740 MR DUNCAN M. Y. SOMMERVILLE ON 
For Class B. the corresponding formule are 
4n' n” 2n' n" 
i ae Sine eae 
; 4y)’ n" 3 4y)” n’ 
eae EAL on ov 
where A=n/n'"(2 — p)+.2(p'n" + pn’). 
The Simple Types. 
§ 23. We proceed now to classify the simple types and investigate their varieties. 
The division into classes according to the number of kinds of polygons can still be 
made, but the subdivision into groups according to the kinds of polygons involved is 
useless, as there are an infinite number of kinds of polygons. We shall therefore, for 
the present, classify them according to the types of nodes. I consider two nodes to he 
of the same type when the values of p,, p., ps, are the same for both. A network 
will not in general admit of variation unless its node does so. But this rule is not 
always true; e.g. the type of angle PQ, is unvaried, but, as we shall see, one of the 
networks corresponding to this type admits of two distinct varieties. We shall give 
for each network the values of N,, N,, N,, etc. Unless otherwise specified, the net- 
work is unique. 
Class Be Wp 1p — 2 
(1) A=2.. @) 7 = 3, N, =20 
n”=10, N,”=12 
N,=60, N,=90, N,=32 (fig. 19). 
(b) n’ =5, N,’ =12 
n’=6, N,”=20 
N,=60, N,=90, N,=32 (fig. 21). 
(2) A=4, (a) n' =3, N, =8 
8, NG 
N,=24, N,=36, N,=14 (fig. 20). 
On =3 Ny = 
n'=6, N,’ =8 
N,=24, N,=36, N,=14 (fig. 22). 
n =n, N, =2. 
N,=2n, N,=3n, No=7 +2 (fig. 24), 
itll p'= ,p"=3 
()A=2. nw =3, Ny ES. 
i =4, N= 18. 
N,=24, N,=48, N,=26. 
This type has two varieties. It contains a group formed by a quadrilateral surrounded 
