82 VISCOSITY OF GASES 209 



so rough and uneven that a regular flow immediately over 

 them is scarcely even conceivable. The forward motion of 

 the gas becomes almost entirely annihilated, so that we are 

 justified in looking on the external friction as infinitely 

 great and in putting the slip equal to zero, as was in 

 general done in the older investigations on the friction of 

 gases. 



In the limiting conceivable case, in which the mean 

 motion of all the particles of gas close by the wall is zero, 

 we must assume that the velocity of flow which those 

 particles have that are coming towards the wall is entirely 

 taken up by those which are coming from it ; each particle, 

 therefore, which meets the wall must not only lose on 

 impact its share of the general velocity of flow, but return 

 with an equal component of velocity in the opposite direction. 

 The loss which it has experienced by the impact would, 

 therefore, in the case considered, amount to double the 

 velocity of forward flow. 



In reality the loss of velocity will probably be less. I 

 represent it then by @v, where v denotes the mean velocity 

 of flow and (3 a constant whose value lies between and 2. 

 By the impact of a particle of gas of mass m against the wall, 

 the amount of momentum in the gas is diminished by ftmv. 

 The whole lessening of the momentum in unit time is 

 obtained from this by multiplying it by the number of 

 particles which strike the w r all in this time. 



In the determination of the pressure by summation of 

 the kinetic energy of all the impacts we found in 11 and 

 12, by the method first employed by Joule, that the number 

 of particles which strike unit area of the wall in unit time is 

 %NG, where, as before, N is the number of particles in unit 

 volume and G is a mean value of the speed. We cannot, 

 without further consideration, apply this to the case under 

 consideration, because the method there employed is strictly 

 admissible only for the calculation of the kinetic energy, and 

 not of other magnitudes. This value, therefore, for the 

 number of impinging particles is only approximately correct, 

 and for accuracy we must replace it by the number JVH calcu- 

 lated in 37 and 41* of the Mathematical Appendices, which 



p 



