208 ON THE RATIONAL TRANSFORMATION BETWEEN TWO SPACES. [447 
been investigated by Cremona. The results may conveniently be stated in a tabular 
form; the tables exhibit in the outside upper line the values of a 1 , a 2 ••• a n-i, and in 
the outside left-hand line the values of a/, a/...a ' n _ 1 , and they are to be read as 
( a/ lines ) 
a 2 ' conics > passes ( ) times through ( ) of the points a u a 
&c. ) 
respectively; the numbers in the table being those of the points passed through, and 
the indices in the table (index = 1 when no index is expressed) showing the number 
of times of passage, that is, showing whether the point is a simple, double, triple, &c., 
point on the curve referred to. 
44. Thus (in the tables which follow) the last of the tables n = 6 gives the con 
stitution of the Jacobian of the first plane, where the principal system is (3, 4, 0, 1, 0); 
and it is to be read: 
Each of the 4 lines passes through 1 of the points and through the point a 4 ; 
The 1 conic „ „ 4 of the points a 2 and through the point a 4 ; 
Each of the 3 cubics „ „ 2 of the points a lt 4 of the points a 2 , and twice 
through the point a 4 (that is, a 4 is a double 
point on each cubic). 
It is hardly necessary to remark that the tables are sibi-reciprocal, or else conjugate, 
as appears by the outer lines of each table. 
Table n = 2. 
a i 
3 
[was originally printed, 
3.] 
Table n = 3. 
ttj a 2 
II II 
4 1 
1 
1 
4 
1 
Tables n = 4. 
a i 
a 2 
a 3 
«1 
«2 
«3 
II 
II 
II 
II 
II 
II 
6 
0 
1 
3 
3 
0 
1 
1 
3 
2 
1 
3 
2 
3 
6 
l 2 
0 
a 3 ' = l