164 Mr E. Hill, On the influence of Geological [May 20, 



III. Mr Darwin suggests that althougli this possible separation 

 must be so minute, it must yet introduce stresses into the rotating 

 earth, which might be relieved by earthquakes restoring co- 

 incidence. This seems probable. In this way an 150 day or 300 

 day period in earthquakes might be produced. It would be in- 

 teresting to investigate whether such a period may not now exist, 



Mr Darwin calculates the path of the pole on the surface 

 supposing the earth plastic. The general problem can hardly 

 be solved without analysis, but the following cases may be noticed. 



The stress will be proportional to the separation. Suppose 

 that whenever the stress reaches a certain amount, the crust yields 

 suddenly, so as to restore the coincidence of the poles. The pole 

 of figure will thus move a uniform distance along its path, and 

 then be deflected a uniform distance at right angles to its previous 

 track. If we suppose these distances very small, we may approxi- 

 mately represent the motion of the pole, by supposing it to possess, 

 in addition to its original velocity, another at right angles to this, 

 and also uniform. If we suppose that the Geologic changes were 

 shifting the pole towards a certain point, its path, as resulting, 

 from the causes above mentioned, would be an equiangular spiral 

 about that point. Since the pole of rotation, starting on its 

 cycloid, moves at right angles to the motion of the pole of figure, 

 if the crust yields at this instant, the pole of figure follows it. 

 This is the case of plasticity amounting to fluidity, and makes the 

 spiral become a circle. 



Should th€ earthquake not restore complete coincidence, th« 

 pole would start on an epitrochoid instead of a cycloid, but if the 

 earthquakes took place as before at a definite degree of stress, and 

 diminished the separation by a constant fraction, the path would 

 be as before an equiangular spiral. This gives a rough idea of 

 the efl'ect of viscosity, and seems to indicate that the path of the 

 pole would on that supposition be some kind of spiral. 



IV. Expansion and contraction will be less effective in 

 changing the position of the principal axes than transference of 

 surface matter. 



The parts of the moments and products of inertia due to any 

 particle will be of two dimensions in the co-ordinates of its 

 position. In consequence, they must vary as the square of its 

 distance from the origin. To elevate the surface at any point by 

 expansion, is equivalent to removing matter from the interior and 

 depositing it on the surface. We may suppose this removal of 

 matter to take place along radii. Such a removal will increase the 

 moments or products of inertia of the body ; but not to the same 

 extent as the addition of an equal quantity to the surface : for 

 there is a loss by subtraction, as well as a gain by addition. Thus 



