ON THE TRIPLE ^-FUNCTIONS. 
452 
[702 
See my “Algorithm of the triple A-functions,” Grelle, t. lxxxvii. p. 165, [701]. 
The (35 + 28 =) 63 hexpairs then are 
35 hexpairs such as 
, say this is 1234.5678 or for 
and 
shortness 567 (the 8 going always with the expressed triad): that is, 567 
denotes the hexpair 
12.34; 13.24; 14.23; 56.78; 57.68; 58.67: 
28 hexpairs such 
2, say this is 12; that is, 12 denotes the 
hexpair 
13.32; 14.42; 15.52; 16.62; 17.72; 18.82. 
It is to be noticed that the odd characteristics, as represented by their duad 
symbols, can be added by the formulae 
12+23 = 13, etc., 
or, what is the same thing, 
12 + 13 + 23 = 0, =^q, etc. 
and 
12 + 34 = 13 + 24 = 14 + 23 = 56 + 78 = 57 + 68 = 58 + 67 = 567, etc. 
Thus, referring to the table, 
and 
which are right. 
The 288 heptads are 
™ no 010 100 
12 + 23= 13 means , 00 + 010 = 110 - 
110 110 000 
12 + 34 = 567 means iqO + 101 = 001 ’ 
8 heptads such as 
2 3 4 5 6 7 8 
the seven duads 12, 13, 14, 15, 16, 17, 18 
, say this is the heptad 1, denoting