Q^ Art. 5. — T. Takenouclii : 



i.e. Ki^ifi), is of relative degree 3''"'. Consequently, K{y,) must Ije 

 at least of the 3''"^th relative degree. 



If follows therefore that the relative degree of Ki^ih?) must be 

 exactly equal to 3''""; and consequently the equation (15) is irredu- 

 cible in ]v(y,,_i). At the same time, it follows tliat 



Jl(yJ = K(yfX (18) 



Now, since 



7/i=0, z,= ±l, 



we find that 



K(y,) = K{.z,) and K{jj,) = it(,3-,). 



More generally, it can he sliewn l)y mathematical induction, that 



for all values of h. For, if we suppose that 



K{y n-i) = K(^k-i)> 

 then, by (17), Jv(z/,) nmst be at most relatively cubic witli respect 

 to Jv(j/n-i). On the other hand, however, since 



-1= l-%fe> 



the same corpus Jv[z/i) contains Jy(f/l). Hence, by (18), it contains 

 Ä"(3//,) ; consequently it must be at least relatively cubic with respect 

 to K(;f/,,.i). We conclude, therefore, that Jv(z/) must coincide witli 



Thus we find that the corpus Jv(x/,) can be decomposed into 

 the following three divisors : 



§. 11. 



Let us now investigate the nature of lv{yi). But. since this 



corpus for a certain value of h is contained in another corpus of the 



same type having a greater value of h, we may confine ourselves 



to the case 



7i = 2;i + 2>3. 



