to be N.N.W. W.; which, therefore, is the course which a ship must steer by compass from Scilly to Cape Clear, provided the variation be as above. Example 2. Required the course, per compass, from Port Royal, Jamaica, to Santa Martha, Columbia; the true course being S. 21:42: E., or S.S.E. nearly, and the variation about half a point easterly? Solution.-The variation a point, being allowed to the left hand of the true course, because it is easterly, shows the magnetic course to be S.S.E.E.; which, therefore, is the course which a ship must steer by compass from Port Royal to Santa Martha, provided the variation be as above, and independent of currents. PROBLEM VI. Given the Magnetic Course, or that steered by Compass, and the RULE. If the variation be westerly, it is to be allowed to the left hand of the course steered by compass; but if easterly, to the right hand in either case, the true course will be obtained. Example 1. : Let the magnetic, or course steered by compass, be E. by N. N., and the variation 1 point westerly; required the true course? Solution. The variation 1 point, being allowed to the left hand of the compass course, because it is west, shows the true course to be N.E. by E. E. Example 2. Let the course steered by compass be N.W. W., and the variation one point and three-quarters easterly; required the true course? Solution. The variation 1 point, being allowed to the right hand of the magnetic or compass course, because it is easterly, shows the true course to be N.W. by N. P P AZIMUTH COMPASS; The card being graduated on an improved principle, so as to be more particularly adapted to the taking of amplitudes and azimuths, the measuring of horizontal angles, &c. &c.; being thus rendered far more applicable to nautical purposes in general than that which is now in common use at sea. The azimuth compass, as well as the mariner's compass, is an aṛtificial representation of the horizon of any place on the terrestrial globe: it consists of a circular card, divided into 32 equal parts, called points or rhumbs; and, since the circle contains 360°, each point is equal to 11:15: for 360: ÷ 32 = 11:15'.* The four principal points of the compass, viz., N., E., S., and W., are called cardinal points; the others are compounded of these, and are named according to the quarter in which they are situated. To the under side of the card, and in the direction of its north and south line, a bar of hardened steel is attached, called the NEEDLE, which, being touched by a load-stone, acquires the peculiar property of pointing north and south, and thus directs the different points on the card to the correspondent points of the horizon. In the centre of the needle there is a small socket, by means of which it is placed, with its attached card, on an upright pin called the pivot or supporter, which is fixed in the bottom of a circular or conical brass box: on this pin the needle turns freely, and, by its magnetic property, the several points of the compass card keep always in the same direction, very nearly; though these do not always indicate the true correspondent points of the horizon, because of the aberration which the needle suffers, owing to that secret, and unknown agency which causes its north and south poles to deviate more or less from the respective correspondent poles of the world. However, since the compass is an instrument with which mariners are well acquainted, it is not deemed necessary, in this place, to enter any farther into its description. Hence, I shall merely point out some of the many advantages which a compass card, graduated on the above principle, possesses over those now in general use at sea. In this card, the circular ring of silvered brass is to be sufficiently broad to admit of four concentric spaces. The outer edge of the ring is to be graduated, mathematically correct, to every 20th minute of a degree * Table XXXIII. contains the different angles which every point and quarter-point of the compass makes with the meridian; and Table XXXIV. contains the logarithmic sinea, tangents, and secants of every point and quarter-point of the compass. (though, for want of room, the present card is only graduated to every 30th minute of a degree), to which a vernier is to be adapted, containing 20 divisions on each side of its nonius, for the purpose of subdividing the divisions on the card into minutes of a degree. The interior surface of the vernier should be ground concave to the segment of a circle, whose radius is equal to that of the card. The remote edge of the inner concentric space, on the silvered brass flat ring, may be graduated similarly to that of the outer edge, so as to render it more convenient in reading off amplitudes, according as they may be reckoned from the prime vertical, or from the meridian. The first space on the broad ring of silvered brass, viz., that next the points of the compass, is particularly adapted to taking amplitudes, when the observations are reckoned from the east or the west points of the horizon; and, therefore, it is numbered both ways, from those points, towards the meridian: that is, from 0 to 90:. The second space being adapted to horizontal azimuths, viz., to amplitudes reckoned from the meridian, is therefore numbered both ways, from the north and south points of the horizon towards the east and west points thereof: that is, from 0 to 90:, in a contrary order to the last. The third space is intended for the accommodation of an azimuth when the observation is reckoned from the south in north latitude, or from the south in south latitude: hence, it is numbered both ways from the south to the north point of the compass, or from 0 to 180:. The fourth, or outer space, is designed for azimuths reckoned from the north in north latitude, or from the north in south latitude, according to the will of the observer; and, therefore, it is numbered both ways from the north to the south, or from 0 to 180°, &c.-See the Frontispiece to this volume. Besides the evident uses of a compass card, graduated after this manner, in observing amplitudes and azimuths, it will also be found of the greatest utility in taking correct surveys of coasts and harbours, and in settling the true positions of places on shore from a known position at sea. It may, moreover, be applied successfully to many astronomical purposes; nay, it may even be applied to the determination of the longitude by lunar observations, as thus :-Let two observers, with two good compasses of the above description, take the azimuths of the moon and sun, or a fixed star, &c., at the same instant; then, if those two azimuths be reckoned from the same point of the horizon, their sum, subtracted from 360, will be the angle at the zenith compréhended between the zenith distances of the objects; with which, and the true zenith distances of the objects, the true central distance may be found by oblique-angled spherical trigonometry, Problem III., Remark 1 or 2, page 203 or 204; and, hence, the longitude of the place of observation, by Problem XXX., page 383. An azimuth compass of this description would be of real advantage to the practical navigator; whereas, the one now in common use at sea is so very ill adapted to the important purposes for which it is designed, that it is very seldom resorted to for those purposes; and, therefore, it is scarcely ever seen upon deck, except for the simple purpose of comparing its parallelism with that of the binnacle, or steering compass. SOLUTION OF PROBLEMS relative to finding the Latitudes and Longitudes, Right Ascensions and Declinations of the Heavenly Bodies, and to the computing of the Central Distances between the Moon and Sun, a fixed Star, or a Planet. PROBLEM I. Given the Right Ascension and Declination of a Celestial Object, to find its Latitude and Longitude. Example. The apparent right ascension of a Arietis, August 1st, 1825, was 15723'. 176, and its declination 22:38:4′′. 44 north; required its apparent latitude and longitude, the obliquity of the ecliptic being 23:27:42".875? « Arietis, right ascen. =157"23'. 176, in degrees =29:20:47′′.64, and north polar distance =67:21:55". 56. CONSTRUCTION. Describe the pri mitive circle PESQ, tangent of its com E plement, viz., 67:21:55",56, describe the parallel of declination a b.— Take the star's right ascension, viz., 29:20:47". 64, in the compasses, from the scale of semi-tangents, and lay it off on the Equator from to R, and with the secant of its complement, viz. 60:39:12". 36, describe the circle of right ascension PRS; the intersection of which with the parallel circle a b, at *, will be the apparent place of the star in the heavens. Make PN, SO=23:27:42". 875 the obliquity of the ecliptic: -draw the polar line N O, and, at right angles thereto, the ecliptic line through the intersecting point, draw the circle of longitude NO, cutting the ecliptic in L;-then, the arc L, will be the longitude of the star, and the arc L*, its latitude; the former being taken in the compasses, and applied to the scale of semi-tangents, will be found to measure about 35 degrees :-the angle PN * (measured by the arc L=54 degrees), represents the co-longitude of the star, and the arc N its co-latitude; the latter being reduced to the primitive circle will be found to measure about 80 degrees. : = Now, in the oblique angled spherical triangle P N*, given the side PN=23:27:42". 875, the obliquity of the ecliptic; the side P* 67:21:55". 56, the star's north polar distance, and the included angle NP119:20:47". 24; to find the side N the co-latitude of the star, or its distance from the north pole of the ecliptic, and the angle PN its co-longitude. = Note. The circle of right ascension which passes through, viz., PQS, is always equal to, or expressed by 270 degrees; and that which passes through v, or, by 0, or 360 degrees; the difference, therefore, between y and, or, which is the same, between Q and y, is 90 degrees; which being added to the arc v R, 29:20:47′′.64, makes the whole arc Q R=119:20:47". 64, which is the true measure of the angle R P Q; that is, the angle N P *, comprehended between the two given sides. Hence, by spherical trigonometry, Problem III., Remark 1, p. 203, An.NP 119:20:47". 64+2=59:40:23.82tw.L.si. 19.8721827.68 Side PN obl. of the ecliptic= 23. 27. 42 .875 L.si. 9.6000350.88 Side P star's N. polar dist. = 67.21.55 .56 L.si. 9.9651914. 48 |