At some periods of the year, the Sun appears five minutes sooner in the morning, and may be seen five minutes later at evening, than if no refraction existed; and about 34 minutes every day at a mean rate. Hence, when the Sun is at T below the horizon, a ray of light T I, proceeding from him, comes straight to I, where, falling on the atmosphere it is turned out of its direct, or rectilineal course, and is so bent down to the eye of the observer at D, that the Sun appears in the direction of the refracted ray above the horizon at S, as seen in Plate vi. Figure 1.

At the Equator, there will be, equal to two days more sunshine in a year, than without refraction; and the higher the Latitude, the greater the benefit from this property of the atmosphere.

MEAN ATMOSPHERICAL REFRACTIONS IN ALTITUDE.

App Refrac.

alt.

frac.

App Re-App) Re- ||App Re- App Relt. frac.alt. frac.alt.

frac.

alt.

How long may the Sun be seen before it rises?

What amount of Sun light in a ycar by refraction

Some Hollanders, who wintered in Greenland about a century ago, had the Sun become visible in the south at noon, 17 days earlier than it would have done without refraction. It doubtless continued 17 days later, making the difference of 34 days in the year.

When the Sun is at the equinoxes, it shines some distance over both poles by refraction, and the twilight may scarcely cease to be visible even at the solstices.

ABERRATION OF LIGHT.

Light is more than 8 minutes in coming 95 millions of miles, in which time the Earth has moved more than 8 thousand miles in its orbit. Consequently a ray of light which left the Sun in the direction of the centre of the Earth, when it reaches the orbit of this planet, falls more than 8 thousand miles behind its centre. A ray that left the Sun in the direction of 8 thousand miles forward of the Earth's centre, is that by which we see the Sun when in the meridian. This is the aberration of light From this cause we never see any of the heavenly bodies in their true places. The Moon being nearest, is least affected by it,

CHAPTER XVII.

PARALLAX.

THE subject of parallar, if attended with some difficulties to minds not conversant with the higher branches of Mathematics, is still of such vast importance in Astronomy, as to merit the most profound attention.

What was witnessed in Greenland ?

What effect has refraction probably at the poles? What is aberration of light? What results from that?

A few definitions will here be given.
Two lines meeting thus form an angle.

If one leg of dividers were set where those lines meet, and the other should describe an entire circle, that part of the circle included between those lines would be an arc. Let A b, in Plate vi. Fig. 1, represent an angle, whose arc between a, b, shall be called 10°, or part of a circle. Measure the distance between a and b, and see what proportion it bears to the radius a A, or b A. We will call that proportion as 1 to 6; that is, the distance from a to A where the lines meet, is six times as great as the distance from a to b. We have now learned a proportion, which will be found the same, whether the circle be large or small. Call that arc 1 inch and the radius 6 inches. Now if a circle were drawn so large that an arc of 10° measured 1 foot, the radius would be 6 feet; if the arc measured one mile, the radius would be six miles; if the arc measured one thousand miles, the radius would be six thousand miles.

Let us now apply this subject to celestial observations; first, in showing the effect of parallax, and secondly, its UTILITY.

The parallax of heavenly bodies is the difference between their apparent altitude, as seen from the surface of the Earth, and their real altitude, as seen from its centre.

Let C (Plate vi. Fig. 2,) represent the centre of the Earth; FD E, part of the Moon's orbit; G de, part of the planet's orbit; Z K, part of the starry

What is an angle? What is an arc? What a radius? About what is the proportion between an arc of 10° and the radius? How would you illustrate this proportion? What is parallax? How illustrate this?

heavens now to a spectator at A, upon the sur face of the Earth, let the Moon appear at E, in the horizon of A, and it will be referred to K; but if viewed from the centre at C, it will be referred to I the difference between these places, or the arc I K, is called the parallax in altitude; and the angle A E C, is called the parallactic angle.

The parallax will be greater or less, as the objects are more or less distant from the Earth; thus the parallax I K, of E, is greater than the parallax ƒ K, of e.

Besides, with the same object, when it is in the horizon, the parallax is the greatest, and diminishes as the body rises to the zenith, where the parallax is nothing. Thus, the horizontal parallax of E and e is greater than that of D and d; but the objects F and G, as seen from either A or C, appear in the same place Z, or in the zenith.

The difference in the Moon's place, as seen in the horizon, or the zenith, may be called its horizontal parallax. The whole difference between its apparent place, when rising and when setting, is twice its horizontal parallax. This being caused by the diurnal motion of the earth, often occasions the Moon's parallax to be called diurnal.

The horizontal parallax of the Moon is about 1° 1' of the nearest planets much less and of the Sun but about 8", proving it about 400 times as distant as the Moon. The diurnal motion of the Earth gives no perceptible parallax to any of the fixed stars. And all attempts have hitherto been unsuccessful, when made to find an apparent

Where will parallax be greatest? What is the Moon's parallax? What the Sun's? What effect has parallax on the heavenly bodies?

change in the position of the fixed stars, as observed the 23d of September or the 20th of March, having the whole diameter of the Earth's orbit, as an angle; called annual parallax.

As the parallax of celestial bodies depresses them, or causes them to appear lower than they really are, the difference must be added to their apparent altitude, to obtain their true altitude.

Thus far the effect of parallax has been described. Let the attention next be turned to its UTILITY. To minds unacquainted with mathematical science, and with the surprising resources of the human intellect, it often seems impracticable to measure distances and magnitudes, when removed many thousands, or even millions of miles from them. But parallax enables man to surmount difficulties of distance, and gauge the heavens.

DISTANCE OF THE MOON.

The distance of the Moon is easily ascertained. The quadrant, an instrument by which degrees and minutes among the heavenly bodies can be accurately measured, shows that the Moon's apparent place, as seen from the surface of the Earth,} varies from its true place, if seen from the centre of the Earth, one degree. Now draw a circle, and divide it into 360 equal parts, called degrees. Let one of these degrees be called the arc; draw a line from each side of that arc, in the centre of the circle. Observe what proportion exists between the length of the arc of 10 and the radius of that circle. Suppose the radius is 60 times as long as the arc. You now have a proportion gained for use. The semi-diameter of the Earth which makes this arc of 10,you may call in round numbers 4000

What instrument is used for finding degrees and minutes in the heavens? How may the Moon's distance be known by its parallax? What other illustration can be given?