﻿380 Prof. A. Anderson on the Theory of the 



It is evident that these equations (la-4 a) must he true 

 no mutter what the velocity between the original system of 

 coordinates and the new observer, that is they are true for 

 all values of </>. The velocities u x , u y , u z , v x , &c, are, how- 

 ever, perfectly definite quantities, measured with reference 

 to a definite set of axes and entirely independent of <£. If 

 these equations are to be true for perfectly definite values of 

 v*, t'y, u e , v x , &c, and for all values of (/>, it is evident that 

 the function /( ) must be of such a form that the equations 

 are identities in <fi. As a matter of fact <fi can be cancelled 

 from all the equations if we make /( ) of the form 



■ — — - ; and we see that the expected relation is a 



solution of the equations. Although this does not exclude 

 the possibility that there may be other solutions of these 

 functional equations, nevertheless from a consideration of the 

 complexity of the equations it appears doubtful if any other 

 simple function would satisfy the necessary requirements. 



In conclusion it is to be noted that in these derivations no 

 reference has been made to any electrical charge which might 

 be carried by the body whose mass is to be determined. 

 Hence, if these considerations are correct, we may reject the 

 possibility of explaining the Kaufmann-Bucherer experiment 

 by assuming that the charge of a body decreases with its 

 velocity*, since the increase in mass is alone sufficient to 

 account for the results of the measurements. 



Cincinnati, Ohio. 

 October 31, 1911. 



XXXIV. Theory of the Behaviour of the Quadrant 

 Electrometer. By Prof. A. Andehson |. 



I^HE following presentation of the theory of the quadrant 

 electrometer has, it seems to me, the merit of sim- 

 plicity, and consequently may be of use to those who are 

 engaged in working with the instrument. The theory given 

 by Mr. G. W. Walker (Phil. Mag. Aug. 1903) is perhaps 

 not elementary enough for the general reader, and the inci- 

 dental reference to the subject by Prof. Sir J. J. Thomson 

 in a paper on the Charge of Electricity carried by the Ions 



* The possibility of explaining the Kaufmann-Bucherer experiment 

 hv assuming that the electrons have less charge at higher velocity was 

 suggested bv Professor More of this University : Phil. Mag. xxi. p. 106 

 (191]). 



t Communicated by the Author. 



