( 827 ) 



published by Kalfmann ') in 1002. From each series lie has deduced 



two quantities ri and g, the "reduced" electric and magnetic dellexions, 



w 

 which are related as follows to the ratio f^ = - : 



€ 



Here if' (|i) is such a function, that the transverse mass is given by 



3 e' 



whereas l\ ank k.^ are constant in each series. 



It appears from the second of the formulae (30) that my theory 

 leads likewise to an equation of the form (35) ; oidy Abraham's 

 function /// (|J) must be replaced by 



3 8 ^ ^ ' 



Hence, my theory requires that, if we substitute this value for 

 If' (^) in (34), these equations shall still hold. Of course, in seeking 

 to obtain a good agreement, we shall be justitied in giving to /(^ and /'.^ 

 other values than those of Kaufmann, and in taking for every measure- 

 ment a proper value of the velocity h', or of the ratio /?. Writing 



3 

 ^>'/' -~ k' .^ and ^' for the new values, w^e may put (34) in the form 

 4 



g 

 ^' = sk,- (3G) 



n 



and 



(i-n"''=^ > (37) 



Kaufmann has tested his equations by choosing for l\ such a value 

 that, calculating ji and /., by means of (34), he got values for this 

 latter number that remained constant in each series as w^ell as might 

 be. This constancy was the proof of a sufticient agreement. 



I have followed a similar method, ushig however some of the 

 numbers calculated by Kaufmann. I have computed for each measure- 

 ment the value of the expression 



r, = (1 - p'VX.^) ^V (38) 



that may be got from (37) combined with the second of the equations 

 (34). The values of tf' ii^) 'i-nd k.^ ha\e been taken from Kaufmann's 

 tables and for ,?' I haxe substituted the value he has found for ^, 

 multiplied by .y, the latter coefficient being chosen with a view to 



1) Kaufmann, Pliysik. Zeilsclir. 4 (^1902), p. uD. 



