88 Proceedings of the Koyal Society of Edinburgh. [Sess. 
(11) It only remains now to examine whether anything is to be learned 
by trying to connect the subject of §§ 1-7 with that of §§ 8-10. The latter 
being the expression of a Pfaffian with general polynomial elements as a 
sum of Pfajfjfians, and the former the expression of a Pfaffian with special 
polynomial elements as a sum of determinants* the possibility is suggested 
that the substitution of the particular elements 
l«AI > !«AI > • • • 
\a 2 b s \ , ... 
for the general elements 
a '\ > ^2 ’ * ■ • 
1*2 ’ • • • 
might lead to a second mode of establishing the less general result. 
The details of the examination need not be entered on. Suffice it to 
say that they seem to shut out all hope of any mode of proof more 
attractive than that originally given. 
* In view of the footnote above (§ 7), it is fitting that I should here point out an 
incorrect footnote of my own bearing on a determinant and a sum of Pfaffians. See Trans. 
Roy. Soc. Edin ., xlv, 1906-7, p. 313. 
Rondebosch, S.A., 
5th January 1920. 
( Issued separately May 29, 1920 .) 
