owing solely to mechanical considerations, which have no more connection with ideas of beauty, than the relation between the arms of a lever, adapted to the raising of a given weight; and yet it is highly agreeable to perceive that such constructive proportion has been duly observed, as it is agreeable to see that anything is fit for its purpose or for ours, and also that it has been the result of intelligence in the artificer of it; so that we sometimes feel a pleasure in apparent non-adaption, if it be a sign of ingenuity; as in the unnatural and seemingly impossible lightness of Gothic spires and roofs.

Now, the errors against which I would caution the reader in this matter are three. The first, is the overlooking or denial of the power of Apparent proportion, of which power neither Burke, nor any other writer whose works I have met with, takes cognizance. The second, is the attribution of beauty to the appearances of con

lessly claimed for the strength-supposed gigantic-of insects and smaller animals; as being capable of lifting weights, leaping distances, and surmounting obstacles, of proportion apparently overwhelming. Thus the Formica Herculanea will lift in its mouth, and brandish like a baton, sticks thicker than itself and six times its length, all the while scrambling over crags of about the proportionate heights of the Cliffs of Dover, three or four in a minute. There is nothing extraordinary in this, nor any exertion of strength necessarily greater than human, in proportion to the size of the body. For it is evident that if the bulk and strength of any creature be expanded or diminished in proportion to each other, the distance through which it can leap, the time it can maintain exertion, or any other third term resultant, remains constant; that is, diminish weight of powder and of ball proportionately, and the distance carried is constant, or nearly so. Thus, a grasshopper, a man, and a giant 100 feet high, supposing their muscular strength equally proportioned to their size, can or could all leap, not proportionate distance, but the same or nearly the same distance-say, four feet the grasshopper, or forty-eight times his length; six feet the man, or his length exactly; ten feet the giant, or the tenth of his length, some allowance being made for the greater resistance of the air to the smaller animal and other slight disadvantages. Hence all small animals can, proportionally, perform feats of strength and agility, exactly so much greater than those possible to large ones, as the animals themselves are smaller; and to enable an elephant to leap like a grasshopper, he must be endowed with strength a million times greater in proportion to his size. Now the consequence of this general mechanical law is, that as we increase the scale of animals, their means of power, whether muscles of motion or bones of support, must be increased in a more than proportionate degree, or they become utterly unwieldy and incapable of motion; and there is a limit to this increase of strength. If the elephant had legs as long as a spider's, no combination of animal matter that could be hide-bound would have strength enough to move them: to support the megatherium, we must have a humerus a foot in diameter, though perhaps not more than two feet long and that in a vertical position under him; while the gnat can hang on the window frame, and poise himself to sting, in the middle of crooked stilts like threads, stretched out to ten times the breadth

structive proportion. The third, the denial, with Burke, of any
value or agreeableness in constructive proportion.

11. The value
Now, the full proof of the influence of apparent proportion, I must
of Apparent
Proportion in reserve for illustration by diagram; one or two instances, however, may
Curvature. be given at present for the better understanding of its nature.

We have already asserted that all curves are more beautiful than
right lines. All curves, however, are not equally beautiful, 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

of his body on each side. Increase the size of the megatherium a little more, and no
phosphate of lime will bear him: he would crush his own legs to powder. (Compare Sir
Charles Bell (Bridgewater Treatise on the Hand), p. 296, and the note.) Hence there is
not only a limit to the size of animals, in the conditions of matter, but to their activity
also, the largest being always least capable of exertion; and this would be the case to a
far greater extent, but that nature beneficently alters her proportions as she increases her
scale; giving slender frames to the smaller tribes, and ponderous strength to the larger.
So in vegetables-compare the stalk of an ear of oat, and the trunk of a pine, the
mechanical structure being in both the same. So also in waves, of which the large never
can be mere exaggerations of the small, but have different slopes and curvatures: so in
mountains, and all things else, necessarily, and from ordinary mechanical laws. Whence
in architecture, according to the scale of the building, its proportions must be altered
constructively, and ought to be so apparently even where the constructive expedients are
capable of disguise; and I have no hesitation in calling that unmeaning exaggeration of
parts in St. Peter's, of flutings, volutes, friezes, &c., in the proportions of a smaller
building, a vulgar blunder, and one that destroys all the majesty that the building ought
to have had-and still more I should so call all imitations and adaptations of large build-
ings on a small scale. The true test of right proportion is that it shall itself inform us
of the scale of the building, and be such that even in a drawing it shall instantly induce
the conception of the actual size, or size intended. I know not what Fuseli means by
that aphorism of his :-

"Disproportion of parts is the element of hugeness—proportion, of grandeur. All
Gothic styles of Architecture are huge. The Greek alone is grand." When a building
is vast, it ought to look so; and the proportion is right which exhibits its vastness.
Nature loses no size by her proportion; her buttressed mountains have more of Gothic
than of Greek in them.

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.

duced in na

The universal forces of nature, and the individual energies of the § 12. How promatter submitted to them, are so appointed and balanced, that they tural forms. 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 decent 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 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 both 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.

in

Not only however in curvature, but in all associations of lines § 13. Apparent whatsoever, it is desirable that there should be reciprocal relation, proportion and the eye is unhappy without perception of it. It is utterly

§ 14. Error of Burke in this matter.

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 nor 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, 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, § 15. Constructive proportion. argument against the second error above named, that of attributing Its influence in the sensation of beauty to the perception of Expedient or constructive plants. 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