431 
1909-10.] The Theory of Persymmetric Determinants. 
can be partitioned. He also gives (§121) a new mode of arriving at the 
canonizant in the form 
a 
b 
c 
d 
b 
c 
d 
e 
c 
d 
e 
f 
In the course of a short “Note on Commutants ” he suggests (p. 146) 
that the two rows of umbrae 
/ 
\ 
a A 
a. 
do 
0 1 
2 
0 
l 
2 
0 1 
2 
should stand for 
a i 
a 2 
a 2 
\ 
/ 
<Z 2 
a 2 
a 4 
in which case the suffixes of any term of the determinant are got by 
adding the first row of umbrae to a permutation of the second row. 
LIST OF AUTHORS 
whose writings are herein dealt with. 
PAGE 
1844. Rosenhain .... 407 
1845. Jacobi 407 
1847. Borchardt . . .411 
1851. Sylvester .... 412 
1851. Sylvester .... 413 
1852. Sylvester . . . .417 
1852. Bruno 417 
1853. Ohio 418 
1853. Sylvester . .419 
PAGE 
1853. Spottiswoode .... 420 
1854. Brioschi 421 
1854. Brioschi 422 
1854. Brioschi 426 
1855. Brioschi 427 
1856. Cayley 428 
1856. Bruno 429 
1857. Bellavitis ... 429 
1859. Salmon 430 
(. Issued separately June 16, 1910 ) 
