miles; which multiplied by the radius 60, make 240 thousand miles, the distance of the Moon from the Earth.

Again, Let us suppose the observer to be under the equator, with the Moon perfectly vertical. He then sees it in its true place among the stars. Bu when it rose that evening, it would appear 1° east of its true place, and when it set it would appear 1° west of its true place; a difference of 2° from its place of rising and its place of setting. This would be occasioned by the diurnal revolution of the Earth, making the observer's place vary the whole diameter of the Earth's orbit, which we call in round numbers 8000 miles. Draw the circle, and take an arc of 2 degrees. Find the proportion between the arc of 20, and the radius, which we will call as 1 to 30. Now multiply 8000 miles, which subtends an arc of 2° at the distance of the Moon, by 30, and you have as before 240 thousand miles.

With the quadrant, or with the micrometer in a telescope, observe how broad the disc of the Moon seems, and it is found to be 31. This is its apparent diameter. If 1° at the Moon's distance is 4000 miles, then 31 minutes, or something more

than will be a trifle more than 2000, or 2180 miles, which is the real diameter of the Moon./ Thus the distance of the Moon from the Earth, and its magnitude, are satisfactorily ascertained.

In one part of its orbit, the Moon is nearer to the Earth, than its opposite. When nearest, it is said to be in Perigee; when remotest, in Apogee. The medium between these, is called its mean distance.

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How can the Moon's diameter be known?

When is the Moon in perigee? When in apogce?

The diurnal parallax of the Sun is so small, that it becomes more difficult to determine with perfect accuracy what it is; and an error of a few seconds in the observation, would occasion an error of millions of miles in the estimated distance. But /Dr. Halley has the honour of having discovered and described, an effectual method of obtaining the true parallax of the Sun. This is by observations of a transit of Venus taken in different parts of the world, and compared together. He gave the necessary directions for such observations, 90 years previous to the transit of 1761. A compliance with his rules by astronomers in 1761, and in 1769, has demonstrated, that the Sun's true parallax is about 8", and its mean distance 95 millions of miles,

TRANSIT OF VENUS.

The following illustration of the transit of Venus is from Guy; and though more lines and more explanation would be needful to render it perfectly correct as a mathematical demonstration, it may aid the learner in appreciating the impor tance and utility of such transit.

Let S (Plate iv. Figure 6,) represent the Sun and V V Venus at the beginning and end of he transit, as she would appear from the Earth's cen tre; also E E' be the corresponding positions o the Earth at those times.

Then, if the observer were situated at C, the centre of the Earth, when Venus entered on the

What difficulty attends determining the distance of the Sun' Who discovered an accurate method of finding the Sun's true parallax? What were the results of observations on the transits of Venus in 1761 and 1769? How can this be illustrated by a plate?

solar disc, she would appear as a small black spot at s, and the true place of both her and the eastern limb of the Sun would be s. But if the observer were situated at any point on the Earth's surface, as P, the apparent place of Venus would be at v, and the apparent place of the corresponding limb of the Sun would appear at P; and consequently Venus would appear to the eastward of the Sun, by a space equal to the arc v P, which is the difference of the parallaxes of these two bodies.

Hence the immersion of Venus would not take place so soon to an observer at P, as to one at C, by the time she would require to describe the apparent arc v P.

Now, as the transit always takes place during the inferior conjunction of the planet, the motions of both Venus and the Earth will then be from east to west, while the motion of the Earth on its axis is in a contrary direction. Consequently, while Venus and the Earth move in their orbits from V to V', and from E to E', the point P, which at the commencement of the motion was west of the centre, will at the end of it be on the east of it, as at P'. Hence the observer, who was supposed to be situated at C, would perceive Venus just leaving the Sun's disc, and her apparent place would be s'; while to the observer at P, her apparent place would be at v' and that of the Sun's western limb at P. The apparent distance of Venus from the Sun at the end of the transit is therefore the arc o' P, which is equal to the difference of the parallaxes of the Sun and Venus, as before.

Consequently, the time of the duration, as observed at the point P, will be less than the absolute duration by the time which the planet would

require to describe the two apparent arcs v P and v' P or twice the difference of the parallaxes of the Sun and the planet.

PARALLAX OF THE SUN.

Here it will be assumed, that the transit of Venus, has given the Sun's horizontal parallax, as 81". Draw a circle sufficiently large to have the 360° divided in 60 parts each, called minutes, and the minutes divided into 60 parts each, called seconds. Take 8 of these seconds and draw lines from each side of them to the centre of the circle. Ascertain the proportion between the arc of 8" and the radius, or one of those lines. Suppose it to be as 1 to 24 thousand. That 1 in the arc is the semidiameter of the Earth, which in miles is 3964. This number, multiplied by 24 thousand, will give 95 millions of miles, the true mean distance of the Earth from the Sun.

Now if the angle of 3964 miles, the distance from the centre to the surface of the Earth, seems at the Sun, but 8", therefore for every 8" in the apparent diameter of the Sun's disc we must compute 3964 miles.

Its mean apparent diameter is 32' 1", which reduced to seconds is 1921". Multiply 1921" by 3964 and divide the product by 84", and you have the Sun's real diameter, which in round numbers, is 890 thousand miles.

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The vast importance of correct observations of a transit of Venus, is thus clearly seen, as it enables man to throw his measuring line through millions of miles in gauge space, and mighty dimensions of the "Sun shining in his strength." Yet this is but one item in many, of its high UTILITY.

When the true parallax of the Sun is found, how determine

its distance-its magnitude?

About the commencement of the 17th century, KEPLER of Wirtemberg, in Germany, by his obser vations and discoveries laid the corner stone of modern Astronomy. He discovered the exact proportions in the distances of the planets from the Sun, before the precise distance of any was known.

PROPORTIONAL DISTANCES.

1

Kepler discovered, by calculations founded on a series of the most accurate observations, that the squares of the periods, in which any two planets complete their revolutions in their orbits, are proportional to the cubes of their mean distances from the Sun.

This proportion requires illustration. Let the period of the Earth's revolution, be called 12 months, and the period of Mercury's revolution, 3 months. By the Sun's parallax learned from a transit of Venus, the Earth's distance is 95 millions of miles. By Kepler's law, the distance of Mercury from the Sun is to be Bought.

The square of any number, is that number multiplied by itself. The square of two is four.

The cube of any number is that number multiplied twice by itself. The cube of 3 is 27; for 3 times 3 are 9; and 3 times are 27. The period of the Earth's revolution 12 months, which multiplied by 12, makes its square 144. The cube of the Earth distance, 95 millions multiplied by 95 millions and that product by 95 millions.

This round sum is again to be multiplied by 9, the square of 3, the period in months, in which Mercury revolves round the Sun. Next, the whole product is to be divided by 144, and the cube root extracted, which will leave 37 millions of miles as the mean distance of Mercury.

What discovery did Kepler make respecting the proportional distances of the planets?

How may this be illustrated? What is a square? What is a cube? How determine the distance of Mercury from the Sun by knowing the period of the Earth's revolution, its mean distance from the Sun, and the period of Mercury's revolution? How determine the distance of Jupiter?