﻿of a Stream of Viscous Fluid. 941 



temperature excess, the three components of its velocity, and 

 the non-hydrostatic part of its pressure. If /, ?», n. are three 

 direction cosines of the general stream of velocity " v^, 9 ' we 

 have as boundary conditions : 



At infinite distance from! u, v, w= v M (/, m, a), 



the origin J (P, t) = 0. 



At the surface of the solid (u,v,w) = 0, t—Q. 



a) 



The hydrodynamical equations of continuity and of 

 motion are 



"du t 'dr "dw IBP , 2 1 



d* oy oz p&v 1 . 



ibp . _ 2 ibp , , ™ 1 



/> 0// P03 J 



i/', */, and bo' being the accelerations of the fluid parallel to 

 the axes. 



Let k be the thermal conductivity of the fluid and c its 

 heat capacity per unit volume, then r', the rate of change of 

 temperature for a given particle with respect to time, is 

 given by 



t' = (£/c)V 2 t (3) 



Also we have 



, , , , d(«, v, iv, t) d(u, v,w,t) 



U , V , IC , T = U s- 1- V ^ 



ox oy 



B K v , ic, r) B (u, v , w, t) . 



+ M; ^ — + gj — . w 



The equations in P, w, r, to are everywhere quite separate 

 from those in 6, and hydrodynamically the problem is the 

 same as that where = 0, the motion of the fluid being- 

 determined entirely by the given general stream and the 

 configuration of the immersed body. Everywhere u, v, and w 

 will be proportional to i\ . , and P proportional to pv^ 2 . 



Let us endeavour to replace the independent variables 

 t, x, y, z and the functions t, u, v, w, P by others t 1} f , rj, f, T, 

 U, V, W, II respectively proportional to them but whose 

 ratios are chosen to eliminate 0, kjc, p, v, v x . 



Let us consider the following substitutions : 



l v, r=0>»(*,y, 0, («. ', »}-».(u,y f w),i 



