MR. LUBBOCK ON THE TIDES IN THE PORT OF LONDON. 
383 
more details, and is, I trust, more accurate ; the time of high water being gene- 
rally well ascertained (as a first approximation) and easily observed on these 
coasts. Lines are drawn round the coast to mark the depth of the water : it 
is to be regretted that this method of indicating the soundings, which, accord- 
ing to Captain Alexander *, is adopted by the Russians in their charts, is not 
more general. The tide which reaches the port of London is principally due 
to the tide which descends along the eastern coast of Scotland and England : 
this branch of the tide meets the tide which comes up the Channel off the sand 
called the Kentish Knock. 
If when the tide is single, the height of the water is represented by a series 
of cosines, affected with constant coefficients ; when the tide results from the 
union of two branches, each of this kind, the height of the water will still be 
represented by a series of cosines of angles, affected with other constant coeffi- 
cients, the periods of the inequalities being the same as before, but the epochs, 
or the times when they arrive at their maxima and minima, different. This is 
shown by Laplace in the Mec. Cel. vol. ii. p. 225. Fresnel has applied the 
same method (Memoire sur la Diffraction de la Lumi&re, p. 279.) to finding the 
resultant of any number of luminous waves of the same length. This method 
l'ests upon the superposition or coexistence of small oscillations, which may not 
be rigorously true ; but it may be stated generally, that when the tide results 
from the union of any number of partial tides, the resultant of the whole may 
be considered as one tide, affected with inequalities, of which the periods are 
the same as the periods of the inequalities of the partial tides of which it is 
composed, but of which the magnitudes and the epochs are different'!'. It is 
owing to this cause that the high water in some places takes place only once 
in twenty-four hours, which is a case of interference. 
I shall now proceed to explain the manner in which the annexed Tables were 
formed. 
Table I. was made by classifying all the transits of the moon which took 
place in the years 1808 to 1826 inclusive, and in each half hour ; thus, all the 
transits were found from the Nautical Almanac which took place between 
twelve o’clock (a.m.) and half-past twelve (a.m.), the moon being above the 
* See Alexander’s Travels to the Seat of War in the East, vol. ii. p. 101. 
f If A cos (9 — A) represent any inequality, the constant A determines its magnitude, the variable 
9 its period, and the constant A its epoch. 
3 D 
MDCCCXXXI. 
