This section is from "The Horticulturist, And Journal Of Rural Art And Rural Taste", by P. Barry, A. J. Downing, J. Jay Smith, Peter B. Mead, F. W. Woodward, Henry T. Williams. Also available from Amazon: Horticulturist and Journal of Rural Art and Rural Taste.
On page 15s (April Number) Mr. Woodward says: "We do say that compound circular curves are practically identical with any curve that can possibly be made use of in any department of landscape adornment, and that there is no curve known, or gracefully flowing line, but what is rigidly mathematical;" and at page 299 (July Number) he says, "It (the circular curve) can be made to pass through any point, adapt itself to any form of surface, and admits of the safe passage of heavy and rapid moving bodies, and for graceful flow and elegance is quite as near perfection as can be attained. To any one who has made a practical examination of curved lines of road laid out by the eye, and compared them with those actually laid out as portions of circular arc*, there can be no question as to the superior elegance of the latter; the difference is so plain, the grace and beauty of flow so decided, that a doubt is not admissible".
Now I take issue with Mr. Woodward in this, and shall attempt to prove that the circular curve is not the curve of " graceful flow and elegance," and that in landscape garden practice it is not adapted for the " passage of heavy and rapid moving bodies." I assert that its elements can not be used as elements in laying out other curves, because they are diverse from them, and governed by altogether different causes and principles. That in laying out other curves, such as the ellipse, the parabola, the cycloid, the catenary, the epicycloid, the hyperbola, etc., in the manner indicated in Mr. Woodward's articles, he is only working by the rule of compensation of errors, which, while they neutralize each other, do not develop the truth.
This is not the place for positive mathematical demonstration of my assertion, as at present we have to do with the circular curve more as a matter of Aesthetics than of mathematics; but let me observe that the circle is not, as Mr. Woodward appears to consider it, the elementary principle of the cone, which is a combination of the triangle with the circle, but that it is rather the elementary principle of the sphere, the circumferential line of any section of which is always a circle, and can be no other figure. The sphere in physics conveys or suggests the ideas of perfection, ponderosity, and quiescence, because it appears as a complete, finished body which will make no further progress in development, and appears as being unacted upon by extraneous counteracting forces. The moment it is acted upon by forces sufficient to overcome the mechanical cohesion of the materials of which it may be composed, it immediately assumes other curved forms, the spheroid and its varieties, the parabola, the cone, the cylinder, the hyperbola, etc., etc., as the case may be: the elements of these curved forms being those of matter in motion, and not at rest; and these elements being produced and governed by laws and principles as diverse from each other as rest and motion are.
The circle being an essential, elementary portion of the sphere, it partakes in its due proportion of the characteristics of the sphere; it incloses the largest space within the smallest circumferential line, and so far is perfect; it is without beginning or end, and so far is complete; and it suggests neither progress nor motion, as, on account of its perfect form, it indicates either having overcome all forces producing motion, or incapacity of being acted upon by such forces; in either case suggesting a state of quiescence.
Now in laying out walks and roads we have to do with bodies in motion, and not at rest, and in order to avoid incongruities and discord of form, we must adopt lines which are produced by, or are in accordance with, the laws of motion or progress; and not with those in accordance with matter in a quiescent state.
As an inclosing line for flower-beds, fountains, statues, monuments, and similar purposes, the circle and its combinations are most beautiful and satisfactory; but for roads or walks it is of all others the most disagreeable and unsatisfactory to a cultivated eye. To reverse two semicircles, joining them at the tangental point, is to dislocate or destroy that which in its proper place is perfect, and so produces an unpleasant emotion in the mind: the very thing to be avoided in all artistic landscape scenes.
Engineers may generally use the circular curve in their operations with tolerable satisfaction, as their works are ordinarily of such a character and on such a large scale that the eye does not generally take in the whole of the curve at once; besides this, the long perspective destroys the bad effect of the curve. But in cases where the eye takes in the whole of the circular curve at once, or the mind instantly comprehends it, the effect is unpleasant.
I can not call to mind any instance in nature of a perfect sphere or circle. The rotation of the earth upon its axis causes it to assume the form of an oblate spheroid, and every thing upon it partakes of forms either original, in combination, or in modification more or less produced or governed by forces causing motion. Not only so, but none of the orbits of the heavenly bodies, or any of their lines of motion, are in the nature of circular curves - they are all curves of motion.
I do not recollect of any painting or piece of sculpture of acknowledged beauty where the circular curve is introduced; and as a fixed matter of taste, the more flowing and delicate the curved lines in a picture or work of art, the more it is esteemed and admired. I think you will admit that the lines in the Laocoon, the Venus de Medicis, the Apollo Belvidere, the Antinous, Niobe and her Children, the Dying Gladiator, and other world-renowned statues, are full of grace and beauty, and yet not one of the lines entering into their composition is a circular curve, nor would any artist ever attempt to lay out their lines by or with a pair of compasses. The ancients well knew the comparative value of flowing curves, (or curves of motion,) and of circular curves; they used the former in their highest and most spiritual works of art, and the latter in their lower works, as in statues of Silenus, Hercules, Bacchus, etc., where, in the roundness of the head, the belly, the calves of the legs, etc., a low degree of intellect, and a certain amount of grossness are admirably indicated, and which it would have been utterly impossible to have indicated by the other class of curves.