[ 57 ] 
VIII. Discussion of Tide Observations made at Liverpool. By J . W. Lubbock, Esq.F.R.S. 
Received and Read January 28th, 1836. 
I AM enabled, through the indefatigable perseverance of M. Dessiou, to present to 
the Society other Tables, in continuation of those published in the Philosophical 
Transactions for 1835, Part II., founded upon the observations instituted by Mr. Hut- 
chinson at Liverpool. 
The chief intention of the Tables now offered is to exhibit the diurnal inequality in 
the height of high water, which is, I believe, insensible in the river Thames, but 
which at Liverpool amounts to more than a foot. So that, for example, in January, 
when the moon is in quadrature, (neap tides,) the evening tide may be a foot higher 
than the morning tide. 
Table XXVII. gives the results as immediately deduced from observation. 
Table XXVIII, was formed by reducing the argument, (moon’s transit,) by inter- 
polation, to the even half-hours, and then taking the differences between the numbers 
so found and those in Table III.* 
The results exhibited in Table XXVIII. are extremely irregular : these irregulari- 
ties were arbitrarily removed in forming Table XXIX., which is intended to be used 
in predicting the phenomena. As the question of the diurnal inequality of the tides 
is important, and as the numbers in Table XXVIII. are so irregular, I have thought 
it desirable to exhibit them in a diagram, together with the inequalities definitively 
adopted in Table XXIX., in order that the nature and extent of the alterations we 
have introduced may be perceived. The diurnal inequality in the interval appears 
to be insensible. 
Bernoulli’s Theory of the Tides leads to the expressions 
h — D -J- E {A cos (2 y — 2 a) -J- cos (2 y — 2 ct!)} 
tan 2 — 
A sin 2 <p 
1 -r A COS 2 
m cos 9 8 P 3 
^ m! cos 9 V P ' 3 
E — Cm! cos 2 b P ’ 3 
h = D + E {cos 2 \p -j- A cos (2 <p — 2 \p)}, 
in which expressions a denotes right ascension, y sidereal time, & declination, m the 
mass of the luminary, P the sine of the horizontal parallax, C a constant depending 
upon geographical latitude, and D a constant depending only on the zero line, from 
which the heights are reckoned. The unaccented quantities refer to the sun, and 
those which are accented to the moon, h is the height of the water above any given 
line, and f is a small variable angle to be added with a certain constant to the time 
of the moon’s transit, in order to obtain the time of high water. 
* Philosophical Transactions, 1835, p. 283. 
WDCCCXXXVI. 
I 
