Theory of Matter and on Radiation. 195 



The interference, and consequent redaction in radiation, is 

 bv no means confined to the case o£ uniform circular motion. 

 For example, n electrons moving in the same ellipse will 

 interfere, it their eccentric angles increase at the same uniform 

 rate, and are in arithmetic progression. 



§ 6. It is a very general assumption that the D lines of 

 sodium can be attributed to steady motion radiation of an 

 electron moving in a circle, as for instance in the elementary 

 explanation of the Zeeman effect. We shall proceed to show 

 that this is not so. 



If possible suppose the D lines to be due to the steady 

 motion of a circle of ?? electrons. 



To account for the frequency of the D lines we must have 

 77/3= -0010 (§§3, 5). Hence n$ is so small that J. J. 

 Thomson's approximation suffices. By §§3, 5, 



p _ 2CV 2 7i(n + l)(n/3) 2n+2 

 p 2 \2n+l 



= t-2.10M0-^+i ^< n+ i I) . 

 \'2n+l 



The kinetic energy, E, of the ring is ^C 2 mnj3 2 . Hence 



It _ 4e 2 n 2 (n +l)(n/3) 2n 

 . E ~~ Cmp 2 2n + 1 



2u + 1 

 These formulae give the following values : — 



71=1, 



2, 



3, 



E = 2-4xl0- 5 , 



3*6 x 10- 12 , 



i-7 xia- 19 , 



E/E = 8-7xl0+ 7 , 



26, 



1-7 xlO- 6 . 



These numbers show that the whole energy would be 

 dissipated by radiation for 1 electron in one millionth sec, 

 for 2 in "04 sec, for 3 in one-fifth year. 



E. Wiedemann* has measured the radiation from the D 

 lines and found it to be 13'45 x 10 10 erg per sec per gram. 

 Assuming the number of molecules in 1 cc of hydrogen at 

 0° C. and 760 mm. to be 4 x 10 19 (J. J. Thomson), and the 

 sodium molecule to be monatomic, this gives 7*7 x 10 -12 erg 

 per sec per atom, or R = 3*9 x 10" 12 for each of the D lines'. 

 This is of the order of the second case above, ?i = 2. In this 

 case the atom can exist for at most *04 sec, whatever the 

 * Drucle. Optik, p. 487. 



