﻿A. M. Mayer — Well- Spherometer. 63 



The interior diameter of the cylinder is found by accurate 



measures with vernier-calipers, or by measures with a dividing 



engine furnished with a micrometer-microscope. Then the 



r 2 h 

 formula E=^7+^r gives the required radius. K=radius o 



Lib 2l 



lens; r=radius of interior of well ; A= versed sine of radius of 

 lens, or, height of section of lens above edge of bottom of 

 cylinder. 



When the radius of a concave spherical surface is to be meas- 

 ured, the outside edge of the cylinder is used. The diameter 

 of this cylinder can be very accurately measured. The same 

 cylinder may do for measurements on either concave or convex 

 surfaces if its outside and inside edges are made by a plane 

 perpendicular to the axis of the cylinder. This form of cylin- 

 der I have generally used. Four or five of these of different 

 diameters will be sufficient for most work. The interior diame- 

 ters, I have selected are *2, '35, '6, 1*00, and 1*7 inches; or, in 

 millimeters, say, 5, 9, 15, 25, and 40*5. The thickness of the 

 cylinders are about T \ in. or, l-5 mm . 



In the account of the measures with this instrument it has 

 been assumed that the tripod of the spherometer rests on a plane 

 surface and also that the plane of the bottom of the well is 

 parallel to this surface. It is not difficult, now that Brashear 

 has reduced to practice the elimination of the errors of an ap- 

 proximate plane, shown by the most delicate test which applies 

 itself to the whole plane at once (namely, the interference 

 bands produced by reflection from the surface of the plane re- 

 quired and the surface of a true plane of glass resting on it), to 

 obtain planes whose departure from truth is less than the indi- 

 cation of the best spherometer. In the planes I use, one of glass, 

 the other of steel, my spherometer, by Briinner, of Paris, does 

 not show a departure from a true plane of xg-gVoo" °^ an inch. 

 These planes, however, when being made were not tested by 

 the optical method. The parallelism of the plane closing the 

 bottom of the well and the plane on which the spherometer rests 

 is, of course, given by the spherometer itself if this be an instru- 

 ment of precision. This it only is when furnished with the 

 means of getting contact by the intervention of a lever, level, or 

 the electric-contact. Every instrument of precision contains in 

 itself the means for its adjustment and for the determination of 

 its errors of measurement. If when the spherometer is brought 

 to the zero reading and the screw is moved over the plane form- 

 ing the bottom of the well, this adjustment remains in all posi- 

 tions of the screw on the plane, then the two planes are parallel. 

 Any want of parallelism can be detected to rgro «rfr inch. I 

 state this quantity so as to be within bounds ; for from nine 

 settings of the Briinner spherometer I found that the extreme 



