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gy: As the time of the Moon's describing the arc EO is to 90 degrees, so is 6 hours 12 minutes to the degrees of the arc Dde, which measures the angle EAL; from which subtract 90 degrees, and there remains the angle O AL, equal to the angle ALC, under which the Earth's semi-diameter AC is seen from the Moon. Now, since all the angles of a right-lined triangle are together equal to 180 degrees, or to two right angles, and the sides of a triangle are always proportional to the sines of the opposite an.
The gles, say by the Rule of Three, as the sine of the Moon's angle ALC, at the Moon L, is to its opposite side distance AČ, the Earth's semi-diameter, which is known to ed. be 3985 miles, so is radius, viz. the sine of 90 degrees, or of the right angle ALC, to its opposite side AD, which is the Moon's distance at L from the observer's place at A, on the Earth's surface; or, so is the sine of the angle CAL to its opposite side CL, which is the Moon's distance from the Earth's centre, and comes out at a mean rate to be 240,000 miles. The angle CAL is equal to what OAL wants of 90 degrees.
191. The Sun's distance from the Earth might The Sun's be found in the same way, though with more diffi- cannot be culty, if his horizontal parallax, or the angle OAS, yet so exequal to the angle ASC, were not so small, as to be actly de: hardly perceptible; being scarce 10 seconds of a as the minute, or the 360th part of a degree. But Moon’s. the Moon's horizontal parallax, or angle OAL, equal to the angle ALC, is very discernible, being 57' 18", or 3438" at its mean state; which is more than 340 times as great as the Sun's : and, therefore, the distances of the heavenly bodies being inversely as the tangents of their horizontal parallaxes, the Sun's distance from the Earth is at least 340 times as great as the Moon's: and is rather underrated at 81 millions of miles, when the Moon's distance is certainly known to be 240 thousand. But
because, according to some astronomers, the Sun's horizontal parallax, is 11 seconds, and according to others only 10, the former parallax making the Sun's distance to be about 75,000,000 of miles, and the latter 82,000,000; we may take it for granted that the Sun's distance is not less than as deduced from the former, nor more than as shewn by the latter : and every one, who is accustomed to make such ob. servations, knows how hard it is, if not impossible, to avoid an error of a second, especially on account of the inconstancy of horizontal refractions. And here the error of one second, in so small an angle, will make an error of 7 millions of miles in so great a distance as that of the Sun's. But Dr. HALLEY has shewn us how the Sun's distance from the Earth,
and consequently the distances of all the planets How near from the Sun, may be known to within a 500th the truth part of the whole, by a transit of Venus over the
Sun's disc, which will happen on the 6th of June, determin- in the year 1761; till which time we must content
ourselves with allowing the Sun's distance to be about 81 millions of miles, as commonly stated by astronomers.
192. The Sun and Moon appear much about the The Sun proved to same bulk; and every one who understands geombe much etry, knows how their true bulks may be deduced than the from the apparent, when their real distances are
known. Spheres are to one another as the cubes of their diameters; whence, if the Sun be 81 millions of miles from the Earth, to appear as big as the Moon, whose distance does not exceed 240 thou. sand miles, he must in solid bulk be 42 millions 875 thousand times as big as the Moon.
193. The horizontal parallaxes are best observed at the equator; 1. Because the heat is so nearly
equal every day, that the refractions are almost con. stantly the same. 2. Because the parallactic angle is greater there, as at A, (the distance from thence to the Earth's axis being greater,) than upon any parallel of latitude, as a or b. 194. The Earth's distance from the Sun being The rela.
tive dis. determined, the distances of all the other planets from him are easily found by the following analogy, the plan. their periods round him being ascertained by obser-ets from vation. As the square of the Earth's period round are known the Sun, is to the cube of its distance from the Sun; to great
precision, so is the square of the period of any other planet, to though the cube of its distance in such parts or measures their real as the Earth's distance was taken; see $ 111. This distances proportion gives the relative mean distances of the well planets from the Sun to the greatest degree of exactness. They are as follows, having been dedu. ced from their periodical times; according to the law just mentioned, which was discovered by KEPLER, and demonstrated by Sir Isaac Newton.*
All the following calculations except those in the two last lines before $ 195, were printed in former editions of this work, before the year 1761. Since that time the said two lines (as found by the transit A. D. 1761) were added ; and also $ 195.
Periodical Revolutions to the same fixed Star, in
Days and Decimal Parts of a day.
from the Sun in English miles, are !31,742,200 1 59,313,060 | 82,000,000 | 124,942,680 I 426,478,720 i 782,284,920 I 1,565,035,600 But if the Sun's parallax be 11" their distances are no more than 29,032,500 | 54,238,570 | 75,000,000 | 114,276,750 | 390,034,500 | 715,504,500 | 1,431,435,000 Errors in distance arising from the mistake of l" in the Sun's
parallax. 2,709,700 1 5,074,490 17,000,000 | 10,665,830 | 36,444,220 | 66,780,420 | 133,600,600 But, from the late transit of Venus, A. D. 1761, the Sun's parallax appears to be only 8' 656 ; and according to that,
their real distances in miles are 36,841,468 | 68,891,486 1 95,173,127 | 145,014,148 | 494,990,976 | 907,956,130 I 1,816,455,526
And their diameters in miles, are, 3100
93601 7970 5150 94,1000 77,9901 35,226 195. These numbers shew, that although we have the relative distances of the planets from the Sun, to the greatest nicety, yet the best observers could not ascertain their true distances until the late long-wished-for transit appeared, in 1761, which we must confess was embarrassed with several difficulties. But another transit of Venus over the Sun, has now been observed, on the third of June, 1769, much better suited to the resolution of this great problem than that in 1761 was; and the result of the observations does not differ materially from the result of those in 1761. No other transit will happen till the year 1874.
196. The Earth's axis produced to the stars, being carried parallel* to itself during the Earth's an
nual revolution, describes a circle in the sphere of Why the the fixed stars equal to the orbit of the Earth. But celestial this orbit, though very large, would seem no bigseem to ger than a point, if it were viewed from the stars; keep still in * By this is meant, that if a line be supposed to be drawn paral
lel to the Earth’s axis in any part of its orbit, the axis keeps parallel to that line in every other part of its orbit: as in fig. I. of plate V. where abcdefgh represents the Earth's orbit in an oblique view, and N 8 the Earth's axis keeping always parallel to the line MN.
and consequently the circle described in the sphere the same of the stars by the axis of the Earth, produced, if the heaviewed from the earth, must appear but as a point; vens, notthat is, its diameter appears too little to be measur.
ding the ed by observation : for Dr. BRADLEY has assured Earth's us, that if it had amounted to a single second, or two
motion at most, he should have perceived it in the number Sun. of observations he has made, especially upon op Draconis; and that it seemed to him very probable that the annual parallax of this star is not so great as a single second: and consequently, that it is above 400 thousand times farther from us than the Sun. Hence the celestial poles seem to continue in the same points of the heavens throughout the year; which by no means disproves the Earth's annual motion, but plainly proves the distance of the stars to be exceeding great.
197. The small apparent motion of the stars, 8 113, discovered by that great astronomer, he found to be no ways owing to their annual parallax, (for it came out contrary thereto,) but to the aberration of their light, which can result from no known cause, besides that of the Earth's annual motion; and as it agrees so exactly therewith, it proves beyond dispute, that the Earth has such a motion; for this aberration completes all its various phenomena every year; and The amaproves that the velocity of star-light is such as car-zing velories it through a space equal to the Sun's distance city of from us in 8 minutes 13 seconds of time. Hence ihe velocity of light is * 10 thousand 210 times as great as the Earth's velocity in its orbit; which velocity, (from what we know already of the Earth's distance from the Sun) may be asserted to be at least between 57 and 58 thousand miles every hour : and supposing it to be 58000, this number multiplied by 10210, gives 592 million 180 thousand miles for the hourly motion of light: which last number divi. ded by 3600, the number of seconds in an hour,
* SMITH's Optic's $ 1197.