or 



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



moving with a velocity of which the part resolved parallel to x is 

 uK The velocity of the plane relative to the molecules we have 

 been considering is u'— (u+ f ) ; and since there are dlS of these 

 molecules in unit of volume, it will overtake 



such molecules in unit of time, and the number of such mole- 

 cules passing from the negative to the positive side of the plane 

 will be 



Now let Q be any property belonging to the molecule, such as 

 its mass, momentum, vis viva, &c, which it carries with it across 

 the plane, Q being supposed a function of f or of f, 97, and £ 

 or to vary in any way from one molecule to another, provided it 

 be the same for the selected molecules whose number is d~N, then 

 the quantity of Q transferred across the plane in the positive 

 direction in unit of time is 



(w-wOjQ^N+jWN. . -. . (57) 



Ifwe put QN for J Q^N, and |QN for f j-QrfN, then we may 

 call Q the mean value of Q, and fQ the mean value of £Q, for 

 all the particles in the element of volume, and we may write the 

 expression for the quantity of Q which crosses the plane in unit 

 of time 



(M-tt')QN+|QN (58) 



(a) Transference of Matter across a Plane. — Velocity of the 



Fluid. 



To determine the quantity of matter which crosses the plane, 

 make Q equal to M the mass of each molecule ; then, since M 

 is the same for all molecules of the same kind, M = M; and 

 since the mean value of f is zero, the expression is reduced to 



(«-«')MN=(a-B , )p (59) 



If u-=u' } or if the plane moves with velocity u, the whole excess 

 of matter transferred across the plane is zero ; the velocity of 

 the fluid may therefore be defined as the velocity whose compo- 

 nents are u, v, w. 



(ft) Transference of Momentum across a Plane.— System of 

 Pressures at any Point of the Fluid. 



The momentum of any one molecule in the direction of x is 



