314 Astronomical and Nautical Collections. 
Mécanique Céleste, Febr. 1824. . He has computed the results of about 6000 
observations made at Brest since the year 1806, and has feund them confirm 
in general those which he had obtained from the more ancient observations. 
There are also some new deductions, which may be made subservient te the 
further illustration of the principles laid down in the Supplement of the Ency- 
clopzdia. 
“I have considered,” says Mr. Laplace, (P. 160,) ‘‘ the tide of which the 
period is abont aday. By comparing the differences of two high and two low 
waters, following each other, in a great number of solstitial syzygies, I have 
determined the magnitude of this tide and the time of its maximum, for the 
port of Brest. I have found its height very nearly one fifth of a metre, and 
one tenth of a day for the time that it precedes the time of the maximum of 
the semidiurnal tide. Though its magnitude is not one thirtieth of that of the 
semidiurnal tide, yet the generating forces of both these tides are nearly eqnal, 
which shows how differently their magnitude is affected by accidental or ex- 
traneous circumstances. This will appear the less surprising, when we con- 
sider that if the surface of the earth were regular and entirely covered by the 
sea, ‘the diurnal tide would disappear, provided that the depths were uniform 
throughout.’ In fact, the observed heights of the diurnal and semidiurnal tides 
are .2134™, and 5,6™ respectively, (P. 227); and the time that the diurnal tide 
precedes the maximum of the evening semidiurnal tide is .095%, (P.226). It 
is not quite clear that the words might not relate to the maximum resulting 
from the most perfect combination of the solar and lunar diurnal tides ; but 
we may suppose, for the sake of the calculation, that the high water of the 
joint diurnal tide generally happens a little more than two hours earlier than 
that of the semidiurnal tide. 
B 
W{(GG—BY + AAGG] 
we assume the mean value of G, for the joint semidiurnal tide, about .98, and 
for the diurnal.49, B being about .g, and 4=.1, the formula becomes=7.83, or 
if A=.2, 4.4 for the semidiurnal, and 1.327 or 1.234 respectively for the diurnal, 
Now supposing, for the determination of the multiplier, 
and a or ces must be such that D sin 2 Decl. x 1.327 may be to D’ x 7.83 
L 
as .2134 to 5.6, or as 1 to 26.25; but sin 2 Decl. = sin 46° 55/.5 = .73045, 
and we have p x .9691 : D’ x 7.83 = 1: 26.25 =D: D’ x 8.07andD ; D’ 
=1; eo 3.25 = cot 17° 6’, which must be the obliquity of the canal to 
8.07 
the equator if 4 = .1, or if A = .2, 10° 30’: either of which may possibly be 
near the truth, though the obliquity of the main channel of the Atlantic to the 
equator is probably greater. With respect to the times of high water, the 
B AG 
tangents —. = become, if A = .2, at 72°59’ and at s° 97’ respec- 
s cs Gco-s ? { ; 7 9 7 pec- 
i 
