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XII. Researches on the Tides. — Fifth Series. On the Solar Inequality and on the 
Diurnal Inequality of the Tides at Liverpool. By the Rev. William Whewell, 
F.R.S . , Fellow of Trinity College, Cambridge. 
Received February 23, — Read March 3, 1836. 
Sect. 1 . Present State of the subject. 
i. The great success with which recent researches on the Tides have been at- 
tended, has encouraged me to attempt some further advances in this subject. The 
laws of the semimenstrual inequality of the times were shown by Mr. Lubbock, from 
the London observations, to agree very closely with the equilibrium-theory : and 
this result has been confirmed by the examination of observations made at many other 
places. I have shown, from the Liverpool observations, that the semimenstrual in- 
equality of the heights presents a still more complete agreement with the equilibrium- 
theory*; and by the help of Mr. Lubbock’s discussions of the London and of the 
Liverpool observations, I have shown, in the Second and Fourth Series of- these 
Researches, that the inequalities depending on the changes of lunar parallax and 
declination may be very well represented by the equilibrium-theory, with certain mo- 
difications, which are far from inconsistent with the best mechanical views we can 
at present form of the laws of the motion of fluids. 
The most obvious points which now remain requiring still to be made out and ex- 
plained, are the diurnal inequality, and the solar inequalities of the time and height 
of high water. 
2. Th e Diurnal Inequality of the tides is that which makes the tide of the morning 
and evening of the same day at the same place, differ both in height and time of high 
water, according to a law depending on the time of the year. This is called the di- 
urnal inequality, because its cycle is a day. 
The existence of such an inequality in the heights of high water has often been 
noticed by seamen and other observers, as I have stated in the First Series of these 
Researches -f\ But its reality has only recently been confirmed by regular and 
measured observations, and its laws have never been correctly laid down. Its ex- 
istence appeared very palpably in the curves which I constructed in order to examine 
the results of the tide observations made by the coast-guard in June 1834, and also 
in the curves drawn by the self-registering tide-gauge erected near Bristol ; although 
the Sheerness machine did not exhibit it, in consequence of the tide at that place 
* Fourth Series: Philosophical Transactions, 1836, page 1. 
f Philosophical Transactions, 1833, page 221. 
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