and its Application to t/te Molecular Motions of Gases. 113 



action, and at the same time denote by e their total volume, 



putting 



N 4 3 (80) 



The equations will then be 



ab*=Y-e, 1 (81) 



§ I4. "We can now limit our further investigations to the case 

 in which, in a rectangularly parallelepipedal vessel a vast num- 

 ber of material points are in motion, not influencing one another, 

 but only subject to forces from the sides of the vessel causing 

 them to rebound. 



The force exerted on a point by a side of the vessel shall be 

 perpendicular to the side, and represented by a function of the 

 distance. If, then, we introduce rectangular coordinates parallel 

 to the edges of the parallelepiped, the origin lying somewhere in 

 its interior, x denoting one of the coordinates, and if further, of 

 the two walls perpendicular to the direction of this coordinate, 

 that situated on the positive side has the distance c, and that 

 situated on the negative side the distance c' from the origin of 

 coordinate, so that c — x and d -\-x are the distances of the moving 

 point from the two walls, we can represent the force which acts 

 on the point along the ^-direction by an expression of the form 



¥{c^x)-¥{c J + x) i 



in which F' signifies a function which, we will assume, is very 

 near equality to zero for all greater values of the argument, and 

 only for very small values does its quantity become sensible, but 

 then, on the argument still further diminishing, increases rapidly. 

 Let F denote the integral of the function F'; the part of the 

 ergal referring to the ^-direction will, for the point under con- 

 sideration, be expressed by 



l\c-x)+¥(c' + x). 



The motions of the material points are to take place in all 

 possible directions, and so that all possible directions are equally 

 represented. 



The velocities of the different points are to be different ; and 

 the law which prevails in this respect we will now express in the 

 following manner. For this purpose we select the quantity 



9 \17/ w ^^ cn we ^ ave au ' ea dy considered; and as in the course 

 of the motion it is indeed constant during the greater portion of 

 Phil. Mag. S. 4. Vol. 50. No. 329. Aug. 1875. I 



