98 
MR. LUBBOCK ON THE TIDES. 
London Docks made under the direction of the late Mr. Peirce ; the latter tables 
differing from those given in the Philosophical Transactions for 1836, Part I., chiefly 
by being founded upon nearly double the number of observations. The high waters 
at Liverpool considered in this paper occur about 48 hours after the transit of the 
moon to which they are referred ; the tides at London which are considered occur 
about 50 hours after the transit to which they are referred in this discussion, so 
that in fact all the intervals of the Liverpool Tables given in this paper ought to be 
increased by 36 hours, and all the intervals in the London Tables by 48 hours. The 
tide which makes high water at Liverpool arrives at the same instant somewhere on 
the north-east coast of Scotland, and at London about fifteen hours later. This is 
proved by the epoch of the semimenstrual inequality. 
I find by interpolation from Table II. the interval for the moon’s transit A 
d h m 
At 3 o’clock ... 1 23 40‘5 
and at 9 o’clock ... 2 1 2-0 
The difference is l h 21 m “5, which converted into space 
= 20° 22' log tan 20° 22' = 9‘56965 = log {A). (See p. 117.) 
If we take the difference between the greatest and least heights = 5*52 from 
Table III., 
(E) = ^2) = 7*4353 for Liverpool, log (E) = 0-87130. 
If we take the greatest height = 17’66 from Table III., 
17-66 = /)+{!+ i A )) (E) ~ D 4- {1'3712} (E ) ; 
and hence definitively for Liverpool in the year 1786, 
log ( A ) — 9-56965, log (E) = 0-87130, 1) = 7*46, 
D being reckoned from the datum in the East Wall of the Canning Dock. 
And I find in the same manner for London in the year 1820 
log {A) = 9-58418, log (E) = 0*64690, D = 16'69, 
D being reckoned from the sill of the London Dock gates at the Wapping entrance. 
I conceive that the best if not the only method of investigating alterations in the 
height of the land above the water in any given locality where the water is influenced 
by the tides, will be to examine carefully whether any alteration has taken place in 
the values of the constants D and (E) for that place, the height of high water being 
of course always reckoned from some fixed mark in the land. 
The semimenstrual * inequality of the interval at Liverpool presents the same re- 
markable agreement with observation which has been noticed before, while the form 
or law of the semimenstrual inequality of the height is also the same as that indi- 
* The semimenstrual inequality is an inequality of high water or of the semidiurnal wave. 
