and that tract has been introduced in this work because the general theorems are few in number, and have their chief applications in propositions relating to astronomy: the transformations which the theorems are made to undergo are, almost always, investigated for the purpose of rendering them convenient in computations; and, as both the investigations and the examples chosen for illustrating the formulæ generally refer to astronomical subjects, it is evident that facilities are afforded and repetitions avoided by comprehending the tract in a work for which it is immediately required.
There is given a description of the principal instruments employed in making observations; and, after investigations of the formulæ for refraction and parallax, there follow outlines of the methods by which the elements of the solar, lunar, and planetary orbits are determined: these are succeeded by formulæ for computing the apparent displacements of celestial bodies, produced by the actions of the sun, moon, and planets on the earth, and by the motions of the latter. In a chapter on Nautical Astronomy there is given a series of propositions relating to the geographical positions of places on the earth, the determination of local time and the declination of the needle; and it may be right to state, here, that the examples which illustrate the several propositions are taken from the book of sextant-observations made by the students at the Observatory belonging to the Institution. Each computation is made from a single observation, and the instruments used are graduated so as to give thirds or, at best, quarters of minutes: these circumstances will account for the discrepancies, generally amounting however to a few seconds only, in the results.
After an outline of the methods of computing eclipses of the moon and sun, and the occultations of stars by the moon, there are given formulæ and examples for determining terrestrial longitudes by those phenomena; and, in the chapter on geodesy, there are given the methods of executing trigonometrical surveys for the purpose of determining the figure of the earth, with propositions relating to spheroidal arcs and angles, also the manner of making pendulum experiments for a like purpose, together with notices of the principal formulæ relating to terrestrial magnetism.