18 ' Art. 5.— T. Takenouchi : 



Sicco A^,(^x) contains only even powers of x, tlie corpus K(x) 



must be relatively quadratic with respect to K{x'). But, this latter 



corpus is identical w^ith the corpus K{y) defined by adjoining to 

 k{f>) tlie number 



which is a root of tlie equation 



SV(7/)^0. ' (12) 



This equation can also bo regarded as an equation for if of degree 

 , — . Hence the corpus K{;y) is relatively cubic witli respect to 

 K{if). Consequently, 7v(a-) is relatively sextic witli respect to 



A'(r)- 



The corpus K{y") can be defined l)y the number 



as well as by y\ The former is an algebraic integer as shewn in 

 §. 3, while it is not the case with the latter. But, as we have 

 found in the preceding section, tlie discriminant D^ of the equation 



(12), considered as an equation for -^, does not contain the prime 



factor 2. Hence the relative discriminant of K{;if) cannot contain 

 the factor 2. 



Next, let us consider the relative discriminant of K{;y). i.e. of 

 Jv(x'), with respect to /v(;y"0- 



Let 



JJi = ^(^0' Z/i = Hv) 



])e two roots of (12), sucli that yi=hy[, then 



y,= ^{it + ü), y{,= ^(u-v) 



are also two roots of (12), •dudijo=kfjL From the relation (7), we 



t^et 



^'(,,) ^ }^'(v), 



and then, from the identity 



Ave see that 



(ur-u'ÙXy-yd^n^^f- 



