Dr T. Muir on the Theory of Determinants. 
493 
of statement. Eemembering that the inner S’s refer always to the 
first suffix, and the outer to the second suffix, we obtain the more 
developed form 
+ “10.1) 
•+“S 2 }(«S+«S+--- 
+ “10.2) 
+ 
+ “1.10 ^ “2.10 ^ • 
••+“:So)(»So + <U- 
+ m^2 j + • • 
• +“m.i 
+ m^2 + ^^2+ • • 
+ m<^> 
+ 
+™So+” 4 !lo+ • • • +™io.io- 
Interpreting now the suffixes and superfixes of the a’s, a’s, and m’s, 
after the manner already described, — any suffix r signifying along 
with the superfix (2) the combination of two numbers taken 
from 1, 2, 3, 4, 5, we finally reach the suitable form 
+ Iai.ia 3 . 2 l 
+ . . . . 
+ 
-f 
to 
+ Ia 3 .ja 5 . 2 l + Ia 4 .ja 5 . 2 l } 
{ !^l*l^ 2 ’ 2 l 
+ Ia 1 .ja 3 . 2 l 4 - . . . . 
.+ Ia 3 .ja 4.21 
+ 
l%’l%' 2 l l%l*^ 5 ‘ 2 l } 
+ . . . 
+ { |ai- 3 a 2 - 5 l 
+ Iaj. 3 a 3 . 5 l 
+ . . . . 
• + |“ 3 * 3 “ 4 * 5 l 
+ 
lo^ 3 - 3 a 5 - 5 l + l« 4 - 3 « 5 - 5 l } 
05 
a 
to 

+ laj. 3 a 3 . 5 l 
+ . . . . 
. + Ia 3 . 3 a 4 . 5 l 
+ 
l% 3 ^ 5 - 5 r+ l% 3 « 5 - 5 l } 
+ { |ai. 4 a 2 - 5 l 4 - lai- 4 « 3 * 5 l 
+ . . . . 
• + ia 3 . 4 a 4 . 5 l 
+ 
k 3 * 4 « 5 - 5 l + K- 4 « 5 - 5 l } 
+ i«l- 4 « 3 - 6 l 
+ . . . . 
.+ Ia 3 . 4 a 4 . 5 l 
+ l<^ 3 . 4 a 5 . 5 | + 1 ^ 4 . 4 %. 5 ! } 
= + i«h'l»*3-2l + + l>«3-l™4-2l + l>»3-l”»5'2l + l»%l«*5-2l 
+ 
+ Im1.3m2.5l + Im1.3m3.5l + + |m 3 . 3 m^. 5 ! + Im3.3m5.5l + K.gmj.jl 
+ im1.4m2.5l + Im1.4m3.5l + + Im3.4m4.5l + Im3.4m5.5l + Im4.4m4.5l, 
where m^'v — + . . . + a^.yxy^ . 
The series of suffixes for the a’s, a’s, and m’s are seen to be the same, 
