THE EQUILIBRIUM OF FLUIDS. 167 



Moreover, it is evident from the equation (10) Art. 4, that 



l-n 

 > 2 



^.. 



1.3 ...2z-l 3.5... 2 



i+2^ 



2.4... 

 and consequently, 



n " * ' 



K n 2 * + * *Q' t2 ' 



the finite integrals extending from t' = to t'co. 



Substituting now for V and V their values in the equation 

 of equilibrium, 



const. = F'+F. (20), 



we immediately obtain 



const. - 



n-2.n... 



2 .4.. 2' 



yi-2.ro... ft + 2'-4 4- n . 6 - n ... 2<-2$' + 2-ro' 

 2 .4... 2^~ 2 . 4 ...2*-2 f 



the constant on the left side of this equation being equal to zero, 

 except when i = 0. 



By equating separately the coefficients of the various powers 

 of the indeterminate quantity r, we get the following system of 

 equations : 



-2 



2 sin , ^ ,. , a 



.-->=*, + ^ + V-^ + & c. 



