Royal Society. 547 
March 3.—A paper was read, entitled, “‘ Researches on the Tides. 
Fifth Series: On the Solar Inequality and on the Diurnal Inequality 
of the Tides at Liverpool.” By the Rev. William Whewel!, F.R.S., 
Fellow of Trinity College, Cambridge. 
The inequality both in the height and time of high water in the 
morning and evening tides of the same day, which varies according 
to a law depending on the time of the year, is termed by the author 
the diurnal inequality, because its cycle is one day. The existence of 
such an inequality has often been noticed by seamen and other ob- 
servers ; but its reality has only recently been confirmed by regular 
and measured observations ; and its laws have never as yet been cor- 
rectly laid down. The author gives an account of the observations 
now in progress at different ports, from which he expects they will be 
ascertained with great precision. He traces the correspondence of 
the observations of the diurnal inequality already made with the equi- 
librium theory; and remarks that the semi-diurnal tides, alternately 
greater and less, which are transmitted from the Southern Ocean to 
Liverpool, may be compared to the oscillations of a fluid mass: and 
that they are augmented by the action of the forces occurring at in- 
tervals equal to those of the oscillations. Hence the oscillations go 
on increasing for a considerable period after the forces have gone on 
diminishing, and reach their maximum a week after the forces have 
passed theirs. 
The remaining sections of this paper are devoted to the investiga- 
tion of the Solar inequalities at Liverpool. By carefully elimiziating 
the Lunar effects, which the author is enabled to do by the aid of the 
preceding researches, he has determined the approximate circum- 
stances of the Solar correction for the height. He has also obtained 
evidence of the existence, and some knowledge of the laws of the 
Solar inequalities of the times ; and these inequalities, as thus dis- 
covered, are found to exhibit the same general agreement with the 
equilibrium theory which has been disclosed in all the inequalities 
hitherto detected. The results of the extensive observations now ob- 
tained are sufficiently precise to indicate the defects of our mathema- 
tical theories of hydrodynamics ; and some of these are pointed out 
by the author, who remarks that although a short time ago the theory 
was in advance of observation, at present observation is in advance 
of theory ; which mathematicians are therefore called upon to re- 
model and perfect. 
The author proceeds to consider the effect of the Moon's declina- 
tion on the Tides at Liverpool; which, as before observed, it is ne- 
cessary to eliminate, in order to obtain the Solar inequality; and 
gives an explanation of various formule and tables constructed for 
that object. He then investigates the laws of the solar inequalities, 
first, as to the heights; and secondly, as to the times of high water at 
Liverpool, by applying to them these methods of calculation. 
March 10,—* Report of Magnetic Experiments tried on board an 
Iron Steam-Vessel, by order of the Right Hon. the Lords Commis- 
sioners of the Admiralty.”” By Edward J. Johnson, Esq., Commander, 
R.N., accompanied by plans of the vessel, and tables showing the ho- 
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