1878.] changes on the EartK s axis of rotation. 165 



the change in these quantities produced by the removal of a par- 

 ticle to the surface, from an original depth of 40 miles, would be 

 less than the change due to the simple addition of such a particle 

 to the same point, in the ratio of 4000^ — 3560^ : 4000^ or of 

 1 — (1 — yJo)^ : 1, or of jfo : 1 approximately, that is 1 : 50. 



Hence Mr Darwin's conclusion clearly follows, that expansion 

 and contraction are vastly less effective in changing the position of 

 the axes than transference of surface matter, at all events when 

 the}^ occur within any moderate depth. We cannot assert a priori 

 that the changes of angle are in simple proportion to the changes 

 of moments and products of inertia. Mr Darwin's analysis shows 

 that they are, and the above result agrees roughly with one of his 

 calculations. 



