Dr T. Muir on the Theory of Determinants. 
519 
only it must be noted that in using Pf« ; s , a\ a this stage, we 
\n h h/ 
leave out of account the signs of the terms composing it, the rule 
of signs being the subject of a separate investigation. Any one of 
the forms 
/n 
1 
2 
\a; 
a , 
a) , 
?(a ; 
a, 
a 
\n 
h 
hJ 
\n 
h 
hJ 
it need scarcely be added, will thus stand for the common 
denominator. 
Of the n 4- 1 equations the first n are taken, written in the form 
nn 7i-\n-\ kk 11 «+l ra+1 | 
ax + ax ax +...+ a.x = s - a x \ 
11 1 111 
nn n-\7i-\ kk 11 n+1 ?i+l I 
ax + ax 4 - . . . + 4 - . . . 4 * = s “ a x I 
2 2 2 2 2 2 > 
nn n-\n-l kk 11 
ax + ax ax ax 
n n n n 
and solved, the results being by hypothesis 
( n ?i+l w+1 1\ 
a ; s - a x , a\ 
n h h h/ 
S 
n 
ra+1 n+1 
a X 
n 
k 
Pi 
>n n+1 n+1 k\ 
a ; s - a x , a) 
M h h h/ 
( n n-\-\n+\ n\ 
a ; s~ a x , a) 
n h h h' 
rp ~ 
ni n n\ 
Pf a ; a , a j 
\n h h/ 
These values are then of course substituted in the {n + 1)‘^ equation, 
which thus becomes 
