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gree: this is, however, what is termed in common conversation the distance as the crow flies.
On Leeway, and Plying to Windward. (55.) WHEN a ship is sailing near to the point from whence the wind blows, a considerable part of the force of the wind is employed in driving her away from that point, or to leeward; but as this action of the wind cannot turn the head of the ship round, or alter her apparent course, the effect produced is a continual drifting of the vessel from the wind with the head still turned in the same direction as if no drifting took place, and consequently the compass showing the same course: but if the ship drifts in this manner, her keel will make a track or wake in the water in a direction opposite to the point towards which she is really moving. Let therefore the figure of a compass be drawn on the stern of the ship, and so placed that the line joining the north and south points of the card shall be in the direction of the keel, or the fore and aft line of the ship; the angle included between this line and the wake is the difference between the ship's apparent and her true course by compass, and is called the leeway: this leeway therefore is always to be allowed for from the wind; that is, if a ship is steering WNW, with the wind at north, the leeway is reckoned to the left of WNW from the wind; and if in this case the angle, or leeway, is found to be two points, the ship's true compass course is due west.
The only method that ought to be relied on in practice of ascertaining the amount of this correction of the apparent course of a ship, is that of actually measuring the angle formed as before mentioned; which angle is in fact the bearing of the wake by the fixed compass: means therefore should be devised for enabling the proper officer to take such a bearing with correctness, and in this respect practical navigation seems to be deficient.
(56.) There are few large vessels that can lie within less than six points of the wind; and therefore, when the wind blows from any point within six points of the bearing of a port for which a vessel is bound, she must tack or ply to windward; that is, she must steer a course as near to the bearing of the port as the wind and other circumstances will admit of, and
she must steer that course, until the bearing of her port is altered so as to become a course, which the direction of the wind will allow her to steer. Suppose, for instance, a ship is bound to a place bearing E, but the wind is ENE, that is, two points from the bearing of her port; the ship's course must be SE or N; for these courses are respectively six points from the direction of the wind, and are, therefore, nearer to the bearing of the port than any other courses which the ship can describe; and the ship, supposing the wind to remain in the same quarter, must sail SE, until the bearing of her port becomes from the alteration of her place due N, or N till it becomes S; and then she must tack and steer N or SE, according as her first course has been SE or N; but if it should be more convenient so to do, the ship may make a great number of tacks, or SE and N courses, before she arrives at her port; and the whole distance sailed will not be greater in this case than in the other.
On Nautical Astronomy.
(57.) THE two first Parts of this treatise have shown, how the situation of a ship on the surface of the globe may be found by a reckoning kept on board of the courses steered, and the number of miles sailed on each course. We have supposed, however, the errors of the compass to be known, and it will be necessary therefore hereafter to point out how they may be found.
The object of the third Part is to explain, how the relative angular posi tions of the celestial bodies, with respect to each other, and the horizon and meridian of any place, enable the mariner to determine the situation of that place, and thus correct the errors of the reckoning. So that these two different methods serve as a check upon each other, and have together been found amply sufficient for all the purposes of the practical navigator.
That part of the heavens which is visible to us, and in which the celestial bodies appear, is in the shape of a hollow hemisphere; and it will facilitate greatly the comprehension of nautical astronomy, if we imagine the earth placed in the centre of a hollow glass sphere, which has the heavenly bodies exhibited on its surface;-that the earth,
instead of revolving round its axis every twenty-four hours from West to East, remains at rest; and that the hollow glass sphere with the heavenly bodies upon it revolves uniformly round the earth in the same time from East to West: the suppositions we have made will accurately represent the diurnal motions of those heavenly bodies: the axis round which the hollow sphere revolves is the axis of the earth produced from each of its extremities till it meets the sphere: let us imagine great circles traced out on the hollow sphere corresponding with and opposite to the great circles of the earth already described; corresponding to the equator, let there be a celestial equator; corresponding to the meridians, celestial meridians; corresponding to the poles, poles of the heavens at the extremities of the axis of the sphere; let the parallels also be represented in the same manner if the circular plane of the equator of the earth were to be enlarged and extended so as to reach the glass sphere, then should its circumference coincide with the celestial equator traced out upon that sphere, and the same observation applies to all the other circles above described; and it is in this sense, therefore, that we use the term corresponding. If a straight line joining the earth's centre, and any place on the earth's surface, be produced until it meet the hollow glass sphere, the point at which it meets that sphere is called the zenith of that place; and as the sphere revolves, every point of it which successively touches the extremity of that line will successively become a zenith to the place; and stars on the sphere, which in succession pass that line, will be said to pass over the zenith of the place. The celestial meridians are called circles of declination: for the arc of a celestial meridian intercepted between any heavenly body and the celestial equator is not called its latitude, but its declination.
As each celestial meridian is brought in succession opposite to the terrestrial meridian of any place, by the revolution of the sphere, it acquires the name of the celestial meridian of that place.
Great circles drawn on the hollow sphere passing through the zenith of any place, are called vertical circles; and that particular vertical circle which passes through the East and West points is called the prime vertical; the angle contained between a vertical circle pass
ing through a heavenly body and the
But though the sun may not have
those meridians contain at the terrestrial; but those celestial meridians contain the hour angle of the sun from the meridian of a, as appears from the definition of an hour angle; therefore the two angles are one and the same angle: if the mariner at e, therefore, be possessed of a watch, which shows the hour angle at a, or what o'clock it is at a, and he have the means also of ascertaining at the same instant of time what o'clock it is at e, he can thus determine the arc A E, or the longitude of e; and it is evident also that any other means of ascertaining what o'clock it is at a, besides a watch, would answer the same purpose. Suppose that the ma
zenith of a place passes through its the straight line which determines the
riner knew that at twelve o'clock at night circles of declination, which by the revoata, two heavenly bodies, whose distance lution of the sphere come in succession from each other is continually varying, would be found at a certain distance from opposite to the meridian of e. each other, say 30°, on a particular day; suppose that on that day at the spot e he watches those heavenly bodies, and ascertains them to be 30° of the arc of a great circle, drawn on the hollow sphere, distant from each other; then let him ascertain the time at e, if he finds that time to be three o'clock in the morning, as three hours difference in time answer to 45° of an hour angle, he may thence conclude, that he is situated at a spot 45° east of Greenwich. The moon is one of those heavenly bodies, which is continually changing its place on the surface of our sphere, moving from some fixed stars and towards others; it seems to revolve rapidly round the sphere from west to east in a great circle, which makes an angle of about 28° with the equator: the sun seems to move also, but not so rapidly, from west to east, and the great circle he seems to trace out is called the ecliptic, making an angle of about 23° with the equator. Now the distances of the moon from the sun and nine principal fixed stars near to her apparent path, are, in fact, computed and set down in the Nautical Almanac, as they would appear at the centre of the earth every three hours of Greenwich time, on those days when the moon is visible; and these distances therefore may be found for any other time at Greenwich by allowing a proportional difference. This mode of ascertaining the longitude by measuring these dis
tances is called the lunar method.
(58.) Let the circle HEZPHQ(fig. 12.) represent one of the great circles of our glass sphere; let it represent the celestial meridian of the place e in fig. 7, that is, it represents in succession all those
meridian, and lies also in the circular plane of its meridian, the circular plane itself extended, or the celestial meridian, must pass through its zenith. Let Z be the zenith of e, let P be the north pole of the sphere, and ECQ the celestial equator, then Z D and Z d are arcs of vertical circles; ifs be the sun, then the angle HZ & represents his azimuth, and 8 PE his hour angle from the meridian of e, or the time before noon at e; if m be the moon, ms may represent the distance between the moon and the sun measured on the arc of a great circle m s, also HDCH' represents the rational horizon of e. Let M and S, also, be two places of the moon and sun; then Sd and M D are called the altitudes of the sun and moon; they are the arcs of vertical circles intercepted between those heavenly bodies and the rational horizon: but we can have no means of measuring how high a celestial object is above that horizon; we can ascertain it, however, by measuring its height above the sensible horizon, and adding a correction to that altitude for the difference between its heights above the two horizons; this correction is called parallax.
corrections to be applied to the observed Besides parallax, there are two more altitudes of heavenly bodies; these are first refraction, which is to be subtracted from those altitudes; for it is the raised above the sensible horizon, in quantity which heavenly bodies appear consequence of their light having to pass
When the eye is in the plane of a circle it appears a straight line.
through the atmosphere of the earth before it reaches us; and 2ndly the dip :the dip is a correction rendered necessary by the peculiar nature of the instruments with which arcs of the great circles of the concave sphere are mea sured at sea; these instruments are called quadrants or sextants: the dip is also to be subtracted from the observed altitudes, for it is occasioned by the circumstance of the eye of theobserver being elevated above the plane of the sensible horizon, from which altitudes are measured by the sextant. In the case of the moon the parallax is greater than the refraction and dip together; in the case of the other heavenly bodies, it is less. Thus the moon appears lower than its true place, while the others, on the contrary, appear higher; therefore m and s may represent the true places of the moon and sun respectively, and M and S the apparent places; then m P and s P will be the complements of the declinations of those two bodies: the distance ms, or true distance at the centre of the earth, is not equal to MS the apparent distance. Pms, MZ S, &c. represent spherical triangles, (Art. 35,) drawn on the concave surface of the heavenly sphere, and if three parts of such triangles be given, the other three can be found. The fixed stars have no parallax, they are found to be at so great a distance from the earth, that the radius of the earth is a mere point compared with that distance.
When we speak of the altitudes of such heavenly bodies as the sun and moon, or their distances, we mean the altitudes or distances of their centres; but altitudes or distances of their limbs can always be converted into altitudes or distances of their centres, by means of the values of their semidiameters given in the Nautical Almanac.
(59.) The latitude of a place e, or its distance from the equator, measured on its meridian, must be equal to the distance of its zenith from the celestial equator, or Z E, for they are corresponding arcs of circles, (Art. 1.) Let B be a heavenly body on the meridian of e, whose declination is given in the Nautical Almanac; let the mariner at e obtain its true altitude B H, by observing its altitude above the sensible horizon, and making the proper allowances for parallax, &c.; let him look for the value of B E, or the declination, in that almanac, and add it to B H, this will give the arc E H, which is the comple
ment of E Z, the latitude. If B had been to the north of the equator, or had had north declination, the declination must have been subtracted; this is the most usual mode of finding the latitude by observation at sea. There is another, however, which remains to be explained; lets and m be two places of the sun before noon; obtain from observation the two altitudes s d, m D, and consequently the complements of those altitudes, called zenith distances, Zs and Zm; note also the time which elapses between the two observations, which will be the angle m P s, then in the spherical triangle m Ps, m P, and s P, the complements of the sun's declination are given by the Nautical Almanac, and the included angle m P s is given, making together three parts, therefore the other parts may be found; that is, the angle Pm s, and the side m s may be found; then in the triangle Z m s, all the three sides are given to find the angle Zms; take away the known angle Pms, from the known angle Z m s, and the angle Z m P remains, which is therefore known; then in the triangle Z m P, m Z and m P are known, and the included angle Z m P, to find the side Z P, which also equals the complement of the latitude. If the ship changes her latitude, as well as place, in the interval between the two observations, a correction is applied, for the difference of latitude made during that interval.
(60.) Suppose the latitude known, and that we wish to find the hour angle ZP s, for the purpose of obtaining the time at e, and also the azimuth & Z H; obtain s Z from observation, as before, and s P by means of the Nautical Almanac; then in the triangle Z s P, all the three sides are given to find the angle Z Ps, which is the hour angle, and the angle s Z P, which is the azimuth from H', and the supplement of the azimuth from H; but the azimuth of the sun, or any other object, is its true bearing from the true meridian of a place; for the true bearing of an object, s, is evidently measured by the arc H d, which measures the angle s Z H. If this true bearing be compared with the bearing by compass, the difference will be the variation of the compass.
(61.) This variation of the compass is the result of a slow progressive alteration of the position of the needle, with respect to the true meridian. It is observed to move towards the west, until it arrives at its maximum on that side;
it then returns, passes over the true meri dian, and moves easterly, until it arrives at its maximum, towards the east, it then returns as before. In the year 1660, in London, the needle pointed to the true north, since which time it has travelled about 24 to the westward, and has lately begun to return. The variation, however, is very different in different parts of the globe, and must, therefore, be determined at sea, by comparing the true bearing of a celestial object with its bearing by compass. For the purpose of taking these magnetic bearings, a particular kind of compass is employed, called an azimuth compass: sometimes the angular distance of the sun from the prime vertical is observed with these compasses when he rises or sets, which is called his amplitude; and then his true distance is computed, and compared with the observed: this is another mode of finding the variation.
(62.) Suppose the latitude of e to be known, and that the longitude is required; then if we suppose M and S to represent the apparent places of the moon and sun, and m and s the true; we can obtain M Z and S Z, by observation as before, and also M S the apparent distance; therefore in the triangle M Z S, the three sides will be given to find the angle MZ S; then in the triangle m Zs, the angle m Zs will be known, and also m Z and s Z, (for they are the zenith distances corrected for parallax, refraction, &c.) therefore m s, which is the true distance, may be
Having found the true distance, and the time at e by Article 60, find out by the Nautical Almanac, at what time at Greenwich the moon and sun are at the true distance m s from each other that day; this time will be the time at Greenwich; and having the corresponding time at e, the longitude is known, (Art.57.) The reader must not, however, imagine that in finding his latitude, variation, time, and longitude, by observation, the mariner is actually compelled in practice to perform all the troublesome calculations
we have adverted to, and to resolve all these different triangles by the rules of spherical trigonometry: for various ingenious devices and contrivances have from time to time been invented by scientific men, for the purpose of shortening his labour, and comprising within a small volume all the requisite tables:-A more useful application of great learning and talents cannot well be imagined, and too much praise can scarcely be awarded to the exertions of those, who are willing to devote their time to the laudable object of devising means of imparting their knowledge to others, comparatively unlearned; and the rather as the task of instruction has never yet been enumerated among the pleasures of science.
We have supposed the circles, on which the altitudes, distances, &c. of heavenly bodies are measured, to be drawn on the concave surface of a hollow glass sphere revolving round the earth: it is evident, however, that the same phenomena will take place, and the same investigations will apply, if the earth be supposed to revolve from west to east every twenty-four hours, and all the heavenly bodies, except the sun and planets, to be at rest. We may likewise suppose the circles that have been defined, to be traced out in the heavens themselves.
(63.) The deviation of the compass was first observed by Mr. Wales, the astronomer of Capt. Čook: it is occasioned by the iron on board a ship attracting the compass. A simple and ingenious method of discovering the amount of this deviation, has been invented by Mr. Barlow of the Royal Military Academy.
Fig. 13 represents a vessel, her com. pass is represented at C. Now it is found that there is a point in which the whole action of the iron of a ship is concentrated, it is called the centre of attraction: let p be this point. When the head of the ship is directed towards the magnetic north, then, if the iron is equally distributed on each side of the compass, it 13.