3:34 
MR. LUBBOCK’S RESEARCHES 
sin (X' — v) ~~i — tan < cos (K' — v) d v = 0 
cos ^5 + tan * sin ( x ' - ") d " + ^ { ( 1 + ^ (^f ) - * (a?) - © (s)} d, '=° 
h d h = - r 2 (^,) d V 
Whence by elimination, 
fi 2 cos / d e + 2 | (l + S *Y cos (V — sr) + e — 
tan is cos (A' — v) sin (A' — ot) 
(1+s 8 )* 
} 
[ sin, cos* , ;•’* cos(X’- v) { (1 + «•) (^f ) - * (^) - (^£) (®) } + cos, r'* (|f) } d X' 
+ 
s cos i r' 4 sin (A' — -sr) 
(i + s*Y 
It 1 r . 
H sin 
1 /X cos I 
{ (1 + * 2 > (ax) - (a£) - (tO (a?) } d 
h 2 cos / e d vs + 2^(1 + s 2 Y sin ( — sr) -f- 
s tan i cos (A' — v) cos (A' — zr) 'J 
(1 + * ¥ J 
| sin , cos® , r' 2 cos (X' - ») { (1 +s 2 ) (^f ) -*(x[f) ” (af ) (£0 } + C °s»-' 2 (cfx) } d,: 
+i2) ( d |)-/(^) - (^)(-)}dx 
(1 + s 2 )* 
A 8 r 
/X cos 
r «• <V -) { - s (i?) - i ® (£) } d v = o 
, r' 2 cos i 2 cos (a' — v) 
a < -j- is 
h* 
j , r ' 9 sin (A' — v) f,, , nN /d 72\ /d E\ /diA/ds\1 , . 
’ + -75 — { 0 + **> 1 dl) ~ s (a? ) - (dXV vTa) } d * = 0 
