99 
MR. LUBBOCK’S RESEARCHES 
7 
— 
2. 10 f 
27 l 
7- 
-7 
2.10/ 
27 1 
7- 
— 
e, cos (4 i + z) 
[135] 
7 
2.28 f 
15 l 
r/- 
-7 
2 .38 r 
17 l 
r 3 '- 
-7 
— 
15 o 1 
T 7 M 
. e 9 cos (4 i — 2 x) 
J 
[136] 
+ l 
+ 
2.20 
27 r ‘ 
' + 
2.20 
27 
1- 
S U7 
i e 2 cos {At + 2 x) 
[137] 
+ l 
2. 180 
23 
W 
— A, 
| r 3 7 
— a 3 
}- 
■ ¥ ^ 
j- e e t cos (4 t — x — 2 ) 
[138] 
r 
L 
2.10/ 
27 1 
-*■} 
2.101 
27 1 
>ee { cos (4 £ + x + 2 ) 
[139] 
+ - 
7 
2.66 1 
59 1 
r/ 
2 . 10 
f 27 
-x; 
1- 
I 7 **'". 
j e e, cos (4 t — x A- r) 
[140] 
+ • 
{+ 
2.83 1 
32 1 
V 
■ + 3{* 
1 — A 
d- 
21 
8 
y 2 Si4 7 je< 
\ cos (4 t + x — 2 ) 
[141] 
+ 
{+ 
2.233 
37 
b 
^1 
! «147 
1 ef cos (4 t — 2 2 ) 
[142] 
^ ^di? maybe obtained immediately from the preceding deve¬ 
lopments. 
Developments required for the integration of the equation 
= „ ii±i!) _ <r±ia/(«)d < + <i±s {/(Jf) d.} ‘ 
d . 
\dx7_ _ 2.2.3 r* 
ds 
4 r 3 
sin (2 A' — 2 A,) *■ 
•=-*(£)* 
= l - % y cos (2 t- y) + ycos (2 t + y) + yecos (2 t - x - y) 
af i zy zy i/ 
[147] [148] [151] 
no OB Of) 
— y C COS (2 « - x + y) — 7" y e cos (2 i + x — y) + — y e cos (2 * + x + y) 
[152] 
t — z 
[157] 
“ ^ y e / cos (2 t-z-y) + ^ ye / cos(2i-z + y) + ye, cos (2* + z — y) 
[153] 
- 2 
[158] 
[154] 
! + 
[159] 
