﻿Equations of Motion of a Viscous Fluid, 447 



This can be transformed into an expression which while it 

 appears more complex, is in reality simpler in application, 

 namely, 



cnrl a curl v = 



[■ -«*$&© w 



This expression is simplified if it is possible to choose one 

 or more of the functions a, /3, 7 so that they are solutions of 

 V 2 = 0, or in the language of Lame, so that they are tliermo- 

 metric parameters. 



It remains to find appropriate expressions for the com- 

 ponents of =p— . In Cartesian coordinates 



and this may be written in vector form 



The component of this vector equation in the a direction is 

 /Dv\ _/3v\ , 7 B?^ , 7 Bw Bit 



Let \ be any fixed direction in space whose direction 

 cosines are I, m,n } then the component of v in this direction 

 is 



v A 



« /,B« , 3« , 3*\ , v/.'dff, ays 1 B/3\ 



