( 424 ) 
By means of the general theorem now proved we find from n = 2 
to n= 10 the following table for the general rational twisted curve 
of minimum order: 
s=n=2... 4, 6, 
s=n= 3 dy doy ie 
s=n=4 10, 18, 24, 28, 
s=n=6... 16, 30, 42, 52, 60, 66, 
s=n=—7... 19, 36,51, 64, 75, 44, 91, 
42, 60, 76, 90, 102, 112, 120, 
s=n=9... 25, 48, 69, 88, 105, 120, 133, 144, 153, 
s=n=10... 28, 54, 78, 100, 120, 138, 154, 168, 180, 190. 
The first line of this table says that the evolute of a general 
conic is a curve of class four and order six, the second that the 
locus Rs of the general skew cubic R3 is a twisted curve of class 
seven, rank twelve and order fifteen, etc. 
If as usual we consider the coefficients uj, uz, uz .... us of the 
equation Sw § = 0,(¢= 1,2,... 8) as the tangential coordinates 
of the space with s—/ dimensions represented by that equation, we 
find from (3) for the normal space 
So dn ee 
= Kvv) 
c— 
ui 
which representation of Zj in space of s dimensions is dualistically 
opposite to that given for Rs. We write it in the abridged form: 
ESL rk Ne aen gy re ce 
3. The degree of the equation (3) or that of the forms z of (5), 
all in ¢, can lower itself in particular circumstances. These, appa- 
rently of five kinds, can be reduced to the following two cases: 
a). The equation y =O has equal roots. 
b). The equations (%=0, (= 1,2,... s) have common equal 
roots. 
