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TRANSACTIONS OF THE SECTIONS. 4] 
is not affected by the occurrence of the tides; nor do his formule reveal any perma- 
nent alteration in the motion of the lunar orb which disturbs the repose of our oceans. 
These results, announced by so high an authority, might be received without a care- 
ful examination if the fundamental principles of natural philosophy did not discoun- 
tenance the idea of an actual creation of power- by lunar attraction. The tides con- 
stitute an important mechanical agent; and, could their whole force be rendered 
available, it would be found adequate to several hundred times the labour of the human 
population. So great an amount of motive power, whether appropriated to the great 
purposes of nature and art, or wasted in overcoming friction, cannot be produced 
without some expense; and my present object is to trace the change which it involves 
in the motions of the earth and the moon. As the extreme disproportion between the 
momentum of the oceanic waters and that of the planetary bodies is the chief source 
of error in these investigations, I shall commence by showing how the tidal action 
should operate, if the moon moved around the earth in an exact circle, situated in the 
plane of the equator, and not more than 34,000 miles in diameter. Her periodical 
revolution in this case would occupy nearly twelve hours, and the lunar day would 
be about twenty-four hours in length. The tidal action on the seas nearest to the 
moon would be almost twice as great as on those most distant; the former being 
about 5000 times, and the latter over 2500 times, the disturbing action now exerted 
by the moon on the watery domain. The aqueous appendage of our planet would 
in this case form two great moveable oceans, sustained on its opposite sides by the 
attraction of our satellite, and keeping pace with her movements. Without taking 
into consideration the oscillations of the solid part of the earth which might possibly 
occur in these circumstances, it is evident that there should be a general flow of the 
waters from west to east ; and though the current may be alternately reversed in deep 
channels, the force propelling it in an eastern direction should always maintain the 
~ ascendency. : A vast body of water, circulating around the earth from west to east, 
could not fail toaccelerate its rotary motion; although the result would not be exhibited 
by the formule of Laplace. The moon in this case would sustain a loss of momentum 
fo a more considerable extent. It is well known that the attraction of mountains 
modifies the direction of terrestrial gravity in their vicinity ; and that a plumb-line 
on that part of the equator immediately west of the Andes would be slightly deflected 
to the east. In the case we have supposed, the direction of terrestrial gravity would 
experience a similar deflection at places in conjunction with the moon from the 
attraction of the excess of waters which swelled behind her. Accordingly, the lunar 
orb would be drawn, not directly to the earth’s centre, but always to a point a little 
westward of it, and a constant loss of motion would be an inevitable consequence. 
It would be different if the earth could preserve an invariable form, for in that case 
its attraction on a satellite being always directed to the centre, or alternately deflected 
east and west of that point, the loss and gain of motion should be evenly balanced 
after one or many revolutions. Other investigations lead to the same conclusion. A 
satellite revolving just beyond the confines of our atmosphere, would alternately 
accelerate and retard the movements of one more distant; and physical astronomy 
shows that in our planetary systems a like periodicity results from the inequality 
of the times in which the several planets perform their revolutions. But as the tide- 
wave rolls around the earth with the same mean angular velocity as the moon, their 
mutual action will not exhibit the periodicity which characterizes planetary disturb- 
ances. In the analytical solution of this problem, the equation depending on the 
difference of motion of the moon and the tide-wave would acquire by integration a 
divisor infinitely small; and this proves its secular character. If Laplace finds no 
- such divisors, it is because all the modifications in the action of the moon on the 
waters of the ocean are not embraced in his investigations on the subject. Leaving 
the supposed case, we shall now pass to the actual condition of the agencies con- 
cerned in tidal phenomena on our globe. At her present distance the revolution of 
the moon occupies more time than the earth’s period of rotation; and the tidal wave 
which has the greatest disturbing influence being always east of our satellite, must 
add to its velocity, while it retards that of the earth. We may remark, however, 
that the additional velocity imparted to the moon would give her a larger orbit, and 
increase the period of her revolution. Hence the orbital motion of the moon, as well 
___as the rotary motion of the earth, sustain a loss depending on the difference of the 
__ tidal force on opposite sides of our globe, and so very insignificant, that some mil- 
ok ae 
