284 Trans. Acad. Sci. of St. Louis. 



Equation (32) may be transformed into one involving a 

 third variable. Thus, the condition that 



is 



^ + ^ J+4^^^'— ^-+^1^^^^ = ^' (^^) 



4 ^ ^ ^ttJc 



provided n = p-, and A = ^27^2 * 



This equation like (32) is not very encouraging in appear- 

 ance, and it may be that no closed solution can be made of 

 it, or that the solution will be too complex for further appli- 

 cation. 



Correction, p. 66, line 21 from bottom, for ten read 

 twenty. 



Issued June 24, 1899. 



