O F THE In which the Principles of the Aftronomical Methods of CHAP. I. Of the Figure and Magnitude of the Earth Upon the Inftruments for measuring angular Distances at V. Of the Corrections to be applied to the altitude of an Of the method of finding the Longitude of a Ship by Lu- nar Obfervations. CHAP. I. Introduction to this method of finding the Longitude64 III. Of the methods of afcertaining Time, and regulating a Chronometer or Watch at Sea or Land IV. Of the methods of clearing the apparent Distance be- tween the Moon and the Sun or a fixed Star, from the effects of Refraction and Parallax CHAP. VI. Of finding the Longitude at Sea or Land, by an Obfervation of the Distance between the Moon and the Sun or a fixed Star, together with the apparent Time of Obfervation VII. A new method of finding the Longitude and Latitude not used in the Nautical Almanac BOOK IV. 131 137 145 150 154 Containing various other methods of determining the CHAP. I. Of finding the Longitude by an Obfervation of the II. The method of finding the Longitude of a place by an III. The method of finding the Longitude of a place by an Eclipfe of the Sun 157 161 167 182 V. Of finding the Longitude of a place by Obfervations IV. The method of finding the Longitude of a place by an VI. The method of finding the Longitude of a ship at 193 200 VII. Of finding the Longitude at Sea by the Variation Chart 209 Containing methods of finding the Latitude of a Place, and the Variation of the Compass. CHAP. I. Of finding the Latitude of a place II. Of finding the Variation of the Compafs 232 251 The Principles of the Aftronomical Methods of finding the Longitude at Sea or Land. W CHA P. I. Of the FIGURE and MAGNITUDE of the EARTH. ITHOUT a previous knowledge of the figure and magnitude of the Earth, the places of the Heavenly Bodies could. not be accurately settled, from obfervations made on its furface; and therefore computations, made from obfervations of these bodies, could not be depended on for afcertaining the fituation of places on the Earth; hence the neceffity of knowing both the figure and magnitude of the Earth is apparently obvious. The opinions of the antients concerning the figure of the Earth were various—the most prevailing one being, that it was an extended plane; fome imagined it to be of a cylindric form, others, that it resembled a canoe, and a few fuppofed it spherical; but the dif covery of its real figure was left to the illuftrious Sir Ifaac Newton. The following are a few of the arguments commonly used to prove, that the figure of the Earth is either fpherical, or nearly fo.. I. The first who attempted to circumnavigate the earth was Ferdinand Magellan, a Portuguefe. He failed from Seville, August 10, 1519, was killed on the island of Sebu; and one of his veffels arrived at St Lucar, near Seville, Sept. 7, 1522. Since that time, the circumnavigation of the Earth has been performed, at different times, by Sir Francis Drake, Lord Anfon, Captain Cook, and others B who who, by failing in a wefterly direction, allowance being made for promontories, &c. arrived at the country they failed from. Hence the Earth muft either be of a cylindric or globular figure; but it cannot be in the form of a cylinder, because then the difference of longitude and meridian diftance between any two places would be equal, which is contrary to obfervation; the figure of the Earth therefore is fpherical. II. LEMMATA.-ft. The diftance of the neareft fixed ftar, when compared with the magnitude of the Earth, is fo immenfe, that rays flowing therefrom to any two points on the surface of the earth, are phyfically parallel. 2d. If in a curve, the arches are proportional to the correspondent angles, it is a circle. Now, if the Earth was an extended plane, the meridian zenith diftance of any given fixed star would be the fame in all places of the Earth, by lemma 1ft; but it is found to be variable, and in fuch a manner, that the difference of the meridian altitudes of the fame ftar is proportional to the intercepted arch of a meridian; that meridian must therefore be circular-and fince this is found to be the cafe in every part of the Earth, therefore, by lemma 2d, its figure must be spherical. III. LEMMA. If the fhadow of any body, when turned in every pofition with respect to the luminous body, be circular, when projected on a plane perpendicular to the line joining the centers of both, the body itself is a sphere. Now fince a lunar eclipfe arifes from the paffage of the moon thro' the shadow of the Earth, and as the portion of the Earth's fhadow projected on the lunar difc is always circular, in every different position of the earth, therefore the figure of the earth muft be that of a sphere. IV. When distant ships are viewed with a telescope, the lower parts are found to be hid by the interpofed water, and more or less is vifible, according to the diftance. The fun is obferved fooner at rifing, and later at fetting, by a perfon at the maft-head, than by one on deck. In making the land, the most elevated parts are first seen; and the lower parts become vifible, as the land is approached.These phenomena evidently arife from the fpherical figure of the Earth, and therefore ferve to prove the Earth to be of that figure. V. The appearance of the fun for a continuance of feveral months above the horizon, in the neighbourhood of one pole, and that in proportion to the distance of the place therefrom, while at a place equally equally distant from the other pole, the fun is as long abfent-is another proof that the earth is fpherical. VI. The planets that have been hitherto difcovered are obferved to be globular; the Earth is alfo a planet, fubject to the fame laws, and revolving round the fun in the fame manner as the other planets-therefore, by analogy, the Earth must also be globular. Although it appears from the foregoing proofs, that the earth is of a spherical figure, yet it is not a perfect fphere, but an OBLATE SPHEROID,* which is a folid generated by the rotation of a femi-ellipfe about its shorteft axis. The circumftance that gave rife to the knowledge of its fpheroidal figure, was Richer's celebrated experiment, made by order of the Royal Academy of Sciences of Paris, at the island of Cayenne, in the year 1672, "That a pendulum of "the fame length vibrates flower at the equator, than in France." This naturally results from the rotation of the Earth; but the difference being greater than what should have arifen from the excefs of the centrifugal force at the equator above that in France, excited the curiofity of Newton and Huygens, who enquiring minutely into the cause of this phenomenon, fhewed that it refulted from the rotation of the earth about its axis, combined with its fpheroidal figure; and Newton fuppofing the Earth to affume the fame figure that a homogeneous fluid would take under like circumftances, computed the ratio of the equatorial diameter to the axis of the earth to be as 230 229. The ratio deduced from actual menfuration feems to confirm the above computation. The determination of the magnitude of the Earth feems to have engaged the attention both of ancient and modern aftronomers and mathematicians, and though the conclufions of the ancients differ very confiderably, yet the measures taken within the lafl 120 years, near the fame place, agree very well. The only perfon in England who performed this problem with any tolerable degree of accuracy, was Mr Richard Norwood, of which an account is given in his "Seaman's Practice"-the fubstance of which is as follows. In the year 1633, he observed the apparent meridian altitude of the fun, at the time of the fummer folftice, near the Tower of London; and June 11, O. S. 1635, he observed the fun's apparent meridian altitude, near the middle of the city of York; from whence he found the difference of latitude between thofe places to be 2o 28'. Now this being compared with the dif- . ference between the parallels of latitude of thofe places, deduced from actual menfuration, which was 9149 chains of 99 feet each, he found B 2 * From obfervations made in different parts of the Earth, it would appear, that its gute is not that of a regular fpheroid. |