306
ASTRONOMY.
Relative diurnal mean motion with re- ispect to the equinoxes ; i. e. her mean >
In supposing the motion of the Sun in a")hundred Julian years 46' 0" above |100 revolutions, the relative secular Vmotion of the Moon above 1236 en- 1
tire revolutions is.J
Diurnal motion of the Apogee, as mea-)
Diurnal motion of the apogee, as mea-sured by the Stars.
Diurnal motion of the Node, as mea-)
Diurnal motion of the Node, as mea-)
sured by the Stars.J
The quantity of the lunar motionwith respect to the Fixed Stars in agiven time, e. g. in one day, 13° 10'33”,890267 being called 1, that ofthe Apogee in the same time is+ 0.00845226444S; and that of theNode -0,004021853526.
The least inclination of the Lunar Or- - )bit, i. e. when the Sun is 90° from >
her Nodes.)
The greatest inclination, i. e. when the )Sun ’s longitude is the same with the >
Lunar Node.J
The greatest elliptic equation, i. e. when 4the Moon is in Apogee, at the time |of her sizygy; or in quadrature with ythe Sun , and at the same time at her I
mean distance from the Earth.J
The least elliptic equation, i. e. when )the Moon is in quadrature with the fSun , and at the same time in her (
12° 11' 26”,697659
.10s. 7° 7' 12”
-j- 6' 41”,069815195|+6' 40”,932238189-3' 10”,638603696— 3' 10”,776180698
4° 59' 30”
5° 17' 30”
7° 39' 0”
4° 58' 4”
The greatest annual equation of the)Moon, depending on the Sun ’s dis- ; .
. 11'
8”,6
The variation of the Moon at a mean, \
41”
(O 90° from apsides).£
The greatest variation of the Moon in j
. 37 '
51"
the octant, (© in perigee).)
The least variation ot the Moon in the (
31”
octant, (O in apogee).)
(156.) The Tides are found to follow periodically the courseof the Sun and Moon, and hence it has been suspected, in all ages,that the tides were somehow produced by the influence of theseluminaries. Of this, Pliny, Ptolemy, Macrobius , and others,seem to have had some knowledge. The celebrated Kepler form-ed some conjectures long ago, as to the true cause of the tides.“ If, (says he,) the Earth ceased to attract its waters towards itself,all the water in the ocean would rise and flow into the Moon .The sphere of the Moon’s attraction extends to our Earth , anddraws up the water.” What Kepler only surmised, has beencompletely verified in the theory laid down by Newton, and byIlalley, from his principles. The principal phenomena of thetides are as follow :
I. The sea is observed to flow for about 6 hours from south tonorth, gradually swelling; after this it seems to rest for a quarterof an hour; and then to ebb or retire back again from north tosouth for 6 hours more. Then after a seeming pause of about *- ofan hour, the sea again begins to flow ; and so on alternately.
II. The time of a flux and reflux is on an average about 12h.24min. the double 24h. 48min. is the period of a luuar day, orthe time between the Moon ’s passing a meridian, and coming to itagan. So that the sea flows as often as the Moon passes the me-ridian, both the arch above the horizon, and that below it; and ebbsas often a!; the Moon passes the horizon, both on the eastern and•western side These are the most obvious appearances : The otherphenomena are as follows:
f;i. 'i ne ‘dew.tion towuds the Mocn exceeds the opposite one
a little, and the quantity of the ascent of the water is diminishedfrom the equator to the poles.
IV'. The Sun raises and depresses the sea twice every day, inthe same manner that the Moon does; but the solar tides aremuch less than the lunar ones, although subject to the samelaws.
V. The tides which depend upon the actions of the Sun andMoon, are not distinguished, but compounded; and thus theyform, to appearance, one united tide, which increasing, and de-creasing, produces Neap and Spring tides.
VI. In the svzygies the elevations from the action of both lu-minaries concur, and the sea is more elevated; but the sea ascendsless in the quadratures; for where the water is elevated by the ac-tion of the Moon, it is depressed by that of the Sun , and viceversa. Therefore, while the Moon passes from the syzvgy to thequadrature, the daily elevations are continually diminished ; ohthe contrary, they are increased, while the Moon passes from thequadrature totiie syzygy. At the New Moon also, catcrisparibus,the elevations are greater; and those that follow one another thesame day, are more different than those at Full Moon .
VII. The greatest elevations and depressions take place on the2d or 3d day after the New 7 or Full Moon , and they are the greater,the nearer the luminaries are to the plane of the equator; beinggreatest in the syzygies, near the equinoxes.
VIII. The actions of the Sun and Moon are greater, the nearerthose bodies are to tiie Earth ; and the greatest tides happen, whenthe Sun is a little to the south of the equator; but this does nothappen regularly every vear, because some variation may arisefrom the situation of the Moon ’s orbit, and tiie distance of the sy-zvgy from the equinox.
IX. The mean force of the Moon , to move the sea, is to thatof the Sun nearly as 4! to 1 ; and therefore if the action of theSun alone produce a tide of 2 feet, which it is said to do; thenthat of the Moon will be 9 feet, from which it follows, that thespring-tides will be 11 feet, and the neap-tides 7 feet. But suchelevations, as far exceed these, happen from the motion of thewater against some obstacles, and from (he sea violently enteringstraits or gulfs, where the force is not broken till the water riseshigher.
T he preceding phenomena take place in the open sea, wherethe ocean is extended enough to lie subject to these motions. Butthe particular situations of places, as to shores, capes, bays, Ac.disturb in a considerable degree these general rules. We are nowto shew how these phxnomena may be explained, from the prin-ciple of universal gravitation.
(157.) If the Earth were entirely (laid and quiescent, its parti-cles, by their mutual gravity towards each other, would form thewhole Inass into the figure of an exact sphere. If a power wereto act on all the particles of this sphere, with an equal force, andin parallel directions, the whole mass would be moved together,but no change would be produced on its spherical figure, and itscentre would have the same motion as eacli particle. But on theprinciple of gravitation the Moon ’s action, on different parts of theEarth , is not equal, those parts, by the general laws of gravity,being most attracted that are nearest to the Moon , and those beingleast attracted that are farthest from her, while the parts, that areat a middle distance, are attracted by a mean degree of force.Besides all the parts are not acted upon in parallel lines; but inlines directed towards the centre of tiie Moon, on both which ac-counts, the spherical figure of the fluid earth must suffer somechange from the action of the Moon . TIeuce it appeal's, (whichmust be carefully observed,) that it is not the action of the Modiiitself, but the inequalities in that action, that cause any variationfrom the spherical figure ; and that if this action were the same inall the particles, as in the central parts, and operating in the samedirection, no such change would ensue. Let A B C D EFG II,(Plate XXIV. fig. 10,) represent a fluid ring forming a great circleof the Earth,let it pass through the point to which the Moon is ver-tical, and adhere to theEarlh bv the force of gravitation; then be-cause the gravity of the points II and F toward the Moon is in theoblique direction B M, F M, part of the force will tend to bringthe particles about B 'and F nearer the centre, and therefore theparticles about D and II will recede till there be an equilibrium.Again, from the laws of gravitation, the Moon ’s force is greater at11 than at O, because II is nearer to the Moon ; but the force at O,in the direction O M, tends to bring II and O nearer together.