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XIV. Researches on the Tides. — Eighth Series. On the Progress of the Diurnal In- 
equality Wave along the Coasts of Europe. By the Rev. W. Whewell, M.A.F.R.S . , 
Fellow of Trinity College, Cambridge. 
Received June 14, — Read June 15, 1837. 
In the Seventh Series of these Researches I have pointed out the laws which the 
diurnal inequality of the height of high water follows, and which I believe had never 
before been collected from the facts of observation, or indeed stated at all. I have 
also shown that these laws are modified so as to exhibit very remarkable differences 
at different places, and to give rise to some difficulty in conceiving the mechanical 
propagation of the tide-wave. I suggested what appeared to me a possible solution 
of the difficulty ; but as this suggestion was founded upon the facts of a few places, 
and as other modes of propagation might perhaps also be conceived and adapted to 
the same facts, the subject remained incomplete. 
I resolved therefore to attempt to trace the progress of the wave which brings the 
diurnal inequality, on some of the coasts on which simultaneous observations were 
made at my request in June 1835, and the present memoir will give some account of 
the conclusions to which I have been led by this investigation. 
The diurnal inequality of the height of high and low water may be conceived to 
arise from an oscillating wave, of which the maximum height comes to each place 
once in twenty-four (lunar) hours ; the minimum height arriving, of course, at the 
intermediate twelve hours. If the time of the maximum height of this wave arriving 
at any port coincides every day with the time of high water, the alternate high water, 
being at twelve hours’ interval, will be affected alternately with the greatest and least 
heights of the diurnal wave ; and the intermediate low waters will coincide with the 
mean height of this wave, and will not be affected at all. In this case there will be 
a decided diurnal inequality in the height of the high water, but no diurnal inequality 
in the height of low water. In like manner if the time of the maximum height of 
the diurnal wave coincide with the time of low water, the height of low water will be 
marked with a diurnal inequality, while the height of high water will exhibit no such 
feature. But if the diurnal wave arrive every day at a time intermediate between 
high and low water, it will elevate both the high water and the low water which are 
nearest to it, and will depress both the high and the low water which happen in the 
other half of the day. Hence both the high waters taken separately, and the low 
waters taken separately will be marked by a diurnal inequality ; and this inequality 
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