﻿60 Prof. G. A. Schott on the 



greater (numerically) when 8, and of course /, is negative. 

 Thas when 8 is positive, we can obtain an upper limit for its 

 value by omitting all positive terms in the factor of FS and 

 all negative ones in the right-hand member of the equation. 

 In this way we find 



F^{tanhF(r-S)-(l+/)F}</{l- sech F(r-S)}. 



This expression can be simplified very considerably without 

 raising the limit appreciably in any actual experiment. In 

 fact we see from (38) that F(r — 8) is less than % or tanh" 1 ^, 

 whence we easily prove that sechF(T — 8) is greater than 

 \/'(l— fi'*), and tanh F(t— 8) greater than j3- F8e T , so that 



F8eT{/3-(l+f)¥-F8er}<f{l- s /(l-F)}. 



From this equation we find, again making use cf (38), that 



/I _ '/Q\1/2F 



&«,.<08/2F)«w»g-p|) , . . 



provided that /'< 



W-w-F)\ 



(43) 



Of course, as we have stated above, (43) presupposes that 

 8 is positive. 



12. Hitherto no experiments appear to have been 

 made in which both the kinetic energy and the work done 

 by the external field have been measured directly as our 

 investigation supposes, but in the course of some determina- 

 tions of e/m the fall of potential has been measured directly, 

 while the speed of the electron has been determined, usually 

 by means of the deflexion produced by a known magnetic 

 field. The calculation of the speed, and hence of the kinetic 

 energy, from the magnetic deflexion involves an error due 

 to the radiation, presumably of the same order as / but un- 

 known, so that experiments of this kind cannot be expected 

 to supply us with an accurate value of 8. Nevertheless they 

 may be expected to give us some information as to its order 

 of magnitude. 



One of the latest determinations of this kind has been 

 made by Hupka * for velocities ranging from one quarter to 

 one half of the velocity of light and falls of potential from 

 4000 to 20,000 volt/cm. measured to within about 1 in 400. 

 Assuming e\m to be 1*77 . 10 7 , Hupka calculated the velocity 

 j3 from the measured fall of potential by means of the Lorentz 

 formula (18) for the kinetic energy, of course neglecting 

 the effect of radiation which we wish to estimate. In his 

 * Hupka, Ann. tier Phys. 3910 (1), p. 169. 



