eter, may be deduced, by methods given in treatises on Navigation. When the true distance has been obtained, and then the time at Greenwich, corresponding to this distance, the difference between this time, and the time of observation, will be the longitude of the place; which will be east or west according as the Greenwich time is earlier or later than the time of observation.

This method of finding the longitude, is of great importance to the mariner, as all others, with the exception of that by the chronometer, require observations that cannot be made at sea.

360. Longitude, by Moon Culminating Stars. Certain stars situated contiguous to the moon's path and passing the meridian at short intervals before or after the moon, are called moon culminating stars. The moon's right ascension increases on an average a little more than half a degree or two minutes in time during a sidereal hour, that is, during the interval that elapses from the time a star is on the meridian of any place till it is on the meridian of a place whose longitude is 15° or one hour, west of the former. Hence, the intervals between the passages of the moon and a star over the meridians of two places differing an hour in longitude must differ about two minutes; and for other differences of longitude there must be a proportional difference in the intervals. It follows, that if the intervals between the passages of the moon and a star over the meridians of two places be accurately obtained by observations, the differences of their longitudes may be easily found by means of the moon's hourly variation in right ascension at the period of observation.

The Nautical Almanac contains a table in which are given for each day in the year, except a few near the times of new moon, the apparent right ascensions of several of the moon culminating stars, the apparent right ascension of the moon's enlightened limb at the instant it is on the

* Dr. Bowditch's Navigation contains several of the best methods.

meridian of Greenwich and the hourly variation in the right ascension of the limb at that time. The difference between the right ascension of the star and the enlightened limb of the moon is the interval between the passages of these over the meridian of Greenwich. From the computed interval for Greenwich, and the observed interval at any other place, the longitude of the latter may be obtained with considerable precision.

361. Determination of the longitude of a place from observations of an eclipse of the sun, or of an occultation. The times of the beginning and end of an eclipse of the sun or of an occultation of a star or planet, at any place, depend on the position of the place. Assuming the computed places of the bodies to be accurate, we may, from the carefully observed time of beginning or end of an eclipse or occultation at any place whose latitude is known, determine the corresponding time at the first meridian, and consequently, the longitude of the place. If the phenomenon is also visible and the times of beginning and end are observed at places whose positions are accurately known, the determination of longitude by this means may be rendered nearly free from any errors in the tabular places of the bodies. The investigation of formulæ for making the equisite computations will be given in the appendix.

362. Longitude by the Eclipses of Jupiter's Satellites This method of finding the longitude of places has been already noticed (321). Although it is not so accurate as several others, its great simplicity, and the frequency of the occurrence of these phenomena, render it very convenient for approximate determinations of the longitude.

CHAPTER XX.

OF THE TIDES.

363. Definitions. The alternate rise and fall which take place in the surface of the ocean, seas, bays and contiguous rivers, twice in the course of each lunar day, or of 24 h. 51m. mean solar time, are called the Tides. When the water is rising it is said to be flood tide, and when it is falling, ebb tide. When the water is at its greatest height it is said to be high water, and when at its least height, low

water.

The swell in the waters of the ocean is called the tide wave, or sometimes, the primitive tide wave; and that in a contiguous bay or river, proceeding from the former, is called a derivative tide wave. A curve line along the summit of the tide wave or through different points or places that have high water at the same instant of time is called a cotidal line.

364. Causes of the tides. The earth in its revolution round the sun is continually drawn, by the attraction of the moon, slightly aside from the place at which it would be, if this attraction did not exist. If the earth was entirely solid, all parts of it would necessarily be drawn aside to the same extent. But as the moon's attraction decreases in the same ratio that the square of the distance increases, and as a large portion of the external part of the earth is composed of water, which can yield to forces unequally impressed on it, it is evident that all parts will not be drawn aside equally. The portion of water nearest the moon, being most attracted, will be drawn farther than the central and solid parts of the earth, and the central part farther than the opposite watery surface. Hence, the distance of the surface of the water from the centre of the earth must be increased, that is, there must be high water, both on the

side of the earth nearest the moon and also on the opposite side. But a swell in the waters of some portions of the earth cannot take place without a corresponding depression in other portions. This depression, it is obvious, must be greatest in the vicinity of the great circle midway between the portions of the earth nearest the moon and most remote from her, and it must there be low water.

The sun's action must also produce similar effects. But although his whole attraction on the earth is far greater than the moon's, yet, as his distance is nearly 400 times that of the moon, the inequality of his attraction at the surface and centre is less; and consequently, his influence in producing a tide is also less. The height of the solar tide is only about one third of that of the lunar tide.

In the open ocean, the average rise and fall of the tides, or height of high water above low water is about 2 feet.

365. Spring and Neap Tides. At the time of new moon, the attractions of the sun and moon are nearly in the same direction, and their actions are, therefore, united in producing the tides. They are also united at the time of full moon, when the moon is in opposition; for each body produces a tide not only on the side of the earth nearest it, but also on the opposite side (364). Hence, at the times of the syzygies, the tides must rise above their average height. The tides occurring at or near these times are called spring tides.

At the times of the quadratures, the action of the sun tends to produce low water, where that of the moon produces high water, and the contrary. The tides occurring at these times will not, therefore, rise to their average height. These are called neap tides.

As the greatest effect of a varying action does not take place at the instant the action itself is greatest, but some time afterwards, so it is with the tides. The most marked spring and neap tides occur about a day and a half after the times of the syzygies and quadratures.

The effects of the separate actions of the sun and moon,

being nearly as 1 to 3, their joint effect must be to their effect when acting in opposition to each other, nearly as 4 to 2. Hence, the height of the spring tides above the medium surface of the water must be about double that of the neap tides. This result is confirmed by observation.

366. Perigean and Apogean Tides. The moon's influence in producing the tides, must evidently be greatest when her distance from the earth is least, and least when the distance is greatest. Consequently, other circumstances being the same, the tides will be higher a short time after the moon is in perigee, and lower, a short time after she is in apogee, than at other times.

Unusually high tides occur, when the moon is in perigee, at or near the time of new or full moon.

The variation in the earth's distance from the sun, has also a slight influence on the height of the tides.

367. Effect of the moon's declination on the tides. The height of the tide at a given place is influenced by the declination of the moon. When the moon has no declination, the highest tides must evidently occur along the equator; and the height must diminish from thence towards the north and south. When she has north declination, the highest tides on the side of the earth next the moon, will be at places having a corresponding north latitude, and on the opposite side, at those which have an equal south latitude. From these parallels of latitude, the height of the tide will gradually diminish to the north and south. It, therefore, follows that when the moon's declination is north, the height of the tide at a place in north latitude will be greater when the moon is above the horizon than when she is below it and at a place in south latitude it will be just the reverse. This is illustrated by Fig. 55, in which the exterior curve is an exaggerated representation of the oval form of the curve through the summit of the tide wave, on the supposition that the whole earth is covered by water. When the moon's declination is south, the whole is