XXXIV 



Trans. Acad. Sci. of St. Louis. 



(5) u^ = cr— ^^ 



k L 



2(2/x + X)^ 



k L 



^\rJo{v,r)+B\rKXri^r) 



^,h^+,-^i^)^ 



(e'^.^+e-^^^) 



(,^/A^+e-'?.-^) 



give a general solution of the equations ( 2 ) where the coeffi- 

 cients A, B, A^, B^ are determined from surface conditions. 

 For the purposes of this paper, however, a simpler method 

 may be pursued. Namely, formulas (4) and (5) show that 

 the general solution may be presented in the form 



w 



^1 ='^ho +^^n ^^ + *'i2 z^ + . . . 

 IV = 2VqZ + iv^z^ + t'V2Z^ + . • • 



where u^^, u^^, . . . , Wo, Wy, . . . are functions of r only. 

 Substituting these expressions of ttj and w in (2) we find that 

 this system of differential equations may be replaced by the 

 following [one 



(7) 





ii d [ div. 





ID, 





