544 
MR. HENNESSY’S RESEARCHES IN TERRESTRIAL PHYSICS. 
might be such as to disturb the rotation, not only by increasing or lessening the an- 
gular velocity, but also by changing the position of the axis. It appears however, 
from the article cited, that the difference of the greatest and least moment of inertia 
of the earth must progressively increase during the process of solidification, and 
hence that the stability of rotation must continually increase until it reaches its limit 
when the mass shall have arrived at the entirely solid state. 
Thus not only does a question closely connected with geological theory seem to 
be definitively settled, but also the future stability of the earth’s rotation appears to 
be completely assured. 
(2.) The Thickness of the EartKs Solid Crust. 
24. In Section II. expressions have been obtained in which the variation of gravity 
at the earth’s surface is a function of the radius and ellipticity of the fluid nucleus 
supposed to exist within it, from which it will be possible to deduce the limiting 
values of that radius, and consequently of the thickness of the solid shell. If we 
refer to the general expression (20.), it will be perceived that the greater is e^, the 
less the thickness of the shell ; hence we would be able to obtain its greatest thick- 
ness consistent with observation, other quantities remaining unchanged, by giving to 
Cl its least value. But from Section IV. the least value of e^ is e, or the ellipticity of 
the surface of the shell, hence in this case m^=m, and 
X=[|-3(/(a) — 
The greatest value which a, can receive will depend on the limits imposed on the 
values of the functions depending on the earth’s internal constitution ; and if we give 
to these values favourable to a large value of e^ must very nearly be equal to e. 
The above expression for X will therefore suffice for this case by attributing the proper 
values to the functions f{a) But when e^=e, we have, by the expression 
deduced in article (5.), 
X=2e+m+|(|?!^-2o;re- ! 
V representing the same quantity as in article (13.), will differ but little from a when 
e, = e, and with a continuous law of density of the strata of the shell; hence in a first 
5 
approximation we may assume their equality. But \=-^—{e), {e) being the value of 
e, deduced by the ordinary theory from observation of the variation of gravity at the 
earth’s surface, hence 
‘ L 3 6c-5<r(2e-»l)J ' 
To find the limiting values of a„ we must make this a maximum or a minimum. If 
we suppose v to differ but little from 1, it will be nearly constant, and therefore 
da^ 2 [■ 
2p<7-p<-\ 
\-^rqp'-pq'-] 
1 
Oi 
( — 
3 q'-q<T\ 
