106 
CHRISTIE. 
for substitution in the form 
c pj cospjt 4 - S pj sinpjt 
or 
% COS (pj t — £ pj ) 
expressing thej-tide of p th order. 
( 4 ) 
Resume equation (2) : Then 
f / TV— 1 \ 
| + sm i T 1 
| -J- /S r sin i T 1 
( N—l 
T 0 =h + Z 1 
r, = a + ^ 
^ (7 r cos i r 1 
f ■ /S/10 0 
1/ 2 mi/T J 
f iV —3 > 
(/ 2 
f t |~ 3 
V 2 m > 
V 2 
21-i=A + 2:-| 
O r cos i x | 
f t-U N - 1 mv r S 
) -j- S T sin ij. 1 
f t , ^-1 
+ 2 to >- ^ 
V + 2 
1 ^ 1 
-mvTj > 
•)} 
are N consecutive derivative ordinates T separated by a com¬ 
plete ^'-period, and hence relating to the same phase of the 
j- tide. Summing, putting 
N 
(^0+^1+ • • • + - l) — Q, 
sin Nmv(3 r 
N sin mv 
U , 
we obtain 
or, putting 
UC = r , 
Q = h -j- 2 (j x cos i r t -f- sin i v t) ; 
2 (y r cos i r t-\- <r r sin i t t) — 2 <p Y , 
(5) 
where i r no longer includes j, we have 
h + r. j cos j t -j- flj sinj t + r v cos2jt + . . . —(Q~2 p r ) = 0. 
1TT ... . ,, . . , . m — 1 m — 3 
Writing m this successively j t== —-- n. —- n. .., 
m 
m 
m — 1 
* ’ ‘ m 
solution is 
7T, we get m equations, of which the least square 
