378 
MR. LUBBOCK’S RESEARCHES 
[0] £ 147 = -0284942 
[5] B 153 = -0061 13 
[10] B 159 = - -0033394 
[2] £ 149 = - -019169 
[8] J3 155 = _ -081170 
[6] B 1M = - -020785 
[11] £ 157 = -071237 
Having found the coefficients of 4-, those of — are easily determined- 
U _____ U U/ j j 
r r ( 1 + s 2 ) r [ 
_ ±f j _ il j 
= v{ 
i _ z!_z! «2 _l y~ 
+ ^r s i47 c os 2 t 
4 4 ” 147 T 2~°147 
+ cos 2 2/ — 2L S 147 cos (2 £ — 2 
4 ' 2 147 
If the coefficients of 4- be called 
y- * y'2 
■^" S 147 r 3 4" S 147 r -i 
’147 
, _ / 1 _ z! _ 1 r + y% r ' 
r O — S 1 4 4 6 147 j r O T s l47 " 1 
r ‘ = I 1 - 4"~ T s3 ' 47 } ri ' 
r °- = {* -^“T s2l47 } ra ' + 
r * = { 1 “ 4" “ V* 147 } ^ + ( l ~ i) 
r4 = I 1 ” 4 - ? S2 ‘ 47 } r4+ ( 1 “f) 
r * = { l f 5 " 147 } rs ' 
- S 147 r 5 
‘ s 147 r 6 
If we suppose 
y = I + r 0 + e (1 +/) cos (n (1 + k) t + e — + e^cos (n (1 + k) t + e ; — -zzr y \ 
a < a ; we find 
r 0 = ^/_^6 30 __^ l ft=: “// fl li 30 _5fl6 31 l 
0 p L2a/ 3,0 2a, 4 3,1 J «, la/ 3 -° 4 a/ 2 3 >>/ 
/-{(’ + ^) 2 (l-3r 0 )-l}=|^- 2 6 3(2 
