﻿<v2 Motion of the Lorentz Electron. 



that if it exists the velocities hitherto found for electrons lie 

 very much below it. If therefore we calculate the value 

 -of ( — 1/8) from the highest value of /3 found for a given 

 value of F, this will certainly give us an upper limit for — 8. 

 In this way we find 



— Of < 6 



■mr « 



With the same experimental data that we have used in § 13 

 we find 



Log 10 (-1/S) > 10' 3 , 



practically the same limit as in the former cnse. 



Hence we may assert as a result of Hupka's experiments 

 that the deviation 8 of the hypothesis of § 6 from the truth 

 amounts to less than one part in the ten-million-millionth 

 power of ten for a field of 20,000 volt/cm. This is the same 

 thing as saying that for an electron moving with a velocity 

 small compared with that of light in an electric field of the 

 intensity stated, the acceleration differs from the mechanical 

 force per unit mass by a fraction 8 at most, in excess or 

 defect. 



It is possible that the deviation 8 may depend upon the 

 intensity of the electric field, but the experiments give no 

 certain information on this point. The probable error seems 

 to be rather smaller for a field of 5000 volt/cm. than for the 

 stronger field, but the number of determinations is too small 

 to afford a decisive result. Consequently it would be unsafe 

 to draw any definite conclusion from the experiments re- 

 specting the dependence of 8 on the field-intensity. What- 

 ever this may be, it does not appear to be very considerable : 

 hence it seems probable that our hypothesis may also be 

 applied to variable fields of intensities of the same order of 

 magnitude as those used in these experiments. 



Since according to § 6 the hypothesis is equivalent to 

 Newton's Second Lruv of Motion for slowly moving electrons, 

 we have verified this law to a degree of accuracy far beyond 

 that attained in astronomical investigations. 



How far the law can be applied to electrons starting from 

 rest in very intense fields such as those inside and close to 

 the atom remains doubtful. 



