294 MR. N. BOHR ON THE DETERMINATION OF THE 



and 



W 



Sr 2 8r 



2a 3 \3S/ a s 3 2 



- ..... < 28 > 



Introducing the values of <, , g, defined by (20), (21), and (26), we get (in order 

 not to make the calculations more extensive than necessary, we will only calculate 

 the terms which have references to the determination of q) 



fc - >coB ^ sin 



cos 2wS- sin 2gi + P 2 sin 2(/ + P 3 cos SnS- sin 3qt 

 + P 4 cos 3n5sin qt + ~P,,cosn9-sm 3qt ...... (29) 



and 



a a 



W 2 (w 2 -l)(40w s -24n 3 +65w-30) A3 3n _ 4 

 = p i - t-i. i A'Vr cos n5 cos 



! cos 2n.^ cos 2qt + Q 2 cos 2w^ + Q 3 cos 2g^ + Q 4 

 + Q 5 cos 3n^ cos 3qt + Q 6 cos 3n5 cos qt + Q 7 cos ?i^ cos 3^. . (30) 



Eliminating from (29) and (30), we get 



3 3n _ 4 . 



= p i - L} V 4 cos n sin 



16(2n a +l)(2w-l) 



cos 2n sn 2(/i + 2 sn 2g^ + 3 cos 3n sn 

 + S 4 cos 3n& sin 5^ + 85 cos nQ sin 3^ ......... (31) 



Setting F (t) = S 2 sin 2qt, (31) will be satisfied by 



Q = Ar" cos n& sin g^ + Ajr 2 " cos 2n& sin 2^f + A 2 r 3 " cos 3n& sin 3gf 



+ A 3 r 3n cos 3w^ sin qt + A 4 r" cos n$ sin 3g, . (32) 

 when 



e _ T . ,_ v A , 2n 

 - n n 



