PARTITIONS OF THE X-ACE AND THE X-GON. 71 
The addition of (+m+n+n'+n"+0), remembering 
the observation (Art. 25), gives, 
141) me m—8 
C. P9+m4y= tN 9 — ity? 
m—8 
+2, > (m+2)(m+6) - 2 ? 
m—9 
42, 1° (m+1)(m+8) -2 2, m>0); 
the number of triedral partitions of the (9 +m)-ace having 
four pairs of rays united pairs, or of the triangular par- 
titions of the (9-+m)-gon having four marginal triangles. 
p. P(11,5) + P(6)=R(6,2 ) = i= R(11, au (4, d’); 
for when every base summit ‘of “R(6,2) 3 is nes as in Art. 4, 
the line j in the axis becomes a line & in the axis. 
2|1 
a) 2 eb 
g RR(OI1 +70) aba #6 22, by (18 and p). 
m i 
aE EP ae. a =? 
. TROL +m5)= GEV. 2 ‘apie ie? 
by (14,p). 
The addition of these gives us, 
D. PQ ae ee gn 
m—8 
+2,,- (m+2)(m+4) + 2 Re (SO; 
the number of triedral partitions of the (11+ )-ace 
having five of the angles about the vertex undisturbed, 
or of the triangular partitions of the (11+mm)-gon which 
have five marginal triangles. 
gs. P(13,6)=P(7,2) + P(7,3) 
== (752) + R72) + R*(7,3) 
ar=C. 
Ly i Pe a a (4,¢,d',9), 
=1%13,6) + R(13,6) + B°(13,6), (Art. 4). 
kax=0, 
t. TI?(13+m,6)=2?->r1— » by (9,8). 
