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one half of the heavens is seen; for those parts which are once visible never set, and those which are once invisible never rise. But the ecliptic Y C X, or orbit which the Sun appears to describe once a year by the Earth's annual motion, has the half Y C constantly above the horizon E C Q of the north pole n; and the other half C X always below it. There. Pheno. fore while the Sun describes the northern half Y C mena at

the poles. of the ecliptic, he neither sets to the north pole, nor rises to the south; and while he describes the southern half C X, he neither sets to the south pole, nor rises to the north. The same things are true with respect to the Moon; only with this difference, that as the Sun describes the ecliptic but once a year, he is for half that time visible to each pole in its turn, and as long invisible; but as the Moon goes round the ecliptic in 27 days 8 hours, she is only visible for 13 days 16 hours, and as long invisible to each pole by turns. All the planets likewise rise and set to the poles, because their orbits are cut obliquely in halves by the horizon of the poles. When the Sun (in his apparent way from X) arrives at C, which is on the 20th of March, he is just rising to an observer at n, on the north pole, and setting to another at s, on the south pole. From C he rises higher and higher in every apparent diurnal revolution, till he comes to the highest point of the ecliptic y, on the 21st of June; when he is at his greatest altitude, which is 23, degrees, or the arc E y, equal to his greatest north declination; and from thence he seems to descend gradually in every apparent circumvolution, till he sets at C on the 23d of September; and then he goes to exhibit the like appearances at the south pole for the other half of the year. Hence the Sun's apparent motion round the Earth is not in parallel circles, but in spirals; such as might be represented by a thread wound round a globe from tropic to tropic; the spirals being at some distance from one an

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Plate II. other about the equator, and gradually nearer to each

other as they approach toward the tropics.

126. If the observer be any where on the terresmena at trial equator e C q, as suppose at e, he is in the plane the equa- of the celestial equator; or under the equinoctial EC Q; and the axis of the Earth n C s is coinci

' dent with the plane of his horizon, extended out to Fig. I.

Nand S, the north and south poles of the heavens. As the Earth turns round the line NCS, the whole heavens MOLl seem to turn round the same line, but the contrary way. It is plain that this observer has the celestial poles constantly in his horizon, and that his horizon cuts the diurnal paths of all the celestial bodies perpendicularly, and in halves. Therefore the Sun, planets, and stars, rise every day, ascend perpendicularly above the horizon for six hours, and, passing over the meridian, descend in the same manner for the six following hours; then set in the horizon, and continue twelve hours below it. Con. sequently at the equator the days and nights are equally long throughout the year. When the observer is in the situation e, he sees the hemisphere SEN; but in twelve hours after, he is carried half round the Earth's axis to q, and then the hemisphere SQN becomes visible to him, and SEN disappears. Thus we find, that to an observer at either of the poles, one half of the sky is always visible, and the other half never seen; but to an observer on the cquator the whole sky is seen every 24 hours.

The figure here referred to, represents a celestial globe of glass, having a terrestrial globe within it: after the manner of the glass sphere invented by my generous friend Dr. Long, Lowndes's Profes. sor of Astronomy in Cambridge.

127. If a globe be held sidewise to the eye, at some distance, and so that neither of its poles can be seen, the equator ECQ, and all circles parallel to it, as D L, y z x,ab X, MO, &c. will appear to be

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straight lines, as projected in this figure ; which is requisite to be mentioned here, because we shall have occasion to call them circles in the following articles of this chapter*,

128. Let us now suppose that the observer has Phenogone from the equator e toward the north pole n, tween the and that he stops at i, from which place he then equator

and poles. sees the hemisphere MEINL; his horizon MCL having shifted as many degrees from the celestial poles N and S, as he has travelled from under the equinoctial E. And as the heavens seem constantly to turn round the line NCS as an axis, all those stars which are not as many degrees from the north pole N'as the observer is from the equinoctial, namely, the stars north of the dotted parallel DL, never set below the horizon; and those which are south of the dotted parallel MO never rise above it. Hence the former of these two parallel circles is called the cir. The cir. cle of perpetual apparition, and the latter the circle cles of

perpetual of perpetual occultation : but all the stars between apparition these two circles rise and set every day. Let us im- and occul. agine many circles to be drawn between these two, and parallel to them; those which are on the north side of the equinoctial will be unequally cut by the horizon MCL, having larger portions above the horizon than below it: and the more so, as they are nearer to the circle of perpetual apparition; but the reverse happens to those on the south side of the equinoctial while the equinoctial is divided in two equal parts by the horizon. Hence, by the apparent turning of the heavens, the northern stars describe greater arcs or portions of circles above the horizon than below it; and the greater, as they are farther from the equinoctial toward the circle of perpetual apparition; while the contrary happens to all stars

• The plane of a circle, or a thin circular plate, being turned edge wise to the eye, appears to be a straight line.

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south of the equinoctial; but those upon it describe equal arcs both above and below the horizon, and therefore they are just as long above it as below it.

129. An observer on the equator has no circle of perpetual apparition or occultation, because all the stars, together with the Sun and Moon, rise and set to him every day. But, as a bare view of the figure is sufficient to shew that these two circles DL and MO are just as far from the poles N and Sas the observer at i (or one opposite him at 0,) is from the equator ECQ; it is plain, that if an observer begins to travel from the equator toward either pole, his circle of perpetual apparition rises from that pole as from a point, and his circle of perpetual occultation from the other. As the observer advances toward the nearer pole, these two circles enlarge their diameters, and come nearer to one another, until he comes to the pole; and then they meet and coincide in the equinoctial. On different sides of the equator, to observers at equal distances from it, the circle of perpetual apparition to one is the circle of perpetual occultation to the other.

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130. Because the stars never vary their distances stars al. from the equinoctial, so as to be sensible in an age, scribe the the lengths of their diurnal and nocturnal arcs are alsame par. ways

the same to the same places on the Earth. But allel of *motion,

as the Earth goes round the Sun every year in the and the ecliptic, one half of which is on the north side of Suna dif- the equinoctial, and the other half on its south side,

the Sun appears to change his place every day; so as to go once round the circle YCX every year, $ 114. Therefore while the Sun appears to advance northward, from having described the parallel ab X touching the ecliptic in X, the days continually lengthen and the nights shorten, until he comes to y, and describes the parallel y z x; when the days are at the longest and the nights at the shortest: for then

as the Sun goes no farther northward, the greatest Plate II. portion that is possible of the diurnal arc y z is above the horizon of the inhabitant i; and the smallest portion : x below it. As the Sun declines southward from y, he describes smaller diurnal and greater noc

, turnal arcs or portions of circles every day; which causes the days to shorten and the nights to lengthen, until he arrives again at the parallel a b X; which having only the small part a above the horizon MCL, and the great part 6 X below it, the days are at the shortest and the nights at the longest : because the Sun recedes no farther south, but returns northward as before. It is easy to see that the Sun must be in the equinoctial E C Q twice every year, and then the days and nights are equally long; that is, 12 hours each. These hints serve at present to give an idea of some of the appearances resulting from the motions of the Earth : which will be more particularly described in the tenth chapter.

131. To an observer at either pole, the horizon Fig. I. and equinoctial are coincident; and the Sun and stars Parallel, seem to move parallel to the horizon: therefore such oblique,

and right an observer is said to have a parallel position of the spheres, sphere. To an observer any where between either what pcle and equator, the parallels described by the Sun and stars are cut obliquely by the horizon, and therefore he is said to have an oblique position of the sphere. To an observer any where on the equator the parallels of motion, described by the Sun and stars, are cut perpendicularly, or at right angles, by the horizon; and therefore he is said to have a right position of the sphere. And these three are all the different ways that the sphere can be posited to the inhabitants of the Earth.

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