146 HEAT. 



y 



But an equal mass p comes up through EF from below, and if we 



suppose that this has on the average the momentum of the layer indi- 

 cated by the lower dotted line, distant L below EF, the momentum parallel 

 to u, brought up through EF, is 



Hence the gas above loses momentum equal to the difference of these, 

 viz. : 



V Lv 

 P 3 ' d 



while the gas below gains an equal amount. But this transfer measures 

 the tangential force F. Then 



3 ' d 



But we also have F = r^-, where 77 is the coefficient of viscosity, 



d 



whence 



pVL 







Maxwell's more exact investigation gives r) = '30967/3LU, where U is 

 the mean value of the velocities. 



We have already seen that L/> is probably constant for a constant 

 temperature. V is also constant for a constant temperature, so that 77 

 should be independent of the density of the gas. This result, first obtained 

 from theory by Maxwell, was afterwards verified by direct experiment. 

 Since V increases with the temperature, 77 should also increase, a result 

 borne out by experiment. 



Maxwell's method of obtaining 77 consisted in principle in allowing 

 a horizontal circular disc suspended by a wire to vibrate about its axis, 

 another horizontal disc being fixed close below and parallel to it. The 

 layer of gas between the two discs was, therefore, sheared by the motion, 

 and the viscous resistance of the gas gradually " damped " the vibrations 

 of the moving disc. From this damping 77 could be calculated, and it 

 was found to be independent of the pressure within a wide range. If, 

 however, the pressure is sufficiently reduced the method fails through 

 slip of the gas on the surface of the discs. And even if there is no 

 slip, it the pressure is so far reduced that the M.F.P. is comparable with 

 the distance between the discs, evidently the method of investigation is 

 no longer admissible. 



The following values of t\ at C. are taken from the extensive tables 

 given by Meyer (Kinetic Theory of Gases) : 



Air ........ -00017 



Hydrogen ....... -00008 



Oxygen ....... -00019 



Water vapour ...... -00009 



While the viscosity increases, as the theory indicates, with the tempera- 

 ture, it does not increase merely in proportion to V or in proportion to 



