436 
Proceedings of Eoyal Society of Edinburgh . [sess. 
remark that can be expressed in terms of n of the quantities 
f g , leads up to a curious set of equations the determinant of which 
belongs to the special class of determinants known afterwards as 
zero-axial skew determinants. The passage is (pp. 300, 301): — 
“ Designemus br. causa per ( Jc , k') expressionem 
io. a £;-(*,*). 
ita ut sit ( k , k') = 
Eit e (8) ipsi g substituendo numeros 0, 1, 2, . 
. , n 
A </>= * + aT \ °> !) + 
^(0.2) . . 
+ 
^(0, 
A ( l /) = « (/ ' ) (l,0) + * + 
<4° (1.2) • • 
+ 
w (1. 
ii. \ 
; A^ ) = a </,) (2,0) + a[ f) ( 2, 1) + 
* • • 
+ 
<> (2, 
A^ = a (/) (w, 0) + ckp (n, 1) + 
AV. 2) . . 
+ 
* 
Similes formulae e (9) derivari possunt. In aequationibus 
(11) ipsorum a [f \ a (f '\ etc. coeflicientes in diagonali positi 
evanescunt, bini quilibet coeflicientes diagonalis respectu 
symmetrice positi valoribus oppositis gaudent. Quae est species 
aequationum linearium memorabilis in variis quaestionibus 
analyticis obveniens.” (lvii.) 
The simple step from the expression of A^ as a differential co- 
efficient to the similar expression for A^’^, is next made (p. 301) : — 
“ Ex ipsa enim aggregati A g ,f gl definitione eruimus formulas 
1 32R _ 02R 
g '* daffWp ddpda<p> 
0.A (/ > 0.A (/ :> 0.A (/,) 0.A (/) 
l _ <L_ _ q__ g » 
da^ d(f f g da ( g ^ 
