and its Application to the Molecular Motions of Gases. 193 



e==u (r 



97) 



The equations resulting from (96) by that addition and subtrac- 

 tion are then : — 



8E = fT81og(g + ?^8c; .... (98) 

 3(U-T) = §TSlogS + 2^5c. . . (99) 



We must now, finally, consider more closely the sum X -j- , 



which occurs in equations (98) and (99), in order to ascertain 

 its signification. 



The sign of summation refers to the six quantities c v d v c 2 , 

 dq, c 3 , c/g, each of which determines the position of one of the 

 six walls bounding the parallelepiped, and only occurs in that 

 part of the ergal which relates to the force exerted by that wall. 

 Calling the coordinates of a point at present <#,, # 2 , and x 3 , we 

 will first consider the wall which is perpendicular to the ^-direc- 

 tion and is situated on the positive side, at the distance c Y from 

 the origin of coordinates. The force exerted by this wall on the 

 point along the ^-direction will, accruing to our former nota- 

 tion, be represented by F'(c,— x^)- } and the part of the ergal 

 referable to this force is ¥(c 1 —x l ). Accordingly we can repre- 

 sent that force which conversely the point exerts on the wall 



by —¥ , (c l — 3s 1 ) or -^ — , and, since in the course of the 



period it is variable, employ the symbol for its mean value : — 



d¥(c l —£c l ) 



dc x 



If we suppose this expression formed for each of the points 

 present in the vessel, and all the resulting expressions added, 

 we obtain the total force exerted by all the points, or the pres- 

 sure which the Wall suffers from them. But the sum of all 



those expressions is no other than — - — ; and hence the pro- 

 duct — - — 8c x represents the external work performed in displa- 

 ac-i 



cing the wall to the extent Sc r 



What we have said of one wall holds good also for the other 

 Phil. Mag. S. 4. Vol. 50. No. 330. Sept 1875. O 



