142 PRINCIPLES OF DYNAMICS. [CHAP. VIII. 



which we cannot take it to be the law of gravitation. No success has attended 

 the efforts of those physicists who have sought after a law of force to account 

 for cohesion, and little success has been attained in seeking similarly to 

 account for the phenomena of elasticity. In the Rational Mechanics of 

 cohesion and elasticity it has been necessary simply to assume that there 

 could be forces between particles in any positions of such magnitudes as 

 would produce agreement with facts of observation; on the other hand no 

 proof has been adduced of the impossibility of such forces. In the absence of 

 such proof, and of more cogent objections, the theory would retain its value. 



The most important of the objections against the theory is directed 

 against the fundamental conception of bodies on which it rests. This 

 conception in fact competes with a different one, which has been deduced from 

 physical and chemical observation and experiment. I mean the molecular 

 hypothesis. Referring to Article 67, it will be observed that we have inferred 

 from the apparent diminution of heterogeneity of a body with the size of the part 

 considered that the smallest parts of bodies are homogeneous, and the whole 

 of our theory really turns on this supposition. Now if we should have any 

 reason to suppose that the approach to homogeneity does not continue in- 

 definitely with diminution of size, but that, after a certain limit of smallness 

 with approximate homogeneity has been reached, further progressive diminu- 

 tion of size would be accompanied by accentuated heterogeneity ; then it 

 would appear that our theory could at best be a first approximation. Now 

 the observed facts on which the molecular hypothesis is founded are all of the 

 kind just indicated ; they all point to the existence of structure in parts of 

 bodies extremely small compared with any parts that we can actually separate 

 from the rest for purposes of observation and experiment. 



Here then we have arrived at an apparent contradiction. Starting* with 

 statical considerations, concerning the mutual actions of approximately rigid 

 bodies, with experiments on falling bodies, and with Astronomical observations, 

 we have been led to a certain hypothesis concerning the structure of bodies. 

 Starting with a different set of experiments and observations we are led to 

 form a quite opposite hypothesis, and there can be no doubt that the second 

 hypothesis is better established than the first. Thus some part of the system 

 of postulates on which we based our Rational Mechanics, though valid in 

 logic, is not a true representation of facts, and it is desirable to endeavour to 

 reconcile the opposing hypotheses by giving up something not really essential, 

 but actually treated as fundamental, when the general problems of Physics 

 are approached from one side or the other. 



To seek ground for reconciliation let us look a little more closely at the 

 results of our theory. That bodies behave as if they were made up of 

 particles possessing what we have called definite mass-ratios, i.e. that bodies 

 have the property we call mass, affects the motions of systems of bodies in a 

 perfectly definite way. There is for each body a definite mass, which is 

 always a constant coefficient entering in the same place in the equations 

 governing its motion. There is absolutely no doubt that we must attribute 



* See Historical Note at the end of Chapter V. 



