It is ascertained that, for an eclipse of the sun to be annular, the most favorable circumstances will be when the sun is in perigee, and the moon in apogee; and, for an eclipse to be total, the most favorable case is when the sun is in apogee, and the moon in perigee. The motion of the moon being much swifter than that of the earth, and the motions of both being directed from west to east, an eclipse of the sun must always begin in the western edge of the sun; and as the moon is a great deal less than the earth, her shadow forms a cone, the section of which is much less than the earth, so that a small portion of the earth only can, at any time, be 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 that is turned towards the sun, and that, in some parts, it will not be seen at all. For instance, a friend of mine, writing from Ceylon in the month of May, (1817,) says, “On the 16th of this month, we had a fine sight of an eclipse of the sun about noon: I think about 3-4ths of the surface were covered.” But in this country we had no solar eclipse at the same time. Again, in different situations, different parts of the sun’s disk will appear eclipsed; but, 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 disk. Hence, eclipses of the sun are much less frequent in any particular place than eclipses of the moon. If the nodes of the moon constantly corresponded with the same points in the heavens, the eclipses of the sun or moon might be expected 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 19½ degrees in a year, the same node will come round about nineteen 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 173 days before the descending node passes by him. If, then, at any time of the year, we have eclipses about either of the nodes, their return may be expected in about 173 days, in or near the other. It may be further observed, that, after the sun, moon, and nodes, have been once in a line of conjunction, they will return nearly to the same state again in 228 lunations, or eighteen years and ten days; so that the same node which was in conjunction 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 for many ages.