PROBLEM XXII.

To find the longitude of a place by an occultation of a star by the moon; the apparent time being estimated from noon to noon, according to the method of astronomers, and the latitude of the place being known.

RULE.

With the longitude by account find the corresponding Greenwich mean time of observation. For this time, take out from the Nautical Almanac the sun's right ascension, the moon's horizontal parallax, and her declination, to the nearest minute.

Reduce the latitude of the place, and the moon's horizontal parallax, by subtracting the corrections found in Table XXXVIII.

To the sun's right ascension add the apparent time of observation; the sum will give the right ascension of the meridian.

Take from the tables "for facilitating the computation of occultations of certain stars by the moon," in the Nautical Almanac, the star's right ascension and declination. The difference between the right ascension of the meridian and the star's right ascension will give the hour-angle of the star, which convert into degrees, &c., naming it west when the right ascension of the meridian is greater than the star's right ascension, and east when less.

To the proportional logarithm of the moon's corrected horizontal parallax add the log. secant of the reduced latitude, and the log. cosecant of the hour-angle, rejecting 10 in each index. To the sum (S) add the log. cosine of the moon's declination and the constant logarithm 0.3010; the result, rejecting 10 in the index, will give the proportional logarithm of an arc, which, subtracted from the hour-angle, will give the hour-angle corrected.

Take out the following logarithms, and place them beneath each other, in two columns: the proportional log. of the moon's corrected horizontal parallax in both columns; the secant of the star's declination in col. 1, and its cosecant in col. 2; the cosecant of the reduced latitude in col. 1, and its secant in col. 2; and the secant of the corrected hourangle in col. 2. The sum of the logarithms in col. 1 will give the prop. log. of an arc of the same name as the latitude, and the sum of the logarithms in col. 2 will give the prop. log. of an arc of a different name from the star's declination, when the hour-angle is less than 90°, but of the same name, if greater than 90°. The sum of these arcs, having regard to their names, will, being applied to the star's declination, give the declination corrected. To the sum (S) add the constant log. 1.1761, and the log. cosine of the star's corrected declination; the sum, rejecting 10 in the index, will be the prop. log. of an arc in time, to be added to the star's right ascension when it is west of the meridian, but subtracted when east, to obtain the star's right ascension corrected.

Find in the Nautical Almanac the time when the moon's right ascension is near to that of the star corrected, and for this time take out the moon's right ascension and declination, and their hourly variations.

Subtract the common log. of the difference between the corrected right ascension of the star and the right ascension of the moon from the common log. of the hourly motion in right ascension; to the remainder add the constant log. 0.4771; to the same remainder add the proportional log. of the hourly motion in declination. The former sum will be the proportional log. of a time to be added to the assumed time when the star's right ascension is greater than the moon's, otherwise subtracted, to obtain the time corrected. The latter will be the proportional log. of a correction of the moon's declination, to be applied with the same name as the hourly variation when the star's right ascension is greater than the moon's right ascension, but with a different name when less.

To the common log. of the hourly motion in right ascension add the log. cosine of the moon's declination; to the sum (S,), rejecting 10 in the index, add the proportional log. of the hourly motion in declination, and the constant log. 7.1427. The result will be the log. cotangent of the first orbitical inclination, and must have the same name as the hourly motion in declination, when the star is north of the moon, but a different name when south of the moon.

To the proportional log. of the difference between the star's declination corrected and the moon's declination corrected add the constant log. 9.4354, and the log. secant of the preceding orbitical inclination, rejecting 10 in the index, and from the sum subtract the proportional log. of the horizontal parallax; the remainder will be the log. secant of the second orbitical inclination, which must be named S. when the observation is an immersion, and N. when an emersion.

Add together the two orbitical inclinations, having proper regard to their names; and to the log. cosecant of this sum add the preceding sum (S), the proportional log. of the horizontal parallax, and the constant log. 8.1844. The sum will be the proportional log. of a correction to be applied to the time corrected to get the mean time at Greenwich; added when the sum of the orbitical inclinations is N., subtracted when S.

Apply the equation of time to this Greenwich mean time, and we shall have the Greenwich apparent time; the difference between it and the apparent time at the place of observation will give the longitude required, west when the time at Greenwich is the greatest east when less.

EXAMPLE.

Suppose, in a place in the latitude 42° 19' 15" north, and estimated longitude 4h. 44m. west of Greenwich, the immersion of y Cancri was observed April 20, 1839, at 10h. 45.n. 35s.9 apparent time. Required the longitude.

Constant Log. 0.4771..........P. L. D's ho. mo. in dec. 953.85....1.2597

....0.6703

ADDENDA.

ON WINDS AND STORMS.

BY W. C. REDFIELD.

THE earth is surrounded by a fine, invisible and elastic fluid, called air; which, when spoken of in its general relations to the earth, is called the atmosphere. Its incumbent weight or pressure upon the earth's surface is determined by means of the barometer, and is equal to a column of mercury of about thirty inches in height, at the sea level. Wind, is air in motion. It is found, that in almost every country and in every sea, the wind is more or less predominant in a particular direction. The most remarkable of these general winds are distinguished by several names, as trade winds, monsoons, variable winds, &c.

The trade winds, are found between the equator and the 30th parallels of north and south latitude, where the wind, for the most part, blows from the eastward: but near the eastern borders of any ocean, the trade winds usually blow more towards the equator than in its more central portions; while on the western borders, the wind not unfrequently, blows in a direction which is more or less outward from the equator.

The monsoons, which are chiefly found in the Indian seas, are regular alternations of the trade winds, which blow for six or eight months in their regular course; but, during the other portions of the year, are replaced by a westerly wind: which is probably a deflection of the trade wind from the opposite side of the equator.

The variable winds, are chiefly found extending from the outward borders of the trade winds to the polar regions; although subject to frequent changes, both of velocity and direction, yet their predominating direction is found to be from a western quarter, being opposite to the general course of the trade winds. The various movements of these winds are often exhibited in different strata, superimposed one upon another; and these movements viewed in their extended relations, are doubtless connected with those of the trade winds.

The land and sea breezes, are daily alternations in the direction of the general winds, near the shores of an island or continent. They appear to be connected with the daily changes of temperature at the earth's surface. The sea breeze generally sets in about ten in the forenoon and continues till about five or six in the evening: at seven the land breeze begins and continues till about eight in the morning.

A whirlwind, is a phenomenon which is often violent and dangerous. The identity of waterspouts and whirlwinds was maintained by Franklin, and although at a later period this has sometimes been questioned, it appears to have been done without sufficient reason. From the equal distribution of the atmosphere as the envelop of our earth, it results, that no violent wind can take place, except by means of a movement which is more or less circuitous in its character, and in cases of great violence, the wind is exhibited in the form of an active vortex or whirlwind; which, if isolated from other violent winds and of small extent, is often called a tornado or waterspout.

Waterspouts and whirlwinds follow the course either of the surface wind, or of a higher current of air from which they are sometimes depended; or their course may be modified by both these influences, without being absolutely determined by either. They abound most in those calm regions which are found near the external limits of the trade winds and in like regions near the equator.

Storms and hurricanes, have from the earliest periods been considered as the chief dangers encountered by the navigator. It was discovered by Franklin, that northeast storms, in the United States, pursued a retrogressive course, commencing sooner in Philadelphia than in Boston. Careful attention having been given to the phenomena of the Atlantic storms, in later years, it has been found that they exhibit certain characteristics of great uniformity. The most violent of these storms, often known by the name of hurricanes, appear to commence in the intertropical latitudes, eastward of the West Indies, where their course is towards the northwest, till approaching the latitude of 30°, their westerly progress ceases and their track becomes recurved to the northward and eastward; in which latter direction their progress usually becomes accelerated. On the annexed chart, the routes of several of these hurricanes are shown by dotted lines, which indicate, somewhat nearly, the center of the track pursued by each hurricane in its daily progress, on such part of its route as has become known.

The rate at which these storms advance in their course, is from eleven to thirty miles an hour; their average progress being about seventeen miles. This cannot explain the velocity of the wind, which, in the most violent part of the gale, sometimes exceeds 80 or 100 miles an hour; but the observations by which their course and velocity have

been determined have also shown, that these storms act in the manner of great whirlwinds, turning constantly to the left around their moving axis of rotation: the most violent portion of the gale being found toward the interior or heart of the storm. Hence it is also found, that the direction of the wind in a gale, for the most part, does not at all coincide with its line of progress.

When a storm is about to commence, the latitude of the ship will indicate its probable course, as is seen on the above chart, and the direction of wind which the storm first presents, may serve to determine the portion of the gale under which the ship is likely to fall, either by preserving, or altering her course; as well as the changes and comparative violence of the wind, to which she will, in either case, be exposed. In the hurricane figures which are found on the chart on tracks 1, 5, and 7, the curved

arrows show the various directions of the wind in different portions of the advancing storm: but in order to exhibit this more perfectly, the annexed diagram may be referred to.. The outward circle of this diagram represents the true points of the compass, and the curved arrows in the figure within, represent the rotary motion of the gale, and serve to show, somewhat nearly, the direction of the wind in all parts of the storm. The indicator C, shows the general course of the storm in the intertropical latitudes, which as the storm moves onward to the higher latitudes, changes gradually round to NE. and ultimately to nearly east. Thus, on the coast of the United States northward of Charleston or Cape Hatteras, the gale, on its central section, will begin from E. to SE. and its close, after the passage of its center, will be from the NW. quarter; for

W

WSW

wind N

wind NW

MS

wind W

wind S

wind Sw

ESE

SE

Diagram for north latitude.