142 
Proceedings of the Royal Society of Edinburgh. [Sess. 
Baltzer, R. (1875). 
[Theorie und Anwendung der Determinanten. . . . 4 te verbesserte 
Aufl viii + 247 pp., Leipzig.] 
The only fresh matter in this edition is the statement that in the case 
of the evanescent determinant 
L(^0 cf) , dj , &2 , . . . y & n _\) 
where 
<f) = ci 0 + af + a 2 6 2 + . . . + a n _ x 0 n ~ l 
the signed complementary minors of the elements of any row form an 
equirational progression whose constant multiplier is 0. In illustration of 
this we may add that the adjugate of 
C(-bO- c$ 2 , b,c), 
if we write M for b 2 0 2 + be + c 2 6, is 
M 
e 2 m 
1 
6 
6 2 
OM 
e 2 m 
M 
i.e. M 3 
6 
e 2 
1 
e 2 m 
M 
6>M 
6 2 
1 
6 
Nicodemi, R. (1877). 
[Intorno ad alcune funzioni piu generali delle funzioni iperboliche. 
Giornale di Mat, xv. pp. 193-234.] 
The section which concerns determinants (pp. 205-210) contains an 
already known proof of Spottiswoode’s theorem, this theorem being there- 
upon used, as Glaisher had already done (1872), to obtain a generalisation of 
cosh x sinh x _ ^ 
sinh x cosh x 
Scott, R. F. (1878). 
[On some theorems in determinants. Messenger of Math., viii. 
pp. 33—37.] 
In § 2 of this paper there are five fresh results, the first two being, if 
X = log CXeq ,a 2 , ... a n ), 
G(a 1 , a 2 
C 
0A 
0a o 
0A. 
da„ 
1 2 
and Hessian of A 
n n , 
( _ jyn(w-l) . 
