JO SI AH WILLARD GIBBS 195 



the spheres of one another's influence, Gibhs finds that the processes of 

 statistical mechanics are to all human perception analogous to those of 

 thermodynamics, the familiar formulae of which appear, as Bumstead 

 puts it, " almost spontaneously, as it seems from the consideration of 

 purely mechanical systems." The differential equation relating to 

 average values in the ensemble is found to correspond with the funda- 

 mental equation of thermodynamics; the modulus of distribution of 

 ensembles turns out to be analogous to the temperature, while the 

 average index of probability in phase is the analogue of the entropy 

 with reversed sign, and being a minus quantity, is found to decrease 

 just as entropy increases. Most of the objections filed against Gibbs's 

 statistical demonstration, turn xipon the fact that it is difficult, perhaps 

 impossible, to apply the reversible dynamics of ideal, frictionless systems 

 to the spontaneous irreversible phenomena of nature without making 

 some physical assumptions. " Entropy," Burbury objects, 134 " may, 

 for all that appears, either increase or diminish in a system which is 

 dynamically reversible. This then can not be strictly applied to an 

 irreversible process." Gibbs has met these objections fairly. " Our 

 mathematical fictions," 135 he says, to quote Burbury's paraphrase of his 

 argument, " give us no information whether the distribution of phases 

 is towards uniformity or away from it. Our experience with the real 

 world, however, teaches us that it is towards uniformity." All actual 

 mechanical systems are, as Gibbs pointed out long before, in reality 

 thermodynamic, 136 and it seems odd that the critics who rejected Boltz- 

 mann's proof, because it did not agree with the facts of nature, should 

 now, for a logical quibble, take exception to Gibbs's because it does. It. 

 has been predicted that future truth in physical science will often be 

 found in the sixth place of decimals, for not everything in nature works 

 out according to specifications. We can, if we choose, regard mathe- 

 matics as a metaphysical diversion or employ it practically as a means 

 of interpreting the physical facts of nature, empirically ascertained by 

 man. In these matters, says Gibbs elsewhere, " Nature herself takes 

 us by the hand and leads us along by easy steps as a mother teaches 

 her child to walk," 137 and he would have agreed with Langley that 

 man may put questions to nature if he will, but is in no position to 

 dictate her answers to them. 138 Nature seems tres femme in this re- 

 spect, especially in regard to mathematical fictions, that is, ideal or lim- 

 iting cases devised by the finite mind of man. 139 Like any other human 



534 Phil. Mag., 1904, 6. s., VIII., 44. 

 i3S Ibid., 45. 



136 Tr. Connect. Acad., III., 108. 



137 Proc. Am. Ass. Adv. Sc, 1886, Salem, 1887, XXXV., 62. 



138 " Let us read Bacon again, and agree with him that we understand only 

 what we have observed." S. P. Langley, Science, 1902, XV., p. 927. 



133 "Physical chemistry is not yet a quantitative science; it is a pseudo- 

 quantitative science. There are all the outward signs of a quantitative science. 



