It is in this manner that the circles of the sphere are projected, as represented in the following diagram, Fig. 2. Here, various circles are represented as projected on the meridian, which is supposed to be situated directly before the eye, at some distance from it. The horizon H O, being perpendicular to the meridian, is seen edgewise, and consequently is projected into a straight line. The same is the case with the prime vertical Z N, with the equator E Q, and the several small circles parallel to the equator, which represent the two tropics and the two polar circles. In fact, all circles whatsoever, which are perpendicular to the plane of projection, will be represented by straight lines. But every circle which is perpendicular to the horizon, except the prime vertical, being seen obliquely, as Z M N, will be projected into an ellipse, one half only of which is seen,--the other half being on the other side of the plane of projection. In the same manner, P R P, an hour circle, is represented by an ellipse on the plane of projection. FOOTNOTE: [1] A small pair of globes, that will answer every purpose required by the readers of these Letters, may be had of the publishers of this Work, at a price not exceeding ten dollars; or half that sum for a celestial globe, which will serve alone for studying astronomy. LETTER III. ASTRONOMICAL INSTRUMENTS.----TELESCOPE. "Here truths sublime, and sacred science charm, Creative arts new faculties supply, Mechanic powers give more than giant's arm, And piercing optics more than eagle's eye; Eyes that explore creation's wondrous laws, And teach us to adore the great Designing Cause."--_Beattie_. If, as I trust, you have gained a clear and familiar knowledge of the circles and divisions of the sphere, and of the mode of estimating the position of a heavenly body by its azimuth and altitude, or by its right ascension and declination, or by its longitude and latitude, you will now enter with advantage upon an account of those _instruments_, by means of which our knowledge of astronomy has been greatly promoted and perfected. The most ancient astronomers employed no instruments of observation, but acquired their knowledge of the heavenly bodies by long-continued and most attentive inspection with the naked eye. Instruments for measuring angles were first used in the Alexandrian school, about three hundred years before the Christian era.