Dr T. Muir on the Theory of Determinants. 
539 
I I bi bo 63 \ II &2 ^3 ^4 \ 
II bi 62 \ II ^2 ^3 \ 
2(-H| AiBg-| B'.,B'3B'J=0, 
2(-)* bv1b'2B'3B',b'J = o, 
welche mit ermudender Weitlaufigkeit bewiesen sind . 
This statement is unfortunately not by any means accurate. As for 
the “ ermiidende Weitlaufigkeit,” there can be no doubt about it, 
and to assert its existence is fair criticism; but to say that the whole 
of Desnanot’s results are to be found in the three identities specified 
is a misrepresentation of the actual facts, and therefore quite unfair. 
The reader has only to turn back for a moment to our account of 
Desnanot’s work, to verify the fact that the two most important 
general results attained by the latter (xxiii. 6 and xlvi.) are 
ignored by Schweins altogether. 
The remaining paragraphs of the chapter are taken up with the 
very elementary case in which the products are three in number, 
and the theorem itself nothing more than one of the extensionals 
so lengthily dwelt upon by Desnanot, viz., the extensional 
= C). 
It is written in several forms, e.g . — 
+ 
^1 ^n+tn \ 
Aj 
^n+m \ 
Aj. • • A,j_jA^_|_ 2 . . . y 
^1 ^w+m\ 
A]^. . . A„_jA,^^j. . . A,j_j_,^I> j 
^«+m+l 
Aj. . . 
• ^n-\-m+\ 
"^1 -h-n+m D 
^n+m +1 
■^1 
) 
) 
) 
= 0. 
The next chapter, the third, concerns the solution of a set of 
linear equations, although according to the title its subject is the 
transformation of determinants into other determinants when the 
elements are connected by linear equations. It presents no new 
feature. 
The fourth chapter deals with a special form of determinant, the 
consideration of which must therefore be deferred. Suffice it for 
the present to say, as an evidence of Schweins’ grasp of the subject. 
