Besolvahiliiy of the Minors of a Compound Determinant. 
101 
\aibo\ \a-J?^\ la-fi^l 
[ctjCgl lo-iCgl hiC^l 
\b-^^do\ \b^d.^\ \h^d^\ 
and is established in the same way as that of § 3. The left-hand member 
being symbolisable by 
i2 M'3 
d^ d. d^ 
we may reason in regard to it exactly after the manner of § 6, obtaining 
first the double result 
125! ~ 0^1^3l^l^2^3^4l 
123 
143 
and thereafter the number of such resolvables to be 96. 
(9) Less general than the immediately preceding, although not thence 
obtainable by substitution, is the equality 
la^b^l \a^b^\ \a^b^\ 
la^Cgl kiCyl \aiC^\ = a-^^la-iboC^d^]. 
\aido\ l^-i^^si Idid^^l 
Here, as in § 7, the change of rows into columns is fruitless, the left-hand 
member being symbolisable both by 
11231 
123! 
f f % ^4 
Lfe^ ! &3 &3 b^ 
and 
L 
^1 ^2 ^3 '^4 
d^ I d^ d^ d^ 
C C ^1 ^1 ^1 
I ^-2 ^2 ^-2 
L a. 63 C3 ^3 
b^ d^ 
The number of minors so resolvable is manifestly sixteen. 
(10) Lastly, by returning to § 8 and changing the d's into cs we obtain 
\aibo\ la^b.J \aib^\ 
123 
124 
= 0. 
'^1^2' l^i^s' '^1^4! 
The construction- symbol for the determinant is either 
C C f ^i ^1 ^1 
I I a.1 bo Co 
f (di a.^ ci^ 
j>??i bo b^ b^ 
L L^i ^2 ^3 ^4 
L ^3 63 C3 
«4 ^4 
