366 Proceedings of Roy cd Society of Edinburgh. 
D 
SESS. 
and 
b c d e f 
9 
abode 
9 f 
abed 
44 
9 f e 
a b c 
tr 
g f e d 
a b 
g f e d c 
a 
g f e d c b 
a 
b c d e 
-9 
abed 
-9 ~f 
a b c 
J_L 
tt 
-9 ~f ~ e 
a b 
-9 ~f ~ d 
a 
~9 ~f ~e -d - c 
6. Besides the results obtained in the preceding, viz., 
= (a + b + c) (a - c) = (a + b + c) • x v say ; 
(a + t) + c + ddj 
a b 
J_L 
C 
a 
tt 
e b 
a b c 
d 
a b 
_L1 
tt 
d c 
a 
deb 
a b 
J_L 
-d 
a 
tt 
~d~e 
= (a 4- & + e 4- d) • x 2 , say ; 
abed 
e 
e d 
e d c 
a b c 
a b c 
a b 
J_L 
tt 
= {a J rb + c J rd-\-e)° 
a b 
tt 
TT 
a 
e d c b 
a 
- e 
- e-d 
e-d — c 
= (a + b + c + 6? + e) • x 3 , say ; 
the following two additional sets are noteworthy, viz 
b 
b a 
a 
b 
J_L 
a 
tt 
a 
b 
c 
a 
b 
44 
TT 
a 
e 
d 
a b c 
a b 
a 
J_L 
C 
c b 
c b a 
d 
d c 
deb 
d c b a 
= 2 (a + b)(a - b ) , 
= 2 (ct + b + c)(a — b + cfx i j 
= 9i(a -f- 5 -+■ c + ddjigx — & + c — dj) % Xo 5 
