55 
1912-13.] Dr Muir on Axisymmetric Determinants. 
X 1 ~ V\ C 12^2 C 13^3 + • • • + C 1 nVni 
X 2 = ^2 + C 232/3 + - • * + C 2n?A, 
= Vn J 
the series A„, A n _ . . . , A 0 does come up for consideration. The only 
property established (p. 7) is : If A n and all its coaxial minors of the (n-1)** 
order varnish, then every other coaxial minor of the said order will also 
vanish. This is easily arrived at by considering any two-line coaxial 
minor of the adjugate. 
We may note that in dealing with a second transformation — the 
orthogonal — Schultze formulates another proposition regarding the evan- 
escence of minors, but that this is identical with the first of Dodgson’s 
pair of 1867. 
Hunyady, E. (1872, January). 
[Question 979 (proposee par H. Brocard). Nouv. Annales de Math. (2), 
xi. pp. 39-44.] 
In seeking to solve anew Lagrange’s interpolation-problem, namely, to 
obtain the values of the A’s in the set of equations 
A x cos 
lr • 7 r 
n + 1 
+ A 9 cos 
’ r ■ 7 r 
n -f 1 
i nr • 77 
+ A n cos = y t 
n + I 
Hunyady finds that 
M-7 T 2-2-7T 
cos — cos 
n + 1 
n + 1 
cos 
n-n-77 
n+ 1 
f Ifn+IY 
] 4V 2 J 
[ 0 
for n even 
for n odd. 
Williamson, B. (1872): Bitchwald, E. (1872). 
[Condition for a maximum or a minimum in a function of any number 
of variables. Quart. Journ. of Math., xii. pp. 48-51 : or his 
Differential Calculus, 1st edition pp. 340-343, 2nd edition pp. 
363-367, etc.] 
[Question 3683. Educ. Times, xxiv. p. 296, xxv. p. 18 : or Math, from 
Educ. Times, xvii. pp. 66-68.] 
[Betingelsen for at den algebraisk rationale homogene Function af 
anden Grad af n variable er positiv for alle Voerdier af de 
variable eller negativ for dem alle. Tidsskrift for Math. (3), ii. 
pp. 20-25.] 
The real object here is to obtain the conditions that must be fulfilled 
in order that a quadric may remain positive for all real values of the 
variables. 
