38G MR. LUBBOCK ON THE TIDES IN THE PORT OF LONDON. 
If the longitude of the sun be introduced by putting for § its value from the 
equation 
sin o = sin w sin l 
l being reckoned from the first point of Aries, 
{ sin <p sin 5 + cos p cos 9 cos 0 } 3 = £“!* ( 1 - 
+ co^^l_suUw\ cos29 
+ cos2 ^ sin Ify | cos (2 0 - 2 l) + cos (2 0 + 2 Z) | 
, ■ „ f cos 2 ® sin 2 <b 1 n , 
+ sin 2 w < 1- > cos 2 l 
14 2 / 
+ S ‘ n -- — sin 2 S cos 0 
Considering the results of many years so as to destroy the effects of changes 
in the moon’s parallax and declination, and taking the mean of the times of 
high water when the moon passes the meridian at any given time, and twelve 
hours later, the tides, owing to the united action of the sun and moon, depend 
on the terms 
3 m II 3 cos 2 p 
4 " 
cos 2 0 
+ 
+ 
3 mil 3 cos q <p sin 2 
16 
— jcos (2 0-2 1) + cos (20+ 21) j 
3 m 
n 3 sin 2 o/ f 
“2 I 
4 2 
} 
+ 
3 m, n ( 3 cos 2 1 p 
( , sin 2 w,\ 0 
1 — -i ) cos 2 0, 
and the height of the water will be represented by 
AmW^\ - cos (2 0 — 2 X) 
+ sin 2 W | cos (2 0 - 2 1 - 2 X) + cos (2 0 + 2 1 - 2 X) 
+ C n 1 sin 2 w cos 2/ 
