Harper's Round Table, November 3, 1896

by Various

"Is there any one here whose vision has been frequently tested, and about which there can be no doubt?"

A young man was sent for, and I was told that his eyesight was as perfect as human eyesight ever gets to be. I took him to the window and pointed out Diana, who now seemed in the act of shooting her arrow directly over our heads, and was therefore facing us.

"How large does she look?" I asked.

"Oh, she is too large," he responded, with a laugh; "she seems fully ten feet high to me." Here was confirmation of my own opinion.

I then went to Mr. St. Gaudens. He told me frankly that the statue was too large, and that it was to be replaced by a smaller one—five feet shorter, a diminished replica. With the modelling he was entirely satisfied, as are all other competent art critics, I believe, but he was convinced that the statue was too tall.

I asked him what the custom was in determining how much a figure that was to be placed at an elevation should be exaggerated. He told me that in modelling ordinary statues a platform could be made of the same size as the base upon which the finished work was to rest, and that then the sculptor's sense of proportion would guide him. In this case, however, where a statue was to be placed at an elevation of 325 feet, such a test was impracticable.

Hence the proportions had to be determined by a scale-drawing which showed all the various parts of the building and tower in relation to each other and to the whole. This drawing was modified until it completely satisfied the sense of proportion of both architect and sculptor. Such a method, however, appears not to have been exact enough to have prevented two of our ablest men from falling into a costly error of judgment.

By marking off a base-line for one side of a right-angled triangle, and letting another side of the triangle be the height of the tower, the length of the hypothenuse, or third side of the triangle, which would also have been the line of vision, could have been easily calculated. Then if another right-angled triangle be constructed, the hypothenuse of which is just as long as the normal human vision can see without diminishing an object of the size that it is desirable that the elevated object should appear when fixed in place, then the height of this given object would be to the hypothenuse of the second or subsidiary triangle as the hypothenuse of the larger triangle is to the height of the desired object. That is, if the normal vision will reach accurately 200 feet, that would be the hypothenuse of the second triangle. Suppose, then, that the hypothenuse of the first triangle be 500 feet, and it was desired that the elevated object should appear six feet high; then the architect would have to make it fifteen feet high for the proper result to be attained.

By applying such a plain mathematical rule as this the costly mistakes made in New York might have been obviated, and by its aid it can be determined at any time just how much an elevated object should be exaggerated so that it will look of a natural size. Such a rule as this can be applied by any school-boy who has mastered his trigonometry; but there are few, if any, architects who resort to calculations to determine a mere matter of size when it does not relate to the strength of the structure. The strength of walls and floors is of course calculated with mathematical nicety, but those matters of construction and ornamentation which only affect the appearance of buildings are determined by the taste and the sense of proportion of the designer.

And it may be that it is scarcely worth while for architects and designers to take any greater pains than they do to arrive at mathematical accuracy in those things which, after all, have only an æsthetic value. The first Diana on the tower was too large; but if a thousand had been randomly gathered in Madison Square Garden, and a census of their opinions taken, it would probably have been found that the vote stood something like this: 50 would have thought the statue 15 feet high; 100, 10 feet; 200, 8 feet; 200, 6 feet; 200, 5 feet; 100, 4 feet; 100, 3 feet; 50, 2 feet.