58 
UR. H. M. TAYLOR ON A SPECIAL FORM OF THE 
Each line represented by a row or a column intersects four of the lines represented 
by the columns or the rows resj^ectively. 
The figure maybe interpreted as representing a closed hexagou, say, a, h, h,j, c, i, 
and four lines, d, e,f, <j, each of which intersects three alternate sides of the hexagon ; 
o)’ it may be ijiterpreted as representing a “ double four,” together with two lines, 
say e,f, eacli of which cuts all the lines of one of the sets of four in the double four. 
Such a combination as 
/ 
e 
d 
c 
b 
a 
(j h i j h I 
is called a “ double six.” 
Each line represented by a row or a column intersects five of the lines represented 
by the columns or the rows respectively. 
The figure may be interpreted as representing two “grilles,” each line of either of 
which intersects two of the lines of the other ; or, as representing two closed hexagons, 
each side of either of which intersects three alternate sides of the other. 
The figure may be interpreted also as representing a “ double four” and four lines, 
each of which intersects the four lines of one of the sets of the double four ; or, again, 
as representing a “ double five ” and two lines, each of which intersects the five lines 
of one of the sets of the double five. 
§ 12. From figure C we see that the number of lines which do not cut the line 26 
is 16. Each of these sixteen lines has the same relation to the line 26 ; take anv 
of them, say 27. Such a pair of lines as 26, 27 is called a “ duad.” 
Again, from figure C, we see that the number of lines which do not cut the duad 
26, 27 is 10. Each of these ten lines has the same relation to the duad; take any 
one of them, say 5. Such a set of lines as 26, 27, 5 is called a “ triad.” 
Again, from figure C, we see that the number of lines which do not cut the triad 
26, 27, 5 is 6. Each of these six lines has the same relation to the triad ; take any 
one of them, say 2. Such a set of lines as 26, 27, 5, 2, is called a “ tetrad.” 
Again, from figure C, we see that the number of lines which do not cut the 
tetrad 26, 27, 5, 2, is 3 : the lines which do not cut are 9, 10, and 13. These three 
lines, however, have not all the same relation to the tetrad. The lines 9 and 10 have 
each one common line of intersection with the tetrad : in fact, the line 4 cuts the lines 
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