MR. LUBBOCK ON THE TIDES IN THE PORT OF LONDON. 
385 
Hence I infer that neglecting the influence of the moon’s parallax and de- 
clination, when the moon passes the meridian at twenty-four minutes past 
twelve mean solar time in January, the time of high water at the London 
Docks is nine minutes past two. 
The other Tables, which result immediately from the observations, were 
formed in the same manner, and are, I trust, sufficiently explained by the head- 
ing which accompanies each. 
In the notation of the Mec. Cel. 
Let m be the mass 
5 . . declination 
6 . . hour angle 
r . . distance from the centre of the earth 
II . . mean horizontal parallax 
l . . longitude 
1 
>-of the sun. 
n . . mean motion in its orbit 
u . . obliquity of the ecliptic 
L 
v 
n t -j- zj — yp 
r 
<P 
m 
e 
The same letters accented at foot refer to the moon, being the inclination 
of her orbit to the equator ; let also <p denote the geographical latitude of the 
port, in the notation of the Mec. Cel. 90° — 0. 
Considering only the terms which are multiplied by the cube of the parallax, 
the forces which produce the phenomena of the tides are the partial differences 
of the function 
3 m 
2r3 
| (sin <p sin $ + cos <p cos S cos 0) 2 
See the Mec. Cel. vol. v. p. 168. 
According to the theory of Laplace, this function being equal to 
2 A cos (0 — X), 6 being any variable angle depending on the time, and A and X 
constants, the height of the water at any given time is equal to 2 ( A ' cos (0 — X'), 
0 being the same angle as before, and A' and X 1 other constants. 
f . . . * „ ] 2 sin 2 c . cos 2 <p . cos 2 0 „ f sin 2 <p cos 2 a 1 0 , 
-j sin <p sin 8 + cos <p cos 8 cos 0 > = — - — + — - — + — - — cos 2 0—^ — - — — — - — > cos 2 5 
+ — | cos (2 0 — 2 S) + cos (2 0 + 2 5) j + s !IlJL£ s in 2 S cos 0. 
3 d 2 
