forth become the bafis of all your obfervations; and to these you will refer the ftars, in order to determine their fituations and motions. The firft thing, therefore, we ought to do, is to difcover the reciprocal fituation of thefe circles: 1. The fituation of the equator with refpect to our horizon. 2. The elevation of the pole. 3. The elevation of the equator at the meridian, or fouth point. If the north or pole-ftar, of which we have already spoken, had been precifely and accurately fituated at the pole of the world, it would have been a fure and permanent mark, and you would have had nothing more than to have taken the altitude of this ftar to have obtained that of the pole; but this ftar is two degrees diftant from the pole. To the naked eye, unaffifted with inftruments, this difference can fcarce be perceived; but with inftruments, and by attentive obfervation, it is found to defcribe a fmall circle about the pole, fo that though it does not mark directly the poles yet the middle of the circle it defcribes being the pole, it's place may be very readily difcovered. Thus the pole-ftar defcribing about the pole, a circle of 2° diftant from the pole, there will be 4° difference between the altitude of this ftar when it is in the upper point of it's circle, and when it is in the lowest point, being 2° on each fide the pole. If therefore the altitudes be taken when it is in both fituations, in order to have the height of the pole, you must fultract 2° from the fuperior altitude, and add two to the lower; thus, if the altitude had been obferved at London first to be 53° 32', and then 49° 32', the difference is 4o, the half of which added to 49° 32'; or fubtracted from 53° 32', gives 51° 32', the altitude of the pole at London; or you may add the two The ele two heights together, and take the half. vation of the pole may be difcovered in the fame manner by any other of the circumpolar ftars. The elevation of the pole being difcovered, you thereby obtain that of the equator. Thus, in the diagram before you, fig. 5, pl. 3, P reprefents the pole, and EQ the equator, HO the horizon, PH the elevation of the pole, Z the zenith; HZO, or the vifible part of the heavens, contains twice go or 180°, it being 90° from Z to H, and 90° from Z to O; but it is alfo 90° from the pole P, to E the equator. If you take away P E, there remains 90° for the other two arcs, or in other words, the elevation of the pole and the equator are together equal to 90°; and the one being known and fubtracted from 90°, gives the other; in technical words, the elevation of the pole is the complement of the elevation of the equator. It follows from hence, that the elevation of the equator is equal to the distance from the pole to the zenith, for the elevation of the equator is the difference between that of the pole and 90°; the fanie elevation fubtracted from 90°, gives it's diftance from the zenith. For the fame reason the distance from the equator to the zenith is equal to the elevation of the pole, for HZ is equal to 90°, and PE is equal to 90°; if, therefore, you take away PZ, which is common to both, the remainders PH, ZE, must be equal to cach other. OF THE APPARENT PHENOMENA OF THE MOON. From confidering the diurnal motion which is common to all the ftars, and obvious even to those who have given very little attention to thefe fubjects, I fhall pafs on to that motion of the plaM m 3 nets nets which is performed in a direction contrary to the diurnal revolutions of the ftars, that is, from weft to caft. Among these there are none fo remarkable as thofe of the moon; every month the changes her figure, and makes the tour of the heaven in a contrary direction to the general motion thereof; fo that though the moon appears to rife and fet every day like the other ftars, by a motion from east to weft, yet fhe feems alfo every day to be retarded in her motion, and to stay as it were behind the ftars, or go backwards towards the east about 13°. This motion of the moon towards the eaft, at the fame time that it partakes of the general diurnal motion, is called her periodical motion, and is fo confiderable, that in 27 days, the moon, which appeared near any remarkable ftar, feparates from it, moving in a contrary direction; the first day it removes rather more than 13 degrees from it, the fecond 26, the third 39, &c. fo that in 27 days it completes the 360, and mects the ftar on the oppofite fide, having made the tour of the heaven. "Her nightly changes in her circling orb" is a phenomenon still more ftriking than the preceding. At the new moon, as soon as the becomes visible The is feen in the western part of the heavens, at no great diftance from the fun, and just as it were immerged from his light. She increases every night in fize, and removes farther and farther from the fun, till at laft fhe appears in the caftern part of the horizon, when the fun is difappearing in the weftern, rifing at the fame time he fets, and appearing with a full round face, equalling if not exceeding the fun in fize. After this fhe gradually removes further and further eastward, till at laft fhe feems to approach the fun as nearly in the eaft as fhe did before in the weft, and rifes only a little before bim in the morning; whereas in the first part of her her course, the fet in the weft long after him. This is a prelude to her total disappearance, and though from her firft appearance in the west she takes almost a month to pass to the eastern part of the heavens, fhe feems to pafs from the eaftern to the western in one or two days; for immediately on her vanishing in the east, fhe appears again in the weft, and very near the fun. All these different appearances happen in the space of a month, after which they recommence in the fame manner. "Sometimes the half reftores day with her waxing brightness; fometimes waning into dimnefs, fhe fcarcely difperfes the nocturnal gloom." This luminary, like the fun, seems to have a motion from north to fouth, but at oppofite feafons; for at fummer time fhe is low in the fouthern part of the heavens, but approaches confiderably nearer to the northern regions in winter. By her phases the divides the times and seasons, and we find that in early ages men were much affected with this twofold confideration of the fervices of the moon, enlightening the night, and regulating their time. I need not here mention the various facrifices, offerings, and proceffions, in honour of Diana, Luna, Hecate, that is, of the moon under different names; her votaries were numerous and fuperftitious. Ignorant of philofophical truth, and uninftructed by revelation, they practifed abfurdities, and believed in lies. OF THE SUN'S ANNUAL MOTION, AND OF THE ECLIPTIC. Though the periodical motion of the moon is quick and remarkable, yet there is ftill one more important, that is, the apparent periodic or annual motion of the fun; on it depend the changes of feafon, the fummer's heat and winter's cold, the different M m 4 different lengths of day and night. This motion is indeed only apparent, arifing from the annual motion of the earth; at prefent, however, we are only confidering appearances, from thefe we fhall afterwards afcend to the contemplation of the caufes which occafion them. A little attention will foon convince you, that the fun does not rife exactly at the fame point of the heaven. Thus if you commence your obfervations of the fun, for inftance, in the beginning of March, you will find him appear to rife more to the northward every day, to continue longer above the horizon, to be more vertical, or higher, at mid-day; this continues till towards the end of June, when he moves hackward in the fame manner, and continues this retrograde motion till near the end of December, when he begins to move forwards, and fo on. It is this change in the fun's place, that occafions him to rife and fet in different parts of the horizon, at different times of the year. It is from hence that his height is fo much greater in fummer than in winter. In a word, the change of the fun's place in the heavens is the caufe of the different length in the days and nights, and the viciffitudes of the feafons. "Sometimes we perceive him very high therein, as if he would come over our heads; at thofe times his rays fall upon us with greater force, he continues longer vifible, the earth and air are confiderably heated, vegetables flourish and arrive at their perfect state, every animal feems cheerful, and this agreeable scafon we call fummer. By and by, however, he removes farther fouth, his time of continuing visible becomes conftantly fhorter and therter, until at laft it is reduced to a few hours; the fun is then funk almoft in the fouthern part of the heavens, the earth is covered |