hundred years before the Christian era, and flourished for several hundred years, numbered among its disciples a succession of eminent astronomers, among whom were Hipparchus, Eratosthenes, and Ptolemy. The last of these composed a great work on astronomy, called the 'Almagest,' in which is transmitted to us an account of all that was known of the science by the Alexandrian school. The 'Almagest' was the principal text-book in astronomy, for many centuries afterwards, and comparatively few improvements were made until the age of Copernicus. Copernicus was born at Thorn, in Prussia, in 1473. Previous to his time, the doctrine was held, that the earth is at rest in the centre of the universe, and that the sun, moon, and stars, revolve about it, every day, from east to west; in short, that the apparent motions of the heavenly bodies are the same with their real motions. But Copernicus expounded what is now known to be the true theory of the celestial motions, in which the sun is placed in the centre of the solar system, and the earth and all the planets are made to revolve around him, from west to east, while the apparent diurnal motion of the heavenly bodies, from east to west, is explained by the revolution of the earth on its axis, in the same time, from west to east; a motion of which we are unconscious, and which we erroneously ascribe to external objects, as we imagine the shore is receding from us, when we are unconscious of the motion of the ship that carries us from it.

Although many of the appearances, presented by the motions of the heavenly bodies, may be explained on the former erroneous hypothesis, yet, like other hypotheses founded in error, it was continually leading its votaries into difficulties, and blinding their minds to the perception of truth. They had advanced nearly as far as it was practicable to go in the wrong road; and the great and sublime discoveries of modern times are owing, in no small degree, to the fact, that, since the days of Copernicus, astronomers have been pursuing the plain and simple path of truth, instead of threading their way through the mazes of error.

Near the close of the sixteenth century, Tycho Brahe, a native of Sweden, but a resident of Denmark, carried astronomical observations (which constitute the basis of all that is valuable in astronomy) to a far greater degree of perfection than had ever been done before. Kepler, a native of Germany, one of the greatest geniuses the world has ever seen, was contemporary with Tycho Brahe, and was associated with him in a part of his labors. Galileo, an Italian astronomer of great eminence, flourished only a little later than Tycho Brahe. He invented the telescope, and, both by his discoveries and reasonings, contributed greatly to establish the true system of the world. Soon after the commencement of the seventeenth century, (1620,) Lord Bacon, a celebrated English philosopher, pointed out the true method of conducting all inquiries into the phenomena of Nature, and introduced the inductive method of philosophizing. According to the inductive method, we are to begin our inquiries into the causes of any events by first examining and classifying all the facts that relate to it, and, from the comparison of these, to deduce our conclusions.

But the greatest single discovery, that has ever been made in astronomy, was the law of universal gravitation, a discovery made by Sir Isaac Newton, in the latter part of the seventeenth century. The discovery of this law made us acquainted with the hidden forces that move the great machinery of the universe. It furnished the key which unlocks the inner temple of Nature; and from this time we may regard astronomy as fixed on a sure and immovable basis. I shall hereafter endeavor to explain to you the leading principles of universal gravitation, when we come to the proper place for inquiring into the causes of the celestial motions, as exemplified in the motion of the earth around the sun.

LETTER II.

DOCTRINE OF THE SPHERE.

Let us now consider what astronomy is, and into what great divisions it is distributed; and then we will take a cursory view of the doctrine of the sphere. This subject will probably be less interesting to you than many that are to follow; but still, permit me to urge upon you the necessity of studying it with attention, and reflecting upon each definition, until you fully understand it; for, unless you fully and clearly comprehend the circles of the sphere, and the use that is made of them in astronomy, a mist will hang over every subsequent portion of the science. I beg you, therefore, to pause upon every paragraph of this Letter; and if there is any point in the whole which you cannot clearly understand, I would advise you to mark it, and to recur to it repeatedly; and, if you finally cannot obtain a clear idea of it yourself, I would recommend to you to apply for aid to some of your friends, who may be able to assist you.

Astronomy is that science which treats of the heavenly bodies. More particularly, its object is to teach what is known respecting the sun, moon, planets, comets, and fixed stars; and also to explain the methods by which this knowledge is acquired. Astronomy is sometimes divided into descriptive, physical, and practical. Descriptive astronomy respects facts; physical astronomy, causes; practical astronomy, the means of investigating the facts, whether by instruments or by calculation. It is the province of descriptive astronomy to observe, classify, and record, all the phenomena of the heavenly bodies, whether pertaining to those bodies individually, or resulting from their motions and mutual relations. It is the part of physical astronomy to explain the causes of these phenomena, by investigating the general laws on which they depend; especially, by tracing out all the consequences of the law of universal gravitation. Practical astronomy lends its aid to both the other departments.

The definitions of the different lines, points, and circles, which are used in astronomy, and the propositions founded upon them, compose the doctrine of the sphere. Before these definitions are given, I must recall to your recollection a few particulars respecting the method of measuring angles. (See Fig. 1, page 18.)

A line drawn from the centre to the circumference of a circle is called a radius, as C D, C B, or C K.

Any part of the circumference of a circle is called an arc, as A B, or B D.

An angle is measured by an arc included between two radii. Thus, in Fig. 1, the angle contained between the two radii, C A and C B, that is, the angle A C B, is measured by the arc A B. Every circle, it will be recollected, is divided into three hundred and sixty equal parts, called degrees; and any arc, as A B, contains a certain number of degrees, according to its length. Thus, if the arc A B contains forty degrees, then the opposite angle A C B is said to be an angle of forty degrees, and to be measured by A B. But this arc is the same part of the smaller circle that E F is of the greater. The arc A B, therefore, contains the same number of degrees as the arc E F, and either may be taken as the measure of the angle A C B. As the whole circle contains three hundred and sixty degrees, it is evident, that the quarter of a circle, or quadrant, contains ninety degrees, and that the semicircle A B D G contains one hundred and eighty degrees.