191. The Sun’s distance from the Earth is found the same way, but with
much greater difficulty; because his horizontal Parallax, or the Angle
_OAS_ equal to the Angle _ASC_, is so small as, to be hardly
perceptible, being only 10 seconds of a minute, or the 360th part of a
degree. But the Moon’s horizontal Parallax, or Angle _OAL_ equal to the
Angle _ALC_, is very discernible; being 57ʹ 49ʺ, or 3469ʺ at it’s 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
understated 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 observations, 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; and much more in the
distances of the superiour Planets. But Dr. HALLEY has shewn us how the
Sun’s distance from the Earth, and consequently the distances of all the
Planets from the Sun, may be known to within a 500th part of the whole,
by a Transit of Venus over the Sun’s Disc, which will happen on the 6th
of _June_, 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.
[Sidenote: The Sun proved to be much bigger than the Moon.]
192. The Sun and Moon appear much about the same bulk: And every one who
understands Geometry knows how their true bulks may be deduced 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 thousand 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 constantly 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_.
[Sidenote: The relative distances of the Planets from the Sun are known
to great precision, though their real distances are not well
known.]
194. The Earth’s distance from the Sun being determined, the distances
of all the other Planets from him are easily found by the following
analogy, their periods round him being ascertained by observation. As
the square of the Earth’s period round the Sun is to the cube of it’s
distance from him, so is the square of the period of any other Planet to
the cube of it’s distance, in such parts or measures as the Earth’s
distance was taken; see § 111. This proportion gives us the relative
mean distances of the Planets from the Sun to the greatest degree of
exactness; and they are as follows, having been deduced from their
periodical times, according to the law just mentioned, which was
discovered by KEPLER and demonstrated by Sir ISAAC NEWTON.
_Periodical Revolution to the same fixed Star in days and decimal parts
of a day._