highest tides known are those, which happen about the change or full, a little before the vernal and after the autumnal equinox; all the causes then, in whole or in part, concurring to produce the greatest effect.

Lakes and small seas have not the extent of water necesry for perceptible tides. The Mediterranean and the Baltic seas, though they communicate with the ocean, are not only too small in themselves; but have straits too narrow to admit an influx of water sufficient for tides of any considerable height.

The preceding system of the tides must correspond to general theory, and, in a great measure, coincide with observation; the following remarks, of Mr. Ferguson, however, are entitled to much consideration.

"It is not to be doubted, but that the earth's quick rotation 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 in a month; for otherwise the tides would be more unequal in their heights and times of their return, than we find they are. But however 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, which 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 by theory,"

Were the surface of the globe entirely water of considerable depth, the tides might always return according to theory. But the case is very different. Islands and continents, straits and shoals, shores, channels, winds and a variety of other causes affect, and sometimes materially alter, the height and return of the tides in different places. These may be considered as exceptions, the preceding theory, the general principle.

The air being a fluid surrounding the earth, and extending much higher than the water, is more unequally attracted in different parts, by the great heavenly bodies, and, moving

without obstruction, must be subject to tides more extensive and higher than those of the ocean.

The vast utility of the tides must be contemplated with admiration by every reflecting mind. They are greatly useful in agriculture and navigation. But this is lost in the far more extensive benefit to health and even to life. Were it not for the action of the tides and saltness, what would the ocean be, but a vast reservoir of contagion and death? Infinite wisdom and goodness are displayed, in giving such inconceivable power of benefiting us, to bodies immensely distant.

CHAPTER VII.

SECTION 1.-ECLIPSES.

An eclipse is a total or partial obscuration of a heavenly body.

All the planets of the solar system are in themselves opaque, and shine only by reflecting the sun's light. Hence dark shadows are cast on the side not illuminated. These shadows are but privations of light in the space hid from the sun. (Plate VII, Fig 6) They are in the form of vast cones extending into the heavens.

If the earth were as large or larger than the sun, its shadow would be co-extensive with the solar rays; and would at times eclipse the other primary planets. But this has never been known. Mars, though often in opposition to the earth, never falls into its shadow. This must therefore terminate before it reaches that planet.

The primary planets can be eclipsed by their secondaries only; and the secondaries, by their primaries. The earth's shadow eclipses the moon; the moon's shadow the earth ;eclipses of the sun, as they are called, being more properly eclipses of the earth. Sanctioned by long established usage, however, the term "eclipses of the sun" will be retained.

The semi-angle of the earth's shadow at the apex, is equal to the apparent semi-diameter of the sun at the earth, minus the sun's horizontal parallax.

For in Plate VII, Fig. 6, let A B E represent the earth's shadow; A B C the semi-angle of the shadow; D A S the semi-diameter of the sun, as seen from the earth; AS C the sun's horizontal parallax. The angle D AS is equal to the angle AS CA B C Euclid, B. I, Prop. 32. From each of these equals take the angle A, S, C, the remainders are equal, viz. the angle A B C is equal to the angle D 1 S-A S C.

This being known, the extent of the shadow may be easily found by trigonometry. It is when longest about 219 semidiameters of the earth; on a mean, about 216 such semidiameters.

The extent of the earth's shadow may be found by subtracting the diameter of the earth from the diameter of the sun, and saying, as the difference is, to the distance of the earth from the sun; so is the diameter of the earth, to the extent of the shadow. Using the semi-diameters will produce the same result.

If the diameters of the sun and earth be taken as in the general table, the extent of the shadow by this computation will be extremely near the same as by trigonometry, the mean distance 217 semi-diameters, equal to 864,094 miles.

If the moon revolved in the plane of the ecliptic, there would be an eclipse at every full or change. But her orbit being inclined to the plane of the ecliptic, in an angle of 5° 9′ 3", subject to a small variation, an eclipse can happen but when she is in or about one of her nodes. (Plate VII Fig. 8.) In every other part of her orbit, she is either too high, or too low, to eclipse the sun, or to be eclipsed by the earth. The limit is greater in solar eclipses than in lunar. For if the moon be within about 17° of either of her nodes at the change, there will be an eclipse of the sun. But she must be within about 11° of one of the nodes for her to fall into the earth's shadow, and be herself eclipsed. The greatest solar ecliptic limit, according to Mr. Ferguson's tables, is 18° 11', the least, 16° 28′; the greatest lunar, 11° 51', the least, 10° 11'. This is a little different from his own statement.

An eclipse of the moon is partial, when a part only of her disk is covered; total, when the whole disk passes through the shadow; central, when the centre of the disk passes through the centre of the shadow.

The moon will be partially eclipsed at the full, if her latitude be greater than the difference, but less than the sum of her own semi-diameter and that of the earth's shadow, at the place of her ingress.

The semi-diameter of a section of the earth's shadow at the moon, subtends an angle at the earth, equal to the sun's horizontal parallax added to the moon's, minus the sun's semi-diameter.

Let A B D (Plate VII. Fig. 14.) be the earth, Cits centre, AGD the earth's shadow; FE the semi-diameter of that circle or section of the shadow, where passed by the moon in a lunar eclipse. The angle AFC is the moon's horizontal parallax ; FCE the angle, which a semi-diameter of the section subtends at the earth.

The angle AF C is equal to the angle F C E and FG E as in the problem from Euclid cited in figure 6; therefore the angle FCE is equal to the angle AF GF GE; but the angle FGE is equal to the semi-diameter of the sun, diminished by the sun's horizontal parallax, as before proved in this plate, figure 6. Add the sun's horizontal parallax to A F C the sum is the moon's horizontal parallax added to that of the sun; and add the sun's horizontal parallax to the angle F G E the sum is the apparent semi-diameter of the sun. But when the same quantity is added to the subtrahend and to the minuend, the difference remains as before. Therefore the semi-diameter of the section subtends at the earth, an angle equal to the sun's hori zontal parallax, added to the moon's, minus the apparent semidiameter of the sun, which was to be demonstrated.

The moon, when wholly immersed in the earth's shadow, is not invisible; but appears of a dusky red colour, like burnished copper. This phenomenon is probably caused by the refracted rays of the sun, which have traversed the earth's atmosphere, and by it have been turned inward, so as to fall on the moon and render it visible.-See the account of Mars, Chap. I. Sec. 8.

All, to whom the moon is visible in her eclipse, see her in the same instant of absolute time.

That hemisphere of the earth, which would be seen as a circle by a spectator at the moon, is called the disk of the earth. The semi-diameter of this is equal to the moon's horizontal parallax.

If at a change the moon's latitude be less than the apparent semi-diameters of the moon and sun and the moon's horizontal parallax added together, there will be a solar eclipse.

The angle subtended by the semi-diameter of the moon's dark shadow at the earth, is equal to the difference of the apparent semi-diameters of the sun and moon.

Let ADF be the moon's dark shadow, A B C the apparent semi-diameter of the moon, (Plate VIII, Fig. 13,) B a station on the earth, touched by the dark shadow, B C E or B C D the angle subtended by the semi-diameter of the dark shadow at the earth, D the apex of the shadow, and B D C taken as the semidiameter of the sun.* In the triangle B DC the side D B being produced, the external angle A B C as before, (Plate VII, Fig. 6,) is equal to the two interior and opposite angles, B C D BD C. The angle B C D is therefore equal to the difference between the angle A B C and the angle B D C which was to be demonstrated.

The dark shadow is largest, when the moon is in perigee and the earth in aphelion. Sometimes the dark shadow is terminated, before it reaches the earth. In this case, the sun at the centre of an eclipse appears like a luminous ring; (Plate VII. Fig. 9.) and the eclipse is called annular. This beautiful phenomenon was seen in some parts of New England, on the morning of April 3, 1791. The dark shadow is shortest, when the moon is in apogee and the earth in perihelion.

The eclipses of September 17, 1811; February 12, 1831; and September 18, 1838, may be enumerated as annular eclipses of the present century within the United States.The total eclipses computed for the same time are that of June 16, 1806, and that of August 7, 1869.†

* See Enfield, Astronomy, Part I. Book VII, Chapter V, Prop. 97, Lemma. It will be seen in the century, and also by inspection of the tables of the sun's and moon's diameter, that annular eclipses are more common than those which are total.