a minute. For though strictly it is the sine of the angle at the centre of the earth, in so short a distance the sine and arch may be taken as equal. A meridian on the earth, and, of course, an observer, passes from the sun one fourth part of a degree in a minute. Subtract this from the distance passed in the same time by the shadow, the difference is the motion of the shadow from the observer, allowance being made for obliquity in the motions. Hence, by knowing the miles passed in a minute and the breadth of the shadow, we may compute how long it will be in passing by a particular place. How the duration of total darkness, may be found geometrically in projecting solar eclipses, may be seen in the directions for projecting the eclipse of July 18, 1860.

V, of this chapter.

See section

When the moon changes in one of her nodes, the centre of the penumbra passes over the centre of the earth, making the largest general eclipse. The duration however varies a little with the distance of the moon from the earth, and a very little with the distance of the sun. It is longest when the moon is in apogee and the earth in its perihelion, being then about 6h. 13. The mean duration of such a general eclipse is about 5h. 46'. The motion of the moon varies with her distance from the earth, being slowest, when she is fartherest distant. This makes an apogeal eclipse a little longer than a perigeal.

The general eclipse begins, when the penumbra first touches the earth; ends, when it leaves the earth. An eclipse begins at any particular place, when the penumbra first touches it; ends, when the penumbra leaves that place.

The position of the earth's axis, as seen from the sun, or moon, at the change, greatly affects solar eclipses. This will be too apparent in projecting those eclipses to need explanation. Compare the eclipse in the projection, Plate IX, with the same eclipse on June 16, 1806.

ECLIPSES VISIBLE AT THE CAPITOL IN WASHINGTON-CITY, AND GENERALLY THROUGH THE UNITED STATES.

As the ingenious student generally wishes to anticipate eclipses, but often finds a difficulty in ascertaining, when those most suited to his genius may happen, the following catalogue was formed for his assistance. The time set to solar eclipses is the middle of each eclipse, as seen from the Capitol; to lunar, the minute of opposition. Both are reduced to apparent time.

5 10 P M Visible in the western parts of the Union. 7 34 A M

It will be seen, that some eclipses are included in the preceding catalogue, which are not visible at the Capitol. A few, however, visible in distant parts, only are not inserted.

SECTION 11.

SOME EXPLANATION OF THE TABLES USED IN CALCULATING

ECLIPSES.

The mean place and motion of a planet at any time, are what the place and motion of that planet would be, if its movement were uniform in a circle.

A mean lunation is the time intervening between one change of the moon and another, calculated in mean motion

The mean anomalies of the sun and moon, are their mean distance from their respective apogees reckoned in degrees, minutes and seconds.*

These anomalies must have been obtained at first by accurate observation at long intervals, and dividing between them. The sun's distance from the moon's ascending node must have been first found in the same manner.

In these and other astronomical calculations, when the signs become 12 or more, 12 or a multiple of 12, are rejected, and the remainder, if any, used as the true number; because 12 signs complete a circle. The distance passed from the apogee and the moon's node, are always taken, and not the remaining distance, however small.

TABLE I, contains the mean time of new moon, in March, the anomalies of the sun and moon, and the sun's distance from the moon's ascending node for the present century. The year is begun in March, to avoid the inconvenience otherwise arising from bissextile. A year in this table includes two months of the succeeding year. The numbers for 1800 were taken from other tables, originally formed from observation.f

*No inconvenience arises from some of these calculations being made on the supposition, that the sun moves round the earth, as he always appears in the ecliptic directly opposite to the earth.

These tables were calculated for the meridian of the capital in Washingtoncity, lon. 76° 55′ 30′′ 54′′. W. of Greenwich; but may be used for any other place, by applying the numbers in table 16, the table for changing longitude into time.