GASES ARISING FROM INEQUALITIES OF TEMPERATURE. 
24.3 
2f—T-O. 
tq, 
VC 
The rate of increase of each of these arising from the encounters of the molecules is 
found by multiplying it by —We may therefore call - the “ modulus of the time 
of relaxation ” of this class of functions. 
The function is not changed by the encounters. 
Homogeneous functions of three dimensions are either solid harmonics of the third 
order or solid harmonics of the first order multiplied by or combinations 
of these. 
The time modulus for solid harmonics of the third order is - 
1879.] 
That of rj, or £, multiplied by Q is \ 
O ft 
(6.) Effect of External Forces. 
The only effect of external forces is expressed by equations of the form 
« =x . oo 
The average values of rj, £ and their combinations are not affected by external 
forces. 
(7.) Variation of Mean Values within an Element of Volume. 
We have employed the symbol S to denote the variation of any quantity within an 
element, arising either from encounters between molecules or from the action of 
external forces. 
There is a third way, however, in which a variation may occur, namely, by molecules 
entering the element or leaving it, carrying their properties with them. 
We shall use the symbol 5 to denote the actual variation within a specified element. 
If MQ is the average value of any quantity for each molecule within the element, 
then the quantity in unit of volume is pQ. We have to trace the variation of pQ. 
We begin with an element of volume moving with the velocity-components U, Y, W, 
then by the ordinary investigation of the “ equation of continuity” 
sCQ/=]+|[Q(«+f-U)]+| y [Q(«+’)-V)]+|[Q(to+c-w)]=4Q . . (37) 
If after performing the differentiations we make U = u, X=v, W =w, the equation 
becomes for an element moving with the velocity (u, v, w) 
2 x 2 
-.—Note added May, 
