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

The most general practice of laying out ornamental roads and walks is by inspection, the lines being decided upon by the eye, one person setting the stakes, while another indicates their positions. The plan, if it may be called a plan, depends for its success on a thoroughly educated eye, a knowledge of the principles of curvature, and the relations curves bear to each other. Without this knowledge, there can not be imparted any instruction of the process of doing such work, and the more one lacks the knowledge of the principles of the beautiful in curved or winding lines, the more complete will be his failure.

A curved line of road, to be beautiful and impressive must have some principle of curvature. "To give curves a character of art," says Mr. Loudon, "they ought to have a certain uniformity in their degree of curvature;" which means nothing more nor less than that they should be laid out by some fixed rule or principle. " To preserve unity," says Mr. Loudon, " curves ought to be so united as not readily to discover where one curve begins and the other ends;" that is, the union of curves must be such that they flow gracefully into each other, and this implies a fixed principle in tracing them.

It is by no means necessary to discuss the advantages or comparative beauties of the many varied forms of curvature. Whatever may be the theoretical value of any but the circular curve, we know by experience that in practice they are of but little or no account. The circular curve, compounded of different radii, is practically identical with any curve of the slightest use in Landscape embellishment. It 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 arcs, 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. The curves of the conic sections are all naturally illustrated; their beauty is of the highest order; beyond them we can not go.

The Circle is the prominent curve, cut from a cone by an intersecting plane; then the Ellipse; then the Parabola and Hyperbola. The three last can be practically laid out by the use of circular arcs of different radii; therefore the only curve we need investigate is the circular one; and we propose to show, by using this in the engineering operations of Landscape embellishments, that a very much higher grade of excellence can be attained; that the field work can be performed in a fraction of time usually required, and with an absolute certainty of a beautiful result. The diagram illustrates the manner by which curves join each other.

Starting from the point A, we pass around a portion of the circumference of circle No. 1, to the place where it is tangent to or touches circle No. 2; from thence pass on to the circumference of circle No. 2 to the point of contact with circle No. 3; then on the circumference of No. 3 to its contact with No. 4. These four circles are tangent to or touch each other internally, and the point of contact between any two can be found by producing a line joining their centres. At this point of contact the passage from one curve to another is harmonious, and is not so at any other point Circle No. 4 touches circle No. 5 at the point B; this is an external contact, and the curve reverses. A line drawn from the centre of circle 4 to the centre of circle 5 passes through the point of contact. The line C D is a tangent line to both curves 4 and 5; that is, it touches both at B, but does not cut either curve. The line C D is at right angles to the line joining the centres of circles 4 and 5; and to pass from a curve to a straight line, it is necessary that the straight line should be at right angles to the radius of the curve at the point of contact.

At the point B, from circle No. 4, we can pass harmoniously on to the straight line in the direction of D, or on to the reverse curve on circle No. 5. At E we pass to curves of different radii, of greater or less radius than circle No. 5, and the union with any of these curves is absolutely graceful. The centres of these curves are always in a line drawn from E through the centre of circle No. 5, and produced. At F the radius is again decreased.

Small garden walks, flower beds, turn-arounds, etc., can be easily laid out by describing portions of circular arcs on the ground from centres in a nearly similar manner to drawing them on paper, using a chain instead of dividers. Curves of large radius, and where objects intervene between them and their centres, are laid out on the circumference. This is best done by the method known as deflection distances; the only accessories required, besides a chain or tape line, can be extemporized on the ground in a few minutes, and the whole problem practically demonstrated in an accurate and rapid manner.