1903 - 4 .] 
Dr Muir on General Determinants. 
87 
Vandermonde’s paper was read afc the very beginning of 1771 and 
Laplace’s in 1772: yet in the History of the Academy for the 
latter year Laplace’s occupies pp. 267-376 and Vandermonde’s 
pp. 516-532, and neither refers to the other’s work. 
It may he noted here that, notwithstanding Terquem’s knowledge 
of the early history of determinants and his manifest desire to 
induce his readers to take up the subject, he does not himself hold 
the new weapon with a very firm grasp. For example, in giving 
in this volume an account of a paper of Grunert’s in Crelle’s 
Journal , viii. pp. 153-159, in which the author says — 
“ Entwickeln wir nemlich x, y', z\ durch Elimination aus 
den Gleichungen : 
x = Ax + By' + Cz, 
y = AV + By' + C V, 
e = A"x + B'y + C"z", 
so erhalten wir : 
, (B'C" - B"C> + (B"C - BC> + (BG - B'C)z 
x ~ : • .. L ’ 
y = 
z = 
wenn wir 
L = AB'C"- A'BC" + A"BC' - AB"C'+ A'B"C - A"B'C 
setzen ” — 
he paraphrases the passage as follows : — 
11 Les equations donnent 
, x[B'C"] + y[B"C] + z[BC] 
x - J- , 
y = ...... 
z — 
oil les crochets represented des binomes alternes ; 
[B'C"] - B'C" - B"C', 
et ainsi des autres : L est la resultante , denominateur 
commun.” 
