1903-4.] 
Dr Muir on General Determinants . 
61 
The Theory of General Determinants in the Historical 
Order of Development np to 1846. By Thomas 
Muir, LL.D. 
(MS. received August 10, 1903. Read November 2, 1903.) 
Since the year 1889, when the last of a series of six papers 
with a title similar to the above appeared, further research has 
led to the discovery of a number of writings belonging to the 
period then dealt with, viz., 1693-1844. Of those an account 
is now given before proceeding to the papers of later date than 
1844. 
Fontaine (1748). 
[Memoires donnes a T Academic Boyale des Sciences, non im 
primes dans leurs temps. Par M. Fontaine* de cette 
Acad^mie. 588 pp. Paris, 1764.] 
These memoirs of Fontaine’s, sixteen in number, cover a con- 
siderable variety of mathematical subjects : it is the seventh of 
the series which indirectly concerns determinants. There is not, 
however, even the most distant connection between it and the 
work of Leibnitz. The heading is “Le calcul integral. Seconde 
methode,” the sixth memoir having given the first method. The 
date is indicated in the margin. 
The matter which concerns us appears as a lemma near the 
beginning of the memoir (p. 94). The passage is as follows : — 
“ Soient quatre nombres quelconques 
a\ , a'2 , a3 , a\ , 
* The full name is Alexis Fontaine des Bertins. The very same collection 
was issued in 1770 under the less appropriate title Traite de calcul differ entiel 
et integral. Vandermonde is said to have been a pupil of Fontaine’s (v. Nouv. 
Annales de Math., v. p. 155). 
