AND ON THE DIURNAL INEQUALITY. 
23 
been given may, for some months, produce the effect of making the afternoon tides 
greater than the morning tides, or vice versa. Suppose the place to be one where the 
tide happens (in general terms*) soon after the moon’s {south or superior) transit ; 
then, beginning from new moon, the afternoon tide for a fortnight follows the south 
transit of the moon. Supposing that during this fortnight the moon has north de- 
clination ; then the diurnal inequality is additive by the rule, and therefore the after- 
noon tide is, during this fortnight, the highest. Now at the end of a fortnight of 
north declination, the declination changes to south. But at the end of a fortnight, 
the afternoon tide begins to be that which follows* the north or inferior transit of the 
moon ; and therefore again, by the second part of the rule, the inequality is still ad- 
ditive, and the afternoon tide is still the greater. And this will continue to be the 
case till the points of no lunar declination are shifted away from the syzygies by the 
motion of the moon’s nodes relative to the sun. But if the declination pass from 
north to south, or the reverse, at a different period from that which transfers the 
afternoon tides from one transit to the opposite one, we shall no longer have this 
apparent constancy in the relation of morning and afternoon tides. If, for instance, 
the tide-hour being such as has already been supposed, the change of declination, 
north and south, takes place when the tide is at four, five, six or seven o’clock ; the 
afternoon tide will then (or rather one or two days later) change from being the greater 
to being the less, or vice versa. Or if the tide-hour be six o’clock, the tide being (in 
general terms) six hours after the moon’s transit, the afternoon tide will follow a 
south transit of the moon from the time when the moon is six hours west of the sun 
to the time when she is six hours east of him, and then change and follow a north 
transit ; and so on alternately. Hence, if in this case the moon’s ascending node 
be at six hours west from the sun, the declination will be north while the afternoon 
tide follows a south transit, and therefore the afternoon tide will be the greater for 
the whole lunation. But if, in this case, the node be in conjunction with the sun, 
the afternoon tide will change from smaller to larger, or the reverse, at the syzygy, 
that is, when the tide is at six o’clock ; or rather, as I have said, a day or two later. 
42. This last-mentioned circumstance, that the change in the features of the tides 
takes place a day or two, or perhaps longer, after the astronomical configuration by 
which it is determined, is common to all the empirical laws of the tides, as I have 
repeatedly remarked in the memoirs on this subject already published in the Trans- 
actions. It has recently been shown by Mr. AiRV'f' that this is a result which 
follows from supposing the tidal motions of the sea to be affected by friction. The 
amount of this retardation of the phenomena for each place, or, as we may term it, 
the age of the tide” relative to this particular phenomenon, the diurnal inequality, is 
different for different places ; and must, for each place, be learnt from observation. 
43. The account which I am now giving of the diurnal inequality supposes it to 
depend upon the moon alone ; and so, for most purposes, it does almost entirely, as 
* I leave out of consideration, in this explanation, the semimensual inequality. 
t Tides and Waves, 452. 
