414 Mr green, ON THE DETERMINATION OF THE 



(22) as before comprising all the ~ — — combinations of the * indices 

 taken in pairs. 



Hence, the quantity on the right side of the equation (17), when 

 we make H = Ho, becomes 



+ 2(22)^^.-^;^,+ («-2^)2^.--^ (23). 



d^rd^r a,«r'2«/ V «r / «^r o, 'v/(2«;^) ^ 



But if we recollect that we have generally 



it is easy to perceive that in consequence of the equation (18) the 

 quantity (23) will vanish, and therefore the foregoing value of Ha 

 will always satisfy the equation (17). 



Having thus a particular value of H, we immediately get the 

 general one by assuming 



H= Hfzdh. 



In fact, there thence results 



H = KHj „„ '^"^^ . 



±l(,~ Ux, Oi, (h a, 



the two arbitrary constants which the general integral ought to con- 

 tain being K, and that which enters implicitly into the indefinite in- 

 tegral. But the condition = V" requires that H should vanish when 

 h is infinite, and consequently the particular value adapted to the 

 present investigation is 



n - jr rr f ^""dh 



J^ Mo'a^, «2 «» 



11. The values of (f> and H being known, we may readily find 

 the corresponding values of V and p. For we have immediately 



