76 
THE REV. W. WH EWELL ON THE 
nighty and vice versa the rest of the year.” But we shall soon see that this way of ex- 
pressing the fact, by speaking of morning and evening tides, is quite inaccurate. 
It is easily seen that the theory of the tides, which supposes them to be produced 
by the ocean assuming its form of equilibrium under the influence of the moon’s 
attraction, would give a diurnal difference of the tides: for if the moon have 20° 
north declination, the tide spheroid will have one pole in latitude 20° north, and the 
other in 20° south latitude ; and as the earth revolves, a place in 50° north latitude 
will have the tide which belongs to these two poles alternately : and as it is 30° from 
one pole and 70 ° from the other, the two tides will be very unequal. 
Now it has been found, with regard to all the other inequalities of the tides, that 
they follow the laws of the tides of the equilibrium-theory, although the constant ele- 
ments (the magnitudes and epochs) can be determined only by observation. Finding 
that the diurnal inequality was very clearly marked in the Plymouth observations, I 
did not hesitate to at mpt to trace its laws, by assuming this kind of correspondence 
with the equilibrium- theory. The result confirmed the assumption in the most 
striking manner, as I shall show. 
According to the equilibrium-theory, the tide which belongs to a south transit of 
the moon should be the greater (of the two on the same day) when the moon’s decli- 
nation is north ; when the moon crosses the equator, the difference of the two tides 
vanishes ; when she has south declination, the tide which belongs to her south transit 
is the smaller. The contrary (as to greater and smaller) will be true of the tide 
which belongs to the north or inferior transit. 
We cannot know, except by observation, to what transit of the moon any tide 
belongs ; but it is manifest that if we begin with any tide, the tides must belong alter- 
nately to south and north transits, and therefore the above alternation of greater and 
smaller tides, as the moon has north or south declination, must come into view. 
Accordingly I set off the observed heights of high water at Plymouth as ordinates 
of a curve, as seen in Plates II. and III. The zigzag form of the lines, appearing, 
vanishing, and reappearing, about once a fortnight, with great steadiness, showed 
that the diurnal inequality really existed in the observations. A line was drawn by 
the eye , cutting off from these zigzags equal portions above and below, and this was 
taken as the mean high water cleared of the<liurnal inequality. The excesses or de- 
fects of the observed height and this mean height were then set off from another axis ; 
those which belonged to the high water next following a south transit forming one 
curve, and the alternate tides, which follow a north transit, forming another curve. 
These curves were both of them found to have their ordinates alternately positive 
and negative at intervals, corresponding to the change of the moon’s declination 
from north to south, and the contrary. 
But though the order and cycles of these changes were the same for the observed 
diurnal inequality and for the lunar declination, the epochs of the changes were not 
the same. According to theory, as we have said, the diurnal inequality ought to 
