﻿64 



A. M. Mayer — Well-Spherometer. 



+ or — departure of single measures from the mean of the nine 

 is onl J ttfoo o inch. 



In one spherometer, which I have, fig. 2, the axis of the screw 

 is made so that it coincides with the axis of the well. In this 



instrument two of its feet rest in conical holes ; the third foot 

 in a V cut in the direction of a line joining this foot with the 

 axis of the well. Any want of parallelism between the planes 

 cannot be determined in this form of apparatus. If this error 

 exist it has to be computed and allowed for ; and for this we 

 have to know the inclination of the planes. This can be meas- 

 ured, in the other forms of spherometers described, by several 

 optical methods. If the plane at the bottom of the well should 

 be tilted 1°, which is an inclination far beyond that which 

 would be made by any one honestly calling himself a skilled 

 mechanic, the error in the measurement from the true height 

 of the section of a lens of 2 in. radius and '2 in. thickness 

 would equal +'000027 inch. This error is however difficult to 

 compute and is not susceptible of a simple expression in terms 

 of the inclination of the planes and of the radii of lens and well. 



If x = the true height of section of lens above bottom of well ; 



a— measure really made, at an angle to plane of bottom of well ; 



6 = angle formed by the two planes of the spherometer ; 



r = radius of curvature of lens ; 



a 2 a 4 



x= a cos 6 h sin 2 #-| -sin 4 tf + etc. or, 



2r ' 8r 3 ' 



x—a(\ + etc. ) + — Id H )H -( 6* J 



\ 2 24 / 2r\ 3 ,30/ 8r 3 \ 3/ 



or 



•99984760c? + -000152284 



<T 



+ 



•00000012-^ 



r 3 



