MR. HENNESSY’S researches IN TERRESTRIAL PHYSICS. 
517 
of the solid stratum in immediate contact with it, its superposition on the spheroid 
will evidently not much increase the mass of the entire attracting body. The equa- 
tion of equilibrium at the surface of the fluid on the greater spheroid is 
a'l being the value of a! at the fluid’s surface, and p the pressure on the stratum. On 
developing and then comparing similar terms, we obtain 
The strata of the shell being bounded by spheroids of revolution and the origin of 
the coordinates being at the centre of gravity, 
W/=0, 
i being different from 2. From the equation for Wo, it can be immediately inferred 
that Wo may receive an arbitrary value. For we obtain 
whence 
(3W2=“jS/i^cos^^ — Ij, (9.) 
in which ^h=nif{a\), (10-) 
m standing for the ratio of centrifugal force to gravity at the equator, and being a 
functional symbol. If we make Wo=— ^/i, and substitute in the expression for r 
these values, we would have 
r'=a'(l— ^Acos^^), 
and therefore (^h must represent the ellipticity of the fluid stratum. 
Similarly for the surface of the fluid stratum on the smaller spheroid, where aj re- 
presents what becomes for the fluid 
ri = a^(l~(i’hcos^d), ( 11 -) 
Besides these general expressions for /3Wo, &c., /3'Wo, &c., it is possible to find others 
in a particular case, which expressions will subsequently be found useful. The par- 
ticular case referred to, is that in which the shell’s strata are supposed to have all the 
same ellipticity. On this hypothesis Wq, Wi, &c. are not functions of a, and conse- 
quently (8.) becomes 
f.aVa-f ...] 
3 X 
MDCCCLI. 
