Mr. J. C. Maxwell on the Dynamical Theory of Gases. 195 



M (u -f- f ) . Substituting this for Q, we get for the quantity of 

 momentum transferred across the plane in the positive direction 



(u-it!)up+fp (60) 



If the plane moves_with the velocity u, this expression is re- 

 duced to pp, where f 2 represents the mean value of f 2 . 



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 attrac- 

 tions 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—v!)vp + gyp, . . . . » (61) 

 and 



(u-u')wp+I%p, (62) 



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



If the plane moves with the mean velocity u of the fluid, the 

 total force exerted on the medium on the positive side by the 

 projection of molecules into it from the negative side will be 



a normal pressure f 2 p in the direction of x, 



" a tangential' pressure %r)p in the direction of y, 



and a tangential pressure f £/? in the direction of z. 



If X, Y, Z are the components of the pressure on unit of 

 area of a plane whose direction-cosines are /, m, n, 



X^lj&p + mijiqp + ngZp, "j 



Y=^p + mfa+nffy, L • .'■-. (63) 



Z = Wfr + ™vSp+nt*p. J 



When a gas is not in a state of violent motion the pressures 

 in all directions are nearly equal, in which case, if we put 



?P + V*P + Fp = 3p, (64) 



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