the question of the number of the Elastic Constants. 24& 



assumption which the rari-constant theorists have employed 

 over and above those equivalent to the laws of energy. If 

 we take Mr. Love's account of Cauchy's deduction of the 

 stress-strain relations * as being fairly representative of de- 

 ductions of the kind (I have not access to the literature of 

 the subject), this seems obvious. For if, in this deduction, 

 the stresses between particles be regarded as functions of the 

 distances of all the pairs of particles of the system, not of the 

 distances between the attracting particles themselves only, 

 while the expressions for the elastic constants will be changed, 

 they will still reduce to fifteen. Hence, so far as the number 

 of independent constants is concerned, the rari-constant 

 theorists may be said to have employed dynamical assump- 

 tions equivalent to the laws of energy. 



This being so, the apparent discrepancy between the 

 results of the two theories must be due to the difference in 

 the assumptions made as to the constitution of bodies. Now 

 the distance-action conception of the constitution of bodies 

 involves a larger assumption than the contact-action concep- 

 tion. This is obvious from the fact that if we assume the 

 molecular hypothesis, or rather the point-atom hypothesis, it 

 can then be proved that bodies may be regarded as consisting 

 of elements exerting forces on contiguous elements only, 

 across surfaces of contact, while the molecular hypothesis 

 cannot be thus deduced from that of contact-action. Thus 

 the point-atom hypothesis may be regarded as consisting of 

 two parts, (a) that bodies may be regarded as consisting of 

 elements exhibiting contact-action; and (b) that this is due 

 to their consisting of point-atoms acting on one another at a 

 distance. Moreover, in the deduction of the rari-constant 

 result, the second part of the hypothesis has been employed. 

 For it is obvious from Mr. Love's sketch of Cauchy's reason- 

 ing, that the possibility of reducing the constants to fifteen 

 is due to the simplicity, one is tempted to say artificiality, of 

 the point-atom conception. It follows at once that unverified 

 deductions from the molecular hypothesis must have a lower 

 degree of probability than similar deductions from the rival 

 hypothesis. 



While the multi-constant result is thus the more probable 

 of the two, it cannot be said to be certain. Mr. Love repre- 

 sents the opponents of the molecular theory as urging 

 against it, " that the known laws of energy lead to results 

 which are certainly true whether the molecular hypothesis be 

 correct or no""t- Even, however, if we regard the laws of 



* ' Treatise ou the Mathematical Theory of Elasticity,' p. 110] 

 f Loc. cit. p. 16. 



T2 



