GENERAL OBSERVATIONS ON ECLIPSES.

If the orbit of the earth and that of the moon were both in the same plane, there would be an eclipse of the sun at every new moon, and an eclipse of the moon at every full moon But the orbit of the moon makes an angle of about 5 degrees with the piane of the orbit of the earth, and crosses it in two points called the nodes: now, astronomers have calculated that, if the moon be less than 17° 21' from either node, at the time of new moon, the sun may be eclipsed; or if less than 11° 34′ from either node, at the full moon, the moon may be eclipsed; at all other times there can be no eclipse, for the shadow of the moon will fall either above or below the earth at the time of new moon and the shadow of the earth will fall either above or below the moon at the time of full moon. To illustrate this, suppose the right hand part of the moon's orbit (Plate II. Fig. 6.) to be elevated above the plane of the paper,or earth's orbit, it is evident that the earth's shadow, at full moon, would fall below the moon; the left hand part of the moon's orbit at the same time would be depressed below the plane of the paper, and the shadow of the moon, at the time of new moon, would fall below the earth. In this case, the moon's nodes would be between E and a, and between G and b, and there would be no eclipse, either at the full or new moon: but, if the part of the moon's orbit between G and b be elevated above the plane of the paper, or earth's orbit; the part between E and a will be depressed, the line of the moon's nodes will then pass through the centre of the earth and that of the moon, and an eclipse will ensue.* An eclipse of the sun begins on the western side of the disc, and ends on the eastern; and an eclipse of the moon begins on the eastern side of her disc, and ends on the western.

* If you draw the figure on card paper, and cut out the moon, her shadow and orbit, so as to turn on the line a E G &c. the above illustration will be rendered more familiar.

NUMBER OF ECLIPSES IN A YEAR.

The average number of eclipses in a year is four, two of the sun and two of the moon; and, as the sun and moon are as long below the horizon of any particular place as they are above it, the average number of visible eclipses in a year is two, one of the sun and one of the moon; the lunar eclipse frequently happens a fortnight after the solar one, or the solar one a fortnight after the lunar one.

The most general number of eclipses, in any year, is four; there are sometimes six eclipses in a year, but there cannot be more than seven, nor fewer than two.

The reason will appear, by considering that the sun cannot pass both the nodes of the moon's orbit more than once a year, making four eclipses, except he pass one of them in the beginning of the year; in this case, he may pass the same node again a little before the end of the year; because he is about 173* days in passing from one node to the other; therefore he may return to the same node in about 346 days, which is less than a year, making six eclipses. As twelve lunations, or 354 days from the eclipse in the beginning of the year may produce a new moon before the year is ended, which (on account of the retrograde motion of the moon's nodes) may fall within the solar limit, it is possible for seven eclipses to happen in a year, five of the sun and two of the moon. When the moon changes in either node, she cannot be near enough to the other node at the time of the next full moon to be eclipsed, and in six lunar months afterwards, or about 177 days,

* The moon's nodes have a retrograde motion of about 191 degrees in a year (see page 133); therefore the sun will have to move 193 (188 ) 170 degrees from one node to the other. But it

2

has been shewn in a preceding note (see page 14), that the sun's apparent diurnal motion is about 59′ in a day; hence, 59′ : 1 day : : 17019: 173 days.

That is, 12 times 29 days 12 hours 44 min. 3 sec., or 354 days & hours 48 min. 36 sec.

she will change near the other node; in this case, there cannot be more than two eclipses in a year, and both of the sun.

The ecliptic limits of the sun are greater than those of the moon; and hence, there will be more solar than lunar eclipses, in the ratio of 17° 21' to 11° 34', or nearly of 3 to 2; but more lunar than solar eclipses are seen at any given place, because a lunar eclipse is visible to a whole hemisphere at once; whereas, a solar eclipse is visible only to a part, as has been observed before; and therefore there is a greater probability of seeing a lunar than a solar eclipse.X

PART III.

CONTAINING

Problems performed by the Terrestrial and Celestial

Globes.

CHAPTER I.

Problems performed by the Terrestrial Globe.

PROBLEM I.

To find the Latitude of any given Place.

RULE. BRING the given place to that part of the brass meridian which is numbered from the equator towards the poles; the degree above the place is the latitude. If the place be on the north side of the equator, the latitude is north; if it be on the south side, the latitude is south.

On small globes the latitude of a place cannot be found nearer than to about a quarter of a degree. Each degree of the brass meridian on the largest globes is generally divided into three equal parts, each part containing twenty geographical miles; on such globes the latitude may be found to 10'

Examples. What is the latitude of Edinburgh?

3. Find all the places on the globe which have no latitude.

4. What is the greatest latitude a place can have?

PROBLEM II.

To find all those places which have the same latitude as any given place.

Rule. Bring the given place to that part of the brass meridian which is numbered from the equator towards the poles, and observe its latitude; turn the globe round, and all places passing under the observed latitude are those required.

All places in the same latitude have the same length of day and night and the same seasons of the year; though, from local circumstances, they may not have the same atmospherical temperature. See page 16.

Examples. 1. What places have the same or nearly the same latitude as Madrid?

Answer Minorca, Naples, Constantinople, Samarcand, Philadelphia, &c.

2. What inhabitants of the earth have the same length of days as the inhabitants of Edinburgh?

3 What places have nearly the same latitude as London?

4. What inhabitants of the earth have the same seasons of the year as those of Ispahan?

5. Find all places of the earth which have the longest day the same length as at Port Royal in Jamaica.

PROBLEM III.

To find the longitude of any place.

Rule. Bring the given place to the brass meridian, the number of degrees on the equator, reckoning from the meridan passing through London to the brass meridian, is the longitude. If the place lie to the right hand of the meridian passing through London, the longitude is east; if to the left hand, the longitude is west.

On Adams' globes there are two rows of figures above the equator. When the place lies to the right hand of the meridian of London, the longitude must be counted on the upper line, when it lies to the left hand, it must be counted on the lower line. Bardin's New British Globes have also two rows of figures above the equator, but the lower line is always used in reckoning the longitude.