ances of the diurnal revolutions, as exhibited to a spectator at the equator and at the pole, that is, in a right and in a parallel sphere, there will be little difficulty in imagining how they must be in the intermediate latitudes, which have an oblique sphere.

The appearances of the sun and stars, presented to the inhabitants of different countries, are such as correspond to the sphere in which they live. Thus, in the fervid climates of India, Africa, and South America, the sun mounts up to the highest regions of the heavens, and descends directly downwards, suddenly plunging beneath the horizon. His rays, darting almost vertically upon the heads of the inhabitants, strike with a force unknown to the people of the colder climates; while in places remote from the equator, as in the north of Europe, the sun, in Summer, rises very far in the north, takes a long circuit towards the south, and sets as far northward in the west as the point where it rose on the other side of the meridian. As we go still further north, to the northern parts of Norway and Sweden, for example, to the confines of the frigid zone, the Summer's sun just grazes the northern horizon, and at noon appears only twenty-three and one half degrees above the southern. On the other hand, in midwinter, in the north of Europe, as at St. Petersburgh, the day dwindles almost to nothing,-lasting only while the sun describes a very short arc in the extreme south. In some parts of Siberia and Iceland, the only day consists of a little glimmering of the sun on the verge of the southern horizon, at noon.

LETTER IX.

PARALLAX AND REFRACTION.

"Go, wondrous creature! mount where science guides,
Go measure earth, weigh air, and state the tides;
Instruct the planets in what orbs to run,

Correct old Time, and regulate the sun."-Pope.

I THINK you must have felt some astonishment, that astronomers are able to calculate the exact distances and magnitudes of the sun, moon, and planets. We should, at the first thought, imagine that such knowledge as this must be beyond the reach of the human faculties, and we might be inclined to suspect that astronomers practise some deception in this matter, for the purpose of exciting the admiration of the unlearned. I will therefore, in the present Letter, endeavor to give you some clear and correct views respecting the manner in which astronomers acquire this knowl edge.

In our childhood, we all probably adopt the notion that the sky is a real dome of definite surface, in which the heavenly bodies are fixed. When any objects are beyond a certain distance from the eye, we lose all power of distinguishing, by our sight alone, between different distances, and cannot tell whether a given object is one million or a thousand millions of miles off. Although the bodies seen in the sky are in fact at distances extremely various,-some, as the clouds, only a few miles off; others, as the moon, but a few thousand miles; and others, as the fixed stars, innumerable millions of miles from us,—yet, as our eye cannot distinguish these different distances, we acquire the habit of referring all objects beyond a moderate height to one and the same surface, namely, an imaginary spherical surface, denominated the celestial vault. Thus, the various objects represented in the diagram on next page, though differing very much in shape and diameter,

would all be projected upon the sky alike, and compose à part, indeed, of the imaginary vault itself. The place which each object occupies is determined by lines drawn from the eye of the spectator through the extremities of the body, to meet the imaginary concave sphere. Thus, to a spectator at O, Fig 16, the several lines A B, C D, and E F, would all be projected into Fig. 16.

arches on the face of the sky, and be seen as parts of the sky itself, as represented by the lines A' B, C D', and E' F. And were a body actually to move in the several directions indicated by these lines, they would appear to the spectator to describe portions of the celestial vault. Thus, even when moving through the crooked line, from a to b, a body would appear to be moving along the face of the sky, and of course in a regular curve line, from c to d.

But, although all objects, beyond a certain moderate height, are projected on the imaginary surface of the sky, yet different spectators will project the same object on different parts of the sky. Thus, a spectator at A, Fig. 17, would see a body, C, at M, while a spectator at B would see the same body at N. This change of place in a body, as seen from different points, is called parallax, which is thus defined: parallax is the apparent change of place which bodies undergo by being ewed from different points.

The arc M N is called the parallactic arc, and the angle A CB, the parallactic angle.

It is plain, from the figure, that near objects are much more affected by parallax than distant ones. Thus, the body C, Fig. 17, makes a much greater parallax than the more distant body D,-the former being measured by the arc M N, and the latter by the arc O P. We may easily imagine bodies to be so distant, that they would appear projected at very nearly the same point of the heavens, when viewed from places very remote from each other. Indeed, the fixed stars, as we shall see more fully hereafter, are so distant, that spectators, a hundred millions of miles apart, see each star in one and the same place in the heavens.

It is by means of parallax, that astronomers find the distances and magnitudes of the heavenly bodies. In order fully to understand this subject, one requires to know something of trigonometry, which science enables us to find certain unknown parts of a triangle from certain other parts which are known. Although you may not be acquainted with the principles of trigonometry, yet you will readily understand, from your knowledge of arithmetic, that from certain things given" in a problem others may be found. Every triangle has of course three sides and three angles; and, if we know

B

Fig. 18.

C

two of the angles and one of the sides, we can find all the other parts, namely, the remaining angle and the two unknown sides. Thus, in the triangle A B C, Fig. 18, if we know the length of the side A B, and how many degrees each of the angles A B C and B C A contains, we can find the length of the side B C, or of the side A C, and the remaining angle at A. Now, let us apply these principles to the measurements of

some of the heavenly bodies.

In Fig. 19, let A represent the earth, C H the horizon, and H Z a quadrant of a great circle of the heav

ens, extending from the horizon to the zenith; and let E, F, G, O, be successive positions of the moon, at different elevations, from the horizon to the meridian. Now, a spectator on the surface of the earth, at A, would