Theory of Matter and on Radiation. 211 



The corresponding complete equation is 



^-(l-^J-i^Co-^H 

 = {^ + (1 + /3 2 )(K-2H)} p|) 2 - 2/3(1 -/3 2 )M^ 4-/(0, 0)-/(*, ?), 



where 



j=»-i i H _ <ss j- 1 sin 2 (Wt/ii) - 



"~ i=1 4 sin 7ri//i' ~~ »= l 4 sin (iri/nf 



M _ i= v _1 sm (2^ 7 ™/ /z ) cos (ni/n) 



1VJL — ^ " 3 ; o - ^ n x ? 



ia£l b snr (iri/n) 



f (h q) =T i 00t (2 '~^ +1),r [- (1 "^) W'.tySJ 



+ ( 1 + 3/3 2 j J/3J ra (Z/3) + { (1 + P) (w» + IW) 



2a 

 withm=2s + l, 1= -± +2s+l. 



With the numerical values of § 3 we find — —- =47,000 



approximately. The constants v, K, H, M are of -order n ; 

 tor small values of k J is of the same order ; small values of k 

 alone are of importance for our purpose. Thus v, K, H, 1VJ, 



and J are all small compared with —~ unless n be larger 



than is physically possible, since the distance between con- 

 secutive electrons must be a large multiple of their radius. 



The largest terms of /(&. q) are generally given by m= + 1, 

 that is, by s = 0, s = — 1 ; these are of the orders 



, (2k + l)ir(q 1 v 2 00 . , 



8 C ° 2n \t ± 2) & res P ectlveJ Jv 



Unless — be very large, f(k, q) is at most of the order 



If it be expanded in a series of ascending powers of V± t 

 the frequency equation takes the form 



where a, a u a 2 , a 3 . . . are functions of n and 0, which 



