500 
MR. HENNESSY’S RESEARCHES IN TERRESTRIAL PHYSICS. 
M^here Q is used for brevity instead of 
25 
The above expression gives 
E=2^{m=Q+P+V2»’t(+P*} 
( 6 .) 
If from any cause, Ej, the present ellipticity of the earth, should not be identical 
with E, and that we should wish to obtain the latter, the numerical value of a, cal- 
culated from the formula 
must be introduced in the value of I' and thence in equation (5.). 
5. The variation of gravity at the surface of the spheroid, during its fluid state and 
during the process of its solidification, may now be considered, the mass being sup- 
posed in both cases to consist of spheroidal shells having a density increasing from 
the external surface to the centre. 
From the supposition which has been just made, if y represent the entire force of 
gravity at the surface of the spheroid, we shall have 
Yo and Yg being rational functions of the coordinates ; and let it be remembered that 
at the surface 
and that 
r=ffi[l-b/3(Yo+Y2)], 
4(677 
“5 
-J§. d.a^Y ^= ^ Y . da^ -f ^/(cos 
Let for brevity 
Let G' represent the attraction at the surface of the earth at present, then if all 
quantities of the order |3^ and ^fd^ be neglected, we shall have after a few reduc- 
tions. 
y=G+(|mG'l^-EG)(cos’' «-|) ; 
the value of/*, being here substituted for it. 
If after the solidification of the external portion of the fluid into a spheroidal shell 
the axes of the shell undergo no great changes in magnitude, then whatever may be 
the physical changes occurring within the exterior surface of the shell, it will follow, 
from the little difference between the figure of the mass and that of a sphere, that 
