218 PROFESSOR A. E. H. LOVE ON THE 



resembles that of a "pear"; but SOLLAS' and JEANS' "pears" have little in common 

 beyond the name. JEANS' ideal distribution would consist of a hemisphere which is 

 nearly all land, and an antipodal hemisphere which is nearly all ocean, with a central 

 island in the middle of this ocean. SOLLAS' account of the actual distribution is that 

 in one hemisphere there is a central continent (Africa) nearly surrounded by a belt of 

 seas, while in the antipodal hemisphere there is a central ocean (the Pacific) nearly 

 surrounded by a ring of land, the belt and ring being broken at three places, which 

 are distributed nearly symmetrically around the centres of the two hemispheres. 

 This description suggests very strongly a mathematical account expressed in terms of 

 surface harmonics of the third degree. 



If we neglect the rotation of the planet, and regard it as at rest under no external 

 forces, we can reach no other result than that reached by JEANS, viz., that, if the 

 modulus of compression was once so small that a spherically symmetrical state of 

 aggregation would have been unstable, the state of the planet would have been one 

 of lateral disturbance with a hemispherical distribution of density. We should not 

 be in a position to account at all for the geographical facts as presented by SOLLAS. 



46. The Earth is a rotating globe, and it is now generally believed to be the 

 larger of two fragments into which a single body has been broken up ; the other 

 fragment is the Moon. In the early history of the Earth-Moon system the two 

 fragments rotated, nearly as a single rigid body ; the period of revolution of the 

 Moon was nearly the same as the period of rotation of the Earth. We wish to trace 

 the consequences of supposing that the average elasticity of the material was once 

 much smaller than it is at present that the average modulus of compression was 

 more of the order of that of mercury, or even water, than of that of glass or steel, 

 and the average rigidity was" smaller in comparison with the modulus of compression 

 than it is to-day. We have the problem of determining the distribution of density 

 within the planet, and the consequent shape of its surface. The problem cannot be 

 solved completely, but we can make some progress with it ; and we can then attempt 

 to discover the extent to which our results accord with geographical observation. In 

 so far as the accord is good we may regard geography as supporting the hypothesis 

 as to the past state of the Earth. 



Illustration of the Nature of a Hemispherical Distribution of Density. 



47. We have reason to think that, in the absence of rotation and external forces, 

 the planet, if of sufficiently small elasticity, would have been in the state which we 

 have described as a state of lateral disturbance with a hemispherical distribution of 

 density. Before proceeding to take account of the rotation and external attractions, 

 we consider further the nature of such a disturbance. For this purpose we take the 

 problem of a spherical body, homogeneous when unstrained, and devoid of all rigidity, 

 and suppose that in the initial state the self-attraction of the body is balanced by 



