1907-8.] Dr Muir on Compound Determinants. 
-/ 12 •••»!' 
\ 1 2 . . . n J > 
207 
where — 1)(^ — 2). Although there is a semblance of reasoning, no 
real proof is given. Passing then to any first minor of A 2 , say the first 
1 2 n 
a 2/ 
minor got by leaving out 
finds that 
from the detailed symbol for A 2 , he 
{CD 
It is next pointed out that if we proceed to the second minors of A 2 it 
becomes necessary to distinguish two cases, — to distinguish, for example, 
the case where we leave out ( ^ ^ from the case where we leave out 
VI 2/ Vf 3/ 
:■ d c 1 
3 4 
and the result is 
In the latter case the row-numbers 1, 2, 3, 4 are all different, 
f/5 6\ /7 8\ /13\ /2 4\ 1 = fl 2 3 4 Wl 2 . . . 
(\5 6/ V7 8/ Vl 3/ \2 4/ j \ 1 2 3 4 /} 1 2 . . . nf; 
in the former case the row-number 1 occurs twice, and the result is 
{CD cd-0-hih: n}{ii::.-:r 
Generally, if (J J ■ ’ (3 4) ’ (5 g) ’ ' ' • ’ Ql! 2i) be le£t ° Ut ’ W ° haVe 
f/2i+l 2i+2\ /2i + 3 2i + 4\ /I 3\ /2 4\ } g f 1 2 . . . 2i\ ( 1 2 . . . n\ v ~ 
(\2t+l 2* + 2/ W+3 2t + 4/ ’ ” \1 3/ \2 4/ J (l 2 . . . 2i] \ 1 2 . . . n J • 
/I 2\ (1 3\ /I i\ 
and if 2/ \1 3/ ’ ’ * \1 i) ou ^ We i iave 
j/l i+lWl t + 2\ _ /2 3\ .... 1 = 11) ^ll 2 ... till 2 ... ra) - <+I 
\\1 i + lAl t + 2/ " \2 3/"" j 1 1 J \l 2 .. . *J \l 2 ... . »J . 
/I 2\ /I 3\ 
Again, a fresh variety of minor may be got by leaving out ( J , ( ) , 
Vl 2/ '1 3/ 
/2 3\ 
^ J the row-numbers being then two l’s, two 2’s, and two 3’s, and the 
result is 
{(! D CD" 
2 4 
2 4 
) _ fl 2 31 f 1 2 . . . nD- 
J “ (1 2 3 / (1 2 .. . n) , 
and so on.” 
