The lenses are now ready to be centered, that is, the circumference so turned that the line which joins the centers of curvature of the two spherical surfaces shall pass through the center of figure. In order to accomplish this, the lens is first cleaned from the pitch used to cement it to the handle used in holding the lens for polishing. For a long time I could find no way of doing this satisfactorily when pitch was the cement; finally, I laid my troubles before Dr. A. M. Bleile, Head of the Department of Physiology, and he suggested to first soak the lens in lard and then wash it in benzol (C6H6). This worked like magic though the first time I tried it I used some lard that had been heated with some pitch in it which made the lard very soft in fact almost as soft as it could be and yet not be an oil, and this same lard was used over and over again. The action is rather peculiar; the lard does not apparently effect the pitch at all but after a few minutes in the benzene it all flakes off and leaves the lens perfectly clean. The actual centering is then carried out on the grinding machine shown in [Fig. 2]; A holder, D, whose front face has been turned in the spherical turning machine to fit one of the surfaces of the lens, is held in the head A. If the lens be cemented to this with a thin coat of pitch, it is obvious that the surface of the lens next to the holder will have its center of curvature coincide with the axis of rotation of the spindle of the head, A, but the center of curvature of the other lens surface will probably fall outside of this axis. A lamp, L, has a tin chimney with a pin hole in it turned towards the lens, this pin hole forming a brilliant point of light, an image of which is formed by each surface and reflected by the total reflecting prism, P, into the telescope, T, where it is seen through the eyepiece. If the centers of curvature of both surfaces do not accurately coincide with the axis of rotation of the head, A, the images of the pin hole will describe circles as this axis is rotated. The back surface will of course be centered if the layer of the pitch used as cement is of uniform thickness which will generally be the case if the work has been carefully done; but in any case the image formed by it should be examined. If the front surface is out of center, as it generally will be, the holder should be warmed and the lens shifted, care being used to keep it tight against the surface of the holder as it is being shifted. As soon as both images remain stationary as the head, A, is rotated, the lens is fed against the wheel, B, and ground true and to size. This worked beautifully and the tests were wonderfully sensitive. As soon as the component lenses of the objective have all been thus centered, they are ready to be assembled in the cell or shutter in which they are to be used; but as this is simply a matter of careful machine work, I need not describe it further.

I know of no literature on the grinding of small lenses though the following memoirs on the making of large reflecting telescopes should be in the hands of any one interested in this work:

Note 1—A Spherometer for Short Radii.

Fig. 6

In [Fig. 6], A is a regular Brown & Sharpe Micrometer Head with the measuring point ground to an angle of 60° and slightly rounded; B is a round steel base all machined at one setting in which the micrometer head is clamped by a set screw not shown.

Let r be the radius of the spherical surface, MNO, and we will have at once r = (a2 + d2) ⁄ 2d. The advantage of this form of spherometer is that it is very easy to make the point of the micrometer exactly central with the base and the value of 2a can be accurately determined by means of an ordinary micrometer calliper. For a convex surface, 2a should obviously be the inside diameter of the base, B.

In using the instrument, two tables, one for concave and one for convex surfaces, should be prepared; these tables to give the power in dioptres for each one thousandth of an inch in the value of d. Using the American Optical Co.’s Standard Index, namely, μ equal to 1.5000 and one dioptre as being the power of a lens of 40 inches focus, we have, for a plano lens, p = 40⁄f = 40d ⁄ (a2 + d2) since f = r ⁄ (μ-1).