and its Application to the Molecular Motions of Gases. 41 

 equations (30) : — 



w = c n u — — \yl) 



du 



The hitherto deduced expressions of h—w, k, and h refer to 

 only one coordinate-direction. But of course equations of pre- 

 cisely corresponding form are valid for all three directions — 

 which equations are obtained when in equations (37), (43), and 

 (50) first the index 1 is annexed to each of the letters h, w, k, i, 

 c, u, and c, then the index 2, and finally the index 3. Remem- 

 bering further that we may put 



V=m{h l + h 2 +h 3 ), 



~E = m(k 1 + k 2 +k 3 ), 

 we get 



+e ^Kwi c ^)l' 



and corresponding equations for E and U. If by the sign of 

 summation we abbreviate the three terms on the right-hand side 

 in each, the three equations become 



n+2> 



/ e n —3\ 



(52) 



wherein (/>, ty, and % are the functions above determined by 

 equations (36), (42), and (49). 



§ 7. In the equations of the preceding section, the quantities 

 h> h) h nave Deen employed for the determination of U— T, for 

 the determination of E the quantities e v e 2 , e 3 , and to determine 

 U the quantities u Xi w 2 , w 3 . For many investigations, however, 

 it is advantageous to effect these determinations by means of one 

 and the same system of quantities, to which purpose the quanti- 

 ties w { , Wq, w b are particularly adapted. Of course, as in all the 

 previous equations, together with them occur also the constants 



C V C 2> C 3* 



When the second of the equations (30) is divided by the first, 



