MR. LUBBOCK ON THE TIDES. 
227 
it is easy to deduce 
. . cos 2 2 sin 2 <p d A sin 2 <p d A 
■ 2(1 + A cos 2 cp ) 3 2(1 + 2^? cos 2 <p + A 2 )' 
The expression d = s ^ n WO uld agree with the empirical expressions which 
Mr. Whewell has suggested* for the variations in the interval; but the terms 
2 A cos 2 <p + A 2 in the denominator have a sensible influence on the value of d 4- 
Table XXI. shows the diurnal inequality in the interval and in the height, which 
is also laid down in Plate XXII. The diurnal inequality of the height at London is 
scarcely sensible ; and when the observations are divided into so many categories, a 
sufficient number does not remain to afford a satisfactory average. I have given a 
comparison with theory of the diurnal inequality for the interval in Table XXXII. 
In the comparison which I have instituted between Bernoulli’s theory and obser- 
vation, it should be remembered that I have employed throughout the same constant 
(A) for all the interval and height corrections. But by assuming the form only of 
the corrections according to theory, and using various constants, expressions might 
perhaps be obtained which would represent the observations a little better. Such 
alterations, however, have not been suggested by theory, nor would they be attended 
with any practical utility. My intention in laying down the results in diagrams has 
been partly to exhibit the nature and extent of their irregularities, which would no 
doubt be diminished by employing a greater number of observations. If even the 
equilibrium-theory were complete and sufficient in the case of a perfect sphere, the 
form of the channel in which a derived tide-wave flows cannot fail to influence in a 
slight degree the form and magnitude of the different corrections. It is easy to see, 
for example, that the corrections for a derived tide-wave flowing through a channel 
bounded by perpendicular sides, would not be exactly the same as in a channel 
bounded by shelving coasts. May not the slight disagreement between the theory 
and observation curves for the semimenstrual inequality of the height in Plate XVIII. 
be accounted for in this manner ? If spring tides and neap tides are propagated with 
different velocities, the value of the constant (A) resulting from observations at 
distant places will not be exactly the same. 
In comparing the semimenstrual inequality as deduced from theory with that de- 
duced from observation, I have supposed the declinations of the sun and moon to be 
equal to 15°, and the horizontal parallax of the moon equal to 57'. The corrections 
which might be required in consequence of deviations from this hypothesis, and which 
are given in Tables XXVIII. and XXIX., are so small, that they may be neglected, 
and the columns headed “ Mean” in Tables II. and III. may be considered as affording 
the semimenstrual inequality. The moon’s average declination corresponding to the 
totality of observations employed is 15°2, and the moon’s average horizontal pa- 
rallax 57 , '0o The agreement between the theory and observation curves in Plates XIX., 
* Philosophical Transactions, 1834. 
2 o 2 
