677 
1907-8.] Dr Muir on General Determinants. 
the expression found for the last coefficient of x 6 is, in later notation, 
I «i h c 3 d± e 5 / 6 | • \a 1 b 2 c 3 d 4 I • I <q b 2 c 3 | 2 • | a Y b 2 | 4 • a x 8 , 
and for the term independent of x 6 
I ^2 ^3 ^4 ^5 ^6 I * I ffi ^2 ^3 ^4 I ’ I ffi ^2 ^3 * I ffi ^2 1^ * j 
with the result, of course, that 
x _ 1 a \ ^2 C 3 ^4 e 5 g 6 I # 
a i ^2 C 3 ^4 e 5/f) I 
It will readily be agreed that this procedure, though fresh, is not an 
improvement on others previously known. 
Chelini, D. (1840). 
[Formazione e dimostrazione della formula che da i valor i delle 
incognite nelle equazioni di primo grado. Giornale Arcadico di 
Sci. . . . , lxxxv. pp. 3-12.] 
The writings known to Chelini were Terquem’s Manuel d’Algebre, 
Bianchi’s paper of 1839, and Molins’ of the same year. The paper, however, 
wffiich his short and clearly written exposition most readily calls to mind is 
Gergonne’s of the year 1813. The “ formazione ” is essentially Bezout’s, and 
the “ dimostrazione ” essentially Laplace’s. 
Terquem, 0. (1846). 
[Note sur les equations du premier degre en nombre plus grand que 
celui des inconnues. . . . Nouv. Annales de Math., v. pp. 551-556.] 
Knowing from the four equations (Terquem uses n) 
a Y x + a 2 y + a 3 z + a^iv = a 5 
b x x + b 2 y + b 3 z + bA = b h 
the usual expressions for w, z, . . . Terquem affirms that if w is to be 
equal to 0 we must have 
I a i l*'2 C 3 dr, j = 0 , 
and that therefore this last equation is the equation of condition for the 
simultaneous existence of four equations between three unknowns. Con- 
tinuing, he says that if we are to have z = w = 0 we must have 
I ~ a \ ^2 c 3 d h | = |oq b 2 c 4 d b | — 0,* (/3) 
and that therefore these two equations are “ les deux equations de condition 
pour que 4 equations entre 2 inconnues puissent etre satisfaites par les 
* The second determinant is incorrectly printed in the original. 
