Intelligence and Miscellaneous Articles. 495 



By applying a few modifications to our apparatus we expect to 

 secure greater precision, and to extend our measurements beyond 

 the line N. — Comjjtes Rendus de VAcademie des Sciences, vol. Ixxxi. 

 pp. 610-613. 



ON THERMIC EQUILIBRIUM AND HEAT-CONDUCTION IN GASES; 

 AND ON THE INTEGRATION OF PARTIAL DIFFERENTIAL EQUA- 

 TIONS OF THE FIRST ORDER. BY PROF. LUDWIG BOLTZMANN. 



At the sitting of the [Vienna] Academy of the 14th October, Prof. 

 Boltzmann presented three memoirs. The first, " On the Thermic 

 Equilibrium of Grases when acted ou by external Forces," contains 

 the demonstration that, even in the case of the operation of external 

 forces, a function E exists of which the value cannot increase in 

 consequence of the molecular motion, and consequently must have 

 a constant minimum value ; indeed this function is perfectly iden- 

 tical with that which possesses this property when no external 

 forces are present ; only the subsidiary conditions are different. 

 In order to furnish the demonstration, in the first place the general 

 partial differential equation for the change of state in consequence 

 of the molecular motion is developed ; it contains some terms which 

 also occur when no external forces act, and others which result 

 from the presence of the external forces. It is then proved that 

 the latter terms supply a vanishing quantity to the expression ob- 

 tained for the differential quotient of the function E according to 

 the time, whence it follows that the laws of the variation of this 

 function with the time undergo no change by the operation of the 

 external forces. But the subsidiary conditions are different, inas- 

 much as the equation of the vis viva must now contain also the 

 ergalof the external forces. By means of this proposition the dis- 

 tribution of state which enters in the case of thermic equilibrium 

 can with facility be determined. In the second memoir, " Remarks 

 on the Conduction of Heat by Gases," some theoretic considerations 

 are attached to the experimental investigations of Stefan, Kundt, 

 Warburg, and Winkelmann. Stefan already remarked that these 

 observations seemed to indicate that the intramolecular motion 

 takes part in a slight degree, as Maxwell assumed, in the heat-con- 

 duction. This is here further elucidated ; and it is shown that 

 perfect accordance with experiment is attained by assuming that 

 the contribution f urniohed by the intramolecular motion to the heat- 

 conduction amounts to only -^ of what it would be according to 

 Maxwell's hypothesis. The author remarks that this is much less 

 than what the intramolecular motion in consequence of the mere 

 diffusion of the molecules would contribute to the heat-diffusion if 

 the proportion of the vis vivaoi the progressive and intramolecular 

 motions were in each layer the same as in a uniformly heated gas 

 of the same temperature. The observations hitherto made appear, 

 therefore, to favour the opinion that such is not the case. It would 

 hence follow that the constancy of heat-conduction is not entirely 

 independent of the thickness of the conducting layer. In conclu- 



