sun.

will then produce a partial eclipse, which would be still greater if the moon were nearer her node, as in the point H. In fine, if, in the moment of the conjunction, the moon is precisely in her node N, the eclipse will be central; for the centre of the moon, if viewed from that of the earth, will appear to coincide with the centre of the And if the apparent diameter AB (fig. 9) of the sun S is greater than the apparent diameter QR of the moon L, it will form round the moon a ring, or a luminous crown; and the eclipse is then called annular. This ring of light will be larger in proportion to the difference between the apparent diameters of the sun and the moon. But if the apparent diameter ON (fig. 10) of the moon L is equally great or greater than the apparent diameter BA of the sun S, he will appear entirely covered by the moon; the eclipse will then be total, and will endure so much longer as the apparent diameter of the moon shall exceed that of the sun.

For an eclipse of the sun to be annular, the case will be most favourable when the sun is in perigé, and the moon in apogé. And for an eclipse to be total, the most favourable case is when the sun is in apogé, and the moon in perigé.

The motion of the moon being swifter than that of the earth, and the motion of both being directed from west to east, that is, that of the moon from Q to R (fig. 9), and from N to O

(fig. 10), and that of the sun from A to B, it will easily be seen that an eclipse of the sun must always begin in its western edge A.

As the moon is considerably less than the earth, her shadow forms a cone NOC (fig. 10) whose section is much less than the earth, so that only a small portion, DE, of the earth is involved in the shadow at one time. Hence it

is that an eclipse of the sun is not perceived at the same instant in every part of the hemisphere which is thus turned towards the sun, and that in some parts it will not be seen at all. Moreover, in different situations, different parts of the sun's disc will appear eclipsed; for those who are in F see him eclipsed in the part I B, and those who are in G see him eclipsed in the part KA. On the contrary, an eclipse of the moon is perceived at the same moment in every part of the earth where this planet is visible, and appears every where to occupy the same portion of her disc. It is for this reason that eclipses of the sun are much less frequent in any particular place than eclipses of the moon.

If the moon's nodes constantly corresponded, with the same points in the heavens, the eclipses, whether of the sun or the moon, would take place in the same months, and even on the same days; but as the nodes shift backwards, or contrary to the earth's annual motion about 191⁄2 degrees in the year, the same node will come round to the sun about 19 days sooner every

year than in the preceding. From the time, therefore, when the ascending node passes by the sun, as seen from the earth, there will be only 178 days before the descending node passes by him. If, then, at any time of the year we have eclipses about either of the nodes, we may expect in about 173 days after to have eclipses about the other node *.

The nodes shift through all the signs and degrees of the ecliptic in eighteen years and 225 days; and in this time there would always be a regular return of eclipses, if any complete number of lunations were finished without a fraction. But this never happens; for if both the sun and moon should set out together from a line of conjunction with either of the nodes, in any point of the ecliptic, the sun would go through eighteen annual revolutions, and 222 degrees over, and the moon through 230 lunations and 85 degrees of the 231st, by the time the nodes came round to the same point of the ecliptic again; and therefore the sun would then be 138 degrees from the node, and the moon 85 degrees from the sun t.

After the sun, moon, and nodes, however, have been once in a line of conjunction, they will return nearly to the same state again in 223 mean lunations, or about eighteen years and ten days, so that the same node which was in con

* Bonnycastle's Astronomy, lett. xxii. + Ibid.

VOL. II.

junction with the sun and moon at the beginning of the first of these lunations, will be within less than half a degree of the line of conjunction with the sun and moon again, when the last of these lunations is completed. In that time, therefore, there will be a regular period of eclipses, or returns of the same eclipses, for many ages. But the falling back of the line of conjunction of the sun and moon, with respect to the line of the nodes in every period, will at length exhaust it, and after that it will not return again in less than 12,492 years*.

If these principles are properly considered, it will not be difficult to conceive how astronomers are able to foretel the exact time when any phanomenon of this kind will happen. For, as an eclipse can only take place at the time of a new or full moon, the chief requisites are to determine the number of mean conjunctions and oppositions that will occur in every year, and the true places of the sun and moon in their orbits at each of those times. And, if from this it appears that the two luminaries are within the proper limits of the node, there will be an eclipse, or otherwise not, agreeably to what has been already observed upon this subject†.

But in order to facilitate these operations, we have astronomical tables ready computed, by which the places of the heavenly bodies and

Bonnycastle's Astronomy.

+ Ibid.

every other necessary particular may be easily found for any given instant of time. Dr. Halley has also given a catalogue of all the eclipses that took place from the year 1701 to 1718, which the author of "L'Art de verifier les Dates," and others, have continued up to the year 1800; and other computers again to the end of the 19th century.

In De Lalande's History of Astronomy for the Year 1800, it is asserted that M. Goudin has, by his analysis, fully determined the eclipse of 1847, the most considerable of the new century. That M. Duvancel, who has delineated eclipses for thirty years past, has likewise delineated this for every country on the globe. By his diagram it appears that it will be annular in England, France, Turkey, and even in Cochin-China. The solar eclipse of September 7, 1820, will be large, and in some parts of the continent beautifully annular.

With regard to the number of eclipses in certain given periods, it may be remarked, that in the space or cycle of 18 years and 10 days, there are usually about 70 eclipses; that is to say, 29 of the moon, and 41 of the sun. These numbers are nearly in the proportion of 7 to 10.

The greatest number of eclipses that can happen in a year is seven; and the least number is If there be seven, five must be of the sun, and two of the moon. If there be only two, they

two.