368 
Proceedings of Royal Society of Edinburgh. [sess. 
( 2 ) 
a 
a 
e 
b 
c 
d 
e 
f 
e 
a 
b 
c 
d 
e 
e 
d 
a 
b 
c 
d 
J_L 
e 
d 
c 
a 
b 
c 
It 
e 
d 
c 
b 
a 
b 
e d 
c 
b 
a 
a 
e 
d c 
b 
a 
b 
c 
d 
e 
/ 
a 
b 
c 
d + e . 
a b +e c + d 
e a + d b+c 
e d c a+b 
deb a 
= -ef 
a b c d + e 
a b+e c+d 
e a+d b+c 
d 
a + b 
ef- 
abed 
e 
a b c 
44 
e d 
a b 
rr 
e d c 
a 
e d c b 
= — ef(a + b + c + d + e) . ^3 . 
It thus appears that for the evaluation of all the determinants 
of these three sets it is necessary only to know the final expansion 
of the set Xl , x 2 > Xv • « • • 
j 
