484 Proceedings of Boy ctl Society of Edinburgh. [july 18 , 
two pages of application to the solution of simultaneous linear 
equations. 
No reference is made by De Prasse to Hindenburg, Rothe, or 
Vandermonde. 
WRONSKI (1812). 
[Refutation de la Th4orie des Fonctions Analytiques de Lagrange, 
Par Hbene Wronski, pp. 14, 15, . . . , 132, 133. Paris.] 
In 1810 Wronski presented to the Institute of France a memoir 
on the so-called Technie de T Algorithmic, which with his usual 
sanguine enthusiasm he viewed as the essential part of a new 
branch of Mathematics. It contained a very general theorem, now 
known as “ Wronski’s theorem,” for the expansion of functions, — a 
theorem requiring for its expression the use of a notation for what 
Wronski styled combinatory sums. The memoir consisted merely 
of a statement of results, and probably on this account, although 
favourably reported on by Lagrange and Lacroix, was not printed. 
The subject of it, however, turns up repeatedly in the Refutation 
printed two years later; and from the indications there given we 
can so far form an idea of the grasp which Wronski had of the 
theory of the said sums. 
At page 14 the following passage occurs: — - 
“ Soient X 1? X 2 , X 3 , &c. pleusieurs fonctions d’une quantite 
variable. Nommons somme combinatoire , et designons par la 
lettre hebraique sin , de la maniere que voici 
^[A a X x . A 6 X 2 . A c X 3 . . . A*XJ , (xv. 3) (vn. 4) 
la somme des produits des differences de ces fonctions, com- 
poses de la maniere suivante : Forrnez, avec les exposans 
a, b, c, . . . , p des differences dont il est question, toutes les 
permutations possibles; donnez ces exposans, dans chaque 
ordre de leurs permutations, aux differences consecutives qui 
composent le produit 
AX 1 . AX 2 . A 3 . . . AX,- ; 
donnez de plus, aux produits separes, formes de cette maniere, 
le signe positif lorsque le nombre de variations des exposans 
a, b } c, etc., considers dans leur ordre alphabetique, est nul on 
