678 Proceedings of the Royal Society of Edinburgh. [Sess. 
memes valeurs.” The words “ et ainsi de suite ” are added to draw atten- 
tion to the general theorem. 
On this we can only remark that the giving of the equations of condition 
in the form (/3) in the second case, even although the real equations of 
condition 
1 «1 
h 
c l 
d x 
a 2 
C 2 
d 2 
=' 0 
\ a 5 
h 
C 5 
d b i 
are thence deducible, seems quite inexcusable, especially in an exposition 
meant to be elementary. 
Hermite, C. (1849, January). 
[Sur une question relative a la theorie des nombres. Journ. (de Liou- 
ville) de Math., xiv. pp. 21-30.] 
As a lemma in the process of attaining the main purpose of his paper 
Hermite gives an identity which for the 4 th order we should nowadays 
write in the form 
«i 
a 2 
a s 
a 4 
1 a 2 b l 1 
| a 3 b 1 | 
1 “A 1 
*1 
c i 
b 2 
C 2 
h 
C B 
h 
C 4 
1 
?i c i 
1 Vi 1 
1 ^3 C l 1 
1 b A i 
*1 
d 2 
d z 
d± 
1 ^ /d j \ | 
1 C B d l 1 
1 C A 1 
This he establishes rather circuitously by taking four quantities (*i , , (Fs > 
which satisfy the equations 
$1^1 + b ^£ 2 + + ^1^4 ~ 1 
^2^1 4" 4" ^2^3 4 ^2^*4 ~ ^ 
4" ^3^2 4" c 3^3 + ^3^4 = 0 
^4^1 4" ^4^2 4 ^4^3 4" ^4^4 — 0 ^ , 
and then multiplying the original determinant columnwise by ( — 1 ) 3 6 1 c 1 in 
the form 
fi • -1 
^2 ~~ a i C 1 • 
. - b 1 d Y | 
^4 • • “ I • 
Salmon, G. (1852). 
[A Treatise on the Higher . Plane Curves : . . . By the Rev. George 
Salmon, M.A. . . . xii + 316 pp. Dublin, 1852.] 
For the convenience of his readers Salmon appended a fifteen-page note 
on the subject of Elimination, and, as was natural, the note opened with a 
