22 
MR. LUBBOCK’S RESEARCHES 
Development 
of $ d R. 
2.101 
27 1 
L r/ — Xl ] 
27 1 
^ 3 '— *3 j 
I-})" 5 '”] 
2 . 28 j 
r r . A ' 
1 
to 
CO 
00 
r r'-A 1 
l 15 y2s 1 
15 
1 1 
1 17 1 
1 '3 A 3 j 
8 7 147 J 
+ {+ r,' + |r 4 '-A 4 j - -|-y B «M 7 J^cos (4 t + 2 x) 
[135] 
L t — 2 3 
[136] 
[137] 
+ {- + t w^{ r3 '~*' 3 } — if y 2 «i4 7 J ee / C0S ( 4< -^- 2 ) 
[138] 
+ {- ^/^{ 7 ' 4,-A4 } ~ 4 y°' s i4 7 jee i cos(4i + x + 2 ) 
[139] 
+ | + {*■/- *,} _ ^7^{ r3 ' _X3 } ~ \v- s ^i\ ee i cos (4 f — x + z) 
[140] 
+ { + j^'-Ai j + { » 4' — } ~ ^ y 2 s 147 |ee / cos( 4 i + * - 2) 
+ { + { r > - A ‘ } “ T r^wje^cos (4 1 - 2 Z ) 
[141] 
[142] 
^• r (trr) anc ^ ma y be obtained immediately from the preceding- deve- 
lopments. 
Developments required for the integration of the equation 
i* . * o±fi _ < + ^ {/(^M * 
d t 
d . 
Q_ 
ds 
2.2.3 r s . 
T~ s Sln 
4 r 3 
(W-2X, >. — *(«) 
_ 2j«£|_ |2 y cos (2t-y)+ |? ycos(2* + ?/) + ^|yecos (2 t — x—y) 
a. 3 I 27 27 17 
[147] [148] [151] 
OQ OA on 
— j|yccos(2«-* + y) - J" y e cos (2 i + x — y) + — ye cos (2 i +x + y) 
[152] 
t — z 
[157] 
[153] 
— 2 
[158] 
^ ye, COS (2 t — z — y) + ^ y e, cos (2 t - 2 + y) + ^ ye, cos (2 t + z — y) 
[154] 
t “}~ 
[159] 
