MR. HENNESSY’S researches IN TERRESTRIAL PHYSICS. 
519 
it being remembered that the surface of the earth is a spheroid of revolution, 
€ representing the ellipticity. The expression for the attraction of a homogeneous 
shell with surfaces of equal ellipticity, is evidently 
Gi = Mfl — — a\)e—^{l—a*) ^cos^^ 
( 1 . 5 .) 
6. Attraction of the Nucleus . — The forces acting on any stratum of the nucleus, 
by changing the arrangement of its particles, must in general influence their action 
on exterior bodies ; hence to obtain the attraction of the nucleus, it is necessary to 
take all such forces into consideration. These forces are in the present case, the 
attractions and pressures of masses of fluid within and without the stratum, the 
attraction of the shell, and centrifugal force. Hence for any stratum we have the 
following equation of equilibrium. 
/ nv \ 
+ 2^^^ + y Wo+ etc.^ 
where p represents the pressure at any point in the stratum ; Y^, Y,, &c. are functions 
of the coordinates satisfying the equation of Laplace’s coefficients, and also possess- 
ing the property of forming the terms of the series into which the radius of the point 
may be developed. 
But as the nucleus is inclosed in a rigid shell, its surface is constrained to take a 
form different from that which it would have if the shell were removed. The in- 
tegral at the left side of the above equation is consequently variable. The condi- 
tions of equilibrium require that it should be constant, and these conditions may be 
fulfilled by separating the variable from the constant terms in that quantity and 
transposing the former terms to the right side, the quantities Yo, Y,, &c. being sup- 
posed to undergo any variations which may be required by the new conditions. 
By article 2, 
;? = n-(/-/)(cos^^-^)^ §ada, 
n being such a pressure that 
p, = n- if-fi) sin" f \ada, 
J 0 
being that value of 6 which makes jo=n, and p^ a function of Uj, and consequently 
a constant for the nucleus. 
3x2 
