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 XIV. Intelligence and Miscellaneous Articles. 



REMARKS ON THE THEORY OF GASES. BY J. STEFAN. 



ACCORDING to the new theory of gases a local excess of tempera- 

 ture in a gas ought to disappear from its place almost instantane- 

 ously; and on many sides this has been urged as an objection to the 

 theory. The objection was based on the consideration of the simple 

 case of the propagation of vis viva in a series of equally large elastic 

 spheres. Each sphere on a central impact with the next one inter- 

 changes velocity with it, and their excess of vis viva propagates itself 

 through the entire series of spheres with their velocity. The new theory 

 gives very large values for the velocities with which the gas molecules 

 progressively move, by which the above objection seemed justified. 



Clausius has answered this in his theory of conduction in gases. 

 He rejects the above simple case of the propagation of vis viva as 

 totally useless, even approximately, for the purpose of leading to a 

 conclusion on the point in question. On the contrary, Clausius lays 

 considerable weight, and justly, on the consideration of the irregular 

 motions of the molecules. His calculation based upon this gives a 

 very small value for the conducting power of gases. This result he 

 adduces in refutation of the above objection. According to his view 

 it appears as if this result were dependent on the consideration of 

 irregular motions. But even under the supposition of a regular 

 arrangement of the molecules, a very small value is obtained for the 

 conducting power, as can readily be shown without tedious calculation. 



If we imagine two superincumbent layers of gas with a common 

 base 1, and each of the height h. Let the temperature of the higher 

 layer be h degrees higher than the lower one. If c is the specific 

 heat of the gas for a constant volume, s its specific gravity, the upper 

 layer has an excess of temperature whose magnitude is csh 2 . If we 

 divide the molecules of a layer into two parts, into those with a pre- 

 dominating upward motion, and those with a predominating down- 

 ward one, then the latter part of the molecules in the upper layer 

 will transfer half their excess of temperature to the downward moving 

 molecules of the lower layer in the time in which a molecule 

 traverses a layer. The thickness of the layer is then equal to the 

 mean of the path of a molecule from one impact to the other, to be 

 taken in the direction normal to the planes of the layers. If r is 



csh 2 . 

 the time which the molecule requires to traverse the layer, -jr— 1S 



the quantity of heat given by the upper to the lower layer, reduced 



to the unit of time. Hence this magnitude must be considered as 



an approximate expression for the conductibility of a gas. Clausius 



Scse 2 

 finds for it y^ — , in which e is the mean path of a molecule from 



one impact to the next, and r the time taken. It is already evident 

 that, on the supposition of a given arrangement of the gas molecules, 

 values will always be obtained for the conductibility of gases which 

 will be of the same order as those found by Clausius. By proving 



