IS RARIFIED GASES 



The rmte of inowwe of each of these arising from the encounters of the 

 i. found by multiplying it by -. We may therefore call the 

 "moduli* of the time of relaxation" of this class of functions. 



The function f +V + C 1 is not changed by the encounters. 



Homogeneous functions of three dimensions are either solid harmonics of 

 the thiid outer or solid harmonics of the first order multiplied by f + V + ', 

 or combinations of these. 



o . 



The time modulus for solid harmonics of the third order is ^-. Note 

 dded May, 1879.] 



That of f 17, or (, multiplied by f + if + C is f*. 



(6) Effect of External Forces. 

 The only effect of external forces is expressed by equations of the form 



The average values of , 17, and their combinations are not affected by 

 external forces. 



(7) Variation of Mean Values within an Element of Volume. 



We have employed the symbol 8 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 3 to denote the actual variation within a specified 

 element. 



It' \IQ 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. 



