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 ; 49* ASTRO N O M Y. curious machine fhews the motion of a comet or excen- This motion is performed in the following manner byr tric body moving round the fun, defcribing equal areas the machine, (Plate XLVIII. fig. 3.). ABC is a woodbar, (in the box containing the wheel-wof^|,' above in equal times, and may be fo’ contrived as to Ihew" fuch enwhich are the wheels D and E, and below it the elliptic a motion for any degree df excentricity. It was inventplates FF and GG ; each plate being fixed cfa an axis in ed by the late Dr Defaguliers. The dark elliptical groove round the letters abcdefghiklrn one of its focufes, at E and K; and the wheel E is fixis the orbit of the comet T: this comet is carried round ed on the fame axis with the plate FF. Ti'.^Toffdates, in the groove according to the order of letters, by the have grooves round their edges precifely of equal diaihev wire W fixed in the fun S', and Hides on the wire as it ters to one another, and in thefe grooves is the teat-gut approaches nearer to, or recedes farther from the fun, ftring gg, gg croffing between the plates at b. On ll, being neareft of all in the perihelion a, and fartheft in the axis of the handle or winch Win fig. 2. is an end • the aphelion g. The areas, aSb, bSc, cSd, &c. or con- lefs ferew ip fig. 3. working in the wheels D and E, tents of thefe feveral triangles, are all equal; and in e- whofe numbers of teeth being equal, and (hould be equal very turn of the winch N, the comet T is carried over to the number of lines aS, bS, cS, Sec. in fig. 2. they one of thefe areas; confequently, in as much time as it turn round their axes in equal times to one another, and moves from / to g, or from g to b, it moves from m to to the motion of the elliptic plates. For, the wheels a, or from « to £; and fo of the reft, being quickeft of D and E having equal numbers of teeth, the plate FF beall at a, and flowed at g. Thus the comet’s velocity in ing fixed on the fame axis with the wheel £■, and the its orbit continually decreafes from the perihelion a to plate FF turning the equally big plate GG by a cat-gut the aphelion g; and increafes in the fame proportion from ftring round them both, they muft all go round their axes in as many turns of the handle N as either of the wheels gto a. The elliptic orbit is divided into 12 equal parts or has teedi. figns, with their refpedtive degrees, and fo is the circle It is eafy to fee, that the end b of the elliptical plate nopqrstu, which reprefents a great circle in the heavens, FF being farther from its axis E than the oppofite end l and to which the comet’s motion is referred by a fmall is, muft defcribe a circle fo much-the larger in proporknob on the point of the wire W. Whilft the comet tion, and therefore move through fo much more (pace in moves from f to g in its orbit, it appears to move only the fame time ; and for that reafon the end b moves fo about five degrees,in this circle, as is (hewn by the fmall much fafter than the end l, although it goes no fooner knob on the end of the ware W but in as ftiort time as round the centre E. But then the quick-moving end k the comet moves from m to a, or from a to b, and it of the plate FF leads about the (hort end bK of the plate appears to defcribe the large fpace tn or no in the hea- GG with the fame velocity^; and the flow-moving end I vens, either of whichv,fpaces contains 120 degrees, or of the plate FF coming half round as to B, muft then four figns. Were the excentricity of its orbit greater, lead the long end k of the plate GG as (lowly about: fb the greater ftill would be the difference of its motion, that the elliptical plate FF and its axis E move uniformly and vice verfa. and equally quick in every part of its revolution; but ABCDEFGHIKLMA is a circular orbit for (hewing the elliptical plate GG, together with its axis K, muft: the equable motion of a. body round the fun S, defcri- move very unequally in different parts of its revolution; bing equal areas ASB, BSC, See. in equal times with the-difference being always inverfely as the diftance of thofe of the body T in its jelliptical orbit above men- any point of the circumference of GG from its axis at tioned ; but with this difference, that the circular mo- K: or in other words, to inftance in two points, if the tion deferibes the equal arcs AB, BC, See. in the fame diftance Kk be four, five, or fix times as great as the diequal times that the elliptical motion deferibes the une- ftance Kb, the point h will move in that pofition four, qual arcs, ab, be, Sec. five, or fix times as faft as the point k does, when the Now, fuppofe the two bodies T and 1 to ftart from the plate GG has gone half round ; and fo on for any other points a and A at the fame moment'of time, and, each excentricity or difference of the diftances Kk and Kh. having gone round its refpe&ive orbit, to arrive at thefe The tooth / on the plate FF falls in between the two points again at the fame inftant, the body T will be for- teeth at k on the plate GG, by which means the revoluwarder in its orbit than the body 1 all the way from a tion of the latter is fo adjufted to that of the former, to g, and from A to G; but 1 will be forwarder than T that .they can never vary from one another. through all the other half of the orbit; and the differ- On the top of-the axis of the equally-moving wheel ence is equal to the equation of the body T in its orbit. D in fig. 3. is the fun S in ’fig. 2.; which fun, by the At the points a A, and gG, that is, in the perihelion and wire fixed to it, carries the ball 1 round the circle aphelion, they will be eqqal; and then the equation va- ABCD, Sec. with an equable motion, according to the nifties. This (hews why the equation of a body moving in order of the letters: and on the top of'th| axis K of the an elliptic orbit, i^idded to the mean or fuppofed circular unequally-moving ellipfis GG, in fig. 3. is the fun S in motion from the perihelion to the aphelion, and fubtrafted fig. 2. carrying the ball T unequabiy round in the ellipfrom the aphelion to the perihelion, in’ bodies moving tical groove abed. Sec. N. B. This elliptical groove round the fun, or from the perigee to the apogee, and muft be precifely equal and fimilar to the verge of the from the*apogee to the perigee in the,moon’s motion plate GG, which is alfo equal tq that of FF. round the earth. In this manner machines may be made to (hew the Von. I. No. 21. 6K true a