﻿448 



Then 



Mr. G. B. Jeffery on the 



/3v\ 3v A 



~dt 



u / 7 3« , 3« j 3*\ , v / 7 3/3 , 3£ 3/3\ 

 "sV 3^ 3y 3~/ 



+ « 





JzAfl^U* 



+ r / 



( 



+ m 



I 3 a V'2 3^/ ' "'3a 



\h 2 "by) 3*W3« 

 1,3/1 3y\, 3/1 3y\ , , 3 /l By\l 



t + " i l vAh s) +m swv +n s U 3^; I; 



Remembering that a = 7^, ft = 7i 2 ?*, 7 = h 3 w, and using 

 the nine relations of the type * 



3 f i B ^ = - ^ ^- f M _ ^7 3 /1\ 



~3*U 3.J a* 3# W a* 3yU/ 



3_/l 3/3\_/^ 2 3« 3 / l\ _3 / 1 3y\_*a 3« J) /1\ 

 3* U 2 3W /'1 3a? 3/3W ' 3*U 3 3^7 ~ Ih 3* 3yU / 



and finally taking for the direction X the normal to the 

 surface a = const., we obtain 



3 /r 



+ similar 

 terms in ff j. 



-htfc±L.(± 



3«vW ] '^nW 



... (7) 



We can now write down the transformed equations of 

 motion. 



Let v be the kinematic viscosity so that v — fijp, and let 



®__3 i _ 7 3 l7 3 , , 3 



^ = 3V f/ ^3« + //2 '3^ + //3?6, 37' 



(8) 



* Ibid. Note on moving axes. p. 539 ; or Lame, Coordonnees Curvilignes, 

 p. 74. 



