351-354] Maxwells Theory of Viscosity 295 



The solution of equation (708) is 



ii?-v* = [u- ^] t= , a- 11 "*, 

 shewing that u* v' 2 decreases exponentially with the time. The value of 



u? v' 2 is reduced to 1/e of its original value in a time . This time is called 



rjv 



by Maxwell, the " time of relaxation." 



Analysis of a similar kind enables us to find the rate at which any other 

 deviation from Maxwell's law subsides. For instance, if in equation (707) we 

 put Q = uv, and use the value of Auv given by equation (697), we obtain 



= - 



ot 



duv 



= rjvuv. 

 ot 



1 

 Thus the value of uv also decreases to lie of its amount in a time . 



f]V 



It is not possible to find the absolute value of this " time of relaxation " 

 from equation (709). We shall, however, be able to compare it with the 

 known values of coefficients of viscosity, and shall find that it is extremely 

 small. 



Viscosity. 



354. We have already seen ( 17 5), that the system of pressures at any 

 point in the gas is given by the equations 



...... -.. .................... (710). 



= /DUV, etc.J 



To arrive at these formulae we have taken nr xx = ^xy = . . . = in equations (363). 

 This does not mean that we neglect the intermolecular forces which vary 

 inversely as the fifth power of the distance, for we have already taken full 

 account of these forces in supposing that two molecules are in collision as 

 soon as these forces become appreciable ; in neglecting the system of pressures 

 T*XX> T^xy* etc. we are merely assuming that no forces exist other than those 

 which vary inversely as the fifth power of the distance. 



When the gas is in its normal state, the quantities P xx , P yy , P zz each 

 become identical with p, the pressure. When the gas is not in its normal 

 state, let us define p by the relation 



p = $p(\j* + \i* + w~ 2 ), 



so that p is still two-thirds of the energy per unit volume, and becomes 

 identical with the hydrostatic pressure in the normal state. 



