GEOLOGICAL CHANGES ON THE EAKTH’S AXIS OE ROTATION. 
281 
be to adjust the form to one of equilibrium about the instantaneous axis. Now the 
principal axis X 3 has (in consequence of the postulated deformation) been travelling 
along the meridian in longitude 7r-f- arc tan measured from the plane containing 
\ and x 3 . 
The earthquake will take place when, to the stresses due to mutual gravitation, are 
superadded the maximum stresses due to centrifugal force ; that is to say, when the 
instantaneous axis is at its greatest distance from the axis of greatest moment of 
inertia. At the instant of the earthquake the principal axis will be moved towards the 
position of the instantaneous axis. And as the circle described by the instantaneous 
axis touches the meridian of displacement of the principal axis, therefore the principal 
axis will be carried by the adjustment towards the centre of the circle described by the 
instantaneous axis, and therefore perpendicular to the meridian of displacement. 
Thus, if the adjusting earthquakes take place at long intervals, the motion of the 
principal axis will not deviate sensibly from continuing along the meridian, along which 
it would travel in consequence merely of the geological deformation. If, however, the 
adjustments are frequent, the path of X 3 will diverge sensibly from the meridian along 
which it started. If the readjustments become infinitely frequent and infinitely small, 
there is a continuous flow of the matter of the earth, which is always seeking to bring 
back the earth’s figure to one of equilibrium, from which figure it is also supposed to 
be continuously departing under the action of internal forces. In this state the earth 
may be considered as formed of a stiff viscous fluid. 
According to these ideas, at each adjustment x l5 X 2 , X 3 will be suddenly reduced to 
nearly their primitive values, A, A, C ; but a, j3, y depend on the rate of accession and 
diminution of matter at various parts of the earth, and remain constant. The only 
effect, then, is that each adjusting earthquake must be taken as a new epoch. 
As far as I can see, it seems quite possible that the earth may be sensibly rigid to the 
tidally deforming influences of the sun and moon, and yet may bring itself back from 
any considerable departure from a form of equilibrium to approximately that form. It 
therefore seems worth while to consider the case of the adjustments being continuous, 
whilst the deformation is also continuous. 
5. Adjustments to the Form of Equilibrium continuous. 
I therefore propose to consider geometrically, but not dynamically, the paths of the 
instantaneous axis, and of the principal axis, where the earth is viscous and continuously 
deformed by internal forces. It is supposed that the velocities of flow of the matter of 
the earth are so small that inertia may be neglected, and that the displacements are so 
small that the principle of the superposition of small motions is applicable. 
As before the paths of the instantaneous and principal axes may be mapped on a 
tangent plane to the spheroid, at the extremity of the primitive pole, the mean radius 
of the spheroid being taken as unity. 
2 e 2 
