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215. The Equinoctial, or Celestial Equator, is the great circle formed by extending the plane of the earth's equator until it intersects the celestial sphere. It is shown in the figure in the line EQW. The equinoctial intersects the horizon in E and W, its east and west points.
216. Hour Circles, Declination Circles, or Celestial Meridians are great circles of the celestial sphere passing through the poles; they are therefore secondary to the equinoctial, and may be formed by extending the planes of the respective terrestrial meridians until they intersect the celestial sphere. In the figure, PB, PS, PB', are hour circles, and that one, PS, which contains the zenith and is therefore formed by the extension of the terrestrial meridian of the observer, intersects the horizon in N and S, its north and south points.
217. Vertical Circles, or Circles of Altitude, are great circles of the celestial sphere which pass through the zenith and nadir; they are therefore secondary to the horizon. In the figure, ZH, WZE, NZS, are projections of such circles, which being at right angles to the plane of projection, appear as straight lines. The vertical circle NZS, which passes through the poles, coincides with the meridian of the observer. The vertical circle WZE, whose plane is at right angles to that of the meridian, intersects the horizon in its eastern and western points, and, therefore,
at the points of intersection of the equinoctial; this circle is distinguished as the Prime Vertical.
218. The Declination of any point in the celestial sjphere is its angular distance from the equmoctial, measured upon the hour or declination circle which passes through that point; it is designated as North or South according to the direction of the point from the equinoctial; it is customary to regard north declinations as positive (+), and south declinations as negative ( —). In the figure, DM is the declination of the point M. Declination upon the celestial sphere corresponds with latitude upon the earth.
219. The Polar Distance of any point is its angular distance from the pole (generally, the elevated pole of an observer), measured upon the hour or declination circle passing through the point; it must therefore
equal 90° minus the decimation, if measured from the pole of the same name as the declination, or 90° plus the declination, if measured from the pole of opposite name. The polar distance of the point M from the elevated pole P is PM.
220. The Altitude of any point in the celestial sphere is its angular distance from the horizon, measured upon the vertical circle passing through the point; it is regarded as positive when the body is on the same side of the horizon as the zemth. The altitude of the point M is HM.
221. The Zenith Distance of any point is its angular distance from the zenith, measured upon the vertical circle passing through the point; the zenith distance of any point which is above the horizon of an observer must therefore equal 90° minus the altitude. The zenith distance of M, in the figure, is ZM.
222. The Hour Angle of any point is the angle at the pole between tbe meridian of the observer and the hour circle passing through that point; it may also be regarded as the arc of the equinoctial intercepted between those circles. It is measured toward the west as a positive direction through the twenty-four hours, or 360 degrees, which constitute the interval between the successive returns to the meridian, due to the diurnal rotation of the earth, of any point in the celestial sphere. The hour angle of M is the angle QPD, or the arc QD.
223. The Azimuth of a point in the celestial sphere is the angle at the zenith between the meridian of the observer and the vertical circle passing through the
point; it may also be regarded as the arc of the horizon intercepted between those circles. It is measured from either the north or the south point of the horizon (usually that one of the same name as the elevated pole) to the east or west through 180°, and is named accordingly; as, N. 60° W.( or S. 120° W. The azimuth of M is the angle NZH, or the arc NH, from the north point, or the angle SZH, or the arc SH, from the south point of the horizon.
224. The Amplitude of a point is the angle at the zenith between the prime vertical and the vertical circle of the point; it is measured from the east or the west point of the horizon through 90°, as W. 30° N. It is closely allied with the azimuth and may always be deduced therefrom. In the figure, the amplitude of H is the angle WZH, or the arc WH. The amplitude is only used with reference to points in the horizon.
225. The Ecliptic is the great circle representing the path in which, by reason of the annual revolution of the earth, the sun appears to move in the celestial sphere; the plane of the ecliptic is inclined to that of the equinoctial at an angle of 23 27£', and this inclination is called the obliquity of the ecliptic. The ecliptic is represented by the great circle CVT.
226. The Equinoxes are those points at which the ecliptic and the equinoctial intersect, and when the sun occupies either of these positions the days and nights are of equal length throughout the earth. The Vernal Equinox is that one at which the sun appears to an observer on the earth when passing from southern to northern declination, and the Autumnal Equinox that one at which it appears when passing from northern to southern declination. The Vernal Equinox is also designated as the First Point of Aries, and is used as an origin for reckoning right ascension; it is indicated in the figure at V.
227. The Solstitial Points, or Solstices, are points of the ecliptic at a distance of 90° from the equinoxes, at which the sun attains its highest declination in each hemisphere. They are called respectively the Summer and the Winter Solstice, according to the season in which the sun appears to pass these points in its path. The Summer Solstice is indicated in the figure at U.
228. The Bight Ascension of a point is the angle at the pole between the hour circle of the point and that of the First Point of Aries; it may also be regarded as the arc of the equinoctial intercepted between those circles. It is measured from the First Point of Aries to the eastward as a positive direction, through twenty-four hours or 360 degrees. The right ascension of the point M' is VD'.
229. Celestial Latitude is measured to the north or south of the ecliptic upon great circles secondary thereto. Celestial Longitude is measured upon the ecliptic from the First Point oi Aries as an origin, being regarded as positive to the eastward throughout 360°.
230. Coordinates.—In order to define the position of a point in space, a system of lines, angles, or planes, or a combination of these, is used to refer it to some fixed line or plane adopted as the primitive; and the lines, angles, or planes by which it is thus referred are called coordinates.
231. In figure 30 is shown a system of rectilinear coordinates for a plane. A fixed line FE is chosen, and in it a definite point C, as the origin. Then the position of a point A is defined by CB = x, the distance from the origin, C, to the foot of a perpendicular let fall from A on FE; and by AB=y, the length of the perpendicular. The distance x is called the abscissa and y the ordinate. Assuming two intersecting right lines FE and HI as standard lines of reference, the location of the point A is defined by regarding the distances measured to the right hand of HI ana above FE as positive; those to the left hand of HI and below FE as negative.
An exemplification of this system is found in the chart, on which FE is represented by the equator, HI by the prime meridian; the coordinates x and y being the longitude and latitude of the point A.
232. The great circle is to the sphere what the straight fine is to the plane; hence, in order to define the position of a point on the surface of a sphere, some great circle must be selected as the primary, and some particular point of it as the origin. Thus, in figure 31, which represents the case of a sphere, some fixed great circle, CBQ, is selected as the axis and called the primary; and a point C is chosen as the
origin. Then to define the position of any point A, the abscissa x equals the distance from C to the point B, where the secondary great circle through A intersects the primary; the ordinate y equals the distance of A from the primary measured on the secondary"—that is, z = CB and y= AR.
233. In the case of the earth, the primary selected is the equator (its plane being perpendicular to the earth's axis), and upon this are measured the abscissae, while upon the secondaries to it are measured the ordinates of all points on the earth's surface. The initial point for reference on the equator is determined by the prime meridian Fhj. 3i. chosen, West longitudes and Nortb latitudes being called
positive. East longitudes and South latitudes, negative.
234. In the case of the celestial sphere, there are four systems of coordinates in use for defining the position of any point; these vary according to the circle adopted as the primaiy and the point used as an origin. They are as follows:
1. Altitude and azimuth.
2. Declination and hour angle.
3. Declination and right ascension.
4. Celestial latitude and longitude.
235. In the system of Altitude and Azimuth, the primary circle is the celestial horizon, the secondaries to which are the vertical circles, or circles of altitude. The horizon is intersected by the celestial meridian in its northern and southern points, of which one—usually that adjacent to the elevated pole—is selected as an origin for reckoning coordinates. The azimuth indicates in which vertical circle the point to be defined is found, and the altitude gives the position of the point in that circle. In figure 29 the point M is located, according to this system, by its azimuth NH and altitude HM.
236. In the system of Declination and Hour Angle, the primary circle is the equinoctial, the secondaries to which are the circles of declination, or hour circles. The point of origin is that point of intersection of the equinoctial and celestial meridian which is above the horizon. The hour angle indicates in which declination circle the point to be defined is found, and the declination gives the position of the point in that circle. In figure 29 the point M is located, according to this system, by its hour angle QD and declination DM.
237. In the system of Declination and Right Ascension, the primary and secondaries are the same as in the system just described, but the point of origin differs, being assumed to be at the First Point of Aries, or vernal equinox. The right ascension indicates in which declination circle the point to be denned may be found, and the declination gives the position in that circle. In figure 29 the point M' is located by VD', the right ascension, and D'M', the declination. It should be noted that this system differs from the preceding in that the position of a point is herein referred to a fixed point in the celestial sphere and is independent of the zenith of the observer as well as of the position of the earth in its diurnal motion, while, in the system of declination and hour angle, both of these are factors in determining the coordinates.
238. In the system of Celestial Latitude and Longitude, the primary circle is the ecliptic; the point of origin, the First Point of Aries. The method of reckoning by this system, which is of only slight importance in Nautical Astronomy, will appear from the definitions of celestial latitude and longitude already given (art. 229).
239. The sextant is an instrument for measuring the angle between two objects by bringing into coincidence at the eye of the observer rays of light received directly from the one and by reflection from the other, the measure being afforded by the inclination of the reflecting surfaces. By reason of its small dimensions, its accuracy, and, above all, the fact that it does not require a permanent or a stable mounting but is available for use under the conditions existing on shipboard, it is a most important instrument for the purposes of the navigator. While the sextant is not capable of the same degree of accuracy as fixed instruments, its measurements are sufficiently exact for navigation.
240. Description.—A usual form of the sextant is represented in figure 32. The frame is of brass or some similar alloy. The graduated arc, AA, generally of silver, is marked in appropriate divisions; in the finer sextants, each division represents 10', and the vernier affords a means of reading to 10". A wooden handle, H, is provided for holding the instrument. The index mirror, M, and horizon mirror, m, are of plate glass, and are silvered, though the upper half of the horizon glass is left plain to allow direct rays to pass through unobstructed. To give greater distinctness to the images, a small telescope, E, is placed in the line of sight; it is supported in a ring, K, which can be moved by a screw in a direction at right angles to the plane of the sextant, thus shifting the axis of the telescope, and therefore the plane of reflection; this plane, however, always remains parallel to that of the instrument, the motion of the telescope being intended merely to regulate the relative brightness of the direct and reflected image. In the ring, K, are small screws for the purpose of adjusting the telescope by making its axis parallel with the plane of the sextant. The vernier is carried on the end of an index bar pivoted beneath the index mirror, M, and thus travels along the graduated scale, affording a measure for any change of inclination of the index mirror; a reading glass, R, attached to the index bar and turning upon a pivot, S, facilitates the reading of vernier and scale. The index mirror, M, is attached to the head of the index bar, with its surf ace perpendicular to the plane of the instrument; an adjusting screw is fitted at the back to permit of adjustment to the perpendicular plane. The fixed glass m, half silvered and half plain, is called the horizon glass, as it is through this that the
horizon is observed in measuring altitudes of celestial bodies; it is provided with screws, by which its perpendicularity to the plane of the instrument may be adjusted. At P and Q are colored glasses of different shades, which may be used separately or in combination to protect the eye from the intense light of the sun. In order to observe with accuracy and make the images come precisely in contact, a tangent screw, B, is fixed to the mdex, by means of which the latter may be moved with greater precision than by hand; but this screw does not act until the index is fixed by the screw C at the back of the sextant; when the index is to be moved any considerable amount, the screw C is loosened; when it is brought near to its required position the screw must be tightened, and the index may then be moved gradually by the tangent screw.
Besides the telescope, E, the instrument is usually provided with an inverting telescope, I, and a tube without glasses, F; also, with a cap carrying colored glasses, which may be put on the eye end of the telescope, thus dispensing with the necessity for the use of the colored shades, P and Q, and eliminating any possible errors which might arise from nonparallelism of their surfaces.
The latest type of sextant furnished to the United States Navy is fitted with an endless tangent screw which carries a micrometer drum from which the seconds of arc are read. By pressure of the thumb the tangent screw is released and the index bar may be moved to any position on the arc by hand, where the tangent screw is again thrown into gear by releasing the pressure of the thumb. The endless tangent screw is accomplished by cutting the edge of the arc with the worm teeth into which the tangent screw gears. At night the reading of this sextant is facilitated by a small electric light carried on it and supplied by a battery contained in the handle.
241. The vernier is an attachment for facilitating the exact reading of the scale of a sextant, by which aliquot parts of the smallest divisions of the graduated scale are measured. The principle of the sextant vernier is identical with that of the barometer vernier, a complete description of which will be found in article 52, Chapter II. The arc of a sextant is usually divided into 120 or more parts, each division representing 1°; each of these degree divisions is further subdivided to an extent dependent upon the accuracy of reading of which the sextant is capable. In the instruments for finer work, the divisions of the scale correspond to 10 each, and the vernier covers a length corresponding to 59 such divisions, which is subdivided into 60 parts, thus permitting a reading of 10"; all sextants, however, are not so closely graduated.
Whatever the limits of subdivision, all sextants are fitted with verniers which contain one more division than the length of scale covered, and in which, therefore, scale-readings and vernier-readings increase in the same direction—toward the left
hand. To read any sextant, it is merely necessary to observe the scale division next F below, or to the right of, the zero of the ~ vernier, and to add thereto the angle corresponding^ to that division of the vernier scale which is most nearly in exact coincidence with a division of the instrument scale.
242. Optical Principle.—When a ray of light is reflected from a plane surface, the angle of incidence is equal to the angle of reflection. From this it may be proved Ui .... that when a ray of light undergoes two
reflections in the same plane the angle between its first and its last direction is equal to twice the inclination of the reflecting surfaces. Upon this fact the construction of the sextant is based.
In figure 33, let B and C represent respectively the index mirror and horizon mirror of a sextant; draw EF perpendicular to B, and CF perpendicular to C; then the angle CFB represents the inclination of the two mirrors. Suppose a ray to proceed from A and undergo reflection at B and at C7 its last direction being CD; then ADC is the angle between its first and last directions, and we desire to prove that ADC = 2 CFB.