1903-4.] 
Dr Muir on General Determinants. 
73 
porro 
ubi 
M = m x x x + m 2 x 2 4 - • • • 4- m n x n 
X n = J(l - Xj 2 + oc 2 2 - • • • - x 2 _^ 
radicali positive accepto ; porro ponamus 
V = ± 2 ± M22 • • * Ki , 
signo ancipiti, ante ipsum 2 posito, ita determinate, ut valor 
ipsius V positivus prodeat. Quibus omnibus positis, erit 
71 Z-y f 4“ &21*^*2 4" * * * 4" bnV^n) 8 Xi$X 2 • * * Sx n _i 
M'v!/ “ ZtK'W 
Yi p 
n z 2 / M(b 12 x x 4 “ b 22 x 2 4 * • • * 4 * b^x^Sx^Sx^ • • • b>x n _ ^ 
z n X^+ 2 > ~~ ’ 
71 z n_ / 1 M(6 1 „ar 1 4- ^2 4- • • • 4- b nn x n )ke x bx 2 • • • &b b _i 
2 n_1 S * V 7 ^X i(n+2) 
integralibus (n - 1 ) tuplicibus extensis ad omnes valores 
reales ipsorum x lt x 2 , . . . , x n _ Y et positivos et negativos, pro 
quibus etiam x n realis sit sive pro quibus 
4- x 2 2 4 - • • • 4- a£_i < 1 ; 
et designante S aut 
2 • 4 • • • • (n-2)\2 
aut 
1.3*5 
(n-2) 
n—1 
IT 
prout n aut par aut impar.” 
Molins (1839). 
[Demonstration de la formule generale qui donne les valeurs 
des inconnues dans les equations du premier degre. Journ. 
de Liouville , iv. pp. 509-515.] 
The real object of Molins was simply to give a rigorous demon- 
stration of Cramer’s rules. His literary progenitors, so far as 
determinants were concerned, were apparently Cramer, Bezout, 
Laplace, and Gergonne, the last of whom, it may be remembered, 
wrote a paper which might well have borne the same title as the 
