JO SI AH WILLARD GIBBS 195 



on, noticeably removed from this condition. The probability of the 

 latter state of affairs is smaller, the further such a state is removed from 

 thermal equilibrium, but it can be made as great as we please to assume 

 the universe to be great. But there is necessary and sufficient prob- 

 ability that our earth as we know it is in its present state. By the 

 second law (irreversible increase of entropy in natural processes) there 

 is still greater probability that it tends to a final state of thermal equi- 

 librium or death; and since the universe itself is so great, there is 

 sufficient probability that other worlds than ours may deviate from 

 thermal equilibrium. As a graphic exposition of this theory, which 

 shows the vast scope of the second law of thermodynamics, a curve can 

 be plotted with the variables H and the time as coordinates, to visualize 

 what takes place in the universe. The II curve is shaped like a suc- 

 cession of inverted trees, the summits of which represent " the worlds 

 where visible motion and life exist." 130 Physicists have found that 

 the Maxwell-Boltzmann distribution of velocities is satisfactory for 

 gases whose molecules move independently and at random; but when 

 the molecules are supposed to be subject to one another's influence, it 

 does not account for certain facts of nature such as the measured 

 specific heats of gases or individual peculiarities of their spectra. In 

 monatomic gases like argon, helium and mercury, the ratio of the 

 specific heats will account for the three degrees of molecular freedom 

 ascribed to them by the mathematical theory, but in the case of dia- 

 tomic gases, like hydrogen or oxygen, the theory calls for six degrees 

 of freedom, while experiment will account for only five. Boltzmann 

 met these objections with frank or ironical admissions as to the ultimate 

 inadequacy of all human hypotheses, 131 and although his theory is to 

 some extent invalidated by facts like the above, 132 his subtle handling 

 of molecular thermodynamics, gives the physicist deeper insight into 



130 " Almost all these trees are extremely low, and have branches very nearly 

 horizontal. Here H has nearly the minimum value. Only very few trees are 

 higher, and have branches inclined to. the axis of abscissae, and the improbability 

 of such a tree increases enormously with its height." Boltzmann, Nature, 

 1894-5, LI., 581. 



131 « N e ith er the theory of Gases nor any other physical theory can be quite 

 a congruent account of facts, and I can not hope with Mr. Burbury that Mr. 

 Bryan will be able to deduce all the phenomena of spectroscopy from the electro- 

 magnetic theory of light. Certainly, therefore, Hertz is right when he says: 

 ' The rigour of science requires that we distinguish well the undraped figure of 

 Nature itself from the gay-coloured vesture with which we clothe it at our 

 pleasure.' But I think the predilection for nudity would be carried too far if 

 we were to forego every hypothesis. Only we must not demand too much from 

 hypotheses." Boltzmann, Ibid., 413. 



132 The principal opponent of the Maxwell-Boltzmann partition of energies 

 was Lord Kelvin in his " Nineteenth Century Clouds over the Dynamical Theory 

 of Heat and Light." When asked what he had against it, he replied point-blank: 

 " I don't think there is a single thing about it that is right " ( Science, Jan. 3, 

 1908, p. 6). 



