gone through 90 degrees, as seen by the observer on the surface; subtract this time, from the aforesaid six hours and 12 minutes, and the remainder is the time that she is moving in her orbit, from a tangent, touching the earth's surface, to a parallel line drawn from the earth's centre; which affords an easy matter of finding the Moon's horizontal parallax, which is equal to an angle made between the last mentioned line, and another drawn from the observer to the centre of the Moon, as seen from the centre of the earth or poles.Then, as the afore mentioned remainder is to 90 degrees, so is 6 hours 12 minutes, to the number of degrces which measures the arc; subtract 90 degrces from this arc, and the remainder is the angle under which the earth's semi-diameter is seen from the Moon. Since all the angles of a right angled triangle are equal to two right angles, or 180 degrees, and the sides of a plain triangle are always proportionate to the sines of their opposite angles; say, (by Trigonometry,) as the sine of the angle at the Moon, is to the earth's semi-diameter, so is radius, (or sine of 90 degrees,) to its opposite side; which is the distance from the observer to the Moon, or subtract the angle at the Moon from 90 degrees, then say as the angle at the Moon, is to the earth's semi-diameter, so is this remainder, to the distance from the centre of the earth to the Moon; which comes out at a mean rate 240 thousand miles. The Sun's distance from the earth might be found in the same manner, if his horizontal parallax were not so small as to be hardly perceptible, being 8,63 K seconds,* while the horizontal parallax of the Moon is 57 minutes and 18 seconds. Therefore, to find the distance to the Sun, say by single proportion, as the Sun's horizontal parallax, (8,63 seconds,) is to the distance that the Moon is from the earth, (240,000 miles,) so is the Moon's horizontal parallax, (57 minutes and 18 seconds,) to the distance of the Sun from the earth, which gives in round numbers, 95 millions of miles. The Sun and Moon appear nearly of the same size as viewed from the earth, and every person who understands Trigonometry," knows how their true magnitudes may be ascertained from the apparent, when their true distances are known. Spheres are to each other, as the cubes of their diameters. Whence, if the Sun be 95 millions of miles from the earth, to appear of equal size with the Moon, whose distance is only 240 thousand; he must in solid bulk, be 62 millions of times larger than the Moon. The horizontal parallaxes are best observed at the equator; Because the heat is so nearly equal every day, that the refractions are almost constantly the same, and likewise, because the parallactic angle is greater there; the distance from thence to the earth's axis, being greater than upon any parallel of latitude. The earth's distance from the Sun being determined, the distances of all the other planets are easily found by the following analogy; their periodical rev * Ascertained from the transits of Venus across the Sun's disk, in the years 1761 and 1769. olutions around him, being obtained by observation.— As the square of the earth's period round the Sun,is to the cube of its distance from that luminary, so is the square of the period of any other planet, to the cube of its distance, in such parts or measures, as the earth's distance was taken. This proportion gives the relative mean distances of the planets from the Sun to the greatest degree of exactnsss. The earth's axis produced to the stars, and being carried parallel to itself during the earth's annual revolution, describes a circle in the sphere of the fixed stars, equal to the earth's orbit. This orbit, though very large, would seem to be no larger than a point, if it were viewed from the stars, and consequently, the circle described in the sphere of the stars, by the axis of the earth, produced, if viewed from the earth, must appear as a point; its diamater appears too little to be measured by observation. Dr. Bradley has assured us, that if it had amounted to a single second, or two at most, he should have perceived it in the great number of observations he has made; especially upon Draconis, (a star of the third magnitude,) 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 more than four hundred thousand times further from us than the Sun. If we suppose that the parallax of the nearest fixed star is one second, and that the mean distance of the earth from the Sun, is 95 millions of miles, we shall have a right angled triangle whose vertical angle is one second, and whose base is 95 millions of miles to find its side, or distance of the star; which would exceed 20 billions of miles, a distance through which light although travelling at the rate of two hundred thousand miles in a second, could not pass in three years. If the brightest star in the Heavens is placed at such an im mense distance from our system, what an immeasureable interval must lie between us and those minute stars, whose light is scarcely visible by the aid of the most powerful telescopes. Many of them are, perhaps so remote, that the first beam of light which they sent forth at their creation, has not yet arrived within the limits of our system. While other stars which have disappeared, or have been destroyed for many centuries, will continue to shine in the Heavens till the last ray which they emitted, has reached the earth which we inhabit. The mean distances of the planets from the Sun, and their apparent diameters as seen from that luminary, being found, the diameters of all the planets can be ascertained by Trigonometry; thus-Subtract the angle or apparent diameter of the planet as seen from the sun, from 180 degrees, and half the remainder will be the an gle at the disk of the planet; then as the sine of the angle at the disk is to the distance of the planet from the Sun, so is half the angle at the Sun to the semi-diameter of the planet. The small apparent motion of the stars discovered by that great Astronomer, (Dr. Bradley,) he found to be owing to the aberation of their light, which can result from no known cause, except that of the earth's annual motion, as it agrees so exactly therewith, it proves beyond dispute that the earth has such a mɔtion; for this aberation completes all its various phenomena every year, and proves that the velocity of star-light is such as carries it through a space equal to the Sun's distance from us, in eight minutes and seven seconds of time. Hence the velocity of light is about 10,313 times as great as the earth's velocity in its orbit, and consequently nearly two hundred thousand miles in one second of time. Interrogations for Section Seventh. From what place can the North and South Poles both be seen? Where will they appear ? What is an angle of elevation? Suppose the north polar star is elevated 43 degrees above the horizon, what is your degree of latitude? How many miles constitute a degree on the surface of the earth? How is that known? How many degrees in a circle? How is the circumference of the earth found? |