fore a meridian section of an element of a spherical surface of which is an axis.
Sections of wave surfaces reflected from the ellipsoid have their centre at and are also sections of wave surfaces reflected from the elementary spherical surface. Evidently the same would be true for any other meridian section passing through of the sphere of which the elementary surface forms a part, and the form of the wave surfaces may be conceived by supposing the whole figure to revolve about as an axis. The arc describes a zone of the sphere, describe wave surfaces, and describes a circumference having its centre on The wave surfaces are portions of the surfaces of curved tubes of which the axis is the arc described by the point The line described by is a focal line, and all the light from the zone described by passes through it, or does so very approximately. If be taken nearer to on the sphere, approaches the axis along the curve and finally coincides with the focus conjugate to is a caustic curve, which, when the figure revolves about the axis describes a caustic surface. It will be noted that all the light from the zone described by passes through the axis between the points and The light coming from and reflected from a small portion of the spherical surface around the middle point of is then concentrated first in a line through at right angles to the paper, and again into the line in the plane of the paper. Nowhere is it concentrated into a point. A line drawn through and the middle of the focal line through is the axis of the re-
