306 Astronomical and Nautical Collections. 
revolution in places differently situated ; and this time being once 
ascertained for any one tide, we may easily infer by calculation 
the time at which every other tide will occur; and we shall find in 
this sequence the most perfect coincidence between theory and ob- 
servation. Thus, if the high water of the spring tides, derived 
from the coincidence of the solar and lunar high waters, soon after 
the new or full moon, happened at any port precisely at noon, the 
next time of the high water belonging to the solar tide would of 
course be at midnight, and that of the lunar high water twenty-five 
minutes later; and the true time of high water will divide this in- 
erval neatly in proportion to the apparent forces, and will occur 
about eighteen minutes after midnight,” [the interval being 12 
18™, and not 1248, as it has been hastily assumed for the table of 
the Supplement :] “ and the next day it will be high water about 
thirty six minutes after twelve. This retardation will increase 
from day to day, since its mean daily value is about fifty minutes ; 
and at the neap tides following the moon’s quadratures, it will be- 
come about twice as great as at the syzygies, its different values, in 
these cases, being nearly proportional to the magnitude of the spring 
and neap tides; so that Bernoulli has considered them as affording 
the most correct estimate of the comparative magnitude of the solar 
and lunar forces; although they are probably less capable of being 
accurately determined by direct observation than the different ele- 
vations and depressions. We can scarcely imagine it possible that 
any individual, acquainted with these simple facts alone, to-say 
nothing of many others, equally well established, could for a mo- 
ment entertain the slightest doubt of the real and immediate de- 
pendence of the tides on a combination of the solar and lunar 
attractions.” 
“In the diurnal and annual variations of the height of the tides, 
there is no peculiar difficulty. The declinations and distances of 
the luminaries modify their forces in a manner which is easily de- 
termined ; and the periods of these changes being much greater 
than the times of spontaneous oscillation in any of the seas con- 
cerned, the effects directly follow their causes, almost in the simple 
proportion of the intensity of the forces concerned. Mr. Laplace 
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