The arrangements for these tests are as follows: Around the flame of a lamp (_a_, Fig. 8) a sheet of tin is bent so as to form a cylindrical screen. Through it at the height of the brightest part of the flame, as at _b_, two holes are bored, a quarter of an inch apart, one 1/32 of an inch in diameter, the other as small as the point of the finest needle will make--perhaps 1/200 of an inch. This apparatus is to be set at the centre of curvature of the mirror _c_--the optical axis of the latter being horizontal--and so adjusted that the light which diverges from the illuminated hole in use, may, after impinging on the concave surface of the glass, return to form an image close by the side of the tin screen. In the case of the first test, the returning rays are received into an eye-piece or microscope, _d_, magnifying 20 times, and moving upon a divided scale to and from the mirror. In the second test the eye-piece is removed away from before the eye, and a straight-edged opaque screen, _e_, is put in its place. The mirror is supported in these trials by an arc of wood _f_, lined with thick woollen stuff, and above two wooden latches, _g_, _g_, prevent it from falling forward, but do not compress it. It is, of course, unsilvered. In the figure the table is represented very much closer to the mirror than it should be. In trials on the 15-1/2 inch it has to be 25 feet distant. The appearance that a truly spherical concave surface presents with the first test is: the image of the hole is sharply defined without any areola of aberration around it, and is surrounded by interference rings. Inside and outside the focus the cone of rays is exactly similar, and circular in section. It presents no trace of irregular illumination, nor any bright or dark circles. With the second test, when the eye is brought into such a position that it receives the whole pencil of reflected rays, and the opaque screen is gradually drawn across in front of the pupil, the brightness of the surface slowly diminishes, until just as the screen is cutting off the last relic of the cone of rays (Fig. 9), the mirror presents an uniform grayish tint, followed by total darkness, and gives to the eye the sensation of a plane. [Illustration: Fig. 9. Action of the Opaque Screen.] [Illustration: Fig. 10. Caustic of Oblate Spheroidal Mirror.]