60 



SCIENCE 



[N. S. Vol. XLVII. No. 1203 



admit that relativists are quite within their 

 rights when they demand an answer to the 

 question, "Fixed with reference to what; 

 rotates relative to what?" Here, it seems 

 to me, is a possible field of usefulness for 

 the ether in addition to its original func- 

 tion of serving as nominative case to the 

 verh "to undulate." This appears the 

 more likely when we consider that the 

 earth's magnetism has never received an 

 explanation — or, if one chooses, a descrip- 

 tion which connects it with other physical 

 phenomena. 



I have left to the end the consideration 

 of the most revolutionary change which the 

 twentieth century has brought about in the 

 outlook and methods of theoretical phys- 

 ics — the rapid development and great suc- 

 cesses of the quantum hypothesis of Planck. 

 As we have seen, the fifty years following 

 the discovery of the conservation of 

 energy were marked by the steady progress 

 of dynamical theories and the conquest by 

 them of one disputed position after 

 another. It is true that the victory was 

 never quite complete, that the models were 

 always in some degree imperfect and ap- 

 proximate; but the success was, on the 

 whole so great that it seemed to justify the 

 hope that only time and labor were neces- 

 sary to clear away present difficulties as so 

 many had been overcome in the past. It 

 had not been easy to bring thermodynamics 

 and irreversible processes into the dynam- 

 ical system, but so far as material systems 

 were concerned, most physicists were in 

 agreement that it had been successfully 

 done. It is true that a violation of the sec- 

 ond law of thermodynamics could not be 

 shown to be impossible ; but its improbabil- 

 ity was so great that there was no reason- 

 able expectation of its ever being observed 

 by finite human beings. The most com- 

 plete and general exposition of this great 



triumph of the dynamical hj^iothesis is con- 

 tained in the "Statistical Mechanics" of 

 Willard Gibbs, which was published in 

 1902, but which had been completed and 

 given in the form of academic lectures by 

 the author for some years previous to that 

 date. As in all of Gibbs 's work the as- 

 sumptions and the results were of a very 

 general character; but he was quite aware 

 that at one point they were too restricted. 

 He says:^" 



Although our only assumption is that we are 

 considering conservative systems of a finite num- 

 ber of degrees of freedom, it would seem that this 

 is assuming far too much, so far as the bodies of 

 nature are concerned. The phenomena of radiant 

 heat, which certainly should not be neglected in any 

 complete system of thermodynamics, and the elec- 

 trical phenomena associated with the combination 

 of atoms, seem to show that the hypothesis of sys- 

 tems of a finite number of degrees of freedom is 

 inadequate for the explanation of the properties of 

 bodies. 



The difficulties involved in the possession 

 by the continuous ether of an infinite num- 

 ber of degrees of freedom were brought 

 more clearly to light in 1900 by Lord Eay- 

 leigh's formula for black body radiation. 

 It was quite irreconcilable with the meas- 

 urements of Paschen and, moreover, it led 

 to a kind of superdissipation of energy into 

 high frequency vibrations of the ether 

 which appeared entirely out of accord with 

 the facts of empirical thermodynamics. 

 Paschen 's observations were well repre- 

 sented by the formula which had been ob- 

 tained by Wien, who assumed the Maxwel- 

 lian distribution of velocities among the 

 molecules of the black radiator, and also 

 that the wave-length radiated by any mole- 

 cule was a function of its velocity. Later 

 experiments by Lummer and Pringsheim 

 and by Eubens and Kurlbaum, with longer 

 wave-lengths and higher temperatures, ap- 

 proximated to the Rayleigh formula. 



10 ' ' statistical Mechanics, ' ' p. 167. 



