means of a greater centrifugal force. At the full, while the Moon raises the tide under, and opposite to her, the Sun acting in the same line, raises the tide under, and opposite to him; whence their conjoint effect is the same as at the change, and in both cases occasion what is called Spring Tides. [Fig. 7th, plate 6th.] But at the quarters, the Sun's action diminishes the action of the Moon on the waters, so that they rise a little under, and opposite to the Sun, and full as much under, and opposite to the Moon, making what we call neap tides; because the Sun and Moon then act crosswise to each other. [Fig. 7th, plate 6th.] But, strictly speaking, these tides happen not till some time after, because in this, as in other cases, the actions do not produce the greatest effect when they are at the strongest, but sometime afterward. The Sun being nearer the earth in winter than in summer, is of course nearer to it in February and October than in March and September, and therefore the greatest tides happen not till some time after the autumnal equinox: and return a little before the vernal. The Sea being thus put in motion, would continue to ebb and flow for several times, though the Sun and Moon should be annihilated, or their influence cease.

When the Moon is in the equator, the tides are equally high in both parts of the lunar day, or time of the Moon's revolving from the meridian to the meridian again, which is 24 hours and 50 minutes. But, as the Moon declines from the equator towards either pole, the tides are alternately higher and lower at places having north or south latitude. One of the highest elevations, (which is that under the Moon,) follows her towards the pole to which she is nearest, and the other declines towards the opposite pole; each elevation describing parallels as far distant from the equator on opposite sides, as the Moon declines from it to either side, and consequently, the parallels described by these elevations of the water, are twice as many degrees from each other as the Moon is from the equator, increasing their distance as the Moon increases her declination, till it be at the greatest: when the said parallels are at a mean state 47 degrees asunder, and on that day the tides are most unequal in their heights. As the Moon returns towards the equator, the parallels described by the opposite elevations approach toward each other until the Moon comes to the equator, and then they coincide. As the Moon declines toward the opposite pole at equal distances, each elevation describes the same parallel in the other part of the lunar day, which its opposite elevations described before.While the Moon has north declination, the greatest tides in the northern hemisphere, are when she is above the horizon, [see plate 6th, fig. 5th,] and the reverse when her declination is south. [See plate 6th, fig. 4th.]

Thus it appears, that as the tides are governed by the Moon, they must turn on the axis of the Moon's orbit, which is inclined 23 degrees and 28 minutes to the earth's axis at a mean state, and therefore the poles of the tides must be so many degrees from the poles of the earth, or in opposite points of the polar circles, going around them in every revolution of the Moon from any meridian to the same again. [Plate 6th, fig. 3d.]

It is not, however, to be doubted, but that the quick rotation of the earth on his axis, brings the poles of the tides nearer to the poles of the world than they would be if the earth were at rest, and the Moon revolved about it only once a month, otherwise the tides would be more unequal in their heights, and times of their returns, than we find they are. But how near the earth's rotation may bring the poles of its axis and those of the tides together, or how far the preceding tides may affect those that follow, so as to make them keep up nearly to the same heights and times of ebbing and flowing, is a problem more fit to be solved by observation than theory.

In open seas, the tides rise but to very small heights in proportion to what they do in broad rivers, whose waters empty in the direction of the stream of tide:-For, in channels growing narrower gradually, the water is accumulated by the opposition of the contracting bank. The tides are so retarded in their passage through dif

ferent shoals and channels, and otherwise so variously affected by striking against capes and headlands, that to different places, they happen at all distances of the Moon from the meridian, and consequently at all hours of the / lunar day.

Air* being lighter than water, and the surface of the atmosphere nearer to the Moon than the surface of the sea, it cannot be doubted that the Moon raises much higher tides in the air than in the sea.

INTERROGATIONS FOR SECTION TENTH.

By whom was the cause of the TIDES first discovered? How does he explain it ?

Who improved the idea of Kepler?

By what does he consider the waters to be attracted? Why are the waters on the side of the earth next to

the Moon, more attracted than the central parts?

Why are the central parts more attracted, than the waters on the opposite side?

From what source is this explanation deduced? By what power is the earth constantly falling towards the Moon, and the Moon towards the earth?

If this be actually the case, why do they not come together?

Is it the centre of the earth that describes the annual orbit round the Sun?

Where is the centre of gravity between the earth and Moon?

How much more matter does the earth contain, than the Moon?

What is the centre of gravity between the two bodies ? How is it found?

Which has the greatest influence in raising tides, the Sun or Moon?

Are the tides at the highest when the moon is due north, or south?

What is the reason?

Do the tides always answer to the same distance of the Moon from the meridian at the same places ?

Does the Moon approach nearer, and recede farther from the earth in each of her revolutions?

At what time does she attract the earth most?

At what time does she attract it the least?

In what positions are the Sun and Moon when the

highest tides are raised?

What are spring-tides?

What are neap-tides?

In what manner do the attractions of the Sun and

Moon act on each other, to produce spring-tides?
In what manner to produce neap-tides?

Where is the Moon when the tides are equally high in

both parts of the lunar day?

What is understood by the lunar day?

What is the length of the lunar day?

At what time are the tides most unequal?

In which hemisphere are the highest tides, when the

Moon has north declination?

Which when in her south declination?

Do the tides rise very high in open seas ?
Are the tides ever retarded in their passage?
What retards them?

What are aerial tides?

How were they discovered, and by whom?

SECTION ELEVENΤΗ.

ASTRONOMICAL PROBLEMS.

PROBLEM I.

To convert time into degrees, minutes, &c. Rule. As one hour is to 15 degrees, so is the time given to the answer.

FXAMPLES.

1. How many degrees are equal to 8 hours, 20 minutes, and 30 seconds?

2d. The Sun passes the meridian of Detroit 1 hour 19 minutes after 12 o'clock, noon, at Boston-How farare those places asunder?

PROBLEM II.

To convert degrees, minutes, &c. into time. Rule.-As 15 degrees are to an hour, so are the num

ber of degrees given to the time.

EXAMPLES.

1. The apparent distance of Venus from the Sun, can never be above 50 degrees, and when at that distance, how long does she rise before the Sun, or set after him?

2. The greatest elongation of Mercury is said to be 28 degrees, 20 minutes and 19 seconds--How long can he set after the Sun, when an evening star?

PROBLEM III.

The diurnal arc of the Sun, or of any planet being given, to find the time of the rising or setting of the Sun. Rule.-Bring the diurnal are into time by Problem 2d. Divide this time by two, and the quotient will be the time at which the Sun sets. Take this time from