( 423 ) 
To prove this we represent Rs by the equations 
peek oe Ale Nete = 
on rectangular axes, where the symbols «aj, @,... «ds and v in- 
dicate polynomia of degree n in a parameter ¢. 
If the equations 
Qi 7 
A MN CSL, A. a) 
V V 
represent the result of the division of the s polynomia a; by v, where 
the s quantities a; are independent of ¢ and the s new polynomia 
?: contain t in the degree n—1 at most, then it is clear that the 
transformation of the system of coordinates to parallel axes corres- 
ponding to the formulae 
Ce ee owe (ch Deal 
simplifies the original representation (1) of Rs into 
We repeat that this simplification consists in the fact that the s 
polynomia /?; ascend only to the degree n—1 in t. 
If moreover /?'; and v' represent the differential-coefficients of (%: 
and v according to ¢, then 
v = (Biv — fiv')&= > (py —fiv)Pi . . « (3) 
represents the normal space with s—1 dimensions of As in the point 
(2) with the value ¢ of the parameter. 
This equation is of degree 3xn—2 in t, which proves what was 
asserted. For the envelope of a space of s—/ dimensions, the equation 
of which contains a parameter to the degree k, has for character- 
istic numbers: 
BEE 10h, SAN ok Seay 
