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Yl. Oa the Distribution of the Molecular Velocities in Gases. 



By C. Cellerieb*. 



THE molecules of a gas are, according to the modern theory, 

 withdrawn from each other's action during almost the 

 whole of their passage, which takes place in this case in 

 straight lines and with a uniform motion. In all that follows, 

 we shall suppose that a homogeneous gaseous mass, every- 

 where at the same temperature, is contained in an invariable 

 enclosure impermeable to heat. It is then in a permanent 

 5:. .:-. The molecular velocities, to which a mean value is 

 often attribute I. are really unequal, constantly modified by 

 the collisions : and after a certain time the proportion of the 

 molecules possessing a more or less great velocity will no 

 longer change : the aim of this investigation is to determine 

 their law — that is to say, the final distribution of the velocities. 

 Ehe men of science who have occupied themselves with the 

 molecular collisions, among others M. Clausius, have in general 

 likened them to that of two solid, perfectly elastic spheres, 

 equal in mass and radius, at least in the conditions of perma- 

 nence which we have just mentioned. We shall attribute to 

 the molecules any form whatever, variable from one to another, 

 so as not to exclude the cases in which they are regarded as a 

 grouping of atoms, those in which they are supposed to pos- 

 sess polarity, &c. "With this exception, we shall admit the 

 other hypotheses contained in the preceding point of view, 

 and which may be summed up thus : — 



1. The sum of the vires vivo? of translation of two molecules 

 is not altered by the collision ; 



2. All the masses are equal; 



3. The collision may be compared to that of two solid 

 bodies. 



It must be remarked that the total vis viva of translation in 

 the whole of the gas, measuring the pressure, is permanent ; 

 it is equally invariable for each of the small portions into which 

 the mass may be divided : therefore the first hypothesis, like 

 the second, consists in neglecting some irregularities which 

 may present themselves in one direction or the other, and 

 which will but little modify the result sought. Hence, if the 

 hypothesis of solidity be admitted, the laws of the collision for 

 two spheres or two surfaces of any kind will certainly be the 

 known laws — that is to say, that the projection of the velocity 

 of one of the centres of gravity upon the common tangent 



* Translated from the Bibliotheque Unh-erseUe, Archives des Sciences 

 physiques et XatureUes, Oct. 15, 1881, t. vi. pp. 3-37-573. 



