measured with a special spherometer and the error in the radius corrected by changing the position of the cutting tool by an amount calculated from the readings of the spherometer. This spherometer we were compelled to build as we could find none of sufficient accuracy on the market and it is described in a note at the end of this article. [Illustration: FIG. 4] [Illustration: FIG. 5] In Fig. 4, R is simply a steady rest made with the large overhang to allow the slide B to swing under it in turning a convex surface. Two master laps, male and female, must be made and carefully ground together. Every effort should be taken to make these as accurate as possible since upon these depends the goodness of our lens. This special tool is easy to make and leaves nothing to be desired in its operation. Detail drawings and directions for making it are given in a note at the end. We now come to the grinding or lapping of the lenses themselves. This is done in a lap turned as above and carefully fitted to the master laps and which must be trued from time to time as the work progresses. This lapping of glass is entirely different from the lapping of metals in that, while in metals the lap is to be kept almost free from the abrasive, in glass the lap must be freely supplied with emery and water or deep scratches will result. The best way to apply the emery is with a paint brush; the brush, saturated with emery, being held in front of the lens as it is ground. The lens may be held in the hand or cemented to a disk of brass having a center hole drilled in the back in which is placed a pointed piece of steel held in the hand, the lens being free to rotate about the pointed steel holder. Of course where the lens has to be ground to a definite thickness it must be held by hand. Flour of emery was used to rough grind though coarser grades would have worked faster. The final smooth grinding was done with a special fine emery made for this purpose by Bausch and Lomb. Great care must be taken in the grinding to keep the lens as nearly centered as possible. A lens is said to be centered when the line which joins the centers of curvature of the surfaces passes through the center of figure. Obviously if a double convex lens could be ground to a knife edge it would be centered but if this were done the edge would be almost certain to crumble in the final polishing and deep scratches result. The centering of a convex lens can be watched by keeping the edge as nearly uniform of thickness as possible with a concave lens, if the original blank is made larger than necessary and care is taken to make the sides parallel, the centering can be watched by keeping a flat edge of _equal width_ around the concave portion, the lens being placed back on the flat tool, from time to time, as the work progresses. If care is used the lens need be made but little larger than the finished size to allow for the final accurate centering to be described later.