On Steady Motion in an Incompressible Viscous Fluid. 343 



in which u, v, w denote the component velocities of a fluid 

 particle in the directions of #, y, z respectively, p is the den- 

 sity of the fluid, /jl the coefficient of viscosity, and 



dt dt dx dy dz 



d? 



d 2 . d? 



V ~ da? + dy* + dz 2 ' 

 Denoting the components of the spin by f , 77, f, we have 



*._±(dw dv\ 

 *~ 2 \dy "IzP 

 , fdu dw\ 



Y _\(^_ __du\ 

 ^~*\dx dy)' 



(2) 



We may observe just here, that from equations (2) we can 

 obtain 



v ^=$-f 



dz 



_d% 



dy 



dx dz 



dy dx 

 In the case of steady motion we have 



du _ dv_ dw _ n 

 dt ~~dt~dt ' 



and equations (1) thus assume the form 



{du du du v 1 dp _~ 



(3) 



{ 



{" 



dv dv dv 



U— +V^r +W^r- 



dy dz 



dx 



dw dw 



dx dy 



; 



Yf + 



dp 

 dy 



f*v\ y 



(4) 



£-*}+£-** 



Assume that the forces X, Y, Z possess a potential V, and 

 write 



2 2 



q' = u' + v' + w<: 



