Mr green, on THE LAWS OF THE EQUILIBRIUM OF FLUIDS. 63 



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 there- 

 fore 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 V, whether p is situated within the ellipsoid or not. I 

 shall therefore only observe, that for the particular value 



(30) , = ^\^-ii^-%-i]' = ^^(^ -'") ' ' 



the series Uo + U2' + U/ + &c. (Art. 2.) will reduce itself to the single 

 term Uo, and we shall ultimately get 



2sin("— .) 



which is evidently a constant quantity. Hence it follows that the ex- 

 pression (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 modifications similar to those of 

 the analagous value for the sphere (Art. 7.)- 



G. GREEN. 



