OF OBSERVATIONS OF COMPLEX PERIODICAL PHENOMENA. 
373 
p =2 a OT costfm;s-j-|jj*(&(— \-\r\— 2 »,(— \ cot^z+O^J 
s 2 i 2 f / n 2 ?i 1 n 3 ra 2 n\ 
IT 1-^*1 Hi '2 . ~s + t + 3~~'2+6/ 
1 x sm 2 — 2 7 
+£.(— J cot^*+0^|j, 
P =5 o cos tfmz+ cot z) J 
s 2 i 2 f (n 3 n 2 n n 2 n 1 \ 
+ £ s (0-|cOt^z)}], 
<ma+^{ffX w “ !)} — w3_w2 + l)}]’ 
> ( 21 ) 
or = 5) a m cos 
according as neither (s-\-t)z nor (s— t)z is 0 or a multiple of 2x; as (s+£)z is not, and 
(s—t)z is 0 or a multiple of 2 t ; as (s + £)z is, and (s— t)z is not 0 or a multiple of 2 tt ; 
or as both ( s-\-t)z and ( s—t)z are multiples of 2r. 
2 
And multiplying both sides by -, 
2 772 = 71 — 1 
cos tmz=-% a m cos tmz-\- 
n m = 0 
[f { “ 2 Zs+Ps (cot S -~z + cot *-£ z) | 
1 
. 1 \ / ,S+t s—t 
+ —&( w cot -g- 3 + 71 cot -jj- 
sin 2 ‘-z- ' 
O 
or o “ m cos tmz + [f { 1s{n - 2) +i> s (cot —z^j | 
-x{^(^ 2_2w +^+~7+t) - ff.(»cot ^)}j, 
or= n f =0 cos [||^-2)+^ s (cot^^| 
Or =^ =o a m coste+[||^2(w-l)J- s -^{ i?s (|w2_2 w+ |)}1 
