MOTION OF ELECTRIFIED SYSTEMS OF FINITE EXTENT, ETC. 169 



The values are calculated to the nearest unit in the third decimal place, and are, 

 I believe, correct. They have been checked by a professional calculator. 



The numbers show that discrimination between ABRAHAM'S formula and No. 2 

 is a somewhat delicate matter, and would require experiments of a high order of 



accuracy. 



If we assume that the mass of the negative particle in Becquerel rays is 

 m + m'f(k) or p,, where f(k) stands for any of the co-efficients in the three formulae, we 

 may apply the calculation to KAUFMANN'S observations. 



In KAUFMANN'S first paper we have the relations 



- , 



C/t 



where F is the strength of the electric field, H the strength of the magnetic field, 

 z' is the magnetic, and ?/ the electric deflexion. 



The constant K t is directly determined by the conditions of the experiment, and 

 since it is free from any theory as to the way in which [L depends on the value of k, 

 this appears the most satisfactory way in which to proceed. KAUFMANN, however, 

 adopting ABRAHAM'S formula and the view that the whole mass is electric, proceeds 

 to determine the constants which will best fit the experimental curve z', y'. This 

 floes not appear to me to be strictly logical, since it gives a bias in favour of the 

 theory adopted. The procedure lias been ably criticised by PLANCK (' Phys. Zeit,' 

 1906, p. 753), and I think we must agree with him in standing by the determination 

 of the constant which is independent of any theory. Unfortunately in the first 

 paper there are not sufficient data to calculate K l5 but \ve may accept the value '257 

 for plate No. 19, which is stated to be in good agreement with the value as reckoned 

 from the conditions of experiment. It ought to be specially favourable to the theory 

 adopted by KAUFMANN. 



Plate No. 19 has been selected as the best, according to KAUFMANN, and two 

 readings omitted as clearly subject to some casual error of observation. The values of 



k are first calculated and then the values of T -, . These ought to be proportional to 



The values are then combined in pairs to give three values of B thus, 



B _ (*)-(!) B _ (5)-(2) B _ (6)-(3) 



/(*<)-/(*,) ' /(*)-/(*) ' /(*)-/(*.) ' 



These ought to give the same values for B. The mean is taken and used to calculate 

 A. This is theoretically the best mode of combining the observations. 



VOL. COX. A. / 



