70 Art. 5.— T, Takonoiichi : 



Hence the relative discriminant of this corpus must contain the 

 factor l + 2e. The relative discriminant of the corpus (b) does not 

 contain the factor 2, since the discriminant of the equation 



is — 27£-, Thus we see that there can be no relatively cyclic, cubic 

 corpus, whose relative discriminant is a power of 2, Q. E. D. 



The relative discriminant of K[m\ must therefore be divisible 

 by 3, when m is divisible by 3, provided that m^d>. 



Thus we arrive at the following conclusion. 



All the prime factors of the relative disc7'iminant of Kirn] are 

 contained in m; and conversely, all the prime factors of m enter into 

 the relative discriminant of K[m\, except when m—2 or 3. 



In the two exceptional cases, Ä"[w] coincides with the funda- 

 mental corpus Ti{p). 



Nagoya, November 1915. 



Published March SOth, 1916. 



