886 
MAJOR P. A. MACMAHOR" OX THE THEORY 
?]5 
contacts 
^25 
(^x.p-1 
yy 
’?15 
yy 
’?25 
a^ao 
yy 
^]5 
«.-«3 
yy 
^25 
«-«3 
yy 
and these numbers must represent also the exact numbers of the contacts in question 
because the sum 
+ + . . . 
gives the whole number of contacts under consideration. 
The number k obviously denotes the number of lines of route through the reticula¬ 
tion of the multipartite 
IhPz- • 
which possess 
essential nodes of the kinds 
^•2 5 5 5 5 5 5 ^X.P-\ 
and so forth. 
67. By an easy arithmetical interpretation the number k also denotes the number of 
permutations in which 
occurs times in the first 'p^ places. 
5 5 ^2 5 5 5 5 5 5 5 5 
„ y]i ,, between the and places. 
>5 5 5 55 5 5 55 5 5 
a. 
-1 
a. 
^3 
yy yy 
yy yy 
yy 
yy 
yy 
