THE EQUILIBRIUM OF FLUIDS. 149 



sm 







...................... &c ...................... &c .................... 



since all the terms in the preceding value of F f (i) in which t' > t 

 vanish of themselves in consequence of the factor 



4 %. 6 n... 2t- 2tf' + 2 n 



2.4 ...2t-2t' 



(when *'> t). 



But F (i) as deduced from the given value of Fmay be expanded 

 in a series of the form 



F"> = r*. { F (i) + F^V + F 2 (i) . r 4 + F 3 (i) r 6 + &c.} 



and if in order to simplify the remaining operations, we make 

 generally 



2?r 3 n-2.?i...rc + 2~-4 



2. 4. ..2* 



sm 



n-l.n+l ... . } 



3. 5.. ,2t ' 



271-2 



-2 



