DIURNAL INEQUALITY OF THE HEIGHT OF THE TIDE. 
77 
vanish when the moon is in the equator. But it appeared that in fact the diurnal in- 
equality did not vanish till about four days after that period. 
By taking the moon’s declination four days anterior to the day of observation, and 
reducing it to a proper scale, it was found that the amount of the diurnal inequality 
could be represented with great accuracy, as may be seen in the Plates, which are spe- 
cimens of a comparison of this kind made for the whole of the years 1833 and 1834. 
It is to be observed, however, that the calculation of the diurnal inequality from 
the declination was made by means of a coefficient which was somewhat different in 
different months. Thus the usual multiplier of the declination for the diurnal in- 
equality of high water at Plymouth is i ; that is, 4° of lunar declination produce a 
difference of height of 1 inch : but in some cases the coefficient is i or more ; in 
others it is i. These differences appear to arise in part from the height of the tide 
itself; for the inequality is theoretically proportional to the whole lunar tide ; partly 
to the effect of the sun, according to different seasons of the year. Yet there appears 
to be still some other unexplained cause of the variation of this multiplier ; for there 
are differences in its value which cannot be referred to the causes just mentioned, 
and which operate, during a lunation or a semilunation, too uniformly to be acci- 
dental. We may take the coefficient at Plymouth to be i, which is the value on 
which the curves represented in Plate II. are constructed. I am persuaded that no 
one accustomed to the comparison of theoretical formulae with observation can look 
at those curves without being persuaded that the formula exhibits the true law of 
nature. 
As has been said, the declination of an anterior period has been taken. The period 
employed was the fifth lunar transit preceding the tide. Thus the diurnal inequality 
of January 6, 1834, is determined by the declination on January 2, at 5 1 ' 44 m a.m., the 
time of the moon’s transit. The assumption of this period is confirmed by the gene- 
ral agreement of the results. 
From what has been said, the inaccuracy of the statements of this inequality, as an 
excess of the evening tide at particular seasons, and of the morning tide at other sea- 
sons, will readily appear ; for the high water at Plymouth is, on the average, five 
hours after the moon’s transit. Suppose the moon to move in the ecliptic, which is 
her average path : when the sun’s right ascension is five hours, (that is, about June 7,) 
the tide which follows the moon’s transit will follow the sun’s transit also, as soon as 
the moon is north of the equator ; that is, if the diurnal inequality were regulated 
by the moon’s place on the same day, the afternoon tide would be greatest ; and so 
it would continue till the moon was seven hours after the sun, at which period the 
tide would be twelve hours after the sun, and the tide following the moon would be- 
come the morning tide. But at the same time the moon would pass to the south of the 
equator ; and therefore the tide following the moon would be the smaller. Therefore 
in this situation the evening tide would be the greater during the whole lunation. 
But suppose the sun’s right ascension to be eight hours, (July 21,) then, when the 
