Tlieory of Matter and on Radiation. 207 



and consequently during the readjustment each electron 

 moves in the same way, so far as these disturbances are 

 concerned. In other words, the vibrations due to these 

 differences are vibrations of class 0. Their amplitudes are 

 of the order of the differences in velocity and radius, and 

 therefore small; nevertheless they may be comparable with 

 the mean amplitudes for classes +1, + 2, because these are 

 much reduced by radiation. We must therefore enquire 

 whether these vibrations of class are powerful enough to 

 produce observable spectrum-lines. 



Let A j3 be the excess of the value of /5 for n + 1 above 

 that for n electrons in steady motion. Then the energy E 

 is of the order ^0 2 mn(A/3) 2 , and the radiation is of the order 



,m (A/3) 2 , that is, of order 10~ 9 . ( -~-~- ) erg per sec. per 



ion. 



The velocity ft is given by an equation of the form 



nU _ p 2 ^(/3) a * 

 g ~ C a 2 ' 



where 11 = 22° [~«i0«J / aBI (2«n£) -sV(l-/3 2 ) P ' J 2s n(2snx)dv] . 



s-i L Jo J 



We find, as in § 6, 



nU//3= v /^.exp.n( 7 -llogf±^\ 7 = v /r^. 

 Hence f3 is given by 



V- 7 . ex p. „( 7 - l logi±^) = v /^^i. 



The right-hand member may also be written 



, Cmp 2 a . 



V'2ir . — — -j where m is the mass of the electron. 

 & a 



The value of y^ — 7 -~~ varies but slightly with /3, that is 



with n ; its value is 4 . 10* 12 . Thus the right-hand member is. 

 nearly constant and small when a/a is small. 1 find 



*A/3 °l a J . 



~W = ~ 2^f ' V6rj a PP roxlmatel J- 



* Schott, loc. cit. p. 23. 

 Q2 



