96 
PROFESSOR AIRY ON AN INEQUALITY OF LONG PERIOD 
'• + l 
i n* + s)(*+s-i) P (*-i) (k- s )(k-s+1 ) ^+i)-) 
— _ a y\ /cs ^ ks ^ J 
in which 
. sin 2 ,3 
/I \2 or (1 - at~f 1S cos*(3 — 2 > 3015505 
U ~v 
o- T\r i • 1 sin 3 /3 4F- 1 /„(* - 0 „(*+i)\ 
3/. Making s = C, = . (C f - C 4 ). Using this 
formula, 
(4) 1 
C 3 =—x 3,403041 
T O, 
(5) 1 
C 3 = — X 2,652559 
T & 
( 6 ) 1 
Cl = 7 x 2,047192 
(7) l 
C, =^X 1,568093 
( 8 ) 1 
C 3 =-r X 1,193991 
■f LL 
(9) 1 
C 3 = -r X 0,904/85 
T ^ 
( 10 ) i 
C 3 = X 0,682935 
T tv 
(11) 1 
C 3 =-7X0,513/99 
T 4 
( 12 ) 1 
C 3 = —X 0,385521 
4 a! ’ 
(13) 1 
C 3 = -r X 0,288655 
T tZ 
(14) 1 
C 3 =-rX 0,215803 
T » 
(15) 1 
C 3 =-7X0,161251 
T LI 
(16) 1 
C 3 = j X 0,120579 
T (6 
(17) l 
C 3 = -r X 0,090452 
t a ' 
38. 
Making s — — _ s * n2 ^ f ( 2 ^ + 3) (2 ^ ] ^ 
Making s g , - Gcos ^- j & W 
C ( 3 + By the use of this formula, 
(2 ft - 3) (2 & - 1) r (*+ U 
k 
cf = ^ X 27,43922 
( 6 ) 1 
c, = 7 x 23,14387 
C ( : ; = ^ X 19,25046 
( 8 ) 1 
C A = 7 X 15,82608 
(9) I 
C 5 = 7 x 12,88246 
T U 
(10) l 
c , = 7 X 10,39741 
( 11 ) 1 
C 4 =^X 8,32969 
( 12 ) 1 
C 5 = —7 X 6,62955 
1r W 
(13) 1 
C. =-7 X 5,24565 
IT LI 
(14) 1 
C V =^7X 4,12790 
_(!5) 1 
C 5 =-/X 3,23120 
T Cl 
(16) 1 
C 5 =-7X2,51561 
t a 
5 sin 2 (3 f (2 A: + 5) (2& + 3) ~(*- 0 
39. Making . = j,C, = . 4 1- £ -C, 
'-!■ 10 cos 2 13 ‘ ^ 
(*+!)■) 
C 5 . Thus we get 
(2 & — .5) (2 £ - 3) ^(* + 1 ) 
& 
