﻿924 Mr. A. H. Davis on Natural 



equal to unity. For gases, therefore, the above substitu- 

 tions should be fairly satisfactory on this ground. 



There is an alternative condition under which the 

 substitutions are satisfactory, even without cv/k being a 

 constant. The condition is that the accelerations u f , v', w r 

 of the particle shall be negligible compared with v\/ 2 u, etc., 

 which would appear to be justifiable for very viscous fluids. 

 It implies that on coming into the region of the hot body 

 a particle of the fluid almost immediately takes up its final 

 velocity and suffers but little subsequent acceleration. 



Consequently, the above substitutions appear satisfactory, 

 and the differential equations (3) and (4) take the following- 

 form. (U' V' W may be retained if cv/k = l, but otherwise 

 they must be omitted since u',v r , and w' are neglected*). 



BU\BV BW T ,_3jT B^T 3*T 1 



d£ + Dn "3? ~ df B>? 2 Br 



b? w s»? 2 as*/' 



dv ~ W BV Bt 2 /' 



3f _ l w + Bf + 3^ 2 + Br ' 

 where (U', V, W, T') = T j B(P, V, W, T) 



Y a(u,v,w,T,) w a(u,v,w,T) 



B»? Bf ' j 



* I am indebted to Mr. W, G. BicMey, M.Sc., for the following 

 notes : — ■ 



(a) If cv/k is not equal to unity, equations 8 are mathematically 



correct if we write — U' for U', etc. Evidently, if cvjh is large, the 

 term — U' is correspondingly small and may be omitted. Ketaining it, 

 however, the solution of (8) becomes 



r u, v, w P . 



0' ffi^tfy/*, ~^W^y73=dehmte functions of 



V &v I P \ c / \l6qac\V*, N cv} 



Kir) <*'*•>'■*}, 



The experimental curve shows that the cccurrence of c^/A; in these 

 functions is in such a manner that large variations in cvjk have 

 imperceptible effects. 



(b) Equation (5), and the resulting one (8), would be more general if the 



term — LI were introduced on the left-hand side. This would 



include unsteady motion, but would in no way affect the changes of 

 variables. 



(8) 



