318 ON THE VIBEATION OF PENDULUMS IN FLUID MEDIA. 



Moreover, by the same means, the last of the equation (4) 

 gives 



which values being substituted in the second member of the 

 preceding equation, evidently cause it to vanish, and we thus 

 perceive that the value (3) satisfies the partial differential equa- 

 tion (2). 



We will now endeavour so to determine the constant quan- 

 tities X and fju that the fluid particles may move along the 

 surface of the ellipsoidal body of which the equation is 



But by differentiation, there results 



and as the particles must move along the surface, it is clear that 

 the last equation ought to subsist, when we change the elements 



dx, dy } and dz into their corresponding velocities -~ , ~~ , 



and -f- . Hence, at this surface 

 az 



x dtp if u(b z U(D 



v == TJJ ~J I T~f9 ~7 i ~7 7 ..(o) 



a dx o dy c dz 

 But the expression (3) gives generally 



' dy~~cibcdy* dz ~ a?bc dz ""^ '' 



