290 
MR. LUBBOCK’S RESEARCHES 
(2 » — 5 «,) a f 3 1 , « a 
^ \ 7273 ~2" r ‘ 33 / r ‘ J73 "]T ^ 273 — u 
(2 77 — 5 77,) 2 f l,w,« -o 
»« 1 312 J + ~~jT 9312 “ U 
R 55 _j_ 5.5 naR xh _j_ 13.5naR-, 
sin (2?7f — 5n t t + 
5 *=| 2 |r 155 + i-^r 55 + r 15 +-| j 
_ m / f 5 77 a ^ 5na R 5S 
p 1 (2 n — 5 77 ,) 155 (3 n — 5 77 ,) 4 (3 n — 4 77 ,) ' 8 . 5 (n — 77 ,) J J (2 n — 5 n,) 
+ | 2 { r i74+ 0 74 + r 34 ) j 
- I 4naR ' 74 , 4 71 a R 74 5.4.«flfi, 4 \ l__ii£l£L_sin (2 77 * - 5 77 / + 2 ® + v.) 
/j. I (2 n — 5 77 ,) (3 n — 5 ?7,) 4 (4 n — 5 ?7,) J J (2 n — 5 7 ?,) 
{2 / r 213 +-L r 1 — ( 3rea-Ra , 3 _ 3 »_a_ fi ii3_I 1 — nee * - — S \n(2nt—5n l t + vr + 2'sr l ) 
\ L ^ 2 3 J fx l (2 ?7 — 5 77 ,) (3 n — 5 77 ,) J J (2» — 5 n ; ) 
+ 
+ 
{*{■ 
r 273 + 
} 77! ( f 3 77 a i ? 273 377aR 193 1 I 
|X 1 (2 77 — 5 77,) (3 77 — 5 77,)/ J 
l, 
n esin 2 
sin(27t<— -5?? ; i+CT-4-2v / ) 
77 e, sin 
2 *7 
(2 77 — 5 77,) 
+ | 2r 3 i 2 — "3 j -A- sin (2nt — 5 72 / + + 2v,) 
l /x(2?7 — 5 77,) J (2 77 — 5 77,) 
The quantities r 55 , r 74 , r 113 and r 133 have the quantity 2 w — 5 n t in the 
denominator, rejecting- those quantities in the value of which have not 
(2 n — 5 w,) 2 in the denominator. 
7* 1 5 r » 
4m,n 3 a e 3 
/X (77 — 5 77,) (3 77 — 5 77,) (2 77 — 5 77,) 
4 7?7, 77 3 a 7? m e 2 e, 
/X (77 — 5 77,) (3 77 — 5 77,) (2 77 — 5 77,) 
i s — 
4m l n 3 a R ns e e, 2 
r i~3 — 
(X (77 — 5 77,) (3 77 — 5 77,) (2 77 — 5 77,) 
4 777 , 77 3 a i? 273 e sin 2 -h- 
JX(77 — 5 77,) (3 77 — 5 77,) (2 77 — 5 77,) 
7" 1 I J 
4 777 , 77 3 a ft J12 e, sin 2 -h- 
/X (?7 — 5 77,) (3 77 — 5 77,) (2 77 — 5 77,) 
fn . 5 777, 77 a ft,,, 1 Tie 3 • /0 . , . , „ . 
‘>•= 2 r li5 + r 45 - —j ^ — — sin (2 n < - 0 77, < + 3 sr) 
l /x(2 77 — 5 77,) J (2 77 — 5 77,) 
{ 
4" 1 2 r i74 "h 
4 777, 
K 2 
naR n , 1 7ie 2 e, . , 0 , c . , 0 , , 
m \ < — sin (2 77 1 — 5 77,t 4- 2 4 - z?,) 
71-577,)/ (2 77 - 5 71,) V ' T " 
