DIURNAL INEQUALITY OF THE HEIGHT OF THE TIDE. 
81 
Among all the irregularities of the Leith tides, it is easily seen from the curves, when 
they are laid down, that there is a diurnal inequality, in consequence of which the 
tide following the south transit of the moon becomes alternately the greater and the 
smaller, as the moon’s declination changes from south to north, and the reverse. The 
times when this inequality is large can be picked out more decidedly than the times 
when it vanishes, and I therefore determined the epoch by means of the greatest in- 
equality, supposing the times when it vanishes to be midway between two successive 
maxima, as may be seen in the preceding Table. 
Rejecting those cases in which the inequality is very small or altogether irregular, 
it appears that the inequality vanishes twelve days after the moon’s inclination vanishes. 
This is certainly a very extraordinary result ; for it is difficult to conceive how the 
effect of the moon’s action can require so much time to manifest itself. Yet there 
can hardly be any doubt of the fact; for it is verified in 11 semilunations out of 17, 
and is inconsistent with none ; the variations in the interval being not greater than 
might be expected, supposing the law to be true. It may be observed, that by these 
variations the inequality is in some cases thrown back more than a whole semiluna- 
tion. Thus the inequality which prevails before April 26, and vanishes about that 
day, is not produced by the series of declinations which vanish on April 24, but by 
the series which vanish on April 11. To suppose the reverse would be impossible; 
for that would make it necessary to suppose that the inequality vanishes on Feb. 27, 
in consequence of the declination vanishing two days later, or March 1 ; that is, that 
the effect precedes the cause. , 
In the system of tide observations made on the coasts of Europe and America in 
June 1835, of the results of which an account was given in the Sixth Series of these 
Researches*, it appeared that the diurnal inequality on the east coast of Scotland 
was, during that semilunation, irregular, passing over a tide in the middle of the 
series. This and other anomalies in the diurnal inequality, as it appears on the 
coasts of the German Ocean, appear to show that the waters in that region are 
affected by the mixture of more than one tide. In the most material point, however, 
the observations of June 1835 confirm the results of our present inquiry ; namely, in 
showing that the diurnal inequality travels more slowly than the other inequalities. 
On the east coast of America, the changes of this inequality appear to be contempo- 
raneous with the corresponding changes of the moon’s declination, and the epoch is 
zero. On the coasts of Spain, Portugal, and France, it is successively two and three 
days. And this is quite consistent with the fact that this epoch is four days on the 
coast of Cornwall and Devonshire, Jive days at Bristol, six at Liverpool, and twelve 
at Leith. That the diurnal inequality should thus creep from place to place on suc- 
cessive days is difficult to explain ; but the laws of fluid motion are so little known, 
that we cannot collect from hydraulical views any good reason for doubting this 
curious fact. The fact is certainly not easily reconciled with our conception of the 
* Philosophical Transactions, 1836, Part II. p. 304. 
MDCCCXXXVIT. 
M 
