204 Mr. G. A. Schott on the Electron 



The first factor depends only on the nature of the system 

 of rings. The second factor depends on the class k or the 

 vibration considered ; its value can be found by means of the 

 table of § 9. 



With the numerical values of § 3 we get 



- 1 i r -=l-9.10 5 . 



71, 



The value of -7^ can be calculated if we assume that the 



/3 2 



value of /3 is fixed by the condition of § 2, in which case it 



depends largely on the value adopted for the rate of expansion 



of the electron. If a be the radius of the electron, the table 



given previously (loc. cit. p. 24) shows that with - = 10~ 16 , 



£=•023 for 7^ = 10, -566 for w = 100, while with -=10~ 46 , 



a 



£ = •00074 for n = 10, '398 for n=100. In these cases we 



have for ra//3 2 the values 1-9 . 10 3 for n = 10, 2'8 . 10 2 for 



n = 100, with- = 10~ 16 , and 1-9 . 10 7 for n=10, 6*3 . 10 2 



a 



for ?i=100, with - =10~ 46 . Except for small values of n, 



a 'a 



n/ft 2 does not vary greatly, even for a small value of - ; we 



may take it to be 1000: with this value —« ri9 „ » is of 



order 2 . 10 8 . _ <*?"? 



The value of T, Ihe average life of a free ion, is unknown 



for the gas in a flame or a vacuum-tube, but it has been 



measured for other cases, e. g. gases ionized by Rontgen rays, 



where it has been found to be of the order of 1/2 second *. 



In default of a better estimate we shall assume T to be of 



wT 

 this order in the present case, and therefore -^77^ — ^ of 



order 10*. ff C ' m & 



The table of values of R /o" 2 of § 9 now shows that for 



£=+3 or more, 7T is of order 10~ 7 or less; for £=+2, 



7T is of order 1 for X = 2 . 10 -5 cm., and of order '001 for 



X= 6 . 10~ 5 cm. ; for k = 0, + 1, 7T is very large. 



Thus the intensities of waves of classes +3 and upwards 



are determined by radiation, those of waves of classes and 



+ 1 by the initial energy, those of classes +2 mainly, if not 



entirely, by the initial radiation. 



In the former case the energy radiated per free ion per sec. 



by the gas is R , in the latter it is B /7T = E /T. 



* J. J. Thomson, ' Conduction of Electricity through Gases,' p. 18. 



