1904 - 5 .] 
Dr Muir on General Determinants . 
911 
X y z\ 
P P P 
x , x x ,y x,z 
x y 
i 
xyz 
P P P 
-*• x,x J x , y M x,z 
X Z 
x y z| 
P P P 
x x, x ■*- y ,y x,z 
x y 
T 
xyz 
P P P 
J z,x M z,y x z , z 
X z 
xyz 
IP P P 
' M y,x y ,y * y ,z 
xyz 
P P P 
\ *- z , x z , y - 1 - z , z 
x y 
p p 
x,x x, y 
+ 
X Z 
p p 
\ -*■ X t X • X - 2 | 
+ 
y z 
p p 
k 1 - x ,y x , z 
1 
« 2/ 
x y 
P P 
x y,* x y,y 
X z 
• 
p p 
i y , x j/,2 
y z 
1 p p 
\ y,y y ,z 
J 
x y 
.r y ' 
P P 
x,x x,y 
+ 
p p 
a?, a; -*• a:, z 
+ 
y « _ 
P P 
\ 
a? 2 
x y 
P P 
z , x z , y 
X z 
P P 
x z, a? x 2: f z 
y z 
P P 
x 2 , 2/ x z , 2 
) 
x z 
® y | 
P P 
y , x y ,y 
+ 
X z 
1 
L 
P P 
y,% y,z 
+ 
y z 
P P 
x y, y x j/ , 2 
y z 
x y 
P P 
x z,x M z,y 
1 
X z 
• 
P P 
■*- Z,X z , z 
J z 
P P 
M z ,y ± z,z 
i 
y z 
or, in still later notation, 
kyi k z i \y z | 
ip pi 
1 fx,x Py,z\ 
\P*,V Py.z 1 
k y ! 
1 P*,x P,,y\ 
\Px,x Pzl 
lc,,„ p,' ,{ 
k z | 
\P*J .. P.. J 
\Py >x P z>z \ 
!-pJ /’..j 
ly z |, 
— a result which loses half its interest if we do not note that each 
element of the initial determinant is presentable in the same form, 
viz., 
P P P 
M x, x x x,y •*- x , 2 
P P P V 
y , x M y ,y y , z y 
P P P 
xyz 
Q i 
y 
z 
y 
z 
The fifth theorem, which is obtained from the fourth by further 
specialisation, viz., by putting in every instance P rs = P sr , is 
enunciated at equal length ; and then, evidently for the sake of 
historical connection, it is illustrated by the two simplest cases, 
that is to say, the case where the number of variables is two and 
where the number is three. In the former case 
