1906-7.] Dr Muir on Axisymmetric Determinants. 
159 
Ferrers (1855, Dec.). 
[Two elementary theorems in determinants. Quarterly Journ. of 
Math., i. p. 364: or Nouv. Annales de Math., xvi. pp. 402-403, 
xvii. pp. 190-191.] 
The first theorem referred to is 
1 
1 
1 
1 
1 
1 + oq 
1 
1 
1 
1 
1 + a 2 * ‘ * 
1 
— 
1 
1 
1 
1 + a n 
the proof being dependent on the fact that, if any one of the as be put 
equal to 0, the determinant vanishes. The second is 
1 + a Y 
1 
1 
l 
1 
1 + a, 
2 ^ • 
i 
1 
1 
1 + a s • • • 
l 
1 
1 
l 
1 + a n 
= a^2 . 
..a n [ 
1 + 1 + 1+ . 
..+1) 
\ 
(Iq 
a n J 
which is made to rest mainly on the fact that if any one of the a’s be put 
equal to 0 the determinant takes the form of the preceding determinant. 
Note is taken that Sylvester’s theorem on p. 55 of the same volume is a 
special case of this second result. 
Faa di Bruno (1855, Dec.). 
[Addizione alia nota inserita nel fascicolo di ottobre ultimo. Annali 
di sci. mat. e fis., vi. pp. 476-479: or § vi. of his Theorie 
generale de l’elimination, x + 224 pp., Paris, 1859.] 
The note referred to in the title professed to be “ Sulle f unzioni 
simmetriche delle radici di un’ equazione,” and contained, besides other 
things, the final expansions of the resultants of two quadrics, two cubics, 
and two quartics. The “ addizione,” on the other hand, draws attention to 
the axisymmetric determinants which represent those resultants, the 
author being apparently unaware that Cauchy had already done this in 
