horizontal moon is the semi-diameter of the earth, farther from the spectator than the moon in the zenith, and consequently ought to appear smaller.

Accordingly, by actual measurement, this will be found to be really the case. This apparent increase of magnitude in the horizontal moon must therefore be considered as an optical illusion, arising from the concavity of the heavens, appearing to the eye to be a less portion of a spherical surface than a hemisphere.

Many astronomers formerly denied the existence of an atmosphere at the moon; principally, from observing no variation of the appearance on the surface, like what would take place, did clouds exist as with us: and also, from observing no change in the light of the fixed stars on the approach of the dark edge of the moon, The circumstance of there being no clouds, proves either that there is no atmosphere similar to that of the earth, or that there are no waters on its surface to be converted into vapour: and that the lustre of the stars not being changed, proves that there can be no dense atmosphere. But astronomers now seem to agree that an atmosphere does surround the moon, although of small density, when compared with that of the earth. M. Schroeter has observed a small twilight in the moon, such as would arise from an atmosphere capable of reflecting the rays at the height of about a mile.

Had the moon an atmosphere of considerable density, it would readily be discovered by the durations of the occultations of the fixed stars. The duration of an occultation would be sensibly less than it ought to be, according to the diameter of the moon. The light of the star passing by the moon, would be refracted by the lunar atmosphere, and the star rendered visible when actually behind the moon; in the same manner as the refraction by the earth's atmosphere enables us to see the celestial objects for some minutes after they have actually sunk below our horizon, or before they have risen above it. Now the duration is certainly never less than eight seconds of time, which proves that horizontal refraction at the moon must be less than 2"; for the duration being lessened by 8", the beginning of the occultation would be retarded 4" of time, during which the moon moves over 2 of space. This, therefore, shows that if a lunar atmosphere mosphere exists, exist it must be 1000 times rarer than the atmosphere at the surface of the earth, because the horizontal refraction by the earth's atmosphere is nearly 2000", With such a rare atmosphere, the lunar inhabitants must be deprived of many of the advantages which we enjoy, from the existence of our own. Indeed the loss of one advantage, that of twilight, is, on account of the length of their day, not of much consequence, and from the apparent irregularities of the lunar surface so much light may be reflected, that the assistance of the atmosphere to make daylight, may not be so necessary as on the surface of the earth..

QUESTIONS.

Which of the heavenly bodies most frequently changes its appearance ?

In what time does the moon perform her sidereal revolution?

What is the real diameter of the moon in miles? In what part of the heavens, in a clear evening, must we look for the new moon?

In what part of the heavens is the full moon shortly after sunset?

Why is a synodic revolution greater than a sidereal revolution?

What is the Metonic cycle?

Have any mountains, or other irregularities, been observed upon the surface of the moon?

Why is that moon whose full happens nearest the autumnal equinox, called the harvest moon?.. Why does the moon appear larger when in or near the horizon, than when in or near the zenith?

CHAPTER XIV.

Of the Tides,

1. That periodical flux, or reflux, caused by the action of the sun and moon, but more particularly by that of the latter, upon the waters of the ocean, is called the Tides.

The tides have been always found to follow, periodically, the course of the sun and moon; and hence it has been suspected, in all ages, that the tides were, some way or other, produced by these bodies.

The celebrated Kepler was the first person who formed any conjectures respecting their true cause. But what Kepler only hinted, has been completely developed and demonstrated by Sir Isaac Newton.

After his great discovery of the law of gravitation, he found it an easy matter to account for the whole phenomena of the tides; for, according to this law of nature, all the particles of matter which compose the universe, however remote from one another, have a continual tendency to approach each other, with a force directly proportional to the quantity of matter they contain, and inversely proportional to the square of their distance asunder. It is therefore evident, from this, that the earth will be attracted both by the sun and moon. But, although the attraction of the sun greatly exceeds that of the moon, yet the sun being nearly 400 times more distant from the earth than the moon, the difference of his attraction upon different parts of the earth, is not nearly so great as that of the moon; and therefore the moon is the principal cause of the tides.

2. There are two tides every 24 hours, 50 minutes, and 28 seconds, agreeing with the mean interval from the moon's leaving the meridian of any place till it returns to the same meridian again. Or, which amounts to the same thing, it is high water at any place every 12 hours, 25 minutes, and 14 seconds.

The mean retardation of the tides, or of the moon's coming to the meridian in 24 hours, is about 48′ 45.7"; and the mean interval between two successive tides is 12 hours, 25 minutes, and 14 seconds hence the mean daily retardation of high water is 50 minutes and 28.4 seconds.

The retardation in the time of high water, or the tide, varies with the phases of the moon.

About the time of new and full moon the interval is least, being only 12 hours, 19 minutes, 28 seconds; and at the quadratures the interval is the greatest, being 12 hours, 30 minutes, and 7 seconds.

If all parts of the earth were equally attracted by the moon, the waters of the ocean would always retain a spherical form, and there would be no tides, except those which would

be produced by the action of the sun. But the action of the moon being unequal on different parts of the earth, those parts being most attracted that are nearest the moon, and those at the greatest distance least, the spherical figure must suffer some change from the moon's action. Now as the waters of the ocean directly under the moon are nearer to her than the central parts of the earth, they will be more attracted by the moon than the central parts.. For the same reason the central parts will be more attracted than the waters on the opposite side of the earth, and, therefore, the distance between the earth's centre and the waters on its surface, both under the moon and on the opposite side will be increased; or the waters will rise higher, and it will then be flood or high water at those places.

But this is not the only cause that produces the rise of the waters at these two points; for those parts of the ocean which are 900 from them, will be attracted with nearly the same force as the centre of the earth, the effect of which will be a small increase of their gravity towards the centre of the earth. Hence, the waters of those places will press towards the zenith and nadir, or the points where the gravity of the waters is diminished, to restore an equilibrium, and thus occasion a greater rise at those places.

But in order to know the real effect of the moon on the ocean, the motion of the earth on its axis must be taken into account. For if it were not for this motion, the longest diameter of the waterý spheroid would point directly to the moon's centre; but by reason of the motion of the whole mass of the earth on its axis, from west to east, the most elevated parts of the waters no longer answer precisely to the moon, but are carried considerably to the eastward in the direction of the rotation. The waters also continue to rise after they have passed directly under the moon, though the immediate action begins then to decrease; and they do not reach their greatest height till they have got about 450 farther. After they have passed the point, which is 900 distant from the point below the horizon, they continue to descend, although the force which the moon adds to their gravity, begins there to decrease. For still the action of The moon adds to their gravity, and makes them descend till they have got about 450 farther; the greatest elevations, Therefore, do not take place at the points which are in a Line with the centres of the earth and moon, but about half

a quadrant to the east of these points, in the direction of the motion of rotation.

Thus it appears, if the earth were entirely covered by the ocean, that the spheroidal form which it would assume, would be so situated, that its longest diameter would point to the east of the moon; or, which amounts to the same thing, the moon would always be to the west of the meridian of the parts of greatest elevation. And as the moon apparently shifts her position from east to west in going round the earth every revolution, the longer diameter of the spheroid fol lowing her motions, will occasion two floods and two ebbs in the interval of 24 hours, 48 minutes, 45", as above.

3. The action of the moon in raising the waters of the ocean, is to that of the sun nearly as 4 to 1. Therefore when the actions of the sun and moon are in the same direction as at the time of new and full moon, the tides rise higher than at any other time, and are called spring tides. But when the moon is in the quarters, the action of the sun diminishes that of the moon, because his action is opposed to that of the moon'; consequently, the effect must be to depress the waters where the moon's action has a tendency to raise them. These tides are considerably lower than at any other time, and are called neap tides.

The spring tides do not take place on the very day of the new and full moon, nor the neap tides on the very day of the quadratures, but a day or two after; because in this case, as in some others, the effect is neither the greatest nor least when the immediate influence of the cause is greatest or least: as the greatest heat, for instance, is not on the solstitial day, when the immediate action of the sun is greatest, but some time after it. And, although the actions of the sun and moon were to cease, yet the ocean would continue to ebb and flow for some time, as its waves continue in violent motion for some time after a storm.

The high water at a given place does not always answer to the same situation of the moon, but happens sometimes sooner and sometimes later than if the moon alone acted on the ocean This proceeds from the action of the sun not conspiring with that of the moon. The different distances of the moor from the earth also occasion a sensible variation in the tides