86 ROYAL SOCIETY OF CANADA / 
favour of the other side, if there were a general concensus that Cauchy’s 
relations hold good and that Poisson’s ratio is + for materials carefully 
examined, that would not amount to a proof of the molecular hypo- 
thesis.”! This must, of course, be admitted. Crucial experiments cannot 
prove an hypothesis; they can only disprove one of two rival hypotheses 
and increase the probability of the other. In the case supposed the mole- 
cular hypothesis would not be proved, but the rival hypothesis would 
surely be disproved.—# It would still be open to us,” he continues, “to 
reject that hypothesis” [i e., the molecular] “as not axiomatic.” What 
is meant by axiomatic is not stated and is not made obvious by the con- 
text ; but it is surely a remarkable statement that an hypothesis, which is 
admitted, for the sake of argument, to be capable of giving deductions 
satisfying the experimental evidence, is to be regarded as not axiomatic, 
while one which is similarly admitted to give results inconsistent with 
experiment is to be regarded as axiomatic. — ‘‘ Modern physics,” he 
says a little farther on, “is perfectly capable of deducing a theory 
of elasticity from the known laws of energy, without the aid of a 
subsidiary hypothesis about inter-molecular force, and being in that 
position, it is bound to discard the hypothesis.” Now it is doubtless 
true that modern physics can do what is asserted of it, but only by 
substituting some other subsidiary hypothesis for that of molecular 
attraction. Mr. Love seems to admit this, for when he proceeds * to show 
that the conception of stress might be obtained independently of the 
molecular hypothesis, he says: “The existence of this stress might be 
taken as a fundamental fact, just as in elementary mechanics the tension 
of a string and the pressure of a fluid are taken as fundamental notions 
derived from experience ;” and that he recognizes this to be merely the 
substitution of another hypothesis for that of the attraction of molecules 
seems to be shown by his remark: “ As an example of a doctrine of stress 
derived from hypotheses other than molecular we may cite the theory of 
hydrodynamics.” In fact, in addition to what are ordinarily called the 
hypotheses of dynamics, one or other of two additional assumptions is 
always made in dynamical discussions, —either that we may regard bodies 
as consisting of particles acting on one another at greater or smaller dis- 
tances, or that we may regard them either as continuous or as connected 
by continuous media, the elements of the bodies or media exerting forces 
only on neighbouring elements across the surfaces of contact. Though 
not usually called distinct hypotheses, these assumptions are so in reality. 
Since, then, modern physics can deduce a theory of elasticity from 
the laws of energy without the aid of a molecular hypothesis, only by 
substituting for it another hypothesis, it surely cannot be held that we 
are bound to discard the molecular hypothesis. The hypothesis which is 


1“ Mathematical Theory of Elasticity,” 1892, vol. i., p. 19. 
2 Ibid., p. 67. 
