288 MR. N. BOHR ON THE DETERMINATION OF THE 



where both a and b are great positive quantities. Thereby the term with e lz will 

 be quite predominant ; we therefore get, neglecting the term with e~", 



and further, by (19), 



J" B (.r) = -J.(a 



In the following calculations we will therefore put 



aud J.(M) = + J.<rf)l + + . (31) 



From (27) we get now, using (29) and (31), 



23 



+ 2 + ^l) = 0, . (32) 

 n \ ad a,dr ] 



and 



-CJ.(rf) = ; (33) 



12ri 2 -8n-3 



from (32) and (33) we get 



* IT/ ;\2fi 2 ^ 2 



= ^A J B (*a6) 7 1 + 7 



cp ' ad\_ 2w(n+l 



and . (34) 



nT/ . JX A IT/- t\*2 3 (-l)ri , 2 ^ 2 Vi 2 2w 3 -3\ 



CJ n (^af^) = -^-A J B (t6) -- i-js ' 1 + / 2 T\ I 1 -- j -- O5~ 

 cp 2 a a o L 2(r 1)J\ ad a'a? I 



From (26) we get now, using (12), (21), (29), (31), (34) and (13), 



V-ibH: M!izl). n + <M_\ \ l + ^ + (!^(^- 8 )1 

 p a?c L n(nl)j L ^ 2a a cP J 



8 ) = 0. . (35) 



Putting p. = in (35), we get the solution of Lord RAYLEIGH,* 



A 2 T ta "oJ n( ^CT ^o) / 2 l , ,,27, 8\ 



V 2 a 3 J n (M,) ( 



T(n'-n)f (3n-l)aV 3(n+3)V 1 



pcV L 2n(n 2 -l) 8n(n-l) (n+1) 2 (n + 2) "J" 



In the following we wilt denote the positive root of this equation by &. 

 * Lord RAYLEIGH, 'Roy. Soc. Proc.,' vol. XXIX., p. 94, 1879. 



