318 
MR. J. C. Me CORNEL ON AN EXPERIMENTAL INVESTIGATION 
therefore 
This term 
T, 
R— (\/l — b 2 am l —\/1 — a 3 sin 2 1 ) 
a 
+ a term involving C. 
. /d cot i" d cot l 
■ 1 sin 
K, 
dK dK 
where K is to be put zero in each differential coefficient after differentiation. 
and 
therefore 
Similarly 
therefore 
d cot d 
1_ dd'_ 
sin 2 l" (iff 
1 _ (h" 
i~ sin 2 1 dK 
sin 3 i" = (a 2 —K) sin 3 1 
• o " dl " ■ 2 
sm 2t — = — sm 2 t 
dK 
d cot i" 
dK a? siu 2 1 " 2d? sin c \/1 —a 2 sin 2 
d cot i 1 
dK 
T 
2 a 3 sin i 1 — a 2 sin 2 
R— -( v 7 1 — b 3 sin 2 l — \/\ —a 2 sin 2 i) 
4tt 2 C 2 T 
a 4 A. 2 (a 2 — b 2 ) sin 2 o a 3 ^/l—a 2 sin 2 1 
• ‘( 9 ) 
This equation is not true for small values of i or <f>, for we have assumed in the 
course of the proof that K is small. We cannot, therefore, put <£=0 and obtain R 0 
from (9), but by putting <f>— 0 in (7) we obtain 
p _ 1__JL_2ttC 
I«b — s'A s'A - a 4 A~ 
( 10 ) 
Equation (9) is not convenient for calculation, for each of the radicles in the bracket 
is very large compared with their difference. And it is on their difference that It 
depends. Remembering that R=??,\, we may put (9) into the form 
(a — b)(a + b) sin 2 i 
an\ 
\/l — b 2 sin 2 l + 1 — a? sin 2 1 T 
a~X 2 
' a 2 —b' 2 
P 
180 
Sill" t 
\/l — 
a- sm- l 
( 11 ) 
Of the quantities involved in this equation a, b, and \ are known with great 
accuracy, certainly within one part in ten thousand. T also is known with consider¬ 
able accuracy, but the value of a~b is uncertain, to the extent of perhaps 1 per cent. 
The third term is small compared with the others, and so requires only approximate 
