So far as I know, there has been only one attempt in modern times, besides my own, to establish a universal system of proportion, based on a law of nature, and applicable to art. This attempt consists of a work of 457 pages, with 166 engraved illustrations, by Dr Zeising, a professor in Leipzic, where it was published in 1854.
One of the most learned and talented professors in our Edinburgh University has reviewed that work as follows:—
“It has been rather cleverly said that the intellectual distinction between an Englishman and a Scotchman is this—‘Give an Englishman two facts, and he looks out for a third; give a Scotchman two facts, and he looks out for a theory.’ Neither of these tests distinguishes the German; he is as likely to seek for a third fact as for a theory, and as likely to build a theory on two facts as to look abroad for further information. But once let him have a theory in his mind, and he will ransack heaven and earth until he almost buries it under the weight of accumulated facts. This remark applies with more than common force to a treatise published last year by Dr Zeising, a professor in Leipsic, ‘On a law of proportion which rules all nature.’ The ingenious author, after proving from the writings of ancient and modern philosophers that there always existed the belief (whence derived it is difficult to say), that some law does bind into one formula all the visible works of God, proceeds to criticise the opinions of individual writers respecting that connecting law. It is not our purpose to follow him through his lengthy examination. Suffice it to say that he believes he has found the lost treasure in the Timæus of Plato, c. 31. The passage is confessedly an obscure one, and will not bear a literal translation. The interpretation which Dr Zeising puts on it is certainly a little strained, but we are disposed to admit that he does it with considerable reason. Agreeably to him, the passage runs thus:—‘That bond is the most beautiful which binds the things as much as possible into one; and proportion effects this most perfectly when three things are so united that the greater bears to the middle the same ratio that the middle bears to the less.’
“We must do Dr Zeising the justice to say that he has not made more than a legitimate use of the materials which were presented to him in the writings of the ancients, in his endeavour to establish the fact of the existence of this law amongst them. The canon of Polycletes, the tradition of Varro mentioned by Pliny relative to that canon, the writings of Galen and others, are all brought to bear on the same point with more or less force. The sum of this portion of the argument is fairly this,—that the ancient sculptors had some law of proportion—some authorised examplar to which they referred as their work proceeded. That it was the law here attributed to Plato is by no means made out; but, considering the incidental manner in which that law is referred to, and the obscurity of the passages as they exist, it is, perhaps, too much to expect more than this broad feature of coincidence—the fact that some law was known and appealed to. Dr Zeising now proceeds to examine modern theories, and it is fair to state that he appears generally to take a very just view of them.
“Let us now turn to Dr Zeising’s own theory. It is this—that in every beautiful form lines are divided in extreme and mean ratio; or, that any line considered as a whole, bears to its larger part the same proportion that the larger bears to the smaller—thus, a line of 5 inches will be divided into parts which are very nearly 2 and 3 inches respectively (1·9 and 3·1 inches). This is a well-known division of a line, and has been called the golden rule, but when or why, it is not easy to ascertain. With this rule in his hand, Dr Zeising proceeds to examine all nature and art; nay, he even ventures beyond the threshold of nature to scan Deity. We will not follow him so far. Let us turn over the pages of his carefully illustrated work, and see how he applies his line. We meet first with the Apollo Belvidere—the golden line divides him happily. We cannot say the same of the division of a handsome face which occurs a little further on. Our preconceived notions have made the face terminate with the chin, and not with the centre of the throat. It is evident that, with such a rule as this, a little latitude as to the extreme point of the object to be measured, relieves its inventor from a world of perplexities. This remark is equally applicable to the arm which follows, to which the rule appears to apply admirably, yet we have tried it on sundry plates of arms, both fleshy and bony, without a shadow of success. Whether the rule was made for the arm or the arm for the rule, we do not pretend to decide. But let us pass hastily on to page 284, where the Venus de Medicis and Raphael’s Eve are presented to us. They bear the application of the line right well. It might, perhaps, be objected that it is remarkable that the same rule applies so exactly to the existing position of the figures, such as the Apollo and the Venus, the one of which is upright, and the other crouching. But let that pass. We find Dr Zeising next endeavouring to square his theory with the distances of the planets, with wofully scanty success. Descending from his lofty position, he spans the earth from corner to corner, at which occupation we will leave him for a moment, whilst we offer a suggestion which is equally applicable to poets, painters, novelists, and theorisers. Never err in excess—defect is the safe side—it is seldom a fault, often a real merit. Leave something for the student of your works to do—don’t chew the cud for him. Be assured he will not omit to pay you for every little thing which you have enabled him to discover. Poor Professor Zeising! he is far too German to leave any field of discovery open for his readers. But let us return to him; we left him on his back, lost for a time in a hopeless attempt to double Cape Horn. We will be kind to him, as the child is to his man in the Noah’s ark, and set him on his legs amongst his toys again. He is now in the vegetable kingdom, amidst oak leaves and sections of the stems of divers plants. He is in his element once more, and it were ungenerous not to admit the merit of his endeavours, and the success which now and then attends it. We will pass over his horses and their riders, together with that portly personage, the Durham ox, for we have caught a glimpse of a form familiar to our eyes, the ever-to-be-admired Parthenon. This is the true test of a theory. Unlike the Durham ox just passed before us, the Parthenon will stand still to be measured. It has so stood for twenty centuries, and every one that has scanned its proportions has pronounced them exquisite. Beauty is not an adaptation to the acquired taste of a single nation, or the conventionality of a single generation. It emanates from a deep-rooted principle in nature, and appeals to the verdict of our whole humanity. We don’t find fault with the Durham ox—his proportions are probably good, though they be the result of breeding and cross-breeding; still we are not sure whether, in the march of agriculture, our grandchildren may not think him a very wretched beast. But there is no mistake about the Parthenon; as a type of proportion it stands, has stood, and shall stand. Well, then, let us see how Dr Zeising succeeds with his rule here. Alas! not a single point comes right. The Parthenon is condemned, or its condemnation condemns the theory. Choose your part. We choose the latter alternative; and now, our choice being made, we need proceed no further. But a question or two have presented themselves as we went along, which demand an answer. It may be asked—How do you account for the esteem in which this law of the section in extreme and mean ratio was held? We reply—That it was esteemed just in the same way that a tree is esteemed for its fruit. To divide a right angle into two or three, four or six, equal parts was easy enough. But to divide it into five or ten such parts was a real difficulty. And how was the difficulty got over? It was effected by means of this golden rule. This is its great, its ruling application; and if we adopt the notion that the ancients were possessed with the idea of the existence of angular symmetry, we shall have no difficulty in accounting for their appreciation of this problem. Nay, we may even go further, and admit, with Dr Zeising, the interpretation of the passage of Plato,—only with this limitation, that Plato, as a geometer, was carried away by the geometry of æsthetics from the thing itself. It may be asked again—Is it not probable that some proportionality does exist amongst the parts of natural objects? We reply—That, à priori, we expect some such system to exist, but that it is inconsistent with the scheme of least effort, which pervades and characterises all natural succession in space or in time, that that system should be a complicated one. Whatever it is, its essence must be simplicity. And no system of simple linear proportion is found in nature; quite the contrary. We are, therefore, driven to another hypothesis, viz.—that the simplicity is one of angles, not of lines; that the eye estimates by search round a point, not by ascending and descending, going to the right and to the left,—a theory which we conceive all nature conspires to prove. Beauty was not created for the eye of man, but the eye of man and his mental eye were created for the appreciation of beauty. Examine the forms of animals and plants so minute that nothing short of the most recent improvements in the microscope can succeed in detecting their symmetry; or examine the forms of those little silicious creations which grew thousands of years before Man was placed on the earth, and, with forms of marvellous and varied beauty, they all point to its source in angular symmetry. This is the keystone of formal beauty, alike in the minutest animalcule, and in the noblest of God’s works, his own image—Man.”
THE END.
BALLANTYNE AND COMPANY, PRINTERS, EDINBURGH.
FOOTNOTES
[1] Sir David Brewster.
[2] No. CLVIII., October 1843.