1907-8.] Dr Muir on General Determinants. 691 
The section (§ 7) on “ determinanti di determinanti ” is founded on 
Cauchy, and contains known extensions of two or three theorems above 
given in the notation of differentiation. 
Cantor [M. B.] (1855, March). 
[Theoreme sur les determinants Crameriens. Nouv. Annates de Math. 
(1), xiv. pp. 113-114.] 
The theorem in question may be formulated thus — If the permutations 
of 1, 2, 3, . . . , n be arranged in order of magnitude as if they were 
integral numbers, the sign of the k /;i permutation is independent of n. 
Reference is appropriately made to Reiss’ paper of 1825, but the theorem is 
virtually contained in Hinderburg’s rule of the year 1784. 
Heger, I. (1856, July). 
[Ueber die Auflosung eines Systemes von mehreren unbestimmten 
Gleichungen des ersten Grades in ganzen Zahlen. Denkschr. d. k. 
Akad. d. Wiss. in Wien: math.-naturw. Cl., xiv. (2)pp. 1-122.] 
Although in this lengthy paper the vanishing of the determinants of a 
2-b y-n array is repeatedly under consideration ( e.g . § 24, p. 87), nothing 
new on the subject presents itself. 
Schlomilch, 0. (1856). 
[Brioschi’s Theorie der Determinante und ihre hauptsachlichsten 
Anwendungen. Zeitschrift f. Math. u. Phys., I. Literaturzeitung , 
pp. 80-87.] 
After a faithful account of Schellbach’s translation of Brioschi’s text- 
book, Schlomilch inveighs against the adoption of “ die miserable englische 
Terminologie,” instancing Unter determinante, Determinante mit reciproken 
Elementen, and Hessian, for the last of which he proposes to substitute 
Inflexionsdeterminante.” 
Rubini, R. (1857, May). 
[Applicazione della teorica dei determinanti. Annali de Sci. Mat. e 
Fis., viii. pp. 179-200.] 
This resembles Chios paper of 1853, having the same fundamental 
theorem, but different illustrative examples. In the mere enunciation of 
