Mr. J. C. Maxwell on the Dynamical Theory of Gases. 197 



On the Rate of Variation of Q in an Element of Volume, Q being 

 any property of the Molecules in that Element. 



Let Q be the value of the quantity for any particular mole- 

 cule, and Q the mean value of Q for all the molecules of the 

 same kind within the element. 



The quantity Q may vary from two causes. The molecules 

 within the element may by their mutual action or by the action 

 of external forces produce an alteration of Q ; or molecules may 

 pass into the element and out of it, and so cause an increase or 

 diminution of the value of Q within it. If we employ the sym- 

 bol 8 to denote the variation of Q due to actions of the first 

 kind on the individual molecules, and the symbol ~d to denote the 

 actual variation of Q in an element moving with the mean velo- 

 city of the system of molecules under consideration, then, by the 

 ordinary investigation of the increase or diminution of matter in 

 an element of volume as contained in treatises on Hydrody- 

 namics, 



where the last three terms are derived from equation (59) and 

 two similar equations, and denote the quantity of Q which flows 

 out of an element of volume, that element moving with the velo- 

 cities u ! , v', w 1 . If we perform the differentiations and then 

 make u'=u, v' = v, and w' = w, then the variation will be that 

 in an element which moves with the actual mean velocity of the 

 system of molecules, and the equation becomes 



► (72) 



(73) 



Equation of Continuity, 



Put Q=M the mass of a molecule; Mis unalterable, and 

 we have, putting MN=p, 



dp , fdu dv dw\ 



which is the ordinary equation of continuity in hydrodynamics, 

 the element being supposed to move with the velocity of the 



