186 Mr. C. Barus on Maxwell's Theory of the 



certain problems in solid elastics. Following Meyer and 

 others, " elastische Nachwirkung " is a possible occurrence in 

 liquids. 



Boltzmann's * theory, amplifying deductions of Lamy and 

 of Clebsch, is based on the assumption that the elastic forces 

 are dependent not only on the present but on the preceding 

 deformations of the body. The effect of earlier states of stress 

 on the existing stress diminishes with the intervening time, 

 but is independent of the intervening states of stress. More- 

 over different viscous deformations are superposable. Boltz- 

 mann's theory therefore subserves a mathematical purpose, as 

 Kohlrausch f remarked, and, by presupposing the phenomena, 

 brings the laws of solid viscosity tersely into formulae. If to 

 is an interval of time reckoned back from t to t — a> when the 

 strain t -o> existed, then Boltzmann's law may be most clearly 

 exhibited, perhaps, in its application to the problem of vibration 

 of a viscous solid. Given a wire of the solid of length I and 

 radius R. Let its upper end be fixed and the lower end be 

 attached to a heavy bob whose moment of inertia for the 

 given conditions is K. Then the equation of motion is (slow 

 oscillation premised) 



D ~ K w = ^{^-j" ,"+«*->»} > 



where D is the moment of the applied couple, fi Lainy's 

 constant, and -\fr some function of co. 



Replying to Meyer's critique that a theory of this kind is 

 at variance with the present state of knowledge in atomistics, 

 Boltzmann J disclaims all present purpose to connect his 

 theory with definite physical hypotheses. He points out, 

 however, that the assumed dependence of the existing states 

 of strain on the foregoing deformations is easily justified 

 when the simultaneous changes of molecular configuration 

 are taken into account. For it is not necessary to suppose 

 that the elastic forces, as such, have any dependence on 

 preexisting stress. The changes of configurations in question 

 are closely similar to Maxwell's, so that in this respect Boltz- 

 mann's theory may be looked upon as one form of mathema- 

 tical development of Maxwell's physical hypothesis. I may 

 add that Boltzmann himself tested his theory with data of 

 Kohlrausch, Neesen, and Streintz. A special series of experi- 

 ments subsequently undertaken by Kohlrausch § give addi- 



* Boltzmann, Pogg. Ann. Erganzb. vii. p. 624, 1876. 

 t Kohlrausch, Pogg. Ann. clx. p. 227, 1877. 

 X Boltzmann, Wied. Ann. v. p. 430, 1878. 

 § Kohlrausch, Pogg. Ann. clx. p. 225, 1877. 



