108 
CHRISTIE. 
are derived is even or odd, be the values of e in thep th term 
of the 7 -tide, as obtained from the several successive and 
consecutive periods or sections by the numerical process re¬ 
flected in the foregoing analysis, I the time-length of a 
period, or section, as the case may be, and dj a correction to 
the assumed value of the speed, so that the corrected or true 
speed of the tide or inequality sought is i — j + dj ; then, 
denoting by £ 0 the true value of e at the middle of the series, 
we have for the determination 
equations 
£ o 
pISj 
or 
2 r — 1 
1 4- - 
2 
h -0 
, 2 
r — 3 
1 + - 
2 
— e 2 =0 
• 
1 
• 
1 +- 
2 
= 0 
1 
1 - - 
2 
- £ r + l =0 
„ 2 
r — 3 
1 - - 
2 
e 2 r — 1 ~ t) 
2 
r — 1 
1 - - 
2 
— e 2 r =0 
of e 0 and dj the conditional 
e o pldj 
1 + S 
— £ i 
= 0 
1 + (8 - 
D-*. 
= 0 
1+ 1 
— £ g 
= 0 
1 zb 0 
“ £ s+l 
= 0 
1 - 1 
“ £ S + 2 
= 0 
1 - s 
~ £ 2s+] 
1 = 0 
whence the most probable values are 
-j k = 2 r 
?0== 27 kli £k 
or 
p I. r (2 r — 1 ) (2 r + 1 ) k = i 
-j k = 2 s 4-1 
1 
k = 2 r 
2 (2 r 
2 k+ 1) e* 
2 6’ 4" 1 k : 
3 _ 
8 (s -f 1 ) (2 s + 1 ) 
k = 2s + 1 
(8—k+ 1 ) 
k = 1 
