244 The Hypotheses of Abstract Dynamics. 



energy themselves as certainly true, the results of their 

 application to the study of elasticity cannot have the same 

 certainty, because of the additional hypothesis (3) which, as 

 seen above, is made in applying them. 



As the point-atom hypothesis may be expressed in the two 

 parts given above, it follows, if the conclusion reached above 

 is correct, viz., that the dynamical hypotheses practically 

 employed in the two theories are of the same hypothetical 

 content, that the rari-constant theorist must accept the multi- 

 constant result. He must hold that with the assumption (a) 

 only the number of independent constants cannot be reduced 

 to less than 21, but that with the additional assumption (6) 

 they are reducible to 15. It is thus obvious that there is no 

 real discrepancy between the results of the two theories. 

 According to the one, all bodies which may be regarded as 

 exhibiting contact-action will be capable of having their 

 elastic qualities completely characterized by 21 constants, and 

 unless we have further data with regard to these bodies, 

 21 constants will be requisite for this purpose. According 

 to the other, in the case of bodies which may be regarded as 

 exhibiting contact-action because of their consisting of point- 

 atoms, the number of the constants may be reduced to 15. 



It would seem to be a simple matter, not indeed to devise 

 and execute conclusive experiments to settle the question of 

 the existence of relations among the 21 constants, but to 

 interpret such experiments when made. For if the elastic 

 constants were found to be reducible to 15, the multi-constant 

 theory would obviously be proved to be inadequate. If other 

 relations were found to hold than those deduced from the 

 point-atom hypothesis, the point-atom conception would be 

 showm to be erroneous and the contact-action conception to 

 be inadequate. If it were found that there were no relations 

 among the 21 constants, the point-atom hypothesis would be 

 disproved and the contact-action conception would be showm, 

 so far as the number of the elastic constants is concerned, to 

 be adequate. Simple logical considerations of this kind are 

 sometimes overlooked by writers in the enthusiasm produced 

 by successful application of the contact-action conception. 

 Thus Mr. Love says * : — " Even if the experimental evidence 

 were all fairly interpretable in favour of the other side, if 

 there were a general consensus that Cauchy's relations hold 

 good, and that Poisson's ratio is J, for materials carefully 

 examined, that w^ould not amount to a proof of the molecular 

 hypothesis. It would still be open to us to reject that hypo- 

 thesis as not axiomatic, and in the present state of science we 

 * Loc. cit. p. 19. 



