Determination of e, N, and Related Constants. 3 



situated between the plates of an air condenser between 

 which a constant electrical field may be thrown on parallel 

 to gravity. If v 1 is the constant speed of descent under 

 gravity, and v 2 the speed of ascent under the influence of 

 the constant field F, then it is found by experiment that 

 when the charge on the drop is changed through the capture 

 of electrons, or their loss through the direct incidence of 

 X-rays or ultra-violet light, the series of speeds imparted to 

 it by the field — namely, the series of values of v ± + v 2 

 constitutes an exact arithmetical progression the greatest 

 common divisor (i\ — v 2 ) of which is the value of the 

 electron measured in terms of a velocity. This is reduced 

 to apparent electrical units by means of the equation derived 

 from Stokes's law, 



*i 



-4 /MV 1 V fol + lfrW m 



-^u) y-gi^pv — *--' ' • (1) 



in which rj is the coefficient of viscosity of air, a the density 

 of the particle, and p that of the air. The radius, a, of the 

 drop is then found to a sufficiently close approximation by 

 inserting an approximate value of e in the equation 



_ 3 / 3 F<? V, 



a ~V ^g{a-p) (tn.+ ffcjo' ■■'■■ {2) 



this equation being derived from 



v. mcf mq . N 



- = ct-^ or e — =^- ( i\ + v 2 ) 



v 2 re — mg Jb v 1 



and m = ^7ra' 6 (a — p). 



Such observations are made on a considerable number of 

 drops at various pressures or on the same drop at different 

 pressures, and, for the sake of obtaining a linear relation, 

 the values of ejt are obtained and then plotted against the 



corresponding values of — . This procedure amounts to 



-adding a first-order correction term to Stokes's law, and 



writing it in the form 



Vl = r- 



2ga 2 , . /. b 



(o-p) 1 + -;. .... (3) 



1 ~ 9 V ^ HJ V ' pa 

 The relation between e 3 and e then takes the form 





pa; 

 B2 



