613] 
ON THE GROUP OF POINTS GS ON A SEXTIC CURVE. 
505 
points; we have then the “ Riemann-Roch ” theorem that these R points form a 
special group Gr, where 
Q + R — 2p — 2, 
as just mentioned, and 
Q — R = 2q — 2r; 
viz. dividing in any manner the 2p — 2 intersections of the basis-curve by an adjoint 
into groups of Q and R points respectively, these will be special groups, or at least 
one of them will be a special group, Gq, Gr, such that their specialities q, r are 
connected by the foregoing relation Q — R — 2q — 2r. 
The Authors give (l.c., p. 293) a Table showing for a given basis-curve, or given 
value of p, and for a given value of r, the least value of R and the corresponding 
values of q, Q: this table is conveniently expressed in the following form. 
The least value of 
and then 
where ^ denotes the integer equal to or next less than the fraction. 
It is, I think, worth while to present the table in the more developed form: 
R =P-„ 
<l = 
P_ 
r+1 
P 
r+1 
+ r 
-1, 
2, 
n 
P 
Dps 
✓ * s 
1 2 3 4 5 6 
4 
3 
0 
G, 1 G? • 
6? #0° • 
5 
4 
2 
G, 1 G* G* 
G 3 1 G,° G 0 ° 
• 
6 
5 
5 
G? G* G* G s * 
GV G 2 ° GS G 0 ° 
7 
6 
9 
GS Gi GS G* GJ 
GS GS GS GS GS 
8 
7 
14 
GS GS GS G,S G u * G V S 
GS GS GS GS GS GS 
where the table shows the values of 
G r R 
G l 
for any given values of p, r. 
C. IX. 
64