MR. HENNESSY’S RESEARCHES IN TERRESTRIAL PHYSICS. 
613 
and nucleus should be favourable to a great amount of friction at their surface of 
contact, it is at least possible to conceive that if the sum of the pressures existing at 
the same surface be sufficiently great, the whole mass might rotate nearly as if solid 
from its surface to its centre. As it will hereafter appear that such conditions must 
almost necessarily exist, it is superfluous for our present object to further examine the 
general problem of the rotation of the shell and nucleus. I shall therefore proceed 
to consider the pressures which might take place at the surface of contact of the 
shell and nucleus. 
2. Abstracting the action of exterior disturbing bodies, the pressure of the nucleus 
at the inner surface of the shell will result from the attractions of all the particles of 
the shell and nucleus, centrifugal force, and molecular actions. Unless the last 
mentioned class of forces should have a tendency to disturb the position of the axes 
of rotation of the shell and nucleus, it is plain that these axes may be considered as 
coincident. 
Of the two resultant pressures mentioned in the preceding article, it is evident that 
the variable pressure may be conceived to result from the difference in form of the 
free surface of the nucleus and the shell’s inner surface. If these surfaces be very 
nearly spheroids of revolution, described about the shell’s axis of rotation, it follows 
that the greatest pressure will be at the equator or poles of the shell, according as 
the tendency of the nucleus may be to become more or less oblate. In either case 
it is evident that every point on certain lines situated between the equator and poles 
will not be subjected to any pressure from this cause, or in other words, the sum of 
all the pressures at the points in question will be equal to the constant pressure. 
The general expression for the pressure at any point of the shell may therefore be 
made to contain the coordinates of the lines in question as constant quantities. As 
these lines in the case considered are evidently circles parallel to the equator of the 
shell, we may call them the parallels of mean pressure. 
Let a straight and indefinitely narrow canal of fluid be conceived to reach from 
the centre to the surface of the nucleus. Let the origin of the coordinates of any 
point in it be fixed at the centre of gravity of the mass, and let the plane of x, y be 
perpendicular to the axis of rotation. Let r represent the radius drawn from the 
origin to a molecule in the canal, & the angle made by this radius with the axis of 
rotation, and u the angle formed by the projection of the radius on the plane of .r, y 
with the axis of y ; then 
%—r cos y=r sin 6 cos a, x=r sin 6 sin a. 
The pressure p at the point in the canal having these coordinates will be expressed 
by the equation 
dp—^[Kdx-\-Ydy-{-74dz-^a^{xdx-\-ydy)\, 
in which, as in art. 2, Part I., X, Y, Z represent the components of the attractions 
parallel to the three rectangular axes of x, y and z, a the angular velocity of rota- 
