MAXWELL'S LAW 47 



But the knowledge of the laws of collision proves to 

 be quite unnecessary for the proof of Maxwell's law. 

 So little indeed is it necessary, that Maxwell was able in 

 course of time to change his views on this point without 

 having to upset or reject the theory established by him. 

 At Erst he thought it probable that two colliding mole- 

 cules, just as two hard elastic bodies, would, after the 

 collision in which they might have come into actual contact, 

 be hurled apart by a suddenly arising and vanishing force. 

 But later, on grounds which I shall examine in Chapter X. 

 123, in discussing the molecular forces, he declared it more 

 probable that two molecules of gas act on each other 

 with repulsive forces, which, varying inversely as the fifth 

 power of the distance, are insensible at greater distances, 

 but at smaller suffice to force apart two molecules coming 

 very near each other. We may hold either the one view 

 or the other without prejudicing the validity of these 

 proofs. 



This shows that for the purpose we have first in view it 

 would be superfluous to indulge in speculations on the \JL- 

 character and the laws of the forces that come into play 

 during the collision of molecules. A decision in favour of 

 a particular hypothesis would only diminish the value of 

 Maxwell's law, as it would seem to limit its validity. JLor_ 

 the law is valid independently of all hypotheses. 



For the proof of Maxwell's law it is therefore sufficient, 

 as Boltzmann 1 has already recognised, to impress the 

 quite general, and on that account jndubitable, propositions^^ 

 of analytical mechanics ; Maxwell too has made use of these 

 alone. So in the proof given in the Mathematical Appendices 

 ( 10*) it stands out clearly that Maxwell's law needs the 

 assumption of these general propositions only. 



The most important of these propositions is that of the 

 Conservation of Energy. The admissibility of its application 

 to molecular motion will not be questioned, but there is one 

 precaution to mind. If the molecules do not consist of 

 single massive points, but are made up of combinations of 

 several atoms, we have to take into account not merely 



1 Wiener Sitzungsber. Ixiii. 1871, pp. 397, &c. 



