152 SOME APPLICATIONS OF 
hypothesis that the nucleus retains its form unaltered. If its material 
possessed the properties of an elastic solid the eccentricity would cer- 
tainly alter, and to an extent probably quite comparable with the alter- 
ation that would have occurred if it had remained fluid. Prof. Roche 
seems in fact to treat his nucleus as possessed of the properties of the 
wholly imaginary perfectly rigid body. He certainly introduces no 
equations such as ought to hold over the surface of an elastic solid 
spheroid. The exact view he adopted as to the properties of solids it is, 
however, difficult to decide. On his page 241 a brief statement would 
imply that he did not regard each elementary layer of a solid sphere 
as of necessity totally self-supporting; but on pages 223, 224, where 
the discussion is fuller, he says, ‘‘Si l’on rejette la complete fluidité de 
la terre,il west plus possible Wattribuer 4 la compressibilité de ses 
couches la méme influence.” - - - ‘Dans un solide, les tensions 
latérales sont variables et acquierent parfois une valeur énorme. C’est 
ainsi qwune couche pourrait se soutenir d’elle méme comme une espece 
de voiite, sans peser sur celle qui est au-dessous.” <A solid layer sup- 
porting itself like an arch under the conditions of matter near the 
earth’s surface treated as an elastic solid, presents strains far in excess 
of those which are regarded here as coming 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 Prof. Prestwich, may 
be strongly urged against Roche’s investigations. 
Some remarks of M. Roche’s, on his pages 240, 241, throw considera- 
ble light on his standpoint and that of many other theorists: ‘Les as- 
tronomes qui persistent a admettre la fluidité - - - cherchent a 
éluder Jes objections de Hopkins et de Thomson, en attribuant - - - 
au liquide central une viscosité assez grande pourque - - - Vensem- 
ble en arrive atourner tout d’une piece - - - La masse tournante 
offre une telle rigidité quelle est assimilable sous ce rapport a un bloc 
solidifié, mais admettre cette assimilation revient a dépouiller le milieu 
interne des propriétés ordinaires des liquides, et a lui en conserver le 
nom tout en V’identifiant 4 un corps solide.” He proceeds to point out 
that the mere question of a name is of no account, considering our 
ignorance of what would be the properties of matter under such pres- 
sures and at such a temperature as the theory of fluidity would lead 
to. His line of argument is not very clear, but there is no hesitation 
apparent in his conclusion: ‘En effet, la pression supportée par les 
couches centrales, dans la supposition dune complete fluidité, dépas- 
serait deux millions et demi d’atmospheres. La grandeur méme de ce 
nombre est a elle seule une objection péremptoire a Vhypothese qui y 
conduit. 
Such a position as this may be all very well for a philosopher who 
supposes the external world a mere idea, the private proverty of his 
own mind and so necessarily obedient to laws which his understanding 
