100 
PROFESSOR AIRY ON AN INEQUALITY OF LONG PERIOD 
(A) 105 (A) (A) (k) 
(4,0) Cx =+-T7- 13,8031342 . C 3 - 6,6980500 . C 5 
fA) (A) 
- 5,9973139 . C 7 + 1,2388750 . C, 
T -T 
(A) Q45 (A) (k) (A) 
(5,0) C § = - 32 C 4 + 84,1230534 . + 15,4872787 . C s 
(k) (A) (A) 
+ 10,2085636 . C 7 + 24,0925995 . C 9 - 3,6747654 . C,, 
45. Making s = ~a, the formulae give 
(A) 
( 1 , 0 ) c; = 
. 1 r (/ ° 
•4 -jj- 
(A) 
— 0,9887370 . C s 
*§■ 
3 ^(*) 
(A) 
(2,0) = 
+ T C 4 
— 1,1812599 . C 5 
"T 
+ 1,6293350 . 
/ x (k) 
15 -(*) 
(A) 
(3,0) C, — 
8 
+ 7,5403278 . C 5 
T 
+ 8,2837785 . 
,(*) 
A*) 
- 3,7589615 . C 
(*) 
46. Making s = 77 , the first formula gives 
(A) 1 (k) (A) 
( 1 , 0 ) C s =-7rC s - 1,6478950 . C 7 . 
TT ^ T *2* 
(Ar) (A) 
47 . Substituting in these the values of C* , C 3 , &c. found in the last sec¬ 
tion for different values of k, we form the following tables: 
For the development of the first term , 
k= 8 
(0,0) c< 8) 
—i 1 x 0,0414571 
a 
(1,0) C' 8) x - 0,414243 
(2,0) C ( , 8) 
"S' 
^ x 4,71815 
/n p(®) 
(o,0) 
x — 61,0595 
