104 PROFESSOR AIRY ON AN INEQUALITY OF LONG PERIOD 
(8) ( 9 ) ( 9 ) 
48. Employing these numbers in the calculation of L , L , & c. M . 
(10) (10) (11) 
M , &c. N and N , from the expressions in (20), (24), and (28), we 
obtain the following numerical values : 
L = X — 333,0969 
_ ( 9 ) m 
L = x 1273,4929 
T ( 10 ) m 
L X - 1945,7913 
(li) m 
L = -, X 1485,3152 
T (12) m 
L = X - 566,5632 
( 13 ) 772 
L =~,X 86,3635 
,,(9) m 
M =-,X — 503,4795 
(10) 777 
M =-, X 1088,9148 
(11) 277 
W -787,0581 
(12) 2?2 
= f,X 190,0487 
(10) 777 
N" = X — 85,3347 
(11) 272 
N = — X 58,8603 
a' 5 
49. The computation of these quantities has been effected by means of alge- 
braical operations of great complexity, and numerical calculations of no in- 
considerable length ; and it is not easy to find in the operations themselves 
any verification of their accuracy. This has imposed on me the necessity of 
examining closely every line of figures before I proceeded to another. I have 
