508 
MR. HENNESSY’S RESEARCHES IN TERRESTRIAL PHYSICS. 
that if a, differed in any way from that semiaxis the difference would most probably 
be owing to the comparative smallness of a^. 
8. The application of equations (5.) or (6.) to the determinations of the earth’s ellip- 
ticity, may now be attempted before proceeding to any further investigations. In 
making use of (6.) or any other similar equation for the determination of the ellip- 
ticity of the spheroid, the numerical results should be always considered as hypothe- 
tical. Such an equation could not give the present ellipticity, unless that which the 
earth had immediately after the solidification of the outer coat of the shell had 
remained unaltered. It is not improbable that many causes may have existed to pro- 
duce such an alteration. 
If from any cause the fluid nucleus exerted unequal pressures upon different parts 
of the shell, it is evident that their tendency would be to alter its form. It is possible 
to conceive that any alteration so produced in the figure of the earth may consist in 
a reduction as well as in an increase of its ellipticity. In a more advanced stage of 
these researches I may be able to fully consider the influence of such causes. It is 
enough for the present to point out the possibility of their existence. 
If it be admitted that the causes which have been referred to in the foregoing para- 
graphs are of sufficient importance to produce appreciable changes in the general 
figure of the earth, it must appear at least a doubtful assumption to assign to n such 
a value in the expression for the density of the strata of the primitive fluid, as that 
which would give precisely the same ellipticity as the present. 
In order to illustrate the application of equation (6.) and to show that from its form 
a change in the value of n can make but a comparatively small change in the value 
of E, I shall now proceed to find an expression for Q. 
If the dimensions of the fluid mass be supposed to be the same as those of the earth 
at present, then g' will be the same as g, gravity at the period of its fluid state. 
It is evident that (p{a) can be expressed under the form 
where 
I=-T §a*da. 
When Qi is taken as unity, we shall have 
where for brevity q is used instead of I— ; but when §=- sin an, 
6)9+ 2wV], 
