4 
MR. LUBBOCK’S RESEARCHES 
From the preceding development, that of r 3 h . y may be immediately in- 
ferred. 
r’ = 1 +3e-(l +.0-3e(l + 
[ 0 ] 
cos x — _ - e 4 cos 2 x + — cos 3 x + — cos 4 x 
8 8 o 
[20] [38] 
[ 2 ] 
[ 8 ] 
The following approximate value of r l — will probably be found sufficient. 
e cos x 
[ 2 ] 
Jy ={( 1 .+ ( r 3 + r 4 )}cos2<+ |r a — r 0 | 
[ 1 ] 
+ |r 3 — j ecos (2 t — a-) + jr 4 — | ecos (2t + x) 
[3] [4] 
+ r 0 e t cosz+ r^cos (2 t — z) + r 7 e l cos (2 t + z) + |r 8 — 1 e- cos 2 x 
[5] 
[6] 
[7] 
I 1 
00 
1 1 
{'•-£ 
_ T x 
4 
1 e 2 cos (2 t — 2 x) + Ir 
r 
10 “"2 
— — | e 2 cos (2 1 + 2 x) 
[9] 
[10] 
\ ee < 
cos (x + z) + < r 12 — 
r 6 1 
2 f 
ee ( cos (2 t — x —z) 
[11] 
[12] 
{ ri3- if. 
>ee t 
cos (2 £ + + z) + < 
*•14 
r 5 
2 
^ e e t cos ( x — z) 
[13] 
[14] 
{ r ‘ 5- if 
>ee t 
cos (2 t — x + z) + < 
fl# 
r«] 
2 „ 
e e / cos (2t + x - 
- z ) 
V. “ J 
[15] 
[16] 
r I7 e, 2 cos 2 
z + 
r 18 e * cos (2 t — 2 z) + t 19 
e, 9 cos 
(2 < 4 - 2 z) 
[17] 
[18] 
[19] 
( 1 \ 2 r 2 p1 r 2 pi r 1 p1 r 2 p 2 r 2 C 2 r 2 
r) = r » , + ^+^ + 4 1 + ! T- + T 1 + - ! T L+!t I i 
[ 0 ] 
+ {2 r 0 r! + e 2 (r 3 + r 4 ) r 2 + e* (r 6 + r 7 ) '5} cos 2 * + {0* + r 3 ) r, + 2r 0 rJ ecos.z 
[ 1 ] [ 2 ] 
+ {rjr 2 + 2r 0 r 3 } ecos (2 t — x) + {r,r 2 + 2r 0 r 4 }cos (2 t + x) 
[3] [4] 
+ {r,r 7 + r,r 6 + 2 r 0 rj ^cosz + {r 5 r t + 2r 0 rJ ^cos {2 t — z) 
[5] [6] 
