ASTRONOMY.

270

tliau 64 to 1. Any person, unassisted by instruments, may ob-serve an inferior planet alternately approach nearer and nearerthe sun, until at last it comes into conjunction with him, and thenrecedes farther and farther, till it is at its greatest elongation, whichw ill IX first on one side, and then on the other: but, if we observethe apparent change of place of an inferior planet in the sphereof the heavens, its direct motions, stations, and retrogradations,measuring its diameter frequently with the micrometer, we shallfind, by its decrease at some times, and increase at others, thatits distance from us is very considerably varied.

(77.) The apparent paths of Mercury and Venus as seen fromthe earth, are delineated on Plate XXIV. Fig. 5. They appear todescribe looped curves, which are extremely complicated. Thedarkest line represents that of Venus , which returns into itselfevery eighth year. The faintest looped curve represents the pathof Mercury, which does not return into itself at any assignableperiod. 1 he double circle, with the months marked upon it, re-presents the apparent path of the sun, (for the earth is here con-sidered as apparently at rest,) and the outer circle represents theecliptic. The apparent stations and retrogradations of these pla-nets, are obviously shewn from this figure. The apparent pathsof Mars, Jupiter and Saturn , are given in Plate XxIV. Fig. 4.Tlie numbers marked on the looped curves, are the years forwhich the motions are shewn. 1 his figure also serves well forshewing the apparent stations, &c. of the superior planets.

(78.) As the superior planets move in a larger orbit than theearth, they can only be in conjunction with the sun, when they areon that side opposite to the earth ; as, on the other hand, they arein opposition to him, when the earth is between (he sun and them.They are in quadrature with him, when their geocentric placesare 90° distant from that of the sun. In order to understand theirapparent motions, we shall suppose them to stand still, in somepart of their orbit, while the earth makes a complete revolutionin hers ; in which case, any superior planet would then have thefollowing appearances: I. While the earth is in her most distantsemicircle, the motion of the planet will he direct. II. While theearth is in her nearest semicircle, the planet will be retrograde.III. While the earth is near those places of its orbit, where a linedrawn from the planet, would he a tangent, it would appear to bestationary. Thus, in Plate XXVI. Fig. 15. let a b cd represent theorbit of the earth ; S the sun : EFG an arc of the orbit of Jupi-ter ; ABC an arc of the ecliptic, projected on the sphere of thefixed stars. Suppose Jupiter to continue at F, while tire earth goesround in her orbit, according to the order of the letters a b c d.While the earth is in the semicircle most distant from J upiter,going from a to b and from b, to c, his motion in tire heavens wouldappear direct, or from A to B, and from B to C ; but, while theearth is in its nearest semicircle c d e, tire motion of Jupiter wouldappear retrograde from C to B, and from B to A ; for a, b, c, d,may be considered as so many different stations, from whence aninhabitant of the earth would view Jupiter at different seasons ofthe year, and a straight line drawn from each of these stations,through F the place of Jupiter , and continued to the ecliptic,would shew his apparent place there to be successively at A, B, C,B, A. While the earth is near the points of contact, a and c, Ju-piter would appear stationary, because the visual ray drawnthrough both planets, does not sensibly differ from the tangent F«or l’c. When the earth is at b, a line drawn from b through S andF to the ecliptic, shews Jupiter to be in conjunction with the sunat 15. When the eartli is at d, a line drawn from d through S,continued lo Ihe ecliptic, would terminate in a point opposite to15 ; which shews Jupiter then to be in opposition to the sun : andthus, it appears, that his motion is direct in the conjunction, butretrograde when in opposition witli the sun.

(79.) The direct motion of a superior planet is swifter the nearerit is to a conjunction, and slower as it approaches to a quadraturewith the sun. Thus, in fig. 16, let 0 be the sun ; the little circleround it, the orbit of the eartli, whereof a b c d ef s' is the mostdistant semicircle; Ol’Q, an arc of the orbit of Jupiter ; andABCDEFG, an arc of the ecfptic in the sphere of the fixed stars.If we suppose Jupiter to stand still at P, by the earth’s motionfrom a to g, he would appear to move direct from A to (j, de-scribing the unequal arcs A15, BC, C D, I) F., EK, FG, in equal limes.When the earth is at d Jupiter is in conjunction with the sun at1), and there Ins direct motion is swiftest. When the eartli is intiiat part of her orbit where a line drawn from Jupiter would touch

it, as in the points e or g, Jupiter is nearly in quadrature with thesun ; and the nearer the earth is fo any of those points, the sloweris the geocentric motion cr Jupiter ; for the arcs CD and IJE aregreater than BC or EF, and the arcs BC and EF are greater thanABorFG.

(80.) The retrograde motion of a superior planet is swifter thenearer it is to an opposition, and slower as it approaches to a quad-rature, with the sun. Thus, let ©, (fig. 17.) be the sun; the littlecircle round it the orbit of the earth, whereof g h i k l m n is thenearest semicircle; OPQ, an arc of the orbit of Jupiter ; NKG anarc of the ecliptic: if we suppose Jupiter to stand still, at P, by theearth’s motion from g to n, he would appear to move retrogradefrom G to N, describing the unequal arcsGII, Ill, IK, KL,LM, MN, in equal times. When the earth is at k, Jupiter ap-pears at K, in opposition to the sun, and there his retrograde mo-tion is swiftest. When the earth is either at g or n, the points ofcontact of the tangents Pg and Pra, Jupiter is nearly in quadraturewith the sun: and the nearer he is to either of these points, theslower is his retrogradation ; for the arcs IK and KI, are greaterthan HI or LM : and the arcs III and LM are greaier than GILor MN. Since the direct motion is swiftest when the earth is atd, and continues diminishing till it changes lo retrograde, it mustpe insensible near the time of change : ami, in like manner, the re-trograde motion being swiftest when the eartli is in k, and dimi-nishing gradually till it changes to direct, must also at the time ofthat change be insensible; for any motion gradually decreasingtill it changes into a contrary one gradually increasing, must at thetime of the change he altogether insensible. The same changes inthe apparent motions of this planet will also take place, if we sup-pose him to go on slowly in his orbit; only they will happenevery year when the earth is in different parts of her orbit;and consequently at different times of Hie year. 'Thus, (fig. 15,)let us suppose, that, while the earth goes round her orbit,Jupiter goes from F to G, the points of the earth’s orbit fromwhich Jupiter will now appear to lie stationary will be a and?/:and consequently his stations must be at a time of the year diffe-rent from the former. The conjunction of Jupiter with the sunwill now be when the earth is at/, and his opposition when it is ate ; for which reason these also will happen, at times of the year dif-ferent from those of the preceding opposition and conjunction.—The motion of Saturn is so slow, that it makes hut little alterationeither in the times or places of his conjunction or opposition ; andthe same will take nlace in a more eminent degree in Ilerschel ;but the motion of Mars is so much swifter than eveii that ofJupiter , that Loth the times and places of his conjunctions and oppo-sitions are thereby very much altered.

(81.) A superior planet is in Apogee when in conjunction withthe sun, and in Perigee when in opposition ; and every one of thesuperior planets is at its least possible distance from the earthwhen it is in perigee and perihelion at the same time. Their ap-parent diameters are variable, according to their distances, likethose of the inferior planets; and this, as might naturally be ex-pected, is most remarkable in the planet Mars , who is nearest us.In his nearest approach, his diameter is 4+ times larger than whenfarthest oft, Jupiter lyt/o', Saturn l-fgj, and Ilerschel 1-^%.As the times of conjunction, utmost elongation, direct or retro-grade motions of the inferior planets, depend on the combinationsof their motions in their orbits with the motion of the earth in itsorbit; anv of these appearances will be more frequent in Mercurythan in Venus , because the former moves with a swifter motion illhis orbit, and consequently must more frequently pass throughthose places where he is in conjunction, &c,

(89.) 'i he time in which any of the inferior planets w ill relitrninto a given situation, may be easily known. Compute the diur-nal heliocentric motions of Venus and of the earth: the differenceof these motions is the diurnal motion of Venus from the earth, orthe quantity by which Venus would be seen to recede from theeartli every day by a spectator placed in the sun : thus the meanmotion of the earth is every day about 59 minutes and 8 seconds;and the difference of the motion of 0 and J about 37 minutes.Therefore, As 37 minutes of a degree is to one dav, so is 3(>0 de-grees, or 91(500 minutes of a degree, to the time wherein Venus,having left the earth, recedes from her 360 degrees; that is, to thetime she returns lo the earth again, or the time between two con-junctions of the same kind. The calculations of the times arehero made according to the mean or equable motions of the pla-nets