an Incompressible Viscous Fluid. 

 then there results 



and also 



If s = <f}ij then 



dx dx dx \ 



ds 3 ds 2 _ ds 



dy dz dx 



dsi ds 3 ^_ ds 



dz dx dy 



ds 2 ds 1 _ ds 



dx dy dz 



} 



351 



(30) 



(31; 



(»+!)& (32) 



Since the functions s l7 s 2 , s s fulfil all the conditions to which 

 f, 7j, f are subject, we may write 



£ = Sl, V = *2, Z=H 



(33) 



5 itself being still an arbitrary function. We can consequently 

 write 



TT dS dS i. ds ds 



dy * dz' * dy J dz 



Tr <rZS dS ds ds 



dz dx dz dx 



^ <iS dS t, ds ds 



* eta <% ' J dx dy 



(34) 



when all the conditions to which these quantities are subject 

 will be fulfilled, provided 



V 2 S=-s and V 2 s=0. 



Using the solution already given for the determination of S, 

 we can now write 



since 



o \ dy 

 dRi dR 



dy y dz 



V 

 O&c. 



202 



