AND ON THE DIURNAL INEQUALITY OF THE TIDES AT LIVERPOOL. 133 
vanishes. The same result would be obtained from the other months, since the sun’s 
right ascension increases on an average two hours in each month*. Hence the 
evanescence of the diurnal inequality which, in the equilibrium-spheroid, would take 
place when the moon is in the equator, does not take place till she has described 5 h 
of right ascension after that time, and this requires six days and a quarter. 
5. In the inequalities hitherto considered, which were the effects of the sun, and of 
changes of the moon’s parallax and declination, the circumstances of the tide agree 
with those of the equilibrium-spheroid one day and a half or two days previous. It 
appears that such an interval suffices for the forces, when near their maximum, to 
accumulate and transmit their effects to Liverpool ; and after this interval the dimi- 
nution of the actual forces overbalances the increase arising from their continued 
action. But in this case of the diurnal inequality we find that above six days are 
required for this accumulation and transfer. The inequality vanishes six days after 
its cause vanishes, and in the same way it reaches its maximum six days after the 
producing force is greatest. On a little consideration we shall not be surprised at 
the great time required to bring this inequality to its full magnitude. The semi- 
diurnal tides, alternately greater and less, which are transmitted from the Southern 
Ocean to Liverpool, may be compared to oscillations of the ocean, and these are aug- 
mented by the action of the forces occurring at intervals equal to those of the oscil- 
lations. Hence the oscillations go on increasing for a considerable period after the 
forces have gone on diminishing, and reach their maximum almost a week after the 
forces have passed theirs. 
6. In January the tide at Liverpool, which follows the moon’s upper transit by 
about eleven hours, is less than the following tide, when the moon is near the sun, 
and consequently when the moon is south of the equator. This agrees with the equi- 
librium-tide depending upon the position of the moon at the time of transit. But it 
is clear that the tide which reaches Liverpool does in fact come from the Southern 
Ocean ; and hence the equilibrium-tide for the time of the moon’s upper transit at 
Liverpool will be greater than the following one, when the moon is near the sun in 
January. Hence the tide at Liverpool is not that which corresponds to the equili- 
brium-tide at the time of transit, but to the equilibrium-tide about either twelve or 
thirty-six hours earlier. The latter is probably the right conclusion, and agrees with 
the inference already obtained from the effects of the solar forces, that the tide agrees 
with an equilibrium-tide thirty-seven hours and a half previous to the moon’s transit. 
8. The succeeding sections of this paper will be devoted to the investigation of the 
Solar Inequalities at Liverpool. By carefully eliminating the lunar effects, which the 
preceding researches enable us to do, I have determined, as I conceive beyond dis- 
* In order to detect the diurnal inequality, the observations have been classed by calendar months ; but as 
this inequality depends mainly on the moon’s declination, it would probably have been obtained more distinctly 
if the observations had been classed according to the moon’s declination, distinguishing north and south de- 
clination, and also increasing and decreasing declination. 
