Henry William Watson. 267 



He published in 1871 a text-book on Geometry (Longman's Series) 

 designed mainly for the use of schools. 



In 1876 he published a treatise on the Kinetic Theory of Gases 

 (Clarendon Press), which reached a second edition in 1893. The 

 foundations of this Theory had been laid by Maxwell in his articles 

 on the collision of elastic spheres, " Philosophical Magazine, 1860." 

 Beginning a new subject, Maxwell naturally adopted the simplest 

 hypotheses. For his molecules he chose, in 1860, as a limiting case, 

 smooth perfectly elastic spheres, supposed to rebound on collisions 

 with each other without loss of kinetic energy. Subsequently, in 1868, 

 he started the hypothesis that molecules were centres of force repelling 

 one another according to the inverse fifth power of the distance, no 

 one objecting at that time to instantaneous action at a distance. 

 Also for the sake of simplicity he assumed, as a limiting case, the 

 motions of his molecules to be mutually independent, the chance of 

 any one having its velocities within assigned limits being wholly 

 independent of the positions and velocities of all the others. Nature 

 might have made matter continuous and not molecular. But if 

 molecules existed, they could not, so it is assumed, have mutually 

 related motions. 



On these assumptions the distribution of velocities among the 

 molecules was found to be, according to the e~ law, generally known 

 as Maxwell's law, and it led to the doctrine of equipartition of energy. 



In the meantime the subject had been treated in Germany with 

 elaboration, but on nearly the same assumptions, by 0. E. Meyer, and 

 by Ludwig Boltzmann in a great series of papers beginning in 1867 in 

 the Vienna Sitzungsberichte. 



Boltzmann accepted Maxwell's second assumption of independence, 

 and deduced therefrom, in addition to Maxwell's results, the H or 

 entropy theorem, according to which Maxwell's law is not only a 

 sufficient, but a necessary, condition for steady motion. He also gave 

 us the law of space distribution known as the e ~ 2A * law, which states that 

 the chance of any group of molecules being in a configuration in which 

 the potential of all the mutual and other forces acting on them is x> 

 varies as e~" x . Such was the state of the theory in 1876. 



Watson's task was to a great extent that of summing up the work 

 of his predecessors. Like Boltzmann before, and Tait after him, he 

 accepted without discussion the limiting case assumption of indepen- 

 dence. It was not until nearly twenty years later, in the discussion 

 of the H theorem and FitzGerald's objection, that the true nature of 

 the assumption was pointed out. And then, and not till then, it was 

 that Boltzmann announced that he would have to make "cine 

 besondere Annahme." 



