PART II. POLAR MAGNETIC PHENOMENA AND TKRRELLA EXPERIMENTS. CHAP. VI. 683 



If we introduce, as before, r = -- , r a , and put 



^o 



X 



r> sin a a = t.M(\ 

 he equation takes the form 



A double root in this must then also satisfy the equation 



(2) .r (kxt + .v) (** + 2 .r) + ^ = 0. 



If we further put 



v = ~ 

 ' 



.'e obtain from (i) and (2) 



vl 2( \}(kn + \)(kn + 2)-f (kn + I) 2 , 



AT. . 



In order that the whole shall have a physical significance, .,.>' j~A<r" an( ^ ^ must a " ^ e P 08 '" 

 ve, and x must be <^ .r , and thus 



(a) n > i 



(b) (k,, H 



nd as 



sin ftu = 

 follows that 



* 



' 



The last relation may however be written 



4)w + 3 ^ , 



(H - !)-((! + ^)-- + (2 

 r, as n^> 1 , more simply, 



(c) (l+)2* + (2 + 4 



The 2 conditions (b) and (c) may be simplified by putting 



* /. 



They thereby assume the form 



(b'l ( 



(c') /- (2 





