Prof. Clausius on the Conduction of Heat by Gases. 425 



side have in general greater velocities than those which pass from 

 the positive to the negative side, so that, compounding the mo- 

 tions of all impinging molecules, we obtain a certain small mo- 

 mentum in the direction of positive x. 



This common momentum remains unaltered by the impacts ; 

 but at the same time a complete change occurs in the directions 

 of the motions, in so far that the molecules are impelled in all 

 directions without distinction. If therefore the motion were, 

 before the impacts, unequally distributed in the various direc- 

 tions (the number of molecules moving in certain directions 

 being greater than the number moving in other directions, or 

 their velocities being different), we must nevertheless assume 

 that all these inequalities would be equalized by the impacts ; 

 and that, excepting the general motion in the direction of posi- 

 tive x } no distinction between the different directions would 

 remain, but that all directions would be equally represented 

 among the new motions. 



It thus becomes easy to give a definite representation of the 

 state of motion of the molecules emitted from the stratum, if, 

 instead of regarding the velocities of the separate molecules, we 

 content ourselves with knowing the mean velocity for each direc- 

 tion. First, let the molecules be conceived as moving equally in 

 all directions, so that an equal number of molecules, and all with 

 the same velocity, move in each direction, and then let a small 

 component motion in the direction of positive x, equal for all the 

 molecules, be conceived as added to all these motions. The 

 directions and velocities of the motions will be thereby somewhat 

 chauged ; and the system of motion so modified represents the 

 motions of the molecules emitted from the stratum*. 



§ 6. "VVe can define this system of motion mathematically as 

 follows. 



Let the velocity possessed by all the molecules before the mo- 

 dification be A. The component velocity to be added to it in the 

 direction of positive x can, according to what has been said 

 above, be only a very small magnitude, of the same order as the 

 mean excursions of the molecules. But as this latter is depend- 

 ent on the density of the gas, it is not the same at every point 

 of the quantity of gas under consideration ; and it will therefore 

 be convenient to substitute for this variable magnitude, in what 

 follows, one which has a determinate value for each gas. For 

 this purpose we will assume a certain condition as a normal con- 



* In the memoir quoted above (Phil. Mag. S. 4. vol. xx.), Maxwell, in 

 determining the conduction of heat, has disregarded the circumstance that 

 the molecules emitted from a stratum have an excess of positive momentum, 

 but has tacitly assumed in his calculations that the molecules are emitted 

 equally in all directions. 



