152 Physical Properties [CH. vn 



173. If we write 



u = u + u, etc., 



as in 26, we have u = u , and u = 0. We therefore have 



o o 



and from this and similar equations, by addition, 



o o _ o 



5- (l/W 2 ) + 5- (l>W>) + 5- (PUW) 



das x 9y 9,0 v 



3 9 9 \ / 9 , , 



+ " + w u + u (l/Mo) + 



^\ r\ *\ 



(^u" 2 ) + E: (J'uv) + 1- (^uw). -(359). 



Also, by the equation of continuity (equation (352)), 



d , . du dv 

 -j- (*&) = v ~TT + u o -r. 

 dt^ dt dt 



du 

 ' ~dt~ 



so that on adding corresponding sides of this equation and (359), we 

 obtain 



W* / \ . t/ / T\ . \j / \ C/ / \ 



d 



The left-hand member of the equation is, however, identical with the bracket 

 in equation (358), so that this equation now becomes 



/ d 9 9 d\ 777 



v T: + u -= h v r- + w n z-} u mdxdydz 

 \dt ox oy ozj 



(vu 2 ) + ^(vUv)+^-(vuw) \mdxdydz...(36Q). 

 9y v 9^ v '\ 



174. We now proceed to examine more closely the system of forces 

 which act upon those molecules of which the centres are inside the element 

 dxdydz the system of forces which we have so far been content to denote 



K-ir V Y" ^ V V 7 



Dy 2^3. , 2t 1 , 2t&. 



