374 
Proceedings of Royal Society of Edinburgh. [sess. 
zero elements of which are (1, 7), (6, 7), (7, 7), (7, 6) , (7, 1), we 
obtain the equivalent expression 
(7, 7)cof + (6,7)(7,6)cof + (l,7)(7,l)cof + ( 1 ,7)(7,6)cof + (7, l)(6,7)cof 
i.e. 
l • • • 
a g Ml a l . . . a b 
6 S C 5 M 
( <h 
\ Cy ... 
1 cq 
- *5 
11111 
1 Cj a 2 & 2 . 
ay by 
1 . C 2 « 3 5 g 
Cy a 2 & 2 • • 
1 . . c 3 a 4 
• c> 2 % ^3 
1 . . . C 4 
• ■ % « 4 64 
Of the two determinants here written at full length the first is 
seen to be 
^ * • • . 
• && 1 “t - c A 1 cq by 
1 Cy a 2 b 2 
1 
1 
/ h- \ / v-- \ /h\ 
— ( (Jy . . . (J 4 \ C 4 ( Oy . . . < 2 g \ +^4^3! aya 2 ] O^C^CfCLy) + ^CgCgCp 
\ C, ... / \ c, . . . / \ 1 c, / 
and the second 
/ 6, 
— ( a-, ... a. 
\ ^1 / \ 'U 
It thus follows that 
c, . . . 
\ 
C, . . 
6, ■ • 
M ( “l • • ■ «(i = «6 M ( “l • • • «5 ) 1 V5 JI 
••• 
+ (%■••%- ( C 5 + 6 5>( “l • • • “4 
/ \ \ 
(C5C4C3 + ^5^ 4 c 3 )( % a 2 \ 
+ (Ws C 2+*5 6 A C 2)( a l) 
— ( C 5 C 4 Wl ^5^4^3^2^l) ’ 0) 
