equator, the fictitious: to which last, the motion of Plate VI. a well-regulated clock always answers.

Let Zz be the Earth, ZFRz its axis, Fig. III. abcde,&c. the equator, ABCDE,&c.the northern half

of the ecliptic from to on the side of the globe next the eye, and MNOP, &c. the southern half on the opposite side from to v. Let the points at A, B, C, D, E, F, &c. quite round from to again, bound equal portions of the ecliptic, gone through in equal times by the real Sun; and those at a, b, c, d, e, f, &c. equal portions of the equator described in equal times by the fictitious Sun; and let Z z be the meridian.

As the real Sun moves obliquely in the ecliptic, and the fictitious Sun directly in the equator, with respect to the meridian, a degree, or any number of degrees, between and F on the ecliptic, must be nearer the meridian Z z, than a degree, or any corresponding number of degrees, on the equator from to f; and the more so, as they are the more oblique and therefore the true Sun comes sooner to the meridian every day while he is in the quadrant

F, than the fictitious sun does in the quadrant f; for which reason, the solar noon precedes noon by the clock, until the real Sun comes to F, and the fictitious to f, which two points, being equidistant from the meridian, both suns will come to it precisely at noon by the clock.

While the real Sun describes the second quadrant of the ecliptic FGHIKL from to, he comes later to the meridian every day than the fictitious sun moving through the second quadrant of the equator from to; for the points at G, H, I, K, and L, being farther from the meridian than their corresponding points at g, h, i, k, and, they must be later in coming to it and as both suns come at the same moment to the point, they come to the meridian at the moment of noon by the clock.

tion of

on the Sun's

place in the eclip

tic.

In departing from Libra, through the third quadrant, the real Sun going through MNOPQ toward

at R, and the fictitious sun through mnopq toward r; the former comes to the meridian every day sooner than the latter, until the real Sun comes to vs, and the fictitious to r, and then they both come to the meridian at the same time.

Lastly, as the real Sun moves equably through STUVW, from toward r; and the fictitious sun through stuvw, from r toward r, the former comes later every day to the meridian than the lat ter, until they both arrive at the point, and then they make it noon at the same time with the clock.

229. The annexed table shews how much the Sun is faster or slower than the clock ought to be, so far as the difference depends upon the obliquity of the ecliptic; of which the signs of the first and A table of third quadrants are at the head of the table, and their the equa- degrees at the left hand; and in these the Sun is time de- faster than the clock: the signs of the second and pending fourth quadrants are at the foot of the table, and their degrees at the right hand; in all which the Sun is slower than the clock; so that entering the table with the given sign of the Sun's place at the head of the table, and the degree of his place in that sign at the left hand; or with the given sign at the foot of the table, and degree at the right hand; in the angle of meeting is the number of minutes and seconds that the Sun is faster or slower than the clock: or, in other words, the quantity of time in which the real Sun, when in that part of the ecliptic, comes sooner or later to the meridian than the fictitious sun in the equator. Thus, when the Sun's place is 8 Taurus 12 degrees, he is 9 minutes 47 seconds faster than the clock;

This table is formed by taking the difference between the Sun's longitude and its right ascension and turning it into time.

Plate III.

230. This part of the equation of time may pera Fig III. haps be somewhat difficult to understand by a figure, because both halves of the ecliptic seem to be on the same side of the globe: but it may be made very easy to any person who has a real globe before him, by putting small patches on every tenth or fifteenth degree both of the equator and ecliptic, beginning at Aries ; and then turning the ball slowly round westward, he will see all the patches from Aries to Cancer come to the brazen meridian sooner than the corresponding patches on the equator; all those from Cancer to Libra will come later to the meridian than their corresponding patches on the equator; those from Libra to Capricorn sooner, and those from Capricorn to Aries later; and the patches at the beginnings of Aries, Cancer, Libra, and Capricorn, being either on or even with those on the equator, shew that the two suns either meet there, or are even with one another, and so come to the meridian at the same moment.

A ma

she wing

equal, and

time.

231. Let us suppose that there are two little balls chine for moving equably round a celestial globe by clockthe side. work, one always keeping in the ecliptic, and gilt real, the, with gold, to represent the real Sun; and the other the solar keeping in the equator, and silvered, to represent the fictitious sun: and that while these balls move once round the globe according to the order of signs, the clock turns the globe 366 times round its axis westward. The stars will make 366 diurnal revolutions from the brazen meridian to it again, and the two balls representing the real and fictitious suns always going farther castward from any given star, will come later than it to the meridian every following day: and each ball will make 365 revolutions to the meridian; coming equally to it at the beginnings of Aries, Cancer, Libra, and Capricorn; but in every other point of the ecliptic, the gilt ball will come either sooner or later to the meridian than the

silvered ball, like the patches above-mentioned. This Plate VI. would be a pretty way enough of shewing the reason why any given star, which, on a certain day of the year, comes to the meridian with the Sun, passes over it so much sooner every following day, as on that day twelvemonth to come to the meridian with the Sun again; and also to shew the reason why the real Sun comes to the meridian sometimes sooner, and sometimes later, than the time when it is noon by the clock; and on four days of the year, at the same time; while the fictitious sun always comes to the meridian when it is twelve at noon by the clock. This would be no difficult task for an artist to perform; for the gold ball might be carried round the ecliptic by a wire from its north pole, and the silver ball round the equator by a wire from its south pole, by means of a few wheels to cach; which might be easily added to my improvement of the celestial globe, described in N° 483 of the Philosophical Transactions; and of which I shall give a description in the latter part of this book, from the third figure of the third plate.

232. It is plain that if the ecliptic were more ob- Fig. IV. liquely posited to the equator, as the dotted circle Y x

, the equal divisions from tox would come still sooner to the meridian Z 0 r than those marked A, B, C, D, and E, do: for two divisions containing 30 degrees, from to the second dot, a little short of the figure 1, come sooner to the meridian than one division containing only 15 degrees from r to A does, as the ecliptic now stands; and those of the second quadrant from x to would be so much later. The third quadrant would be as the first, and the fourth as the second. And it is likewise plain, that where the ecliptic is most oblique, namely, about Aries and Libra, the difference would be greatest; and least about Cancer and Capricorn, where the obliquity is least.