450 Mr. STOKES, ON THE STEADY MOTION 



1 dp ds ds ., „. 



- p £ = - S d-r- W T*> (15) ' 



di" - S Wr~ W di' W> 



1 dp dw t „dw 



P 

 and the equation of continuity becomes 



■*+*t.*.T.« m 



In the case where udx + vdy + wd% is an exact differential, it will 

 be found that the three equations 



du _ dv du die dv _ die 

 dy dx ' dz dx' dz dy ' 



are equivalent to only one equation, which is 



■ % = % w- 



In the general case we get, by eliminating p from (15) and (16), 



d I ds ds\ d_ ( dw_ 



d% \ dr dz) dr \ dr 

 or 



ds ds ds dw d 2 s d*s 



dr dz dz d% drd% dz* 



dw dw dw ds d"w d ! w . 



dr dz dr dr dr dz dr* '' 



The differential equation, between ■ and r, to a line of motion is 



dz _ w 



dr s ' 



Let /j. be a factor which renders sdz — wdr an exact differential, 



then 



d/xs d/uw _ 

 ~dr~+~dz~- 0i 



ds , dw\ du du 



dw\ 



dz) 



fas aw\ r//u du 



Orf >[Tr + dz) +8 dr +W Tz= > 



