ARISING FROM INEQUALITIES OF TEMPERATURE. 693 



volume, and p a new coefficient which we shall afterwards find to be the 

 coefficient of viscosity. 



Equation (15) may now be written 



(20) 



where the integrations are all between the limits oo and + <x> , and f t and /, 

 are of the form 



...................... (21) 



(> V' ) being small compared with unity. 

 We may write F in the form 



F= (2A) (o 



(22) 



where each combination of the symbols afty is to be taken as a single in- 

 dependent symbol, and not as a product of the component symbols. 



(4) Mean Values of Combinations of 77, . 



To find the mean value of any function of f, 77, for all the molecules 

 in the element, we must multiply this function by f, and integrate with respect 

 to f, r), and . 



If the non-exponential factor of any term contains an odd power of any 

 of the variables, the corresponding part of the integral will vanish, but if 

 'it contains only even powers, each even power, such as In, will introduce a 



into the corresponding part of the integral. 

 First, let the function be 1, then 



1 = Ifl&ndt (23) 



