When the moon approaches the earth, her action in every part increases, and the differences in that action, upon which the tides depend, likewise increase. For the attraction of any body is in the inverse ratio of the square of its distance; the nearer, therefore, the moon is to the earth, the greater is her attraction, and the more remote, the less. Hence, her action on the nearest parts increases more quickly than it does on the more remote parts, and therefore the tides increase in a higher proportion as the distance of the moon diminishes.

Newton has shown that the tides increase as the cubes of the distances decrease; so that the moon at half her present distance, would produce a tide eight times greater. Now the moon describes an ellipse about the earth, and, of course, must be once in every revolution nearer the earth than in any other part of her orbit; consequently, she must produce a much higher tide when in this point of her orbit than in the opposite point. This is the reason that two great spring tides never take place immediately after each other; for if the moon be at her least distance at the time of new moon, she must be at her greatest distance at the time of full moon, having performed half a revolution in the intervening time, and therefore the spring tide at the full will be much less than that at the preceding change. For the same reason, if a great spring tide happens at the time of full moon, the tide at the following change will be less.

The spring tides are highest, and the neap tides lowest about the beginning of the year; for the earth being nearest the sun about the 1st of January, must be more strongly attracted by that body, than at any other time of the year; hence, the spring tides which happen about that time will be greater than at any other time. And should the moon be new or full in that part of her orbit which is nearest to the earth, at the same time the tides will be considerably higher than at any other time of the year.

When the moon has north declination, the tides are higher in northern latitudes; when she passes the meridian above the horizon, than when she passes the meridian below it; but when the moon has southern declination, the reverse takes place.

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Newton has shown that the moon raises the waters 8 feet 7 inches, while the sun and moon together raise them 10 feet, when at their mean distances from the earth; and about 12 feet when the moon is at her least distance. Such

would the tides regularly be, if the earth were all covered with the ocean to a great depth; but as this is not the case. it is only in places situated on the shores of large oceans, where such tides, as above described, take place.

The tides are also subject to very great irregularities from local circumstances; such as meeting with islands, shoals, headlands, passing through straits, &c. In order that they may have their full motion, the ocean in which they are produced ought to extend 900 from east to west, because that is the distance between the greatest elevation, and the greatest depression produced in the waters by the moon. Hence, it is that the tides in the Pacific Ocean exceed those of the Atlantic, and that they are less in that part of the Atlantic which is within the torrid zone, between America and Africa, than in the temperate zones, on either side of it where the ocean is much broader.

In the Baltic, the Mediterranean, and the Black Seas, there are no sensible tides; for they communicate with the ocean by so narrow inlets, and are of so great extent, that they cannot speedily receive, and let out water enough to raise or depress their surfaces in any sensible degree.

At London the spring tide rises 19 feet, at St. Maloes, in France, they rise 45 feet, and in the bay of Fundy, in Nova Scotia, about 60 feet.

CHAPTER XV.

Of Refraction, Parallax, &c.

1. The density of the atmosphere surrounding the Earth continually decreases, and at a few miles high becomes very small; and a ray of light passing out of a rarer medium into a denser, is always bent out of its course towards the perpendicular to the surface, on which the ray is incident. It follows, therefore that a ray of light must be continually bent in its course through the atmosphere, and describe a curve, the tangent to which curve, at the surface of the Earth, is the direction in which the celestial object appears. Consequently the apparent altitude is always greater than the true

2. The refraction or deviation is greater, the greater the angle of incidence, and therefore greatest when the object is in the horizon. The horizontal refraction is 32'; at 45° in its mean quantity it is 57 seconds.

The refraction is affected by the variation of the quantity or weight of the superincumbent atmosphere at a given place, and also by its temperature. In computing the quantity of refraction, the height of the barometer and thermometer must be noted. The quantity of refraction at the same zenith distance varies nearly as the height of the barometer, the temperature remaining constant. The effect of a variation of temperature is to diminish the quantity of refraction about part, for every increase of one degree in the height of the thermometer. Therefore, in all accurate observations of altitude, or zenith distance, the height of the barometer and thermometer must be attended to.

The refraction may be found by observing the greatest and least altitudes of a circumpolar star. The sum of these altitudes, diminished oy the sum of the refractions corresponding to each altitude, is equal to twice the altitude of the pore; pole; from whence, if the altitude of the pole be otherwise known, the suin of the refractions will be had; and from the law of variation of refraction, known by theory, the proper refraction to each altitude may be assigned.

Otherwise, when the height of the pole is not known, the ingenious method of Dr. Bradley may be followed, who observed the zenith distances of the Sun at its greatest declinations, and the zenith distances of the pole star above and below the pole. The sum of these four quantities must be 1800 diminished by the sum of the four refractions, and then by theory apportioned the proper quantity of refraction to each zenith distance. In this manner he constructed his table of refraction.

The ancients made no allowance for refraction, although it was in some measure known to Ptolemy, who lived in the second century. He remarks a difference in the times of rising and setting of the stars in different states of the atmosphere. This, however, only shows that he was acquainted with the variation of refraction, and not with the quantity of refraction itself.

Alhazen, a Saracen astronomer of Spain, in the 9th cen

tury, first observed the different effects of refraction on the height of the same star, above and below the pole. Tycho Brahe, in the 16th century, first constructed a table of refractions. This was a very imperfect one.

3. As the atmosphere refracts light, it also reflects it, which is the cause of a considerable portion of the daylight we enjoy. After sun-set the atmosphere also reflects to us the light of the Sun, and prevents us from being involved in instant darkness, upon the first absence of the Sun.

Repeated observations show that we enjoy some twilight till the Sun has descended 180 below the horizon. From whence it has been attempted to compute the height of the atmosphere, capable of reflecting rays of the Sun sufficient to reach us; but there is much uncertainty in the matter. If the rays come to us after one reflection, they are reflected from a height of about 40 miles; if after two, or three, or four, the heights will be twelve, five, and three miles. The computation requires the assistance of the theory of terrestrial refractions.

The duration of twilight depends upon the latitude of the place, and declination of the Sun. The Sun's depression being 180 at the end of twilight, we have the three sides of a spherical triangle to find an angle, viz. the Sun's zenith dis tance (1080,) the (108) the polar distance, and the complement of lati tude, to find the hour angle from noon. At or near the equator, the twilight is always short, the parallels of declinanation being nearly at right angles to the horizon. At the poles, the twilight lasts for several months: at the north pole, from the 22d of September to the 12th of November, and from the 25th of January to the 20th of March. When the difference between the declination and complement of latitude of the same name is less than 180, the twilight lasts all night.

4. Refraction is the cause of the oval figures which the Sun and Moon exhibit, when near the horizon. The upper limb is less refracted than the lower, by 5', or nearly of the whole diameter, while the diameter parallel to the horizon remains the same.

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The rays, from objects in the horizon, pass through a

greater space of a denser atmosphere than those in the zenith, hence they must appear less bright. According to Bougier, who made many experiments on light, they are 1300 times fainter, whence it is not surprising that we can look upon the Sun in the horizon without injuring the sight.

5. A spectator observing a planet not in his zenith, refers it to a place among the fixed stars, different from that to which a spectator at the centre of the Earth would refer it. The observed situation of the body is called its apparent place, and the place seen from the centre of the Earth, is called its true place. The arc of the great circle, intercepted between these two imaginary points, is called the diurnal parallax. This parallax, when the apparent zenith distance of the body is 90°, or when the body is in the horizon, is called the horizontal parallax.

Let C be the centre of the Earth, H the place of a spectator on its surface, Pany object, Vomnrs the sphere of the fixed stars, to which the places of all the bodies in our system are referred; V the zenith, and HS the horizon.