242 Mr. C. Chree on some Applications of 



matical theory to hold, a solid isotropic sphere tinder a uniform 

 surface-pressure shows none but negative strains, and the 

 three principal stresses are everywhere equal. Thus the 

 greatest strain is everywhere negative, and the stress-dif- 

 ference everywhere zero. This is true irrespective of the 

 magnitude of the surface-pressure, and so, according to both 

 theories, the stress-strain relation would be linear and the 

 mathematical theory would apply, however large the pressure 

 was. According to the theories, one might continue to em- 

 ploy mathematical formula? which indicated a reduction of 

 the sphere to one millionth of its original volume. It is 

 obvious, however, that a reduction of the volume by even a 

 tenth would produce strains which are probably far in excess 

 of those admitted by the principle (C). In formulating an 

 objection to the universal application of the theories, I have 

 preferred to attack them on the side of the principle (C) so 

 as to show clearly that the high authority of Thomson and 

 Tait is on my side. The example considered raises, however, 

 what seems to me at least an equally strong argument against 

 the theories from the side of the principle (B). For we must 

 remember that the stresses inside the material are determined 

 by the intermolecular forces. Now, whatever molecules may 

 be, and however they may act on one another, it seems in- 

 credible that the molecular forces should lead to one and the 

 same stress-strain relation, however much the mean molecular 

 distance may be reduced. The fact that Sir W. Thomson 

 regards the existence of an irreducible minimum volume as 

 possible may, I think, be taken as proof that he is opposed to 

 the view that it is possible for the stress-strain relation to 

 remain linear under such circumstances. It thus seems to 

 me, on various grounds, that the inevitable conclusion is that 

 while one or other of the two theories may, under ordinary 

 circumstances, be sufficient to define the limits of the mathe- 

 matical theory, the result must always be checked by reference 

 to the condition (C), or, what comes to the same thing, we 

 must give up the mathematical theory when the strains it 

 indicates are such as would markedly alter the mean mole- 

 cular distance. 



I next proceed to discuss the possibility of the earth's 

 possessing an elastic solid structure, deriving the necessary 

 data from three papers published in the * Transactions' of the 

 Cambridge Philosophical Society. For brevity these will be 

 referred to as (a)*, (7>)|, and (c)J. 



* Vol. xiv. pp. 250-369. 



t Vol. xiv. pp. 467-483. | Vol. xv. pp. 1-36. 



