A question like the following naturally arises :— Why is it that the Sun is not Eclipsed at every change, if the Moon actually passes between the Sun and the earth. And why is not the Moon Eclipsed at every full, if the earth passes between the Sun and Moon in every month?

One half of the Moon's orbit, is elevated 5 degrees -and twenty minutes above the ecliptic, and the other half is as much depressed below it; and, as before has been observed, the Moon's orbit intersects the ecliptic, in two opposite points, called the Moon's NODES.

When these points are in a right line with the centre of the Sun at new or full Moon, the Sun, Moon,and earth are all in a right line; and if the Moon be then new; her shadow falls upon the earth, but if she be full, the earth's shadow falls upon her. When the Sun and Moon are more than 17 deg's. from either of the nodes at the time of conjunction,the moon is generally too high or too low in her orbit to cast any part of her shadow on the surface of the earth. And when the Sun is more than 12 degrees from either of the nodes at the time of full Moon, the Moon is generally either two high or too low to pass through any part of the earth's shadow; therefore in both these cases there can be no Eclipse.

This howevever admits of some variation, for in apogeal Eclipses, the solar limit is only sixteen degrees and thirty minutes, and in perigeal it is eighteen degrees and twenty minutes. When the full Moon is

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in her apogee, she will be Eclipsed, if she be within 16 degrees and thirty minutes of the node; and when in her perigee, if within twelve degrees and two

minutes.

The moon's orbit contains 360 deg's. of which the limits of seventeen degrees at a mean rate for Solar Eclipses, & twelve for lunar are only small portions, and the Sun generally passes by the nodes only twice in a year, and consequently impossible that Eclipses should happen in every month. If the line of the nodes, like the axis of the earth, were carried parallel to itself around the Sun, there would be exactly half a year between the conjunctions of the Sun and nodes. But the nodes shift backward, or contrary to the earth's annual motion, nineteen degrees and twenty minutes every year; and therefore the same node comes round to the Sun nineteen days sooner every year, than in the one preceeding. 173 days, therefore, after the ascending node has passed by the Sun, the descending node also passes by him. In whatever season of the year the luminaries are Eclipsed, in 173 days after, we may expect Eclipses about the opposite node. The nodes shift through all the signs and degrees of the ecliptic in 18 years and 225 days, in which time there would always be a regular periodical return of Eclipses, if any number of lunations were completed without a

* The fartherest point of each orbit from the earth's centre is called the apogee, and the nearest point is called the perigee. These points are directly opposite each other, and consequently exactly six signs asunder.

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fraction. But this never happens, for if both the Sun and Moon should start from a line of conjunction with either of the nodes in any point of the ecliptic, the Sun would perform 18 annual revolutions and 222 degrees of the 19th, and the Moon 230 lunations, and 85 degrees of another by the time the node came around to the same point of the ecliptic again.

The Sun would then be 138 degrees from the node, and the Moon 85 degrees from the Sun. In 223 mean lunations after the Sun, Moon and node, have been in a line of conjunction, they return so nearly to the same state again, that the same node which was in conjunction with the Sun and Moon at the commencement of these lunations, will be within 28 minutes, and 12 seconds of a degree of a line of conjunction with the Sun and Moon again, when the last of these lunations is completed. In that time, there will be a regular period of Eclipses, or rather a periodical return of the same eclipse for many ages. In this period, (which was first discovered by the Chaldeans,) there are 18 Julian years, 11 days, 7 hours, 43 minutes, and 21 seconds, when the 29th day of February in leap years, is four times included; but one day less when included 5 times. Consequently, if to the mean time of any Eclipse, whether of the Sun or Moon, the above named time be added, you will have the mean time of its periodical return. But the falling back of the line of conjunctions, or oppositions of the Sun and Moon, namely, 28 minutes, 12 seconds, with respect to the line of the nodes in every period, will wear it out in process of

time, so that the shadow will not again touch the earth or Moon, during the space of 12,492 years. Those Eclipses of the Sun which happen about the ascending node, and begin to come in at the north pole of the earth, will continue at each periodical return to advance southwardly, until they leave the earth at the south pole; and the contrary with those that happen about the descending node, and come in at the south pole. From the time that an Eclipse of the Sun first touches the earth, until it completes its periodical returns, and leaves the same, there will be 77 periods equal to 1388 years. The same Eclipse cannot then again touch this earth, in a less space than 12492 years as above stated.

If the motions of the Sun, Moon, and nodes were the same in every part of their orbits, we should need nothing more than what has been said to find the exact time of all Eclipses; but as this is not the case, we are under the necessity of forming Tables so constructed, that the mean time can be reduced to the true. By the following example, it will be found, that by the true motions of the Sun, Moon and nodes, the Eclipse calculated, leaves the earth five periods sooner than it would have done, by mean equable motions. To exemplify this matter more fully, I will take the Eclipse of the Sun, which happened in the year 1764, March 21st. Old Style, (or April 1st. in the new,) according to its mean revolutions, and also according to its true equated time.

The shadow, or penumbra of the Moon, fell in open space at each return, without touching the earth ever since the creation, until the year of our Lord, 1295 then on the 14th day of June, at 52 minutes, and 59 seconds in the morning, Old Style, the Moon's shadow touched the earth at the north pole. In each succeeding period since that time, the Sun has come 28 minutes and 12 seconds nearer the same node, and the Moon's shadow has gone more southwardly. In the year 1962, on the 18th of July, Old Style, (or 31st. in the new,) at 10 hours. 36 minutes, 21 seconds in the afternoon, the same Eclipse will have returned 38 times. The Sun will then be only 24 minutes and 45 seconds from the ascending node, and the centre of the Moon's shadow will fall a little north of the equator.-At the end of the next following period, in the year 1980, July 29th, Old Style, (or August 11th in the new,) at 6 hours, 19 minutes and 41 seconds in the morning, the Sun will have receded back three minutes and twenty-seven seconds from the ascending node; the Moon will then have a small degree of south latitude, and consequently cast her shadow a little south of the equator. After this, at every following period, the Sun will be 28 minutes and 12 seconds further back from the ascending node than at the preceding, and the Moon's shadow will continue at each succeeding period to approach nearer the south pole, until September 13, Old Style, (or October 1st. in the new,) at 11 hours, 46 minutes and 22 seconds in the morning, in the vear 2665, when the Felinse will have