4:2 I Prof. Clausius on the Conduction of Heat by Gases. 



poncnt the motion of the common centre of gravity of the two 

 spheres ; the second component must then he the motion of the 

 two spheres in question relatively to their common centre of gra- 

 vity. The former motion is equal and in the same direction for 

 both spheres ; the latter motion is equal and opposite for the 

 two spheres. The former is not altered by the impact ; the latter, 

 on the other hand, is altered exactly in the same way as it would 

 be if it existed alone and there were no common motion. In 

 relation to it, what has already been said of the case of two 

 spheres moving in parallel straight lines, and which assume 

 various directions after impact, according to the point at which 

 they strike each other, is applicable. It thus becomes evident 

 how far the motions after impact, of molecules which impinge 

 upon each other irregularly, are dependent upon their motions 

 before impact, and how far they are independent of them. The 

 motion of each sphere consists of two components, the first of which 

 is entirely determined, both as to magnitude and direction, by the 

 motions before impact, and the second of which has also a deter- 

 minate magnitude, but may have an infinite number of different 

 directions, every direction in space being equally probable with every 

 other*. 



§ 5. In applying this result to the impacts which occur among 

 the molecules, we may assume that here .also only that portion 

 of the motion possessed before impact by two impinging mole- 

 cules remains unchanged in magnitude and direction which is 

 common to both molecules, that is, the motion of their common 

 centre of gravity ; while the direction of the second component 

 of their motions may be altered in so many ways that it may 

 with equal probability assume any direction in space whatever. 



Let us now consider the whole number of molecules which 

 impinge upon each other in one unit of time within the infinitely 

 thin stratum spoken of in § 3. The motions which they possess 

 before the impact have already been discussed in § 3 : all possible 

 directions are represented among their motions ; but the mole- 

 cules coming from the warmer side have in general somewhat 

 greater velocities than those which come from the colder side. 

 Since, according to our assumption, the temperature diminishes 

 as x increases, the warmer side is the negative side, that is, the 

 one on which x has a smaller value than it has in the stratum : 

 hence the molecules which pass from the negative to the positive 



* This result shows very plainly what a great departure it is from the 

 real state of the case to regard, like Jochmann and Hoppe, in an approxi- 

 mate consideration of it, only central impact, since, instead of an infinite 

 number of different directions, there is thus obtained only one determinate 

 direction, and that one which is especially favourable to the transmission 

 of vis viva. 



