MR. HENNESSY’S RESEARCHES IN TERRESTRIAL PHYSICS. 
505 
should be formed, the densities of its strata may be supposed such, as to be ex- 
pressible according to the same function of their axes as the densities of the fluid 
strata. 
Let the fluid mass be conceived to consist of an infinite number of pyramids or 
columns meeting at its centre. Let, in conformity with the supposition mentioned 
by Laplace, the relation between the pressure 11 at any point in one of these fluid 
columns, and the density § be expressed by the equation* 
2k being a constant depending on the peculiar physical properties of the fluid. The 
value of deduced from this equation, may after a few reductions be expressed under 
the form 
A . 
p=— sin an ; 
s a ’ 
where a is the semipolar axis of the spheroidal stratum in which the point may be, 
A a constant, and n a constant depending on the constitution of the fluid, for n is 
here used to express 
Let Ml, as before, represent the mass of the spheroid which is supposed to remain 
constant, let ^ represent its density at the surface when fluid, and let D represent 
its mean density, so that we shall have very nearly 
D= 
3Mi 
47rflj’ 
«! representing the semipolar axis of the fluid mass, and nr, as in every other part of 
this memoir, representing the ratio of the diameter of a circle to its circumference. 
Let c represent the amount of compression of the fluid produced by the pressure of 
a column I units in height, and the ratio of which to the earth’s radius is represented 
by w?i. Then the values of n and a.^ can be determined from the equations 
wfl] c _ D 3c 
tan na~ ~ m ’ g' ~ mr?(i^ ' 
Remembering the value of D, and that m^——, we can obtain from the second of the 
«i 
above equations. 
Let for brevity the quantity under the radical be called 
nation of n, we shall have the equation 
cnh 
rfih 
= 0 . 
2 tan 
Then for the determi- 
( 10 .) 
* Mec. C41., tome v. p. 49. 
