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 467 ASTRO N O M Y. the curve Je, and is again in conjunction at e with the defcribed by the nail will referable in miniature as much fun the earth is at E, between the 29th and 30thof the earth’s annual path round the fun, as it defcnbes day when moon’s age, accounted by the numeral figures whilft the moon goes as often round the earth as the pin ofthethenew moon at A. In defcribing the curve abode, does round the nail; and the curve defcribed by the from the moon goes round the progreffive earth as really as if nail will have fome refemblance of the moon’s path du- ftie had kept in the dotted circle A, and the earth contiring fo many lunations. in the centre of that circle. Let us now fuppofe that the radius of the circular nued immoveable thus we fee, that although the moon goes round curve defcribed by the nail in the axle is to the radius of theAnd earth in a circle, with refpedt to the earth’s centre, the circle which the pin in the nave defcribes round the her in the heavens is not very different in apaxle, as 3374- to i ; which is the proportion of the ra- real path from the earth’s path. To ftiew that the moon’s dius or femidiameter of the earth’s orbit to that of the pearance is concave to the fun, even at the time of change,. moon’s, or of the circular curve ^1234567 .5, path &c. to the little circle ; and then, whilft the pro- itt0 is carried on a little farther into a fecond lunation, as greffive nail defcribes the faid curve from A to E, the moon’s abfolute motion from her change to her pin will go once round the nail with regard to the cen- firft^The quarter, or from a to b, is fo much flower than the tre of its path, and in fo doing, will defcribe the curve earth’s, that ftie falls 240 thoufahd miles (equal to the abode. The former will be a true reprefentation of the femidiameter he*f orbit) behind the earth at her firft earth’s path for one lunation, and the latter of the moon’s quarter in b, ofwhen the earth is in 5; that is, ftie falls for that time. Here we may fet afide the inequalities of back a fpace equal to her diftance from the eajth. From the moon’s motion, and alfo, the earth’s moving round fhat time her morion is gradually accelerated to her opits common centre of gravity and the moon’s : All which,if they were truly copied in this experiment, would not pofition or full at e, and then ftie is come up as far as fenfibly alter the figure of the paths defcribed by the nail the earth, having regained what ftie loft in her firft quarand pin, even though they fhould rub againft a plain up- ter from a to b. From the full to the laft quarter at d,. right furface all the way, and leave their tracks vifible her motion continues accelerated, fo as to be juft as far upon it. And if the chariot was driven forward on fuch before the earth at D, as flie was behind it at her firft a convex piece of ground, fo as to turn the wheel feve- quarter in b. But, from d to e her motion is retarded ral times round, the track of'the pin in the nave would fo, that flie lofes as much with refpedt to the earth as is ftill be concave toward the centre of the circular curve equal to her diftance from it, or to the femidiameter of defcribed by the pin in the axle ; as the moon’s path is her orbit; and by that means ftie comes to e, and is always concave to the fun in the centre of the earth’s then in conjunction with the fun, as feen from the earth at E. Hence we find, that the moon’s abfolute motion annual orbit. In this diagram, the thickeft curve line ABCD, with is flower than the earth’s fjom her third quarter to her the numeral figures fet to it, reprefents as much of the firft ; and fwifter than the earth’s from her firft quarter earth’s annual orbit as it defcribes in 32 days from weft to her third : Her path being lefs curved than the earth’s to eaft; the little circles at abode ftiew the moon’s orbit in the former cafe, and more in the latter. Yet it is ftill in due proportion to the earth’s ; and the fmalleft curve bent the fame way towards the fun; for if we imagine abodef reprefents the line of the moon’s path in the hea- the concavity 5f the earth’s- orbit to be meafured by • vens for 32 days, accounted from any particular new moon the length of a perpendicular line Cg* let down from the at a The machine, Plate XLIX. fig. 2. is for delineating earth’s.place upon the ft'raight line bgd at the full of the. the moon’s path, and will be defcribed,.with the reft of moon, and connecfling the places of the earth at the end tbe aftronomical machinery, in the laft chapter. The of the moon’s firft and third quarters, thqt length will fun is fuppofed to be in the centre of the curve A 1 2 y be about 640 thoufand miles; and the,moon, when new,. 4567.#, &c. and fheTmall Ndotted circles upon it repre- only approaching. nearer to the fun, by 240 thdufand lent the moon’s orbit, of which the radius is in the fame miles than the earth is,- the length of the perpendicular proportiomto the earth’s- path in this fcheme, that the let down from her place at that rime upon the fame radius of the moon’s brbit in- the heavens bears to the ra- ftraight line, and which (hews the concavity of that part dius of the earth’s annual path round the fun j that is, as: of her path, will be about 400 thoufand miles. The moon’s path being concave to the fun throughout,, 240,000 to 81,000,000, or as i to 3374.. When the earth is at A, the new moon is. at a; and- demoftrates that her gravity towards the fun, at her in the feven days that the earth defcribes' the curve 1 2 conjunction, exceeds her gravity towards the earth. 34567, the moon, in accompanying the earth de- And if we confider that the quantity of matter in the fun fcribes the curve ab- and is in her firft quarter at b is almoft 230 thoufand times as great as the quantity of when the earth is at 2?. As the . earth defcribes the matter in the earth, and that the attraction of each body curve 2? 8 9 10 11 12 13 14, the moon defcribes the' diminifties as the fquare of the diftance from it increafes, curve d; and is at c, oppofife to the fun, when the we (hall fdon find, that the point of equal attraction beearth is at C. Whilft the earth defcribes the curve tween the earth and the fun is about 70 thoufatad miles C 15 16 17 18 19 20 21 22, the moon defcribes the nearer the earth than the moon is at her change. It may curve <r<2; and is in her third quarter at <2 when the . now appear furprifing, that the moon does not abandon earth is at Z). Once more, whilft the earth defcribes. the earth when (he is between" it and the fun, .becaufe the curve D 23 24 25 26 27 28 29, the moon defcribes: (he k confiderably more nitrated by the fun than by the : earth:s