general kind; so that the determination of right or wrong proportion is as much a matter of feeling and experience as the appreciation of good musical composition. Not but that there is a science of both, and principles which may not be infringed; but that within these limits the liberty of invention is infinite, and the degrees of excellence infinite also. Whence the curious error of Burke, in imagining that because he could not fix upon some one given proportion of lines as better than any other, therefore proportion had no value or influence at all. It would be as just to conclude that there is no such thing as melody in music, because no one melody can be fixed upon as best.

The argument of Burke on this subject is summed up in the following words:" Examine the head of a beautiful horse, find what proportion that bears to his body and to his limbs, and what relations these have to each other; and when you have settled these proportions as a standard of beauty, then take a dog or cat, or any other animal, and examine how far the same proportions between their heads and their necks, between those and the body, and so on, are found to hold; I think we may safely say, that they differ in every species, yet that there are individuals found in a great many species so differing, that have a very striking beauty. Now if it be allowed that very different, and even contrary, forms and dispositions are consistent with beauty, it amounts, I believe,

$14. Error of matter.

Burke in this

§ 15. Constructive Proportion.

plants,

to a concession, that no certain measures operating from a natural principle are necessary to produce it, at least so far as the brute species is concerned."

In this argument there are three very palpable fallacies. The first is, the rough application of measurement to the heads, necks, and limbs, without observing the subtle differences of proportion and position of parts in the members themselves; for it would be strange if the different adjustment of the ears and brow in the dog and horse, did not require a harmonizing difference of adjustment in the head and neck. The second fallacy is that above specified, the supposition that proportion cannot be beautiful if susceptible of variation; whereas the whole meaning of the term has reference to the adjustment and functional correspondence of infinitely variable quantities. And the third error is, the oversight of the very important fact, that, although "different and even contrary forms and dispositions are consistent with beauty," they are by no means consistent with equal degrees of beauty; so that, while we find in all animals such proportion and harmony of form as gift them with positive agreeableness consistent with the station and dignity of each, we perceive, also, a better proportion in some (as the horse, eagle, lion, and man, for instance), expressing the nobler functions and more exalted powers of the animals.

And this allowed superiority of some animal forms is, in itself, Its influence in argument against the second error above named, that of attributing the sensation of beauty to the perception of Expedient or Constructive Proportion. For everything that God has made is equally well constructed with reference to its intended functions. But all things are not equally beautiful. The megatherium is absolutely as well proportioned, in the adaptation of parts to purposes, as the horse or the swan; but by no means so handsome as either. The fact is, that the perception of expediency of proportion can but rarely affect our estimates of beauty, for it implies a knowledge which we very rarely and imperfectly possess, and the want of which we tacitly acknowledge.

Let us consider that instance of the proportion of the stalk of a plant to its head, given by Burke. In order to judge of the expediency of this proportion, we must know, First, the scale of the

plant; for the smaller the scale, the longer the stem may safely be: Secondly, the toughness of the materials of the stem, and the mode of their mechanical structure: Thirdly, the specific gravity of the head: Fourthly, the position of the head which the nature of fructification requires: Fifthly, the accidents and influences to which the situation for which the plant was created is exposed. Until we know all this, we cannot say that proportion or disproportion exists: and because we cannot know all this, the idea of expedient proportion enters but slightly into our impression of vegetable beauty, but rather, since the very existence of the plant proves that these proportions have been observed, and we know that nothing but our own ignorance prevents us from perceiving them, we take their accuracy on trust, and are delighted by the variety of results which the Divine intelligence has attained in the various involutions of these quantities; and perhaps most when, to outward appearance, such proportions have been neglected; more by the slenderness of the campanula than the security of the pine.

What is obscure in plants is utterly concealed in animals, owing § 16. And anito the greater number of means employed and functions performed. mals. To judge of Expedient Proportion in them, we must know all that each member has to do, its bones, its muscles, and the amount of nervous energy communicable to them; and yet, as we have more experience and instinctive sense of the strength of muscles than of wood, and more practical knowledge of the use of a head or a foot than of a flower or a stem, we are much more likely to presume upon our judgment respecting proportions here; and are not afraid to assert that the plesiosaurus and camelopard have necks too long, that the turnspit has legs too short, and the elephant a body too ponderous.

But the painfulness arising from the idea of this being the case is occasioned partly by our sympathy with the animal, partly by our false apprehension of incompletion in the Divine work1; nor in either case has it any connection with impressions of that typical beauty of which we are at present speaking; though some, perhaps, with that vital beauty which will hereafter come under discussion.

For the just and severe reproof of which, compare Sir Charles Bell, On the Hand, p. 31, 32.

§ 17. Summary.

I wish therefore the reader to hold, respecting proportion generally:

1st, That Apparent Proportion, or the melodious connection of quantities, is a cause of unity, and therefore one of the sources of all beautiful form.

2ndly, That Constructive Proportion is agreeable to the mind when it is known or supposed, and that its seeming absence is painful in a like degree; but that this pleasure and pain have nothing in common with those dependent on Ideas of Beauty.

Farther illustrations of the value of Unity I shall reserve for our detailed examination, as the bringing them forward here would interfere with the general idea of the subject-matter of the Theoretic faculty which I wish succinctly to convey.