INDETERMINATE QUARTIC EQUATIONS 75 

 which is an algebraical solution of the equation 



where X, (i, vj, ^ 2 , v 3 , . . ,,v r are arbitrary coefficients, positive 

 or negative, which are unrestricted except that >. and \>. are 

 both finite, and the v's do not all vanish a result of consider- 

 able generality. 



