219 
1888-89.] Dr T. Muir on the Theory of Determinants. 
and 
P = (b'c"){ca')-(bc')(c'a") i /3" = . . . , /r = . . . , 
y' = (Ve”){ab')-(a'b")(bc' ), y" = . . . , y'" = . . . , 
0 , = (6'c")(a5c)-(5c , )(aW), 0''=. . . , 0"' = . . . . 
Minding then continues (pp. 399, 400) 
“ Man setze 
a"\bc') - a(0V') + a\b"c"') - a'\b'"c) = M. 
“ Nach den nothigen Reductionen erhalt man : 
p = ~(c" -c' )M, y = -(V -b") M, 0' = ~(b'c" - b" d )M , 
P' = + (c" - c" )M, y " = + (0" - V") M , 0" = + (0" d" -b'c )M 
P'"=-(C - c"')M, y"= -(0"'-0 )M, 0"'=-(0"'c -0 c'")M 
“ Hieraus erhalt man weiter : 
A = - M 3 (0" c -V c") . (0V"), 
A' = - M 3 (0"'c" - 0" c'") . {(0"c" # ) - (0"'e)} , 
A" = -M 3 (0 c"'-0"'c ).(0'c"). 
“ Eine weitere Reduction ergiebt : 
(0c'" - 0"'c)(0'c") - (0"'c)(0'"c" - 0V") = {c'"b' - c'U") . 
“ Hieraus folgt A. + A' + A" = M 3 (0'c")(0V"), und als Resultat: 
nn'irir" m 3 „ 
A B C D q.ff'f" ’ 
The first point to be noted here is, that since 
(be') , (ca!) , (ah’) , 
are in modern notation 
b 
V 
b" 
c 
c' 
c" 
a 
a 
a!' 
c 
c' 
c" 
a 
a' 
a" 
0 
V 
b" 
1 
1 
1 
} 
1 
1 
1 
> 
1 
1 
1 
the identity 
a(bc') + b(ca f ) + c(ab') = a(b'c" - b"c') + a\b"c - be") + a" (be - be) 
