120 On the Tides. 
nuch greater than the others. For by considering at the same | 
time the observations at the’two cquinoxes and at the two 
solstices, the effect of the small inequality, whose period is 
nearly a day, is mutually destroyed. The sums in question 
are consequently entirely owing to the great inequality. The 
winds can have little influence on them; for, if they raise the high 
water, they must equally depress the low water. I have deter- 
mined the law of these sums for each year, by observing, that 
their variation is very nearly proportional to the square of their 
distance in time from the maximum which has given tne this 
maximum ; its distance at the mean of the times of the syzygy 
tides, and the coefficient of the square of the times in the law 
of the variation, With regard to this coefficient, the little dif- 
ference which the observations of each year present, proves the 
regularity of these observations: and according to the laws 
which I have elsewhere established, on the probability of results 
deduced from a great number of obsenatitis: some judgement 
may be formed of the accuracy of results determined from the 
whole of the observations of eight years. 
In the same manner I have considered the quadrature tides, 
by taking the excess of the high water in the morning above the 
low water of the evening of the day of the quadrature, and of 
the three following days. The increase of the tides, beginning 
from the minimum, being much more rapid than their decrease, 
beginning from the maximum, | have thought it necessary to 
confine the law of the variation proportional to the square of the 
time within a much shorter interval. 
In all these results the influence which the declinations of the 
heavenly bodies have on the tides, and upon the law of their va- 
riation in the syzygies and in the quadratures, is evidently 
shown. In considering, by the same method, eighteen equinoc~ 
tial syzygy tides towards both the perigeum aid the apogeum of 
the moon, the influence which the changes of the lunar distance 
have upon the height and upon the law of variation of the tides, 
is manifested with the same degree of evidence. It is thus that 
by combining observations in such a way as to biing out every 
element, which we are desirous of knowing, we are able to se- 
parate the laws of the phenomena when mixed and confounded 
together in the collections of observations. 
After having obtained the results I have just mentioned, I 
compared them with the theory of the tides delivered in the 
fourth book of the Mecanique Céleste. This theory is founded 
on a principle of dynamics, which renders it very simple, and 
independent of the jocal cireumstances of the port, which cir- 
cumstances are too complicated for the possibility of submitting 
them to calculation, By means of this principle, they enter 
into 
