﻿942 Mr. A. H. Davis on the Cooliiui Poiver 



It is readily found that the substitutions effect the 

 eliminations satisfactorily i£ cv/k = l. For gases cvjk is 

 approximately equal to unity, and the substitutions should 

 be satisfactory on this ground. Also they are satisfactory 

 if the accelerations u v' w' of the particle are negligible 

 compared with vV 2 w, etc., as would appear justifiable for very 

 viscous fluids. 



In either of these circumstances the equations take the 

 form (U' V W being omitted unless cv/k=l): 



BU BV BW T'-^l 1 .^ 1 VI 



it &i &.■ ■ ~ap B'? 2 Br 



BJ?_ tt'i /B 2 U B 2 U B 2 U\ 

 Bf ~ + ^ 3f + 3i? 2 + B?V' 



Bn__ v ,^/B!_v yv yv\ 

 + \Bf + c^+Br 2 /' 



B»? 



Bn_ w , . f yw yw a»w\ 



Br - \a? 2 + a*? 2 + apr 



where 

 T a(U,Y,W ,T) B(U,V,W,T) 



B(U,V,W,T) 3(U,V,W,T 

 + "~ B? ^ + _ B«i 



Let us put the equation of the solid in the form 



m-»Jv){x,y,z)-]=0 (7) 



Thus, if v m /v changes, this amounts to considering instead 

 of the actual solid, similar bodies having linear dimensions 

 inversely proportional to v^/v. The direction cosines l u m l9 ?/ f 

 of the normal will remain the same at corresponding points, 

 and the boundary conditions become : 



At the surface U = V = W = 0, T=l, 1 



At the distance VT+^TF infinite U = l, V=m,W = n.F 



The system of equations (6) and (8) determine TJ V W II T 

 as functions of f , rj, f, and t l9 and substituting in the integrals 

 for the new variables their equivalents, we obtain 



TV, - ' , s = definite functions of 



