1907-8.] Dr Muir on Compound Determinants, 
and pointing out that this is evidently the same as saying 
I aa, cl (3 bo. + b /3 
209 
\ a (3 
a b 
\ a (3' 
a b' 
In later phraseology, it may be said that the specialisation necessary for the 
purpose is 
matrix of 
(tj « 2 . . . a , 
b 1 b 2 ... b r 
s = r , 
= 1 , matrix of 
Uj r + 1 M 'r’+2 
b r + 1 br + 2 
a 2r 
b 2r 
= 0.* 
Brioschi (1854, March). 
[La Teorica dei Determinant^ e le sue principali applicazioni ; 
del Dr Francesco Brioschi; viii + 116 pp. ; Pavia. Translation 
into French, by Combescure; ix + 216 pp. ; Paris, 1856. Trans- 
lation into German, by Schellbach ; vii + 102 pp. ; Berlin, 1856.] 
After proving (p. 100) Jacobi’s theorem, above referred to, regarding a 
compound determinant whose elements are functional determinants, Brioschi 
bids the reader make the functions , f 2 , . . . linear, say 
fr d r -^Cy + CL r <2PC2 + • CL r< n+irftn+m j 
and note that the outcome is 
2±A (1, Af ...A ( ™> = {2 
where 
} TO-1 
• y ; + CL i X ®22 ‘ ‘ ’ 
v n+m , n+m ) 
A r — 2 — a n a 22 • 
n+s , n+r 
— that is to say, is Sylvester’s first result of March 1851. 
The same course is followed by Bellavitis in his Sposizione of 1857 
(see §§ 71, 72, p. 56). 
* Some of the pages of Spottiswoode dealt with in the foregoing are, by reason of mis- 
prints and other neglects, not easy reading. On p. 360 there are at least nine misprints. 
(Issued separately, April 8, 1908.) 
YOL. XXVIII. 
14 
