1904 - 5 .] 
and thence 
Dr Muir on General Determinants. 
927 
V x d" ^2^2 "h l^’ 2 ^1^3 T ^2^3 ^3^3 
v 2 + m 2 & 2 + W 3 C 2 ^i®3 + m 2 & 3 + m 3 c 3 
v 3 n x a 2 + n 2 b 2 + n 3 c 2 n x a 3 +njb z +n z e z 
l i$i + ^2^1 T ^3^1 ^1^2 "h ^2^2 ^3^*2 ^1^3 "b / 2 & 3 ~b ^3^3 
m-p^q + m 2 &j + m 3 c x m x a 2 + m 2 b 2 + m 3 c 2 m^g + m 2 & 3 + m 3 c 3 
+^2^1 + ^3 C i ^1^2 + w 2^2 +^3 C 2 7i i a s + ^2^3 + ?? '3 C 3 
Secondly, — and here he differs from Joachimsthal, — by writing the 
six equations as one set in the form 
a x x 
+ a -iV + 
a 3 z - 
% 
= 
0 ' 
b x x 
+ \y + 
h z 
- 
U 2 
= 
0 
e x x 
t o 2 y t 
c z z 
- 
w s = 
0 
h w i 
+ 
l 2 u 2 
+ 
/ 3 W, 3 = 
m l u l 
+ 
m 2 u 2 
+ 
m z u 3 = 
^2 
n x u x 
+ 
n 2 u 2 
+ 
= 
V 3 
he obtains directly for x the value 
a 2 
a z 
- 1 
. 
a x 
a 2 
a 3 
-1 
b 2 
h 
- 1 
\ 
^3 
- 1 
C 2 
c 3 
- 1 
c i 
C 2 
C 3 
- 1 
V 1 
h 
l 2 
h 
h 
h 
h 
V 2 
m x 
m 2 
m 3 
m x 
m 2 
m 3 
V Z 
n x 
n 2 
n 3 
n x 
n 2 
n 3 
A comparison of the denominators in the two values of x then 
gives the desired result.* 
The theorems of § 6, though, for some unexplained reason, 
not formulated and numbered like the others, are of the 
highest importance, the subject-matter being the determinant 
* Spottiswoode, like Joachimsthal, it will he observed, deduces nothing from 
a comparison of the numerators. Thus, by equating the two cofactors of v lf he 
might have obtained 
I m i 
m 2 
m 3 1 | a 2 
b 2 c 2 1 
1 n i 
n 2 
n 3 1 1 a 3 
h c 3 | 
a. 2 a 3 — 1 
b 2 b 3 . - 1 
c 2 c 3 . . - 1 
. . m x m 2 m 3 
. . n x n 2 n 3 . 
