ASTRONOMY.

gravitation of anv one of them, arising from the attractions of therest, may be determined by the rule lor composition of motion;and if the law of gravity be such as obtains in the Solar System , itsgravitation will not be always directed to the centre of gravity ofthe oilier bodies, or indeed to any fixed point, hut sometimes toone side of that centre, and sometimes to the other, and thereforeequal areas will not be described in equal times about any pointin the system ; and some irregularities will therefore arise in themotions of the bodies. Hut if one of these bodies should bevastly greater than the others, so that the actions of the other bodiesmay be neglected, when compared with its action ; and the centreof gravity of the system be always found near it, the irregularitiesof such a system will he very small, the areas described in equaltimes about the centre of the great body will be nearly equal, andthe orbits described will be nearly elliptic, having that centre intheir focus. Now this is the case with the Sun and planets, and thuswe see that not only the regular motions of the latter are to be de-rived from the principle of gravity, but also their minute errorsand irregularities.

(99.) Though the actions of the Sun and of the inferior planetscompounded together do not always produce, in a superior planet,a gravitation exactly directed towards their centre of gravity, yet,as; upon the whole, it is more directed to that point, than to anyother, the motions of a superior planet will be found more regular,by supposing that point to be the centre of its attraction, ratherthan any other ; and its ellipse will be just, by placing its lowerfocus there. A planet, that is higher than this, will, by its attrac-tion, have some effect on the motion in this ellipse ; but as it alsoacts on the inferior plamts at the same time, there will no irregu-larity arise from that part of its action which is equal, and in thesame direction with them all; hut from the differences of its ac-tions only, which being very minute, and having contrary effectsin the opposite situations of that higher planet, can produce effectsscarcely sensible in many revolutions.

(100*) The action of Jupiter on Saturn , when greatest, (that is,when their distance is least,) is found by calculation to be ofthe action of the Sun upon Saturn . This produces an effect notaltogether insensible ; but the elliptic orb of Saturn will be foundto be more just, if we suppose its focus not to be in the centre ofthe Sun, but in the centre of gravity of Jupiter and the Sun , orrather in the centre of gravity of the Sun and of all the planets be-low Saturn ; and the same observation applies to the orbit of anyother planet. The whole action of Jupiter disturbs the. motion ofSaturn in their conjunction, because Jupiter then acts upon Saturn and upon the Sun in opposite directions. Hut because Saturn thenacts upon Jupiter and upon the Sun in the same direction, if it actedalso with the same force on both, it would have no effect on the mo-tion of Jupiter about the Sun ; and it is by the excess of its actionop. Jupiter, above its action on the Sun , that it disturbs the motionof Jupiter . This excess is found to be one-192.3 part of the actionof the Sun on Jupiter ; and therefore is much less than the forcewith which Jupiter disturbs the motion of Saturn . The actions ofthe other planets on each other are incomparably less than these,and the irregularities proceeding from those actions are always lessin any planet, as it is nearer the Sun ; only the orbit of the Earth may appear a little more irregular than its neighbogring planets,because it revolves about the centre of gravity of tlieEarl h and Moon .

(101.) Eig. ti, Plate XX11. is intended to illustrate the effects ofthis general power. Let E represent the Earth, M the Moon , Kan inferior planet, S the centre of the Sun , G the centre of gra-vity of the Earth and Moon , and (,' the centre of gravity of thesystem. Then because of the mutual attractions, the centre of theSua S will describe a curve S, S', S", round C, while the planet Kand point G revolve, about the same point C, and the bodies Eand M instead of describing similar curves about G, w ill, in con-sequence of the progressive motion, describe curves intersectingEGA, the path of the centre of gravity, somewhat in the manner ofthe curve BEAU. The distance of the Earth and Moon is hererepresented about 40 times their proportional distance from G : iftruly delineated the real paths of the Earth and Moon would heconcave to the Sun , and not any where convex as at II: we hadnot room here to draw them in their proper proportions. Theinferior planet at K is accelerated, and E retarded, but at I- theinferior planet is retarded, and E accelerated by their attractionson each other.

(102.) What has been advanced respecting the planets will ap-

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ply equally to the comets, they being planets whose orbits arevery much elongated. The planes of their orbits cut (he eclipticin very different angles; some of them are nearly perpendicular to it.

Sect. IV. Of the Orbits and Motions of the Secon-dary Planets.

(103.) I lie same general principle of gravitation by which themotions ot the primary planets are produced, extends’ also to themotions of the secondary planets, and from observations on themwe get an additional proof of this general law, that all matter gra-vitates to all other matter with a force reciprocally proportional to-fhe square of the distance. That each secondary planet is kept inits orbit by a power directed toward its primary, &c. is proved iromthe phamomena of the satellites of Jupiter, Saturn , and Herschel ;because they move in circles, as far as we can observe, about theirrespective primaries with an equable course, the primary beingthe centre of each orbit: and by comparing the times in whichthe diilerent satellites of the same primary perform their periods,they are found to observe the same relation to the distances fromtheir primary, as the primary planets observe in respect to theirmean distances from the Sun . The same thing holds good alsow ith regard to the Earth and Moon ; for she is found to moveround the Earth in an ellipsis after the same manner as the primaryplanets do about the Sun , excepting only some small irregularitiesin her motions, the cause of which will he particularly explainedin what follows. The power of Jupiter and Saturn maybe measuredto a very considerable distance, by the number of satellites whichmove round them : for the distance of the outermost satellite-ofeach of them exceeds several times that of the innermost. Theforce of the Earth upon the Moon , however, at different distances,is more confirmed by the following consideration than any analo-gical reasoning :

(104.) Let A, in Plate XXII. fig. 7, represent the Earth , B theMoon, BCD the Moon ’s orbit; which differs little from a circle,of which A is the centre. If the Moon in B were left to itself tomove with the velocity it has in the point B, it would leave theorbit, and proceed straight forward in the line BE which touchesthe orbit in B. Suppose the Moon would upon this conditionmove Irom B to E in the space of one minute of time: bv theaction of the Earth upon the Moon , whereby it is retained in itsorbit, the Moon will really be found at the end of this minute bythe point F, from whence a straight line drawn to A shall makethe space BE A in the circle equal to the triangular space BEA ;so that the Moon , in the time wherein it would have moved fromB to E, if left to itself, has been impelled towards the Earth fromE to E. And when the time of the Moon ’s passing from B to F issmall, as here it is only one minute, the distance between E and Fscarcely differs from the space through which the Mcon would de-scend in the same time, if it were to fall directly down from. Btoward A without any oilier motion. AB, the "distance of theMoon from the Earth , is about bo of the semidiameters of the lat-ter; ami the Moon completes her revolution round the Earth inabout 27 days, 7 hours, and'43 minutes: therefore the space EFwill here be found by computation to be about l(ii feel. Conse-quently, if the power, by which the Moon is retaiiied in its orbit,be, near the surface of the Earth , greater than at the distance ifthe Moon , in the duplicate proportion of that distance, the num-ber of feet a body would descend near the surface of the Earth ,by the action of this power upon it, in one minute, would beequal to the number 1 ti-jmultiplied twice into the number bO;that is, to 38050.

(105.) IIow last bodies fall near the surface of the Earth may beknown by the pendulum ; and, by exact experiments, they arefound to descend the space of lti-JTeet in one second; and thespaces described by falling bodies being in the duplicate propor-tion of the times of their fall, the number of feet a body woulddescribe in its fall near the surface of the Earth in one minute oftime, would be equal to 1(>J- twice multiplied by (30 ; the same asthe power which acts upon the Moon would cause. The Earth , inthis computation, is supposed to be at rest; but it would havebeen more exact to suppose it to move, as well as the Moon ,about their common centre of gravity. The action of the Sun upon the Moon is also here neglected ; and Newton shews, ifjou take in both these considerations, the present computationwill best agree to a somewhat greater distance of the Moon andEarth , viz. to boj; semidiamoters of the latter, which distance