and its Application to the Molecular Motions of Gases. 33 

 and from it we can at once derive the following equations — 



n + 2 



e = mx' :2 i= Cc(mx' 2 ) 2 " » 



_ 2 



« = ^=:C'¥K)'S 



from which, conversely, the following equations also can be 

 formed — 



2)i 2n n 



-"-(t) = fe) =(ov)- (^ 



From these, taking into consideration (13), result : — 



-^ m—rz 2 — n 



H — — r' 2 = 

 11 2 2« 



■mx l2 = 



2-n /CcV- 2 

 2/i 



can 



H^7^^ m ^^riY +2 . 



H+~^ 



2n 



2n X 



e \ n+2 

 Cc) '' 



H=- w^ /2 =-(^ 1 ) 

 n n \C V/ 



(18) 



Equations of this form are valid for all three coordinate-direc- 

 tions ; and when we form the sum of each three equations belong- 

 ing to one another, at the same time designating the total vis 

 viva by T, and the total ergal by U, and the total energy by E, 

 we obtain : — 



2n 2a 2n "^ 



2n 2n 2n 





^ 



j 



§ 5. As a further example we will discuss a case which we shall 

 be able to make use of subsequently, in the investigation con- 

 cerning the molecular motion of gaseous bodies. 



Namely, let us suppose that a material point moves in a rec- 

 tangular parallelepiped-shaped vessel, by the sides of which it 

 is repelled. The force exerted upon the point by one of the 

 walls shall depend only on its distance from that wall, and be 

 proportional to a negative power of the distance. It may further 

 be supposed that the force diminishes so rapidly as the distance 



Phil. Mag. S. 4. Vol. 50. No. 328. July 1875. D 



