XXXI V 



Trans. Acad. Sci. of St. Louis. 



(5) « 

 + 



. = cr- 2 [A^/.d*'-) + B.i^.(hr) (e? '^+ e"^*^) 



__ Z^ + X -yf 



(VO + ^I^/V) ( 



e^^+e-'^*") 



Vi^a_-Vk^ 



e'^+e 



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

 cients A^ B, A^f 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 



(6) 





where Wj^, i/n, . . . , 2(;o» ^i» • • • ^i*^ functions of r only. 

 Substituting these expressions of u^ and ?/? in (2) we find that 

 this system of differential equations may be replaced by the 

 following f one 



d Idu. 



dw. 









'C?t^,, u. 



y^ d I dw^ 

 r dr 





