58 Mr green, ON THE LAWS OF THE EQUILIBRIUM OF FLUIDS. 



then compare it with the forrnulag (25) of the present article, we 

 shall have generally E^^ = 0, and 



C"'=-2ga-^.l^(r;O)+0(e;l)^+«^(/; 2) ^ +,^ («; 3) J + &c.^ 



except when i = 0, in which case we must take only half the quantity 

 furnished by this expression in order to have the correct value of C*"'. 

 Hence whatever u may be, 



2 sin I ^-Q— T I 

 ^ - 0, and cf = ^^ qa} -"-*-^" ; 



TT 



the particular value f=0 being excepted, for in this case we have agreeably 

 to the preceding remark 



and then the only remaining exception is that due to the constant 

 quantity on the left side of the equation (27). But it will be more 

 simple to avoid considering this last exception here, and to afterwards add 

 to the final result the term which arises from the constant quantity thus 

 neglected. 



The equation (26) of the present article gives by substituting for 

 d" its value just found. 



^ . (n-l \ 

 2 sm I—- — tt) 



«»= l^f L qa'"-'-'". {1 + '^.a-' 



n — 3.n-l ^, n — 3.n-l.n-l ., . , 

 2.4 2.4.6 ' 



^ • /«-! 

 2 sm 



(n-1 \ 



l^i i qa'-'-'-"- (1 - a-')— 



2 sin I -—^ 



TT^ 



