J. Trowbridge — Vorle.r Riw/s in Liquids. 329 



do not exist. For the components X 1 , Y 1 , Z 1 , of the attraction, 

 which tend to make the non -diffusible drop reassume its spher- 

 ical form, we have in the case of the diffusible the components 

 X, Y, Z, of an external force arising from the superficial tension 

 of the liquid, and the impulse given to the drop. 



If we follow the notation of Poisson* and Helmholtz,f we shall 

 have for the general equations of internal motion of a liquid : 



--^ 1 dp _du du du du "] 



hfa-~dt + U 7lx^ V d~y + W dz I 

 v I dp dv , dv , du , du ! . 



Y -hdy = llt + u dx + v 4y + W Tz\ (3) 

 „ 1 dp die dw dw dw \ 

 L ~hdz=Tt+ U te + V -dAj + W irz) 



dh . dh , dh , dh dh /t . 



-di +u dx + % +w dz = Tt (4) 



du dv die ... 



& + ^ + & = ° (5) 



In which p is the pressure in a liquid at the point x, y, z: 

 X, Y, Z, are the components of the external forces acting on a 

 unit of mass ; and h is the density. When the variation of h 

 v small, we have Eq. (5). The forces X, Y, Z, are 

 considered to have a potential V. So that 



and the velocities m, v, to, a velocity potential #. So that 



or udx + vdy + wdz = dep, 



and cp satisfying the equation 



tfcp d^ <Fq>_ Q 

 W + dy* + dz* ~ 

 which is what equation (5) becomes under the conditions e: 

 pressed above. We must therefore have 



du _ch dv _ dw dw_du^ „ .. 



