THE DYNAMICAL THEORY OF GASES. 53 



(a) Tramference 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 is zero, the expres- 

 sion is reduced to 



(u-u')MN=(u-u')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 components are u, v, w. 



(ft) Transference of Momentum across a Plane System of Pressures at am/ 



point of the Fluid. 



The momentum of any one molecule in the direction of x is M(u + ). 

 Substituting this for Q, we get for the quantity of momentum transferred 

 across the plane in the positive direction 



(u-u')up + ?p (60). 



If the plane moves with the velocity u, this expression is reduced to 'p. 

 where f l represents the mean value of f . 



This is the whole momentum in the direction of x of the molecules projected 

 from the negative to the positive side of the plane in unit of time. The 

 mechanical action between the parts of the medium on opposite sides of the 

 plane consists partly of the momentum thus transferred, and partly of the 

 direct attractions or repulsions between molecules on opposite sides of the plane. 

 The latter part of the action must be very small in gases, so that we may 

 consider the pressure between the parts of the medium on opposite sides of the 

 plane as entirely due to the constant bombardment kept up between them. 

 There will also be a transference of momentum in the directions of y and z 

 across the same plane, 



(u-u')vp + fr)p (61), 



and (u-u')wp + i%p (62), 



where 77 and f represent the mean values of these products. 



