42 ^rt. 5.— T. Tak-enouchi: 



of the same equation. In fact, if 



be a root of (24), then evidently the other three roots are 



/ , ^/\ o7/,. + 2,0- 



Putting 



Ave get 



Vic- 



5^. + :^^ = 47/,.,, 



r,Y;: = -4(7/,., + l), 



y.+2 - 7/,7/r. 



Thus the solution of the biquadratic equation (24) can be reduced 

 to those of the following two quadratic equations : 



Y|-47/,_ir^-4(7/,_i+l)=-0, 



7/|-r,7/,+(r,+2) = o. 



The discriminants of these equations are I'ospectively 



4= 17-4(7, + 2). 

 Dk can be transformed as follows. 



This shews that the corpus J^iYi.) can l)e derived from K{i/,,_-^ l)}- 

 adjoining a:;/,_i to it; in other words, K{Y,) is identical with K{xj,_-i). 

 It follows therefore that K{xk-^ cannot coincide with /vXva-i), if 

 k>2. 



