illumination of the mirror decreases, and just before the light disappears the irregularities will plainly appear, showing themselves by patches of light, which prove that those parts still bright are so inclined as to reflect the rays by the side of the true focus. By moving the metallic edge so as to advance upon the focus from all sides, a very good idea of the irregularities may be obtained. If, however, the surface be truly spherical, the light will disappear regularly over the whole surface. M. Foucault commences by making the surface truly spherical, and then by polishing off in concentric circles, increasing the polishing from the centre, an elliptic and at last a parabolic curve is attained. The ellipse is tested from time to time by removing the perforated plate further and further away from the mirror until the ellipse becomes practically a parabola. The great advantage of this method is, that the effect of the polishing can be examined as it proceeds, and the work can always be applied wherever necessary, and the test is entirely independent of hot-air currents which are seen to fluctuate over the mirror as waves of light, leaving the irregularities of form permanently marked. It further appears that the method may be varied to form a first-rate test of a finished mirror already mounted; for one has nothing to do but bring a star into the field of view, and remove the eyepiece, and bring the eye into such a position as to receive the diverging rays from the focus of the star. A knife is then gradually moved across in front of the eye, say from the right; then if the mirror commences to get darkened on the right side distinctly before the left the knife is on the mirror side of the focus; if, however, the left side of the mirror becomes darkened first it is on the eye side of the focus. After a few trials it can be got to cut across the focus and darken the mirror at all points at once, and show up all irregularities. We have now, then, by one system or another, got our mirror, either of speculum metal or of glass, and if of the latter substance we have to silver it; processes have been published by Mr. Browning, and M. Martin,[7] by which, on the plan proposed in the first instance by Liebig, an extremely thin coating of silver is deposited on the glass. This film is susceptible of taking a high polish, which, in the case of small mirrors, can be renewed as often as is wished without repolishing the mirror; the resilvering of one of large aperture however is a most formidable affair. To those who wish to silver their own mirrors, let us say that it should be done in summer, or in a room kept by a stove at an equable summer heat, and the silvering solution should be kept for a day or more to settle, and for probably some chemical change to take place before the reducing solution is added. It will be found easy enough to silver the small planes for Newtonian reflectors, but large mirrors require much greater care and trouble. -----