AND ITS APPLICATION TO MR. B. TOWER’S EXPERIMENTS. 
195 
r=2 go 
A o =-X-2,. =2 i 
(r + i)r\r-l) . . . ^ (r + 2)(r + l)r(r- 1) . . . ^ 
-— c r ~ lJ r 
2 r 
+i 
2r+l 
r 
2 
c r X 
A 2 „ = (-i)" +1 < 
(2tt + 1)2^„ +1 + (2 n + 2)(2n + 1) ^ 
2 2tl 
92« 
+2 
r= 2oo 
r=2m+2 
/ , h \ jr r + 2?i + 2 , ON . 1N r + 2?t + 2 
(r + l)r\r — l) . . . -^- (r + 2)(r + l)r . . .-^- 
' C'" 1 +-~- ° r X 
r 
2~ n 
— n 
_ , ,J (2n + 2)(2 W + l) (2n + 3)(2n + 2) 
^2^+1 \ 1 2 2w+1 ° 9.2»+l 
22^+1 
-c 3 « +] ^ 
r=2oo + l 
+2 
— 2?i + 3 
( r _|_l) r 2( r . 
-1) . . . r+2 ^ +3 (r + 2)(r + l>. . .r 
1 1 . 
Or 
r —2?i —1 " 1 
?• —2?i —1 
2 
2 
-c’-x 
B n = 
r=2 oo 
l-3c x +S 
r=2 
(4-3(r+l))n(r-l)...i±2 
2 r 
3(?’+ l)r(r — 1) 
r + 1 
2 r 
° r+1 x 
B 2 , — 
/_, u J [£- 3(2«, + l)]c 2 ” — 3(2n + l)c 2,t+1 % 
V i / 1 02 b—1 
+2 
r=2m+2 
[4—3(r+l)]c'—3(r+l)c’ +I x 
r.(r— 1) . 
r + 2n + 2 
2 
£r-l 
r — 2n 
2 
E +| _ ( ^..n { [i-mn + 2)y+'-3(2n + 2y*° x 
02b 
r=2oo + 3 
r- 
r.(r + 1) 
. . . r + 2w + 3 
+2 
r=2»+3 
[4 — 3(r +!)>/-3(r +1 )c r+1 x 
2 r-a 
r — 2n — 1 
2 
(53) 
(51) 
2 c 2 
