1904-5.] Dr Muir on G-eneral Determinants. 947 
where A rs = a rs + h r + Jc s , and the h’s and &’s are perfectly arbitrary 
quantities, the transformation being of course effected by adding 
multiples of the last column to the other columns, and thereafter 
multiples of the last row to the other rows. 
The geometrical applications which follow, it may be interesting 
to note, are connected with the subject of Cayley’s paper of 1841, 
— his well-known first paper on determinants. 
LIST OF AUTHORS 
whose writings are here dealt with. 
1844. 
Cauchy . 
PAGE 
. 908 
1851. 
Sylvester 
page 
. 929 
1844. 
Cauchy . 
. 908 
1851. 
Sylvester 
. 932 
1846. 
Hansen . 
. 913 
1851. 
Sylvester 
. 933 
1847. 
Cayley . 
. 913 
1851. 
Cayley . 
. 934 
1847. 
Cauchy . 
. 915 
1852. 
Sylvester 
. 939 
1849. 
JOACHIMSTHAL 
. 919 
1852. 
Betti 
. 942 
1850. 
Sylvester 
. 923 
1852. 
Bruno, Faa di 
. 943 
1851. 
Spottiswoode 
. 924 
1852. 
Sylvester 
. 944 
( Issued separately September 30, 1905.) 
