Physics and Mathematics to Geology. 351 



molten matter such as appears at the surface in volcanic out- 

 bursts, but the total volume occupied by this must be small. 

 Professor Roche takes three results as given ; viz. the earth's 

 total mass, the eccentricity of its surface, and the ratio of the 

 principal moments of inertia, the last quantity being deduced 

 from astronomical data. He satisfies all the conditions he 

 recognizes by the aid of the following hypothesis regarding 

 his nucleus : — "Ce bloc a pris sa forme definitive sous l'influ- 

 ence d'une rotation moins rapide qu'elle n'est aujourd'hui, 

 et il a conserve Paplatissement correspondant, malgre les 

 accroissements successifs de vitesse du systeme resultants de 

 sa contraction progressive " (p. 232). In other words, he 

 assumes the nucleus to have solidified before the crust and that 

 it retains its shape unaltered. Thus as he regards the angular 

 velocity as increasing in consequence of the diminution in the 

 moment of inertia through contraction in cooling, the nucleus 

 possesses a smaller eccentricity than the crust. He supposes 

 only a small difference in the length of the day at the dates of 

 the two solidification s, so that the difference between the 

 eccentricities of the nucleus and crust is also small. This, 

 however, in no way justifies his hypothesis that the nucleus 

 retains its form unaltered. If its material possessed the pro- 

 perties of an elastic solid the eccentricity would certainly 

 alter, and to an extent probably quite comparable with 

 the alteration that would have occurred if it had remained 

 fluid. Professor Roche seems in fact to treat his nucleus 

 as possessed of the properties of the wholly imaginary per- 

 fectly rigid body. He certainly introduces no equations 

 such as ought to hold over the surface of an elastic solid sphe- 

 roid. The exact view he adopted as to the properties of solids 

 it is, however, difficult to decide. On his p. 241 a brief state- 

 ment would imply that he did not regard each elementary 

 layer of a solid sphere as of necessity totally self-supporting; 

 but on pp. 223, 224, where the discussion is fuller, he says, 

 " Si Ton rejette la complete fluidite de la terre, il n'est plus 

 possible d'attribuer a la compressibility de ses couches la meme 

 influence." . . . " Dans un solide, les tensions laterales sont 

 variables et acquierent parfois une valeur enorme. C'est 

 ainsi qu'une couche pourrait se soutenir d'elle-meme comme 

 une espece de voute, sans peser sur celle qui est au-dessous/'' 

 A solid layer supporting itself like an arch under the con- 

 ditions of matter near the earth's surface treated as an elastic 

 solid, presents strains far in excess of those which are regarded 

 here as coining within the range of the mathematical theory. 

 On various grounds it seems to me that the criticism of a 

 want of elasticity, though hardly in the sense intended by 



