32 
Transactions of the Royal Society of South Afr 
(^1 ~ (^1 — ^-3)'" ■ (^1 — 
(«2 - ^'J" (^2 — ^i)' 
5 
-10 
This, for shortness'' sake, may be written 
-10 
and with the same notation the next case 
(^h 
. . 7 
. -21 . 
35 . . 
the general theorem being thus evident. 
a^a,,a~^a^ 
2«'irt'2'^3 
a-^ac^a^a^ 
(6) On account of the number of their zero elements the Pfaffians on 
the right may be condensed into the forms 
- 10 
- 5c 
-5c. 
1 ^2 
be, 
C^C•^ 
35 
— 21 — 7ciC2 
— 7C2C3 
- 7C3C4 
8c^. — CiC- 
where, however, the law of formation is not quite so evident. If we divide 
every element outside the last frame-line by 5 in the one case and by 7 in 
the other, we are thereby removing the factors 5, 7^, respectively. This 
suggests a third form, which in the next case is 
-14 
- C3C4 
lOc^— C^Cy 
