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is: and there remains the uncertainty arising from our ignorance of the
law of interior density in our earth; so that our chief reliance should still
be on mathematical measurement, conducted with due care.
An interesting question belonging to the hydrostatic theory of the
planetary forms is of the conditions of stability of equilibrium of the
fluids which are collected on a part or the whole of the surface of the
planets. LaPlace shows this stability to depend, under all circumstances,
on the density of the fluid being less than the mean density of the planet;
a view established with regard to the earth by Cavendish s fine experi-
ment.
Section III
The Tides
There remains the question of the tides, the last important inquiry un-
der the head of celestial statics. Under the astronomical point of view,
this is evidently a statical question, the earth being, in that view, re-
garded as motionless: and it is not less a statical question in a math-
ematical view, because what we are looking at is the figure of the ocean
during periods of equilibrium, without thinking of the motions which
produced that equilibrium. Moreover, this inquiry naturally belongs to
the study of the planetary forms.
A particular interest attaches to this question, from its being the link
between celestial and terrestrial physics, the celestial explanation of
a great terrestrial phenomenon. Descartes did much for us in estab-
lishing this. He failed to explain the phenomenon, but he cast aside the
metaphysical conceptions which had prevailed before; and showed that
there was a connection between the change of the tides and the motions
of the moon; and this certainly helped to put Newton in the way of the
true theory. As soon as it was known that the cause of the tides was to be
196/Auguste Comte
looked for in the sky, the theory of gravitation was certain to afford its
true explanation. Newton therefore gave out the simple principle that
the unequal gravitation of the different parts of the ocean towards any
one of the bodies of our system, and particularly towards the sun and
moon was the cause of the tides: and Daniel Bernouilli afterwards per-
fected the theory. The same theory answers for the atmosphere: but we
had better study it in the case of the seas alone; on account of the uncer-
tainty of our knowledge of the vast gaseous covering of our globe, whole
diffused mass almost defies precise observation.
Suppose the earth joined to any heavenly body by a line passing
through the earth s centre. It is clear that the point of the earth s surface
which is nearest the other body will gravitate towards it more, and the
remoter point less, than the centre, inversely to the squares of their re-
spective distances. The first point tends away from the centre: and the
centre tends away from the second point; and in each case the fluid
surface must rise; and in nearly the same degree in both cases. The
effect must diminish in proportion to the distance from these points in
any direction: and at a distance of ninety degrees it ceases. But there the
level of the waters must be lowered because of the exhaustion in that
place caused by the overflow elsewhere. And here enters a new consid-
eration, difficult to manage: the changes in the terrestrial gravity of
the waters, occasioned by their changes of level. Thus the action of
any heavenly body causes the ocean to assume the form of a spheroid
elongated in the direction of that body. Newton calculated the chief part
of the phenomenon of the tides on the supposition of an ellipsoid of
homogeneous structure, as he had done in estimating the effect of the
centrifugal force on the earth s figure, substituting for the centrifugal
force the difference between the gravitation calf the centre of the globe
and that of its surface next the proposed body. After that, Maclaurin s
theorem served Daniel Bernouilli for a basis of an exact theory of the
tides.
Thus far, we have regarded the tides only as if they were a fixed
accumulation of waters under the proposed star. This is the mathemati-
cal basis of the whole question; but the most striking part has yet to be
consulted, the periodical rise and fall. It is the diurnal motion of our
globe which causes this rise and fall, by carrying the waters succes-
sively into all the positions in which the other body can raise or depress
them. Hence arise the four nearly equal periodical alternations, when
the two greatest elevations take place during the two passages of the
Positive Philosophy/197
heavenly body over the meridian of the place, and the lower levels at its
rising and setting; the total period being precisely fixed by combining
the terrestrial rotation with the proper daily movement of the heavenly
body. The last indispensable element of the question is the valuation of
the powers of the different heavenly bodies. This calculation is easily
made from the difference between the gravitation of the centre of our
globe and that of the extreme points of its surface next the observed
body. Guided by the law of gravitation, we can determine which, among
all the bodies of our system, are those which can participate in the phe-
nomenon, and what is the share taken by each. We thus find that the sun
by its immense mass, and the moon by its proximity, are the only ones
which produce any appreciable tides: that the action of the moon is from
two and a half to three times more powerful than that of the sun; and
that, consequently, when they act in opposite directions, that of the moon
prevails; which explains the primary observation of Descartes about the
coincidence of the tidal period with the lunar day.
Thus far, we have considered only the effect of a single heavenly
body upon the tides; that is, the case of a simple and abstract tide. The
complication is very great, when the action of two such bodies has to be
considered. But the resources of science are sufficient to meet this case,
even deriving from it new means of estimating the mass of the sun and
moon; and also of calculating the modifications arising out of the vari-
ous distances of the earth from either body; and again, of tracing the
changes of direction caused by the diurnal movement of the proposed
body, whether in accordance with the earth s axis of rotation, or parallel
with the equator, which makes the difference between the tides of our
equinoctial and solstitial lunar months. As for the difference of the phe-
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