130 
THE REV. W. WH EWELL ON THE SOLAR INEQUALITY 
Declination Table (W. T.). To be used in ‘predicting the Time of high water at Liver- 
pool, for the mean parallax. 
Declination Table (W. H.). To be used in predicting the Height of high water at 
Liverpool, for the mean parallax. 
When these tables are used in predicting the tides, the times and heights found by 
these must be corrected for parallax by Mr. Lubbock’s Tables XXIII. and XXIV., or 
by the formulae given in my Memoir on the Empirical Laws of the Tides in the Port 
of Liverpool. I will insert, at the end of this paper, Tables of the correction for 
parallax given by these formulae. 
§ 3. On the Solar Inequality of the Heights of High Water at Liverpool. 
13. By means of the Declination Tables (W. T.) and (W. H.) we can reject from 
Mr. Lubbock’s Tables II. and III. the part which depends on the moon’s declination, 
and we thus have the remainder, which is the solar correction as far as it can be ob- 
tained from the observations of Mr. Hutchinson. This is what I have done in the 
following calculations (Table A.). The third column of each table, marked (W. H.), 
contains the height due by the declination table ; the fourth column, marked (L. III.), 
contains the observed height as given by Mr. Lubbock’s Table III. ; and the column 
(Diff. H.) is the excess of the latter, and is therefore the residual height due to the 
solar effect. In like manner the columns marked (W. T.), (L. II.) and (Diff. T.) con- 
tain the Intervals due to the moon’s declination, the observed intervals, and the resi- 
dual solar effect. 
I shall consider the solar effect on the Heights in the first place, since its law is 
more manifest. It may be expected, like the other tidal inequalities, to be resolvable 
into a non-periodic and a periodic part. In order to effect this, I take the mean of 
each monthly column of differences, and subtract it from each number in the column. 
In this manner I obtain Table (B. II.). 
In order to trace the law of the periodical part, which exists in the remainders, if 
at all, I lay down these remainders by coordinates, as in Plate XVII. 
14. If we draw lines through the dots belonging to each hour of the moon’s transit, 
it becomes manifest that these remainders really result from a solar inequality. For 
the curves (the dotted curves in Plate XVII.) have all the same general form, having 
a reference to an annual cycle. Thus there are, for all of them, a maximum or mini- 
mum in March, another in July, another in October, and another in December. 
Hence the effect of lunar declination has been nearly or altogether eliminated ; for 
this effect is a maximum for different hours at different times of the year, as appears 
by the reason of the case, and as is shown in Mr. Lubbock’s Tables IV. and V. 
It appears also by the curves, that the effects of the changes of the solar force are 
the greatest for the hours of moon’s transit, l' 1 30 m and 7 h 30 m , and are in these two 
rases t he opposite of one another, which agrees with the nature of the case; for th" 
