80 
Proceedings of the Royal Society of Edinburgh. [Sess. 
by 
The product then is 
CL i CL 2 ^ 
A 9i A 
f 2 92 A 
f 3 9% A 
m. 
l • 
«1 
a 2 
a 3 
a x 
a 2 
a 3 
a x 
a 2 
a 3 
A 
A 
m 1 
A 
9i 
A 
m 2 
A 
9i 
A 
m 3 
A 
92 
h 2 
n i 
ft 
92 
h 2 
n 2 
A 
9 2 
h 2 
U 3 
A 
9s 
A 
r i 
f» 
93 
A 
r 2 
A 
93 
A 
r 3 
A 
h 2 
a 
A 
A 
A 
A 
h 2 
A 
A 
9i 
a 
m x 
A 
9i 
A 
m 2 
A 
9i 
A 
m 3 
A 
92 
A 
n i 
A 
92 
h 2 
n 2 
A 
92 
h 2 
n B 
A 
9s 
A 
r i 
A 
93 
A 
V 2 
A 
93 
JI3 
r 3 
c i 
C 2 
C 3 
c i 
C 2 
C 3 
c i 
C 2 
C 3 
A 
9i 
A 
m l 
A 
9i 
A 
m 2 
A 
9i 
A 
m 3 
/. 
92 
A 
n i 
A 
92 
A 
n 2 
A 
92 
A 
n B 
/s 
93 
A 
r \ 
A 
93 
lis 
v 2 
A 
93 
A 
V 3 
and the minor which is the cofactor of the element in the place 1,1 , con- 
sisting as it does of terms in b x , terms in b 2 , and terms in b 3 , may be dealt 
with in three portions. The aggregate of the terms in \ is evidently 
i.e. 
A* 
f\ A <A ^2 
m 2 ? 2 A 9 1 A 
/ 2 92 A 
f b 9% A 
A 
f\ f <2 f 3 ^2 
m 3 n 3 r 3 A 9l A 
f 2 92 A 
/a 9s A 
( m 0 i 
AA . ffi 9s 9 b _ AJjJ s . 0 'i ga g« l 
2 w 2 r 2 m 3 w 3 r 3 m B w 3 r 3 m 2 n 2 r 2 
m, 
^.e. 
+ 5 c / -A A A . A A A _ A A A . A A A l 
1 3 1 n 9 r 9 m 3 w 3 r 3 m 3 w 3 r 3 m 2 n 2 r 2 J ’ 
A C 2 
1 A A A 
• 
m 2 m 3 
+ b 1 c B • 
A f 2 A 
• m 2 m 3 
9i 92 93 
n 2 n 3 
A A A 
j w 2 w 3 
r 2 T 3 
1 r 2 ^3 
Similarly, the aggregate of terms in b 2 is found to be 
b 2 c v 
9 1 92 9 3 
A 1 A A 
m 2 m 3 
To 
Vs- 
j ft % % 
A A A 
m 2 m 3 
