70 Electric Endosmose and other Allied Phenomena. 



clu 



dx \ 



du 

 ' dx 

 du 



dy dxdz 



du_-.( 



dy-\' 



dx \ 



dy \ dx 



b=_o£"+45»+b 



dx dy dydz 



;dv' -ftdv d?v B 





dy ay dz 



°£> j 



(55) 



If we neglect Ik, IB, 10, as before, these equations combined 

 with the equation of continuity- 



reduce to 



du ' dv dw 

 dx dy dz ' 



:0 



du 

 dx'' 



, d 2 u 

 JxTz' 



du_ 7 d 2 u 

 dy~ dydz' 



dv 

 dx 



(56) 



dxdz 

 d 2 v 



dv _, 



dy dydz J 



If there is no slipping 1=0, and the preceding equations then 

 show that the following quantities all vanish at the origin — 



du 

 dx 

 dv 

 dx 

 dw 



du 



¥' 



dv 



dy' 



dio 

 dy' 



dw 

 Tz> 



d-i 



,'-■' 



d 2 w 

 dxdy' 



dho 



the last three quantities vanishing in virtue of (49). 

 therefore write in this case — 



We may 



V 2 »=xf, 



d 2 w 

 'd: 



a result which must also hold good approximately when I is 

 not zero, provided it be small in comparison with the other 

 linear magnitudes concerned. 



