distances found. Then in the figure, p. 275, S and M representing the true places of the sun and moon, P the pole, and Z the zenith; in the triangle M Z S are given M Z and S Z the true zenith distances, and M S the true distance of the objects, to find the angle MSZ; and in the triangle P M S are given P M and P S the polar distances of the objects, and M S their. true distance, to find the angle M SP, the difference between which and MS Z is P SZ; and in the triangle ZSP there are then given Z S and PS, the zenith distance and polar distance of the sun, and the included angle ZSP, to find Z P the co-latitude, and Z PS the sun's meridian distance, whence the apparent time at the place of observation is known; and as the apparent time at Greenwich at the same instant is found from the distance, the difference of those times, or the longitude in time, is known.

Note. If S were the place of a star, the latitude and the star's meridian distance would be found as above; and from the star's meridian distance, its right ascension, and the right ascension of the sun, the apparent time at the place of observation, and thence, as above, the longitude might be found.


1. If in N latitude the altitude of @be 26° 48' +, and of 2 72° 10' +, when the distance of their nearest limbs is 53° 27' 17", on September 2, 1823, height of the eye 20 feet, required the latitude and longitude ? Answer, latitude 32° 44' N, and longitude 31° 45' E.

2. On September 8, 1823, in N latitude, the altitude of 0 was 26° 50 –, and of 2 31° 30' distance of their nearest limbs 470 26' 58", height of the eye 26 feet, required the latitude and longitude?

Answer; latitude 37° 50' N, and longitude 19° 36' E.

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1. Given the sun's declination 3° 16' 6" S +, and right 'ascension 12h 30m 14:4s, required his longitude, and the obliquity of the ecliptic?

Answer, longitude 6s 8° 13' 57", and obliquity 23° 27' 46''. 2. In latitude 40° 48' N, the sun bore S 79° 16' W, at 3h 37m 59s P. M., required his altitude and declination?

Answer, altitude 36° 46', and declination 15° 32' N. 3. In N. latitude, when the sun's declination was 14° 20' N, his altitudes, at two different times, on the same forenoon, were 43° 7' +, and 67° 10' +, and the change of hïs azimuth in the interval 45° 2', required the latitude ?

Answer, 34° 20 N.


4. In latitude 16° 4' N, when the sun's declination is 23° 2' N, required the time in the afternoon, and the sun's altitude and bearing, when his azimuth neither increases nor decreases ?

Answer, time 3h 9m 26s P. M., altitude 45° 1', and bearing S 73° 16' W.

5. The sun set S W } S, when his declination was 16° 4', required the latitude ?

Answer, 69° 1. 6. The altitude of the sun, when on the equator, was 14° 28' +, bearing ES E, required the latitude and time?

Answer, latitude 56° 1', and time yh 46m 12s A. M. way. The altitude of the sun was 20° 41', at 2h 20m P. M., when his declination was 10° 28' S, required his azimuth and the latitude ?

Answer, azimuth S 37° 5' W, latitude 51° 58' N. 8. If on August 11, 1840, Spica set 2h 26m 14s before Arcturus, height of the eye 15 feet, required the north latitude ?

Answer, 36° 46' N. 9. If on November 14, 1829, Menkar rise 48m 3s before Aldebaran, height of the eye 17 feet, required the north latitude ?

Answer, 39° 45' N. 10. If on January 4, 1825, Castor and Alphard be observed on the same vertical in the eastern hemisphere, at the same time that Betelgeuse and Rigel are on the same vertical in the western hemisphere, required the N latitude ?

Answer, 35° 12' N, 11. In latitude 16° 40 N, when the sun's declination was 23° 18' N, I observed him twice, in the same forenoon, bearing N 689 30' E, required the times of observation, and his altitude at each time ?

Answer, times 6h 15m 40s A. M. and 10h 32m 48s A. M., altitudes 9° 59' 36'' and 68° 29' 42''.


The chief causes of winds are the expansion and contraction of the air from heat and cold; and, though in our climate nothing is more proverbial than the inconstancy of the winds, in some parts of the earth they appear to be governed by laws which operate with considerable regularity.

The most remarkable of these winds are the Trade Winds, which in a zone extending in general about 30° on each side of the equator, blow from the eastward nearly quite round the globe; inclining towards the north in north latitude, and towards the south in south latitude, and forming what are called the N E and S E trade winds. blows from the eastward. In this space sudden squalls and heavy rains frequently occur.

When the sun has his greatest north declination, the S E trade wind extends several degrees N of the equator ; and, in the opposite season, the N E trade wind extends in like manner to the south side of the equator ; but in all seasons these winds are found to be greatly modified by local circumstances, particularly near land. In the vast expanse of the Pacific Ocean they prevail almost uninterruptedly out at sea ; but in the Atlantic, on the coast of Brazil, they blow from N E to E N E, from September till March, and from SSE to ES E during the other half of the year. Near the African coast, the winds in general tend towards the coast; but, in the Gulf of Guinea, there is sometimes found a moderate breeze from the N E. Off this coast, about ro N latitude, and 20° W longitude, there is a considerable space, where almost continual calms are found, attended with thunder and lightning; and the rains are so frequent and heavy, that the space has acquired the name of the Rains.

İn the Indian Ocean, from about latitude 28° S to the equator, the SE trade wind blows pretty constantly; but in the Arabian Sea and the Bay of Bengal, there are certain periodical winds, called monsoons, which, from April till October, blow from S W, and from the opposite point from October till April. The S W monsoon is frequently attended with tempests and rain ; but, during the prevalence of the N E monsoon, the weather is in general dry and pleasant. About the change from one monsoon to another very violent storms of wind are usually met with.

Monsoons are found also in the Mozambique Channel, but the fair season there is during the S W, and the rainy season during the NE monsoon.'

On the coasts of Sumatra and Java, and along the coast of China, monsoons also prevail; but they blow more nearly from the north and south than those in the Arabian Sea, and they are, besides, much less regular, and are frequently interrupted by violent hurricanes, called tyfoons. Off the western coast of New Holland, there are regular monsoons, which blow from N W from October till April, and from S E during the remainder of the year.

Beyond the limits to which the trade winds extend, the winds are so variable, that all attempts to deduce the laws by which they are governed, have hitherto been unsuccessful ; westerly winds however are observed to be, on the whole, most frequent.

From what has been said, it will readily be perceived that a mariner, bound to the westward, will avail himself of the trade wind, when he can reach it without going too far out of his way;

but this wind, so favourable in running towards the west, is directly adverse

in sailing eastward, and it would therefore be a mere waste of time to attempt to sail to the eastward in the trade winds.

Indiamen, both outward and homeward bound, generally cross the equator between 18° and 23° west longitude, and thus avoid the coast of America, as well as the calms off the coast of Africa ; and steering to the south westward across the S E trade wind, till they reach the latitude where variable winds prevail, they then make towards the east. In sailing outwards in the Indian Ocean, they generally run down their longitude on the parallel of the Cape of Good Hope, and then steer across the SE trade wind towards India.

Ships bound from Europe for the West Indies, and the southern parts of North America, avail themselves of the trade wind, which they endeavour to reach as soon as possible; and, in returning, they steer towards the north, till they get without the limit of the trade wind, where they find the winds variable, and they then work their way towards the east.

Ships from the coast of Guinea sail from S to E S E, as the wind will permit, till they reach the Island of St. Thomas ; and with the wind which is generally found in that quarter, they run to the westward till they meet the SE trade wind.

Near the shore in tropical climates, there are daily land and sea breezes, the wind blowing from the sea during the heat of the day, and from the land during the night. In very warm weather these breezes are often observed to blow pretty regularly, even in temperate climates.


Tides are the daily rising and falling of the waters of the ocean, and they are produced by the attractions of the sun and moon, but chiefly by the attraction of the moon.

The attractive force of the moon, like that of every other body, varies in the inverse proportion of the square of its distance from the object which it attracts; and, consequently, the particles of the earth immediately under the moon are more, and those on the opposite side less attracted by her, than the intermediate parts are. And as the attraction of the moon, in the former case, acts in opposition to the gravity of the particles towards the earth's centre, their tendency towards the centre will be diminished ; and, consequently, if they were at liberty to move freely among themselves, they would rise above the level of the place which they would otherwise occupy, and form a wave, which would follow the moon in her diurnal circuit

same direction with the gravitating force of the particles on the opposite side of the earth, yet, as she exerts a greater force in the same direction, on the central parts, the relative gravitation of the central parts, and the particles on the opposite side towards each other will also be diminished; and, therefore, if at liberty to move freely, these particles will also rise above the general level, and form a wave or tide on the side opposite the moon.

The tide on the side next the moon, or that which happens when the moon is above the horizon, is called the superior, and the other the inferior tide.

Now it is only the particles of fluids that can be sensibly affected by such small variations in the gravitating forces; and it is only in the ocean, and large seas, that there is sufficient water to admit the effect, even in fluids, to be distinctly observable.

The time of full tide, however, even if the earth were covered with water, would not be at the time at which the moon is on the meridian of any place; for the waters, having been once put in motion, would continue to rise for some time, even if the moon's action were to cease altogether; and they, of course, continue longer to rise when her force is only a little diminished.

The waters of the ocean are similarly affected by the attraction of the sun ; , but though his attractive force on the earth is immensely greater than the moon's, yet, from his great distance, the effect is more nearly equal upon every particle, and therefore the tides which he produces are, with respect to the moon's, comparatively small ; and, in fact, they are only perceived in the modifications which they produce in the times and the heights of those which are primarily regulated by the moon.

In the interval between two successive transits of the moon, she produces two tides; and the sun, in every twenty-four hours, produces two tides also. The tides produced by the sun and moon coincide at the times of full and new moon; and the consequence is, that the tides at those times are higher. At the quarter of the moon, the effect of the solar is to diminish the lunar tide; and hence, at those times, we find the tides are below the average height. The tides at full and change are called spring tides, and those at the quarters neap tides; but the highest and lowest tides are generally about the third tide after the full and change, and the quarters.

As the action of the sun increases or diminishes the height of the lunar tide, so it also accelerates or retards the times at which high water happens.

When the moon is in the first and third quarters, the observed tide, or that compounded of the solar and lunar ones, is to the westward, and in the second and fourth quarters to the eastward of that raised by the moon alone ; hence the action of the sun makes high

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