H. A. Lorentz. Electromagnetic phenomena in a system moving with any velocity smaller than that of light. // Proceedings Royal Acad., Amsterdam. Vol. VI., 1904

( 827 )

published by Kaufmann¹) 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 k₃ 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 k₃ 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 k₃, 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 Kaufmann¹), which have been calculated by Runge⁵) by means of the method of

Kaufmann, Goll. Nadir. Matli. phys. Kl., 1903, p. 90.

*) Runge, ibidem, p. 326.

IV. * = 0,954.