APPENDIX. Page. PROP. I. The Time from a Star's Rising to coming to the Me- II. Given the Sun's Longitude to find the Right Ascen- III. To find the Time when the Sun rises: when due East: the Time from Altitude given XIII. From Error in Altitude to find Error in Time. . . 263 XIV. To find when the Part of the Equation of Time arising from the Obliquity of the Ecliptic is XVI. To Deduce the Change of Altitude in a given Time, when the Object is near the Meridian PROP. XVII. To investigate nearly the Quantity of Atmosphe- rical Refraction XVIII. From given small Variations in the Longitude of a Celestial Object and in the Obliquity of the Eclip- tic, to deduce the Variations of the right Ascension XXIII. To find the Longitude from the Transits of the Moon and a Fixed Star, observed in two Places . . . 282 INTRODUCTION. THE science of astronomy has advanced to its present state, by means of a series of observations and discoveries made during a long course of ages. We can now select from these, such as will best conduce to demonstrate the true system, and explain the various phenomena. Astronomy, by making known to us the immensity of the creation, necessarily increases our reverence of the Divine Creator. This alone, is a sufficient reason for making it a part of general education. It also, perhaps, furnishes a more satisfactory application of the abstract sciences, than any other part of Natural Philosophy. Its practical utility is also considerable. It has always been useful in Geography and Navigation, and lately has afforded splendid assistance to the latter, by the lunar method of finding the longitude at sea. When the student first applies himself to subjects of Natural Philosophy, it is of much importance that he should proceed by the same strict and accurate manner of investigation, to which he had been accustomed while engaged in the rudiments of Mathematics. The perfection of modern instruments, and of modern observations, admits of an arrangement, which will afford, with respect to the most important facts in Astronomy, nearly the same degree of conviction to the mind as it receives from the elements of Euclid, and which requires little more preparatory knowledge. Such an arrangement has here been had in view. The phenomena of the celestial bodies observed by a spectator fixed in one place are noticed. The uniform apparent diurnal motion of the concave surface carrying with it the sun, moon, planets and fixed stars, leads to the definitions of the celestial equator, poles, meridian, declination, &c. The considerations of the apparent motions of the sun, moon, and planets, on the apparent concave surface, lead to the definitions of the ecliptic, of right ascension, longitude, &c. The various problems of the sphere have their origin from the apparent motion of the concave surface and the apparent motions of the sun, moon and planets on this surface. This is almost all the astronomical knowledge that could be attained to by a spectator fixed to one spot, and not possessing observations made in distant places. He could form no accurate notions of the actual magnitudes, and actual distances of the sun, moon and planets. All the certain astronomical knowledge that existed for many ages was limited to the doctrine of the sphere. The next consideration is, in what manner we can ascertain the actual magnitudes of the celestial bodies and their |