156 Proceedings of Royal Society of Edinburgh. 
and 
D. 
1 1 . 
- 1 1 
- a s _ 2 1 0 
- a s _ i 0 1 
1 0 0 
— 1 1 
- a n _ i 1 1 
-a n 1 
1 1 
1 1 
-«* 1 1 
0 1 j 
- a s+ 2 1 1 
1 o ' 
- a s _ 3 1 1 
- a n _ i 1 1 
- « S - 2 1 
-a n 1 
_ _ TV - 
- 1 - 1 &,s— 2- 1 - 1 s+2,w j 
and thus reaches the result 
“ -^fc.s-l^s+l.w d* tt s-N*,s-2-^Vj-2, n 
already obtained in a different way by Schlafli. 
Lastly, taking a determinant of the same form as hut 
having 
— a s , — a s _i , . . . , — a k+li — a hi — a k , — a k+ 1 , . . . , — a n _ 1} — a n 
for its minor diagonal of a’s, he obtains for it by isolating the first 
a k the expression 
s,fc+2-Nfc+l,« J 
and by isolating the second a k 
+ a ^s,A:+l^+2 ( n > 
and thus deduces 
-Nfc.n-Nfc+l.s — Nfc jS N’fc +ljn — — tt A (N fc+ i >n N A+ 2 )S — N s+ljS N a+ 2,w)* 
It is then noted that the bracketed expression on the right differs 
