lower circle, that is, from the celestial equator. On this account the upper circle is called the declination-circle. Supposing also the zero point of graduation of the lower circle to be that marked by the index when the telescope is directed to the meridian, the reading of the lower circle will give the angular distance of the star from the meridian at the time of observation, measured along the celestial equator. This angle will be the same as that between the meridian and the declination-circle of the star. It is commonly called the hour-angle of the star, and the circle on which it is measured is called the hour-circle. Let P be the pole, EQ the celestial equator, S a star. The equatoreal gives the arcs SM and EM, the former of which is the declination, and the latter is equal to the angle EPM, included between PE the meridian, and PS the declination-circle of the star. E M EPM is called the hour-angle, because whatever part it is of 360°, the same part of 24 hours is the time of S from the meridian, that is, the time S will take in getting to the meridian, or the time by which it has passed the meridian, according as it is on the east or the west of the meridian at the time of observation. In practice the equatoreal is not much used for accurate determinations of declinations and hour-angles, which may be more certainly made by other methods. Its chief use is in giving approximate positions of bodies observed out of the meridian, and in such observations as occupy any considerable time, as those of double stars by micrometers; for by turning the telescope about the polar axis, which is parallel to that of the diurnal motion of the heavens, a star may be kept continually in the field of view, the space commanded by the telescope in its revolution being in fact the star's diurnal path. In the case of large instruments the telescope is made to move in this manner by clockwork, properly regulated, so that the observer may devote his whole attention to micrometrical measurements, or whatever other object he may have in view. 49. Hadley's Sextant. From the preceding descriptions it is evident that the instruments which have hitherto occupied our attention depend for their efficiency on the firmness of their supports, without which all modes of adjustment would be vain. Such instruments, therefore, are inapplicable to a very large and important class of observations, namely those made at sea. In fact, the roughest determination of the position of the observer by means of the heavenly bodies, would be perfectly hopeless except in the calmest weather, if we had no instruments to depend on excepting such as have been already described. The instrument of which a representation is subjoined is found completely to answer all nautical purposes. It is called by the name of its reputed inventor, Hadley, but we have Sir J. Herschel's authority for ascribing it to Newton.* It consists of a strong frame in the form of a sector of a circle, including, as the name imports, one-sixth of the circumference. The two extreme radii are firmly braced together, as represented in the figure. A moveable radius, having a vernier at its extremity to read off the divisions on the arc, carries a small mirror called the index-glass, which stands upon it at right angles to the plane of the instrument, and in such a position as to be bisected by the axis of revolution produced. On the extreme radius, and facing the index-glass, is fixed the horizon-glass, which is half silvered, the other half being left so that objects may be seen through it. It is of about the same size as the index-glass, and is fixed in such a manner that it is parallel to the index-glass when the index is at the opposite extremity of the arc. Its plane is therefore perpendicular to that of the instrument, and nearly parallel to the extreme radius on the other side. A telescope is so fixed that its line of collimation passes through the centre of the horizon-glass, meeting its surface at the same angle as the line drawn from the same point to the centre of the index-glass. Hence a ray of light reflected from * Outlines of Astronomy, p. 115. the centre of the index-glass to that of the horizon-glass is again reflected along the line of collimation of the telescope. In the accompanying figure, I is the index-glass, H the horizon-glass, T the telescope, and V the vernier-index. The object of the instrument is to measure the angle between two distant objects. Let S be such an object. If the light from S fall upon the index-glass at I in such a way that the lines SI and HI make equal angles with the surface, it will be reflected at I and H, and will emerge from the horizon-glass in the direction of the line of collimation of the telescope, so that an image of S will be seen through the telescope by reflection at the silvered part of the horizon-glass. Since there have been two reflections, the deviation of the course of the light, that is the angle which the line of collimation makes with SI, is double the angle of inclination of the mirrors. And if another object S' be at the same time in the line of collimation produced, the angle between IS and HS', or between the directions of S and S', is twice the angle of inclination of the mirrors. Therefore, if the observer can bring the image of S, seen by reflection at I and H, to coincidence with that of S' seen directly, which may be done just at the common edge of the silvered and unsilvered parts of the horizon-glass, he may conclude that the angular interval between S and S' is twice the angle by which the index-glass is inclined to the horizon-glass. If then the limb be so graduated that every division of one degree shall count for two, and the zero point be that marked by the index when the index-glass and horizon-glass are parallel, the vernier will give the exact angular interval required; for the arc passed over by the index is the measure of the angle through which the index-glass revolves. In this way a sextant is capable of measuring an angle of 120°. It is obvious that when the index-glass is parallel to the horizon-glass, there is no deviation, or SI is parallel to the line of collimation. Hence, when the index is at zero, the image of S seen by reflection ought to coincide with that seen directly through the unsilvered part of the horizon-glass, (S being a distant object, and therefore its direction from H being the same as from I). This gives an easy test of the right adjustment of the instrument. The horizon-glass is furnished with a screw by which it may be turned on its axis through a small angle, and so may be brought to parallelism with the index-glass when the index marks zero. In practice, however, it is usual to bring the direct and reflected images of some well-defined object to coincidence by moving the index only, and then to observe the reading of the limb, which may be applied as a correction to the angles afterwards observed. This is called the index-error, and must be added to or subtracted from the angles afterwards observed, according as the index was behind or before the zero point at the time of coincidence of the images. In this way the angle between two stars may be observed, or the angle between the moon and a star, the image of the moon's limb as seen by reflection being made to touch the direct image of the star. The latter observation, as will afterwards appear, is of great use in navigation. The principal use, however, of the sextant at sea is in taking altitudes, the reflected image of the observed body being brought into contact with the sea-line or offing seen through the unsilvered part of the objectglass. The following is the usual mode of finding the altitude of a star. The observer holding the sextant in his right hand, with its plane vertical, directs the telescope to the star, the index being in such a position that the mirrors are parallel. The reflected image therefore coincides with that seen by direct vision. The observer then moves the index gradually forward with his left hand, causing the reflected image to leave the direct image, and, by the principle of the instrument, to descend through twice the angle described by the index. The observer follows the image in its descent by gradually lowering the telescope until at last the sea-line appears in the field of view. If the plane of the instrument were accurately vertical, it would be sufficient to bring the star into coincidence with the middle point of the sea-line in the horizon-glass, and then the observed angle would be the altitude of the star above the visible horizon: but if the plane of the instrument be not vertical the observed angle will be too great, the distance of the star from the point in the offing vertically below it being less than its distance from any other point. Thus, if S be the star, AB the sea-line, it would not do to observe the distance of S from any point P in the offing, the altitude required being SD, where the arc SD is perpen- A dicular to AB. Р D P B There is, however, a very easy practical method of determining the right altitude. If the plane of the instrument be turned through any angle, without altering the inclination of the index-glass to the direction of the star, or moving the index, the reflected image of the star will still remain visible, and will appear to describe a circular arc, since it is always at the same angular distance from the star itself. This kind of motion is easily communicated to the instrument with the hand; and if the index be moved |