CONSTITUTED OF SPHERICALLY SYMMETRICAL MOLECULKs 437 



Tin- value. of A,,Q may IK- obtained from A U Q by making in' m, v = v, 



throughout. 



Thr problem l*forr us consists in the evaluation of the integral on the right-hand 

 side of the last equation, with certain special forms of Q. Before proceeding with 

 this we shall first write down the forms assumed by the equation of transfer (l) in 

 these cases. 



2. SfH-rin/ /'..///* of tin- Kijiintinn of Transfer. 

 The equation (l) is more convenient for use in the equivalent form 



[DQ_ _ _ 



v [_Dt 3V Dt dv ' Dt dw ' Dt 



In dealing with the problem of heat conduction we shall have to put 

 Q = u(u 1 + v a +tif t ) and Q = u'+v 3 + u?; but in this case it will be sufficient to 

 consider the case of a gas at rest, so that M O = v = w = 0, and the left-hand side of 



tin- above equation becomes simply vr*- On the right-hand side, in finding 

 ^r> : i we must, of course, not put u a = v = w = till the differentiation has 



been performed. Thus, when Q = w a +v s +w* we have Q = u 3 +v i +w 3 +\J 3 + V 3 + W, 

 so that r- 3 ^- = TT 3 ^ = ^- = 0, and the equation of transfer becomes* 



(9) 



where we have written q for ^ U'+V^+W 2 ; A n (u 3 + v*+tt?) vanishes because the 

 energy of the molecules, being wholly translational, is unaltered by the encounters of 

 the molecules m among themselves. 



In writing out these equations of transfer, it is customary and sufficient to neglect 

 the mean values of odd functions of U, V, W in comparison with the mean values of 

 even functions, and also to neglect the differences between the mean values of 

 f<>rr<'sj)<ni(l/ii</ even functions (such as U*, V a , W J ) in comparison with these mean 

 values themselves ; thus we may write tP = V a = W a = g, and neglect UV, VW, WU 

 in comparison with </. Similarly we may neglect UV(U !l -l-V a -i- W) in comparison 



with U^IP + V+W), and the latter we may calculate as if MAXWELL'S law of 



* The suffix on tin- right-hand side is to indicate that we are considering a gas at rest. Similarly in 

 eijuation (10). 



