1895.] 



of a Viscous Incompressible Fluid. 



317 



Equations (9) may be written in the form 

 dr 



If we write 





.(10). 



and therefore 



f ?7 — i^ — log roojdz—iV—V'^ log ro) 1 rfr = mdx, 



U—v^ log r(o 



dz' 



V— V ^ lo£C rw = — m ^ 



97^ 





•(iiX 



then equations (10) may be written in the form 



3^ + 2mft):^ = 0, 



or or 



oz oz 



Eliminating <^ from equations (12) we obtain 



a (mo), x) _Q 



d(r, z) 



.(12). 



or 



2mco=f(x) (13). 



Multiplying the first of equations (12) by dr, and the second 

 by dz, and adding, we have 



d<l>+f(x)dx = ^> 

 from which by integration we readily deduce 



P^W 



where 



+ F + 2 2' + -^ (%) = const. 

 F(X) = (fix) dx- 



.(14), 



Also from equations (11) we readily obtain 



or 



dr \ dr 



