1901 - 2 .] Dr Muir on the Theory of Jacobians. 
153 
Si, pour plus de simplicity on fait usage de la notation 
adoptee par M. Cauchy dans son Memoir e sur les f auctions 
symetriques ,* 1’equation prendra la forme suivante : 
le signe S etant relatif a la permutation des trois lettres 
Here we have clearly the Jacobian of x, y , z with respect to 
«, b, c : and we have it expressed also in the determinant notation 
then in use. 
The second point of interest is centred in the note to which the 
formal statement of a theorem, and extends to only ten lines, is as 
follows : — 
“ Si Ton rapporte la position des sommets d’un parallelepi- 
pede a trois plans rectangulaires des x, y, et z ; que l’on 
designe par A, B, C, les longueurs des trois aretes de ce 
parallelepipede qui aboutissent a un meme sommet, et par 
les projections respectives des memes aretes sur les axes des 
x, y, et z>, le volume du parallelepipede aura pour mesure 
Here we have one of those so-called “ applications of deter- 
* There is a curious oversight here. In a footnote, Cauchy says “ Le 
Memoire dont il estici question a ete imprime en partie dans le xvii e . Cahier 
du Journal de Vltcole Poly technique." Now, as a matter of fact, there is no 
memoir bearing this title. The well-known memoirs contained in Cahier xvii. 
are headed “ Memoire sur le n ombre des valeurs . . . .” and “Memoire sur 
les fonctions qui . . . .” The second part of the latter, it is true, bears the 
approximate designation, “ Des fonctions symetriques alternees . . . but 
the notation in question occurs in both parts. 
It is also not clear what was intended by the words ‘ imprime en partie ’ 
in Cauchy’s footnote. 
author directs his reader. This note, which consists merely of the 
