Mcanique Cleste volume 2

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Mcanique Cleste volume 2
Pierre Simon Laplace
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S' nearly, we have -4' — ^ = — ^ [2733/]. The mean of [2760a] these two values, using [2578a, &€. ], is 4, ' — ^ = ^ . Tv A cos. S' -j ;- i = tv=:the mean synodical motion. [27606] Therefore if we take as many tides in the equinoxes as in the solstices, we may suppose the mean synodical motion, after the maximum. , to be 4^' — 4'j and before it, 4-' — 4'; so that 2 . (4'' — -4) is nearly equal to the synodical motion, in the whole interval [2761]. [2760c] 764 THEORY OF THE TIDES COMPARED WITH T...HE [Mcc. C^l.
the middle of the interval comprised between these observations ; therefore [2761] we may suppose 2. (V — J. ) to be equal to the sjnodical motion of the moon during this interval [2760c]. Moreover, the hour of the greatest tide [2762] is determined by the equation* w ^ -f -. — — x := [2479c] ; therefore [2762'] 2. (nt'-^r - — ^ — ^) is the retardation of the tide, in the interval comprised between the observations. This retardation, estimated in degrees, supposing the whole circumference 400° to correspond to one day, being put equal to fA, we shall have, t Ratio of the lunar Xv and solar — -tj- forces.


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