696 
Proceedings of the Royal Society of Edinburgh. [Sess. 
as the assertion of the vanishing of an aggregate of products of pairs of 
determinants. 
The theorem formulated by Bella vitis regarding a zero determinant is 
appropriately based (§ 7, 5 ) on the vanishing of the two-line minors of the 
adjugate determinant — a course suggested by what Lebesgue did in 1837. 
Cayley’s development of 1847 is well stated (§ 8, 6) in the form 
D + A/ + • • • +«ii«22 ■<■••«»»> 
where D is what the given determinant becomes when all its diagonal 
elements are made 0, and D;* is the minor of D got by deleting the 
i t}l , k th , . . . rows and the i th , k th , . . . columns ; and the proof consists in 
showing that no term is thus neglected or repeated. 
Newman, F. (1857). 
[On determinants, better called eliminants. Proceedings Roy. Soc. 
London, viii. pp. 426-431 : or Philos. Magazine (4), xiv. p. 392.] 
The author’s object was merely to recommend the introduction of the 
subject into elementary text-books. 
Del Grosso, R. (1857). 
[Sulla regola secondo la quale debbono procedere i segni nello sviluppo 
d’un determinante in prodotti di deter minanti minor i. Rendic. 
. . . Accad. Pontaniana, Ann. v. pp. 196-198.] 
When a determinant is expressed in accordance with Laplace’s theorem 
as an aggregate of products of complementary minors, Del Grosso directs 
that the sign of any product is to be ( — l) 0- , where cr is the sum of the odd 
row-numbers and odd column-numbers of one of the factors. The rule is 
not stated with sufficient care, and the author in reaching it concludes too 
hastily that the simplest case is all that need be established. 
Janni, G. (1858). 
[Saggio di una Teorica Elementare de’ Determinants del 
Sacerdote Giuseppe Janni. ... 40 pp. Napoli.] 
Janni’s professed object was to make determinants more readily 
accessible, previous text-books having, he says, either totally neglected 
demonstrations or used those of great difficulty. He speaks of the work 
as the first of a series, and its contents certainly look like the first five 
