244 
ON COMPOUND COMBINATIONS. 
[668 
as is very easily verified; but if the number of letters A, B,... be greater (say this 
= 8), or, instead of letters, writing the numbers 1, 2, 3, 4, 5, 6, 7, 8, then the question 
is that of the number of types of combination of the 28 duads 12, 13,..., 78, taken 
1, 2, 3,..., 27 together, a question presenting itself in geometry in regard to the 
bitangents of a quartic curve (see Salmon’s Higher Plane Curves, Ed. 2 (1873), 
pp. 222 et seq.): the numbers, so far as they have been obtained, are 
No. of types = 
1, 2, 3, 4, 
1, 2, 5, 11, 
24, 25, 26, 27 
11, 5, 2, T 
It might be interesting to complete the series, and, more generally, to determine 
the number of the types of combination of the \n(n— 1) duads of n letters.