244 EEV. T. P. KIEKMAJ^ ON THE K-PAETITIONS OP THE E-OON AND E-ACE. 
r-gons will have only n sides of the w-gon loaded with (l+So)'PaJditioned (3-f-2c4o)-gons 
71 ^71 
monogonally reversible, namely the wth, the ^th, the ^th, &c. sides. And half the 
interval between the nth. and ^th, namely sides, will be loaded, the TTith with a 
(l+^m)-partitioned (2-l-«^)-gon, which will be placed also on the (^—ni^th side, so as 
to form a figure reversible about the diagonal bisecting that interval. 
Our equations of condition are now 
r = W' -}- 2 csq^-}- 2 A 
A— w-|“A2q -}-2A^gt ~f~^2 H" ■ • ~i~ € n—}^ 
(C-.) 
I5 
where and g,, are any numbers we select from our list of monogonally reversibles. 
Keasoning as in the previous constructions, we deduce that the entire sum, made from 
every solution of (C'.), of products MA of 
M=2„,R”*-'”'’(3+2ao, go), and 
An-^ = I)( 2 61) £2} •• • dn—h^ 
2h \ ifT 2h ) 
is the complete number of configurations about a loaded axis, of ?’-gons ha^fing 
^ equidistant loaded, and bisecting the intervals between these, | clear, diagonal axes of 
reversion. 
Now one of these configurations about a loaded axis is seen in each of A)„ ; 
for it has in the intervals of any equidistant ^ loaded axis 2^4-l clear ones, one of them 
bisecting each interval. But none of the class E|f •*'(r, A)„ has that configuration, 
because in the equal intervals of | loaded axes it has an even number of clear ones, and 
none bisecting an interval. And no ago-diagonally reversible can have this configuration, 
because the diagonal axes are in these all clear or all loaded. 
Wherefore 
and 
27 * 
Rr(n A)„=2M.A^-S,Ef;+^>'^-‘'‘(r, A)„; (z>0). 
2 /* 
n — h! . 
where (27-1- 3) A is a value A' that makes ■ integer. 
XLIII. The greatest value of A in (C'.) is A=?z, when there is no interval between the 
axes. Then, 
r—2n 
k—n 
= Za„ 
■ = £n 
n n 
Ao=l = SAo M=2M, 
and 
which =0, iir and k are not multiples of n. 
