ELLIPSE' is the name of a figure in geometry, important from its being the approxi mate shape of the planetary orbits. It is a curve of the second order, and is a conic section, formed by cutting a right cone by a plane passing obliquely through its oppo site sides. It may be defined as a curve, the sum of the distances of every point in which from two fixed points within the curve is always the same. These two fixed points are called the foci; and the diameter drawn through them is the major axis; the minor axis bisects the major at right angles. The distance of either focus from the middle of the major axis is the eccentricity. The less the eccentricity is compared with the axis, the nearer the figure approaches to a circle; and a circle may be considered as an E. whose foci coincide.
There are various contrivances for describing an E. called ellipsagraphs or elliptic compasses. The simplest method of description is to E., on a plane the two ends of a
thread with pins in the foci, and make a pencil move on the plane, keeping the thread constantly stretched. The end of the pencil will trace an E., whose major axis is equal to the length of the thread.
The equation to an E. (see CO-ORDLNATES), referred to its center as origin, and to its v2 major and minor axes as rectangular axes, is — = 1, where a and b are the semi major and semi-minor axes respectively. From this equation, it may be shown, by the integral calculus, that the area of an E. is equal to nab; or is got by multiplying the product of the semi-major and semi-minor axis by 3.1416. It may also be shown that the length of the circumference of an E. is got by multiplying the major axis by the quantity Tr (1 — d2 3d2 etc.), where d 1