THE EQUILIBRIUM OP FLUIDS. 183 



Under the present form it is clear the determination of V 

 can offer no difficulties after what has been shown (Art. 2). 

 I shall not therefore insist upon it here more particularly, as it 

 is my intention in a future paper to give a general and purely 

 analytical method of finding the value of F, whether p is situated 

 within the ellipsoid or not. I shall therefore only observe, that 

 for the particular value 





the series U '+ Z7 2 '+ U 4 ' + &c. (Art. 2) will reduce itself to the 

 single term J7 ', and we shall ultimately get 



2 sin 



which is evidently a constant quantity. Hence it follows that 

 the expression (30) gives the value of p when the fluid is in 

 equilibrium within the ellipsoid, and free from all extraneous 

 action. Moreover, this value is subject, when n < 2, to modi- 

 fications similar to those of the analogous value for the sphere 

 (Art. 7). 



