(532 ) 
of these equations cannot be expelled by applying the method of 
the first lemma or by making use of the lacking of ¢* in (3), 
by which equations /()=0 etc. of still lower degree are obtained. 
For, these operations correspond with the diminishing of the elements 
of a row of the determinant indicated above by the corresponding 
elements of another now multiplied by a form in ¢, and by this 
method of transformation, much in use with determinants, the degree 
of the determinant in ¢ cannot be lowered. So it is only appa- 
rently that by applying the first lemma the degree of the general 
eliminant is lowered from 
ee) eo eye ee ee ee 
2 ’ 
~ 
in reality the eliminant of the equations 
Ned de 
fO=0, FHA... a =O 
is already of degree (s + 1) (k —s), although judging by the form it 
seems to be of a higher degree. On the other hand in the case of the 
skew parabola 
ob 725" O18 3 OT ee4 
| | | 
ae, Lape Hi 7-2) 3° B 
== 0 passes into =0 and = 0, 
0240 1001 (0000 0000) 
AR lo 00 0 00001 
if in succession we make use of the method of the first lemma or 
of the two cubic equations used in the direct solution; so the deter- 
minant remains of degree six in t. 
4. We are now able to treat the general case completely, where 
n and s <n are arbitrary and k is equal to 2x — 1. If as is custo- 
mary we represent the analytical faculty 
P(p+r)(p+2r)..-.tpt+q—1r} 
by per the equation under investigation appears in the form 
