By Geo. E. Woodward, Civil Engineer And Architect, No. 87 Park Bow, New York.

It would appear, on carefully reading the article in the August number, page 367, by Mr. James Hogg, that he condemns the use of the circular curve in laying out ornamental roads, for the reason that he has no knowledge of any heavenly body having a circular orbit. Thus he says: "None of the orbits of the heavenly bodies, or any of their lines of motion, are in the nature of circular curves." And again he says: "I call attention to the fact that the circular curve does not exist in nature, or among the celestial bodies." It would have been proper to establish these assertions by proof, as they are made in reply to well-known principles, and which we are in the act of demonstrating. When one advances a new theory, facts should not be ignored, nor false assertions made. "He succeeds best who brightly illuminates his work by the lamps of Truth, Power, and Beauty; if the first is at all dimmed, the others will be more than correspondingly darkened".

It is necessary for us, in reply, to prove beyond all question that the circular curve does exist as a line of motion among the celestial bodies; this done, and his whole superstructure, statues, ships, water-cart horses, etc., is completely demolished. If heavenly bodies have circular orbits, then, according to Mr. Hogg, the circular curve is a curve of motion, and, consequently, must be flowing, graceful, beautiful; precisely what we claim for it.

We think Mr. Hogg misunderstands us. While we speak of compound circular curves, he refers to semi-circular arcs, judging from his allusions to ships and statues.

He misrepresents us by quoting us as saying, on page 299, July number: "It (the circular curve) can be made to pass through any point," etc. We said, "It (the circular curve, compounded of different radii) can be made to pass through any point," etc. Black and white do not differ more than the misquotation and the true one.

How Mr. Hogg can assert that the circle is not a "curve of motion" we can not understand, when it is one of the four curves in which a satellite of the sun can move. Newton proves in the "Principia"- (Book I., Prop. 11, 12, and 13) that the path of a planet affected by the power of gravity will be one of the conic sections; and in the 2d Corollary to Prop. 13, he expressly includes the circle among the conic sections.

The orbits of two at least of the heavenly bodies are not only "in the nature of circular curves," but are actually circular, as far as has been ascertained by the delicate astronomical instruments now used. These are the satellites of Jupiter, Nos. 1 and 2. The orbit of the planet Neptune is very nearly circular, the eccentricity being less than one per cent. of the semi-axis major. The orbits of Mercury, Venus, the Earth, and Saturn are gradually approaching circles.

"The axis of the Earth," says Herschell, " it is true, remains unaltered, but its eccentricity is, and has been since the earliest ages, diminishing, and the diminution will continue till the eccentricity is annihilated altogether, and the Earth's orbit becomes a perfect circle." - Herschell, p. 413.

It is needless to multiply proofs on this point; those who desire to follow this subject farther are advised to consult any of the popular elementary works on astronomy.

"True lines or curves of beauty," says Mr. Hogg, "are those composed of the various curves of motion," and we agree with him exactly.

We assume the position that curves of motion can be practically laid out for ornamental roads by using the elements of the circular curve, which is also a curve of motion, and that, when a circular curve is properly compounded of different radii, no eye, however accurate, can distinguish between it and the curve it is intended to represent. To execute the field work necessary to lay out a mathemati- cal elliptic or parabolic curve, independent of their foci, involves more labor and calculation than any but a first class fool would care to pay for. The elements of the circular curve are the most simple; and that curve and all its combinations can be more readily and rapidly laid out than any other, not excepting the guess-work curves of the gardener.

Our object is to so simplify the field operations in landscape embellishment, that curves of acknowledged beauty may be traced in the easiest and quickest manner, and that shall not involve the use of expensive instruments, nor the necessity of abstruse mathematical calculations.

We have stated that compound circular curves are practically identical with any curve of the slightest use in landscape embellishment. We will go still farther, and assert that the compound circular curve can be made to coincide so exactly with any other curve, that if both be laid out on a large sheet of drawing paper, and one be superimposed on the other, no difference could be detected except by a powerful microscope. We do not say, but, on the contrary, distinctly deny, that the circular curve, or its combinations, is mathematically identical with any other curve; and we also deny most emphatically that any person can walk or; drive over an ornamental road, and show which portion of said road is laid out with elliptic, parabolic, or other mathematical curves, and which with compound circular curves.

The combination of curves is a matter of taste; like words or sounds, or colors, the manner in which they are put together will indicate the talent that controls them. It is possible, as we have said in previous articles, to make a combination that will be destitute of grace and beauty, and positively disagreeable to an artistic eye; and it matters not whether the curves used be circular curves or otherwise.

We said the circular curve was adapted to the safe passage of heavy and rapid moving bodies. In the report of experiments made on the New York and Erie Railway in 1855, a train of 100 loaded freight cars, weighing, with engine, etc., 3,530,000 pounds, or about 1765 tons, was run forty-three consecutive miles on the Susquehanna Division at an average of twenty miles an hour, including four stops, from one third to one half of which was over circular curves. The time made through the reverse curve at Cameron was ten miles an hour.* Is it not splitting very fine hairs to say that an ornamental road laid out on a circular arc is not adapted to the passage of rapidly driven vehicles?

The remarks on the sphere we do not precisely understand. Admitting there is no example of a perfect sphere in nature, we could not quote a section of a sphere as a perfect circle; but as the form of the earth is an oblate spheroid, that is, a solid generated by the revolution of a semi-ellipse around its major axis, every section of an oblate spheroid at right angles to the axis must be a perfect circle; we therefore give this as an example.

The tendency of a body traversing a curved line is to fly into a straight line or tangent, when all centripetal and other attractive force is removed. We, therefore, consider it better to pass from a curve to a straight line, and from that straight line on to the reverse curve, or else make the degree of curvature on both curves as slight as possible at the point of reversing; the line is more beautiful and the motion easier. Contrary curvatures are the most beautiful when their radii are equal, and the most graceful bends, says Mr. Hay, are those in which two ellipses touch at points having the greatest equality of curvature.

We thoroughly understand the practical values and beauties of the elliptic and parabolic curves, and constantly make use of them in our practice; but whether they are more beautiful than the circular curve is merely a matter of taste. Mr. Alison, in his Essays on Taste, thinks the circle the most beautiful; Mr. Ruskin thinks it the least beautiful of all curves. We think the right curve in the right place has the most beauty.

Unless the eye be exactly in the axis where the circle can be seen as a circle, which is almost an impossible case, as far as an ornamental road is concerned, "perspective," says Mr. Garbett, "makes it appear elliptical or hyperbolic" It would thus seem that if the circular curve is objectionable, its appearance must be, except from one point, the perfection of grace and beauty.

That vehicles should delineate natural, and therefore beautiful lines, depends altogether upon the horse and his driver. The best drivers find it sometimes impossible to make a young horse follow any regular line, and the natural instinct of a well-broken horse, on entering his master's grounds, is to take a straight line to the stable. We therefore find, in most country places, the turf' edged by wheels, where horses turn too sharp to get the straight direction.

The principal drives of the Central Park are grand in their conception and execution. Their width is such that numerous beautiful curves might be traced by vehicles, and not be parallel with the border. We know that every curve described by all the heavenly bodies can be laid out through their entire length, and yet be confined to the gravel.

* The experiment was net made for the purpose of testing safe speed, bat to ascertain the com-paratite cost of moving freight. - N. Y. and E. R. R. Report, 1865.

As to the water-cart horses, we would suggest that their instincts be discouraged and their tastes educated. We should like to buy, and will pay a high price for a horse, or any other animal, that can delineate an elliptic or parabolic curve.

In this intelligent age, it is folly to write down the results of civil engineering, a profession whose limits have not as yet been defined, nor can they by any possibility be kept outside the field of art. As long as civil engineering covers the arts of construction, it must include the arts of design. Proportion, harmony, light and shadow, and other artistic appliances, must be thoroughly understood by every engineer who seeks a prominent position in his profession. Our practice of it carries us into the highest walks of art, and we presume to say, after thirteen years' practical experience, that a first-class civil engineer must necessarily be an accomplished architect; he must understand every principle of construction, and the value and strength of every class of building material; and unless he be content to copy others, he must be familiar with the principles of design; but the fling at the engineering profession falls short in its aim at us. Our education as an artist is thorough and complete, and equally so as an architect and a civil engineer.

We have served our time in every grade of the three professions, and have found them indispensably necessary in the pursuit of the profession of Landscape Adornment We attribute our uniform and gratifying success to the ground work so well and thoroughly laid.