62 
Proceedings of the Royal Society of Edinburgh. [Sess. 
It is an inference from a property of the multiple integral 
n 
e~ iq dx 1 dx 2 . . . dx n 
where Q is the n — ary quadric 
x 2 
X 3 
2 “ll 
a i2 
a i3 
X } 
« 2 1 
2«22 
a 23 
X' 
a 31 
a 32 
2 a 
ZlU 33 
Xc 
Trzaska, W. (1876, Dec.). 
[Question 201. Nouv. Gorresp. Math., ii. p. 401. Solution by Even, 
iii. pp. 91-92.] 
Exactly in Cayley’s manner it is shown that higher-order determinants 
formed like his third of 1841 {Hist., ii. p. 110) vanish also. 
Jamet, V. (1877); Longchamps, G. de (1877). 
Paige, C. Le (1879); Wolstenholme, J. (1879). 
[Sur une application des determinants. Nouv. Annates de Math. (2) 
xvi. pp. 372-373.] 
[Des fractions etagees (p. 325). Giornale di Mat., xv. pp. 299-328.] 
[Question 514. Nouv. Gorresp. Math., v. p. 452. Solution by Jamet, 
vi. pp. 92-93.] 
[Question 6038. Educ. Times, xxxii. pp. 243, 315 : or Math, from 
Educ. Times, xxxii. p. 91.] 
None of these is of any moment, the first and third being but instances 
of the square of an oblong array, the fourth a simple instance of the 
multiplication of two determinants, and the second a reproduction of 
Ferrers’ first result of 1855. 
