I have not had occasion to use this instrument in my own work, as a more simple, delicate, and efficient method was at my command, but for one measurement of convex surfaces I know of nothing that can take its place.  I will briefly describe the method of using it.

[Illustration:  FIG. 10.]

The usual form of the instrument is shown in Fig. 4; a is a steel screw working in the nut of the stout tripod frame, b; c c c are three legs with carefully prepared points; d is a divided standard to read the whole number of revolutions of the screw, a, the edge of which also serves the purpose of a pointer to read off the division on the top of the milled head, e.  Still further refinement may be had by placing a vernier here.  To measure a plane or curved surface with this instrument, a perfect plane or perfect spherical surface of known radius must be used to determine the zero point of the division.  Taking for granted that we have this standard plate, the spherometer is placed upon it, and the readings of the divided head and indicator, d, noted when the point of the screw, a, just touches the surface, f.  Herein, however, lies the great difficulty in using this instrument, i.e., to know the exact instant of contact of the point of screw, a, on the surface, f.  Many devices have been added to the spherometer to make it as sensitive as possible, such as the contact level, the electric contact, and the compound lever contact.  The latter is probably the best, and is made essentially as in Fig. 5.

[Illustration:  FIG. 11.]

I am indebted for this plan to Dr. Alfred Mayer.  As in the previous figure, a is the screw; this screw is bored out, and a central steel pin turned to fit resting on a shoulder at c.  The end of d projects below the screw, a, and the end, e, projects above the milled head, and the knife edge or pivot point rests against the lever, f, which in turn rests against the long lever, g, the point, h, of which moves along the division at j.  It is evident that if the point of the pin just touches the plate, no movement of the index lever, g, will be seen; but if any pressure be applied, the lever will move through a multiplied arc, owing to the short fulcri of the two levers.  Notwithstanding all these precautions, we must also take into account the flexure of the material, the elasticity of the points of contact, and other idiosyncrasies, and you can readily see that practice alone in an instrument so delicate will bring about the very best results.  Dr. Alfred Mayer’s method of getting over the great difficulty of knowing when all four points are in contact is quite simple.  The standard plate is set on the box, g, Fig. 4, which acts as a resonater.  The screw, a, is brought down until it touches the plate.  When the pressure of the screw is