280 
MB. GrEOBGE H. DABWIN ON THE INFLUENCE OF 
meridian, along which the axis of figure is travelling with uniform velocity, in conse- 
quence of the geological deformation of the earth. 
The motion of the instantaneous axis in the earth is a prolate cycloid. 
4. Adjustments to a Form of Equilibrium. 
If the earth were a viscous fluid there is no doubt but that the pole of figure would 
tend to displace itself towards the instantaneous axis, whose mean position would be the 
centre of the circle above referred to. 
But Sir William Thomson has shown* that the earth is sensibly rigid; and in any 
case the earth is not a viscous fluid, properly so called, although it may be slightly 
plastic. 
M. Tresca has shown that all solids are plastic under sufficiently great stresses, hut 
that, until a certain magnitude of stress is reached, the solid refuses to flowf . Now in 
the case of a very small inequality like this, the stresses introduced by the want of coin- 
cidence of the instantaneous axis with the axis of figure are very small, even when at 
their maximum ; and every 306th day they are zero. It seems, therefore, extremely 
improbable that the stresses can be great enough to bring the earth into what M. Tresca 
calls the state of fluidity ; and therefore it is unlikely that there can be any adaptation 
of the earth’s form to a new form of equilibrium in consequence thereof. 
In all the other inequalities introduced, whether arising from the first three terms 
above given in &> L and a 2 , or arising from the impressed forces, to he treated hereafter, 
the centre of the positions of the instantaneous axis is coincident with the pole of 
figure, and therefore there can hardly be any adaptation of figure eccentric to the axis 
of greatest moment to balance the stresses introduced by centrifugal force. 
It would appear probable that, whilst a geological change is taking place, the earth 
is practically rigid for long periods. But as the earth comes to depart more and more 
from a form of equilibrium, the stresses due to the mutual gravitation of the parts, and 
to the rotation, increase gradually, until they are sufficiently great to cause the solid 
matter to flow. A rough kind of adjustment to a form of equilibrium would then take 
place. The existence of continents, however, shows that this adjustment does not take 
place by the subsidence of the upheaved part ; and as this adaptation of form would 
he produced by an entirely different cause from that to which the upheaval was due, that 
upheaval would probably persist independently of the approximate adoption of a new 
form of equilibrium by the earth. 
M. Tresca’s experiments on the punching of metals would lead one to believe that 
the change would take place somewhat suddenly, and would, in fact, be by an earth- 
quake, or a succession of earthquakes. On each of these occasions the tendency would 
* In his Address to the British Association, 1876, he states that the argument derived from precession 
(Thomson and Taix’s Nat. Phil. p. 691) is fallacious ; he adduces, however, a number of cogent arguments on 
this point. 
t “ Sur l’ecoulement des Corps Solides,” Mem. des Sav. tom. xviii. 
