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4$ 2 ASTRO N O M Y. degrees at o, in the edge EC •, but if he elevates the which ftie is then viewed, will be at d, 90 degrees from quadrant fo as to look through the fight-holes at any D, where it was when flie was feen *t E. Now, let the part of the heavens, fuppofe to the fun at S ; juft fo exadt moment when the moon is feen at 0 (which will be many degrees as he elevates the fight-hole b above the when fhe is in or near the fenfible horizon) be carefully horizontal line HOX, fo many degrees will the plumb- noted, that it may be known in what time fhe has gone line cut in the limb CP of the quadrant. For, let the from E to 0-, which time fubtradted from 6 hours 12 obfcrver’s eye at yV be in the centre of the celeftial arc minutes (the time of her going from E to L) leaves the XT’/ (and he may be faidto be in the centre of the fun’s time of her going from 0 to L, and affords an eafy meapparent diurnal orbit, let him be on what part of the thod for finding the angle OAL (called the moon's horiearth he will) in which arc the fun is at that time, fup- zontal parallax, which is equal to the angle ALC) by pofe 25 degrees high, and let the obferver hold the qua- the following analogy. As the time of the moon’s dedrant fo that he may fee the fun through the fight-holes; feribing the arc EO is to 90 degrees, fo is 6 hours 12 the plumb-line freely playing on the quadrant will cut minutes to the degrees of the arc DdE, which meafures the 25th degree in the limb CP, equal to the number of the angle EAL; from which fubtradt 90 degrees, and degrees of the fun's altitude at the time of obfervation. the're remains the angle OAL, equal to the angle ALC, —[N. B. Whoever looks at the fun, mult have a under which the earth’s femidiameter AC is feen from fmoked glafs before his eyes to fave them from hurt. the moon. Now, fince all the angles of a right-linfcd The better way is not to look at the fun through the triangle are equal to 180 degrees, or to two right angles, light-holes, but to hold the quadrant facing the eye, at and the fides of a triangle are always proportional to the a. little diftance, and fo that the fun fhining through fines of the oppofite angles, fay, by the Rule of Three, one hole, the ray may be feen to fall on the other.3 as the fine of the angle ALC at the moon L is to its In fig 2. Plate XLI. let BAG be one half of the oppofite fide AC, the earth’s femidiameter, which is earth, AC its femidiameter, S the fun, rn the moon, and known to be 3985 miles, fo is the radius, viz. the fine of EKOL a quarter of the circle defcribed by the moon in 90 degrees, or of the right angle ACL, to its oppofite revolving from the meridian to the meridian again. Let fide AL, which is the moon’s diftance at L, from the CRS be the rational horizon of an obferver at A, ex- obferver’s place at y^, on the earth’s furface , or, fo is tended to the fun in the heavens; and HAO his fenfible the fine of the angle CAL to its oppofite fide CL, which horizon, extended to the moon’s orbit. ALC is the is the moon’s diftance from the earth’s centre, and comes angle under which the earth’s femidiameter AC is feen out, at a mean rate, to be 240,000 miles. The angle from the moon at L, which is equal to the angle 0 AL, CAL is equal to what OAL want^ of 90 degrees. becaufe the right lines AO and CL which include both The fun’s diftance from the earth is found the fame thefe angles are parallel. ASCs the angle under which way, but with much greater difficulty; becaufe his boithe earth’s femidiametef AC is feen from the fun at S, rizontal parallax, or the angle OAS equal to the angle and is equal to the angle OAf becaufe the lines AO ASC, is fo fmall as to be hardly perceptible, being only and CRS are parallel. Now, it is found by obferva- icfeconds of a minute, or the 360th part of a degree. tion, that the angle OAL is much greater, than the an- But the moon’s horizontal parallax, or angle OAL, equal gle OAf; but OAL is equal to ALC, and OAf is e- to the an^le ALC, is very difcernible, being 5/ qf, qual to ASC. Now, as ASC is much lefs than ALC, or 3469 at its mean ftate ; which is more than 340 it proves that the earth’s femidiameter AC appears much times as great as the-fun’s: And therefore the diftances greater as feen from the moon at L, than from the fun of the heavenly bodies being inverfely as the tangents of at S; and therefore the earth is much farther from the their horizontal parallaxes, the fun’s diftance from the fun than from the moon. The quantities of thefe angles earth is at leaft 340 times as great as the moon’s ; and is are determined by obfervation in the following manner. rather underftated at 81 millions of miles, when the Let a graduated inftrument, as DAE (the larger the moon’s diftance is certainly known to be 240 thoufand. better) having a moveable index with fight-holes, be But becaufe,* according to feme aftronomers, the fun’s fixed in fuch a manner, that its plane' furface may be horizontal parallax is 11 feconds, and according to oparallel to the plane of the, equator, and its edge AD thers only 10, the former parallax making the fun’s diin the meridian: fo that when the moon is in the equi- ftance to be about 75,000,000 of miles, and the latter jnoftial, and on the meridian at E, (he may be feen 82,000,000.; we may take it for granted, that the fun’s through the fight-holes when the edge of the moveable diftance is not lefs than as deduced from the former, index cuts the beginning of the divifions at o, on the nor more than as ffiewn by the latter: And every one graduated limb DE; and when (he is fo feen, let the who is accuftomed to make fuch obfervations, knows precife time be noted. Now, as the moon revolves a- how hard it is, if nqt impoffible, to avoid an error of a bout the earth, from the meridian to the meridian again, fecond, efpecially on account of the inconftancy of hoin 24 hours 4?8 minutes, ftie will go a fourth part round rizontal refractions : And here, the error of one fecond, it in a fourth part of that time, viz. in 6 hours 12 mi- in fo fmall an angle, will make an error of feven millions nutes, as feen from C, that is, from the earth’s centre of miles in fo great a diftance as that of the fun’s. or pole. But as feen from A, the obferver’s place on The fun and moon appear much about the fame bulk; -the earth’s furface, the moon will feem to have gone a and every one who underftands geometry, knows how quarter round the earth when (he comes to the fenfible their true bulks may be deduced from the apparent, horizon at 0 ; for the index, through the fights of when their real diftances are known. Spheres are to one another
