50 Proceedings of the Royal Society of Edinburgh. [Sess. 
that it was first communicated in a number of papers to the Naples 
Academy of Sciences in the year 1857. This being so, it was two years 
in advance of Zeipel’s memoir on the same subject {Hist., ii. pp. 370-372) 
and Bruno’s text- book, a fact which it is important for the reader to recall 
if any small point of similarity between two modes of treatment should 
attract attention. 
Salmon, G. (1866). 
[Lessons Introductory to the Modern Higher Algebra. 2nd ed. 
viii + 296. Dublin.] 
In a table of resultants (pp. 283-285) the final expansion of R 25 is given ? 
and the discriminant of {a, b, c, d, e \ x 4 , x s y, ... , y 4 ). 
Sardi, C. (1866) : Rajola, L. (1866) : Torelli, G. (1866). 
[Questione 47. Giornale di Mat., iv. pp. 239-240 : solution by L. Rajola, 
iv. p. 297.] 
[Teorema sui determinant a due scale, e soluzione della questione 47. 
Giornale di Mat., iv. pp. 294-296.] 
We have already seen how, from equating two forms of the resultant of 
a pair of rational integral equations, interesting identities may be obtained 
{Hist., i. p. 487 at bottom: ii. pp. 369-370, 374-375). Another instance is 
here reached, the forms of eliminant used being Sylvester’s bigradient and 
the eliminant which arises from successively substituting the roots of one 
of the equations in the non-zero member of the other equation and taking 
the product of the resulting expressions. If in connection with the latter 
we make use of Spottiswoode’s determinant expression {Hist., ii. p. Ill) 
for such a non-zero number, the identity evolved will be purely and almost 
alarmingly determinantal. 
Baltzer, R. (1864, 1870, 1875). 
[Theorie und Anwendung der Determinanten, ... 2 te Aufl. 3 te Aufl. 
4 te Aufl. Leipzig.] 
Putting (§ 11, 4 ) 
A{x) = a 0 x m + aqa?™ -1 + • • • + a m = a 0 (x - a 1 ){x - a 2 ) . . . {x - a m ) | __ 
B(a?) = b 0 x n + l x x n ~ x +••• + &„ = b 0 (x - j8 x )(aj - /3 2 ) ... {x - f3 n ) f > n 
