MR. HENNESSY’S RESEARCHES IN TERRESTRIAL PHYSICS. 
539 
Let V represent the distance from Che centre of the spheroid of any element of the" 
section of rupture, v■^ the distance of the centre of gravity of that section, then 
k = — (39.) 
Jo §2^^^ 
But distance ; hence, substituting its value for the 
distance aj+^+^j we obtain 
/? 2 («i + 4 + 0 l‘'dl= C^fl^ sin (a, + 4 + l)n4l. 
Let a,+/2+/=M, and the preceding factor of Cg becomes 
fu^ sin un^du — 2(ai + 4)y*^ sin un^du-\-{a^-\-l^‘^f sin un^du. 
Integrating between the limits 4 and 4, and we have 
/ u^ sin un<idu=.\{n\d\ cos a^n^—nl{a^-\-l^-\-l^) cos («i + /, + 4)^*2 
+2(a,+4+4)w2 sin (a, + 4 + 4)w2— 2u,W2 sin a,W2+2 cos (a, + 4 + 4)w2— 2 cos a^n^), 
Ju sin un^du=^\_{a^-\-l^-\-Qn^ cos (aiH-4 + 4)w2+aiW2 cos aiW2+sin (a,4-4 + 4)w2— sin a,W2], 
^sin un^du—^ [cos a{a^— cos (Ui+4+4)w2]- 
But 4+4=1 — «i; hence 
/ +^i f 1 
zrz[inla\—2) cos a{n 2 —{nl — 2) cos ^2+2^2 (sin Wa — sin aiW 2 )] ( 40 .) 
2(fflt + 4)r • ‘ill (®i4"4)^/ xl 
+ — — [sm U 1 W 2 — cos a^n^ — sm W 2 +W 2 cos nJ -\ — ^ ^ (cos a^n^— cos n^) k 
^2 J 
To determine 4 and 4, I substitute for ^2 its value in (39.) and integrate, then 
cos — cos Wg) + sin Wg— sin <* 1^2 
y,=- 
4 = 
«2 (cos a^n^— cos 
(1— flj) cos fflj/Jg 
\_ \ 71 
2 sm -(1 +<ii)n2.sm-(l— flj)n2 ' 
^ oi\{\ -\-a,)n^ 
If we make 
we shall have 
, 11 , (1 — ®l) cos 712 
4=- cot 2 ( 1 +«.)W 2 — ^ f . 
® 2sin -(l + «j)w2.sin-(l— «i)n2 
J=|(l -«i) cot ^(1 — a,)« 2 — 1| cot i(l +a,)w. 2 , 
. ( 41 .) 
It appears, from the value of deduced by observation, that when 1— u, is a small 
