It was now ready for the second stage of the operation the grinding of the correct shape for the upper reflecting surface. In order to bring the light of a star to an accurate focus this surface must be a paraboloid of revolution, the same kind of curve given to the reflectors of search lights or automobile headlights. The curve for this reflector of 30 feet focus is very nearly a section of a sphere of 60 feet radius, within one-thousandth of an inch, and consequently would nearly fit a huge globe 120 feet in diameter. The upper surface of the disc was fine ground and polished to this spherical surface and was then ready for the final stage, the “figuring” a continuation of the polishing process until the centre is deepened about a thousandth of an inch and the surface becomes accurately paraboloidal. This “figuring,” an exceedingly delicate and difficult process especially over such a large surface as the 72-inch, with the added difficulty of a central hole, occupied about two years and was not completed until nearly a year and a half after the mounting was ready. When it is remembered, however, that the surface nowhere deviates from the true theoretical form more than one four-hundred-thousandth of an inch and that if one part is accidentally polished too deep, the whole surface has again to be brought down to this level, the exceeding delicacy of the operation is evident and the time taken not excessive. Accurate quantitative tests showed that the final figure is of the highest order of accuracy and this is further clearly shown by the practical test of direct photographs at the principal focus. Figure 4, a six fold enlargement of a photograph at the principal focus, of the Ring Nebula in Lyra shows how sharp and small are the star images. Actual measurement on the original negative gives a minimum diameter of two one-thousandths of an inch equivalent to only a second of arc at the focus. As the images are enlarged considerably by unsteadiness of the air and errors in guiding the star light reflected from the whole surface of the mirror is collected into a little disc less than a thousandth of an inch in diameter indicating the extraordinary accuracy of the reflecting surface. Mr. J. B. McDowell, head of the firm since Dr. Brashear’s death, and Mr. Fred Hegemann, his chief optician, are to be highly congratulated on the perfection of figure obtained under specially difficult circumstances. Further the fine rendering of the detail in the ring and the strength of the two bands in the interior indicate not only perfect figure but exceptionally high polish. Mounting of Mirror