132 
THE REV. W. WHEWELL ON THE SOLAR INEQUALITY 
being a compound of two others. But this inequality had never been obtained in 
numbers till the recent discussion of the Liverpool tides. Under Mr. Lubbock’s 
direction, Mr. Dessiou has obtained it from the observations of Mr. LIutchin- 
son. Mr. Bywater, who has calculated Tide-Tables for Liverpool for the present 
year, has also obtained this inequality from his own calculations, (suggested, as he 
states, by the remarks made in the First Series of these Researches,) and has in- 
troduced it, for the first time, into published tables ; and I have just learnt from 
Mr. Bunt, who is at present employed in forming Tide-Tables for Bristol, that he has 
also obtained the general form of this inequality, agreeing, on the whole, with the 
other results, although with some discrepancies. These arise, I conceive, principally 
from the shortness of the series of observations which he had at his command (less 
than two years). The tide observations now going on at these ports, when hereafter 
discussed as the preceding ones have been, will, I have not any doubt, lead to the 
production of tide-tables possessing a degree of accuracy which, a little while ago, 
would have been considered unattainable. 
3. It is natural for us to wish to refer the effects of the diurnal inequality, so far 
as they have yet been obtained, to the equilibrium-theory. I will say a few words on 
this subject. 
The general relation of these results to the equilibrium-theory it is not difficult to 
see. When the moon is south of the equator, the equilibrium-tide corresponding to 
her upper transit at any place having southern latitude, would be greater than the 
tide corresponding to her lower transit : when she is north of the equator the con- 
trary would be the case. When she is in the equator the two tides are equal. Now 
in one lunation she moves in an orbit inclined to the equator. Hence, while she 
moves from the sun to the sun again, (that is, while the time of her upper transit 
passes through the whole twenty-four hours from noon to noon again,) the tide 
which corresponds to her upper transit will, during one lunation, be greater during 
half the period, and less during the other half, than the tide of the next half-day ; and 
at two particular times in the lunation the difference will vanish. The times of moon’s 
transit for which the diurnal difference vanishes, correspond to the times when the 
moon is in the equator, and are therefore different at different seasons of the year. 
Now from the general correspondence of the phenomena of the tides with the equi- 
librium-theory, we may expect that the circumstances of the diurnal inequality will 
be the same as those which have been described ; but that the time when the diurnal 
inequality vanishes will not be the time when the moon is in the equator, but some 
time afterwards. 
I. By the statements above referred to on this subject it appears that the time at 
which the diurnal difference vanishes is when the moon’s transit takes place about 
9 h 30 m in January, and two hours earlier in each succeeding month, taking the general 
average of the facts. Now in the middle of January the sun is 4 h 30 ra from the vernal 
equinox, and hence the moon is 5 h beyond the equinox when the diurnal inequality 
