PHILOSOPHICAL TRANSACTIONS 
I. Researches on the Tides. — Fourth Series * On the Empirical Laws of the Tides in 
the Port of Liverpool. By the Rev. W. Whewell, M.A. F.R.S. 
Received November 10, — Read November 19, 1835. 
i. In the Philosophical Transactions for 1831 Mr. Lubbock published the results 
of a discussion of nineteen years of the London tide observations ; and from the 
materials there given, I endeavoured to obtain the mathematical laws of the inequa- 
lities of the phenomena, in a memoir which was published in the Transactions for 
1834. Mr. Lubbock having now, in Part II. of the Transactions for the present year, 
published the results of a similar discussion of nineteen years of the Liverpool tide 
observations, I intend in the present paper to use these results in testing and improv- 
ing the formulae to which I was led by the London observations. 
Perhaps the precise object of such investigations as this may be best understood by 
comparing them with corresponding steps in the history of other parts of astronomy ; 
as, for instance, in the progress of our knowledge respecting the Moon’s motions. 
After Hipparchus had singled out and reduced to rule the great inequality of the 
Moon’s motion, th e Equation of the Centre, it was the employment of succeeding astro- 
nomers, as, for instance, Ptolemy and Tycho, to discover, by examination of long- 
continued observations, other smaller inequalities, and the laws which they follow ; as 
the Variation, Erection, and others. In the same manner, the great inequality of the 
tides, the Semimenstrual Inequality of the time, is now well understood ; and the 
agreement which Mr. Lubbock showed to exist between the London observations 
and the formulae leaves nothing to desire. But formulae for the observed effects of 
lunar and solar parallax and declination (although some such formulae may have been 
* For convenience of reference I shall take the liberty of thus numbering the papers in the Philosophical 
Transactions in which I have attempted to make out the Laws of the Tides. The preceding papers are. 
First Series. Essay towards a First Approximation to a Map of Cotidal Lines. — 1833, Part I. 
Second Series. On the Empirical Laws of the Tides in the Port of London. — 1834, Part I. 
Third Series. On the Results of Tide Observations made in June 1834 at the Coast Guard Stations in Great 
Britain and Ireland. — 1835, Part I. 
MDCCCXXXVI. B 
