809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831  
( 827 ) published by Kaufmann^{1}) in 1902. From each series he has deduced two quantities ■>] and g, the “reduced” electric and magnetic deflexions, which are related as follows to the ratio .... (34) Here (0) is such a function, that the transverse mass is given by • (35) whereas k^ ank k_{3} 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); only Abkaham’s function tp (/?) must be replaced by Hence, my theory requires that, if we substitute this value for tf>(0) in (34), these equations shall still 'hold. Of course, in seeking to obtain a good agreement, we shall be justified in giving to l\ and k_{s} other values than those of Kaufmann, and ui taking for every measurement a proper value of the velocity iv, or of the ratio Writing 3 sk_{v} — k\ and ft for tb« "aw vjiIhas we may put (34) in the form .........(36)and .......(37)Kaufmann has tested his equations by choosing for k^ such a value that, calculating ? and k_{t} by means of (34), he got values for this latter number that remained constant in each series as well as might be. This constancy was the proof of a sufficient agreement. I have followed a similar method, using however some of the numbers calculated by Kacfmann. I have computed for each measurement the value of the expression ......(38) that may be got from (37) combined with the second of the equations (34). The values of {$) and k_{3} have been taken from Kaufmann’s tables and for /J' I have substituted the value he has found for 0, multiplied by s, the latter coefficient being chosen with u view to ^{l}) Kaufmann, Physik. Zeitschr. 4 (1002), p. 55.  ( 828 ) obtaining a good constancy of (38). The results are contained in the following tables, corresponding to the tables III and IV in Kaufmann's paper. III. s = 0,933.
The constancy of is seen to come out no less satisfactory than that of k_{3}, the more so as in each case the value of s has been determined by means of only two measurements. The coefficient has been so chosen that for these two observations, which were in Table III the first and the last but one, and in Table IY the first and the last, the values of h'_{s} should be proportional to those of I shall next consider two series from a later publication by Kaufmann^{1}), which have been calculated by Runge^{5}) by means of the method of Kaufmann, Goll. Nadir. Matli. phys. Kl., 1903, p. 90. *) Runge, ibidem, p. 326. IV. * = 0,954.
