590 Mr. H. Jeffreys on the Compression 



If, then, the third part is able to counterbalance the other 

 two, the spherical state of the earth is unstable and a 

 departure from it will occur. It has been shown by Love 

 that such instability will occur first for deformations ex- 

 pressed by spherical harmonics of the first order, in the 

 case of a homogeneous sphere. If the outer layer of the 

 sphere is of somewhat lower density than the rest, as in 

 the actual earth, the problem is more complex ; if the outer 

 layer is, however, thin and of small strength, the effect 

 of the change can be predicted. For the same displace- 

 ments inside, the changes (1) and (3) in the energy are 

 the same as before ; but if displacements of mass occur 

 over the outer surface to such an extent as to compensate 

 isostatically the displacements below it, the change (2) 

 attains its minimum value : this is seen at once from the 

 fact that the isostatic state, being that in which the interior 

 of the earth is in hydrostatic equilibrium, must be a state 

 of minimum potential energy for a given thickness of the 

 surface layers. Hence one of the causes making for 

 stability is reduced if heterogeneity is allowed for and 

 the inequalities are supposed compensated. Gravitational 

 instability will then be first manifested in the case of those 

 degrees of freedom that are consistent with the isostatic 

 state. Thus if inequalities can be produced at all in this 

 way, it is highly probable that they will be isostatically 

 compensated from the start. The explanation of the low 

 density of the continents and the high density of the 

 matter below the oceans may then be connected with 

 gravitational instability, accelerated by the mechanism of 

 isostasy. 



VIII. The effect of changes in the rotation of the Earth, 



An essential feature of the present investigation is the 

 hypothesis that the earth was formerly in a very heated, 

 and probably fluid, condition. This leads directly to several 

 other consequences. In this liquid state the coefficient of 

 viscosity must have been practically zero ; but at present 

 it is exceedingly high, probably greater than 10 17 c.g.s., 

 units. Now, as the substances of which the earth is. 

 formed are not in general pure, they would pass through 

 a pasty state in solidifying and the viscosity would thus 

 increase continuously. Hence it would take in the process 

 every value between its initial and final values. Now 

 Sir Gr. H. Darwin showed that if the viscosity had a certain 



