QUADRANT AND SEXTANT. 200. The Quadrant and Sextant* are reflecting astronomical instruments for measuring angles, and are the instruments chiefly in use for taking the observations required for the solution of a number of the most useful problems in navigation, such as to find the time, the latitude and longitude of a place. The Quadrant contains an arc of 45° in real extent, and measures a few degrees more than 90°;† it is usually of wood, and the graduated arc, which is ivory, reads to minutes, and sometimes to 30". The Sextant is constructed on the same principles as the quadrant; has a graduated limb of more than 60° in real extent; and furnishes the means of measuring the angle between two objects in whatever direction they may be placed, so that the angle does not exceed 140°. The quadrant serves for common purposes at sea; but the sextant is used when considerable precision is required, as, for instance, in taking a lunar observation. 201. The form of a sextant, as at present in common use, consists of a single frame of brass, so constructed as to combine strength with lightness; and in others a double frame connected by pillars (see Fig., page 278). The graduated arc, inlaid in the brass, is usually of silver, sometimes of gold, or platinum. The explanation of the parts of a sextant, and of the adjustments of that instrument, will answer for the quadrant, since the parts and appendages are common to both. 202. The flat surface of the sextant is called the plane of the sextant; the circular part B C is the arc or limb, which is graduated from right to left from the zero point 0° to about 140°, and each degree in the best instruments is again sub-divided into six equal parts of 10' each, while the vernier g, used in estimating the sub-divisions of the arc, shows 10". The divisions are also continued a short distance in the opposite direction on the other side of zero (O), towards C, forming what is termed the arc of excess, for the purpose of determining the index error in the manner that will be subsequently explained. The microscope M, and its reflector r, secured at the point d by a movable arm dr to the index bar A E, may be adjusted to read off the divisions on the graduated limb and the vernier g. AE is the radius, or index bar, movable along the arc and round a centre, and having a dividing scale (called the vernier) close to the arc, by which the sub-divisions of the arc are read off. The index bar is secured to the arc B C by the intervention of a mill-headed clamp screws at its back, which must be loosened when the index has to be moved any considerable distance, and when the contact nearly has been made The first inventor of the sextant (or quadrant) was NEWTON, among whose papers a description of such an instrument was found after his death, not, however, until after its re-invention by THOMAS GODFRAY, of Philadelphia, in 1730, and perhaps by HADLEY in 1731. + This depends on the properties of light, which we cannot consider here. The principle of the sextant is this: the angle between the first and last direction of a ray which has suffered two reflections in one plane is equal to twice the inclination of the reflecting surfaces to each other. by hand, the screw is again to be fixed, and a tangent screw & enables the index bar and the vernier* upon it to be moved by a small quantity along the limb, so as to render the contact of the objects observed more perfect than could be effected by moving the index solely by hand; the other extremity of the index bar has a silvered glass or reflector, I, fixed perpendicular to the plane of the instrument, with its face parallel to the length of the index bar, and directly over the centre; another glass, b, is fixed perpendicular to the Fig. 61. plane of the instrument frame H, and facing the index-glass, the lower half only is silvered (being a reflector), and the upper transparent; it is usually provided with screws, by which its position with respect to the plane of the sextant may be rectified; the plane of this glass, usually termed the horizonglass, is made parallel to the plane of index-glass I, when the vernier g is adjusted to zero on the divided arc BC, or if not so made, the want of parallelism constitutes what is termed the index error of the instrument. The telescope t is carried by a ring fastened to a stem E, which can be raised or lowered by a mill-headed screw s" at the back of the frame, for the purpose of so placing the field of the telescope that it may be bisected by the line on the horizon-glass, separating the silvered from the unsilvered part, whereby the brightness of the reflected object and that seen by direct vision may be made equal, and the quality of the observations improved; the ring and its elevating apparatus are technically known as an "up-and-down piece." It is usual to supply a direct and inverting telescope, of which the latter is to VERNIER-SO called after its inventor, PETER VERNIER, of France, who lived about 1630. By some it is called a nonius after the Portugese, NUNEN or NONIUS; but the invention of the latter (who died in 1577) was quite different. be preferred, as possessing greater magnifying power, and thus showing a better contact of the images of the objects. Two wires parallel to each other, and to the plane of the instrument, are placed in the inverting telescope, within which limit the observation should be made. In the quadrant the telescope is omitted, and the eye is applied to a small circular orifice in a piece of brass, placed in the same position as the telescope in the drawing. Dark glasses of different colours and shades are a necessary accompaniment to the sextant to enable the sun to be observed, and they are usually attached to a hinged joint at K. Four of these glasses or shades are placed at a, between the index and horizon-glasses, so as to admit of one or more of them being interposed between the index and horizon-glass, to moderate the light of any brilliant object seen by reflection. Three more such glasses, sometimes called back shades, are placed behind the horizon-glass at K, any one or more of which can also be turned down to moderate the intensity of the light before meeting the eye when observing a bright object, such as the sun. There is also a dark glass which can be placed at the eye-end, t, of the telescope, which method is preferable to the other, as no error in this is liable to be introduced in the passage of the rays from the index to the horizonglass.* When observing, the instrument is to be held with one hand by the handle P placed at the back of the frame, while the other hand moves the index. 203. Reading off the Angle.-The following brief directions for reading off will be more readily understood by the learner, if he place a sextant before him for reference and examination. It will be seen that the arc (limb) is divided into degrees and parts of a degree, from 0° (zero) to about 140°; every 10th degree is numbered from 0° to 140°; the space between every 10° is divided into 10 equal parts by straight lines; consequently every part is 1°; every fifth line is made a little longer than the others, to represent every fifth degree; and (in the best instruments) every degree is sub-divided into six equal parts by lines shorter than those which represent the degrees; those short lines divide every degree into sixths of a degree, or 10', every third line of these short ones being made a little longer to denote 30'. On any part of the arc, therefore, the first short stroke is 10', the second is 20', the third is 30', the fourth is 40', and the fifth is 50'. We will suppose it is an instrument of this kind before the learner. The index, up to which an arc is read off, is a line cut in a plate at the end of the movable radius, and is generally distinguished from the other lines on the plate by a diamond-shaped mark, resembling a spear head, and sometimes by O. Supposing this index to stand exactly at any of the long lines on the arc, that is, so that the two lines are in the same direction; in such a case the reading off is easily known, for it must be a certain number With respect to the dark glasses, when it is possible (as in observing altitudes of the sun in the mercurial horizon, &c.) to make the observation with a single dark glass on the eye-end of the telescope, without using any shade, this should always be done, for the error of this dark glass does not affect the contact at all, and the distortion caused by it is not magnified, whereas any fault in the dark shade between the index and horizon-glasses produces actual error in the observation, and the distortion is magnified subsequently by the telescope. of divisions, of which the value is seen at once, the reading being degrees and no minutes; it may be 10°, 12°, 20°, 30°, &c.-any number: but if the index exactly coincides with a short stroke in the arc, on such a case the reading off must be a certain number of divisions and sub-divisions. Thus, if it coincide, for example, with the second line to the left of 40°, then the reading off will be 40° 20′, or if it coincide with the fifth stroke to the left of 30°, the reading will be 30° 50', since each line on the arc represents 10'. But suppose the index not to stand exactly at any line whatever on the arc, but somewhere between two, as in the above example, between the second and third line from 40°, suppose it appeared to be about half-way between the second and third lines (the learner may place it in that position). But as this is a rough and imperfect way of estimating the additional minutes and seconds beyond the second division from 40°, the exact value of this small space is known by means of a few divisions on the index plate to the left of the index, and called the Vernier. These divisions are made less than the arc divisions, so that the line on the plate immediately to the left of the index is somewhat nearer to the corresponding one on the arc than the small space to be determined. It is nearer thereto, as is manifest by difference of a division on the arc and one on the index plate. In like manner the second line, reckoning from the index, must be nearer to the corresponding line by two differences, the third by three, and so on. At length, therefore, there must be a coincidence of two lines, or nearly so; that is, they must appear to an eye placed directly over them to lie in the same direction, or nearly so. And since, upon the whole, the lines on the vernier have approached those upon the arc through the small part the index is in advance of 20', this excess must be equal to as many times the difference of two divisions, as there are lines, reckoning from the index, before this coincidence takes place. Hence, if we know the value of a difference, we shall know the value of the small arc to be measured. This difference is known as follows:-By examining the arc of the sextant before us, it will be seen that 60 divisions of the vernier just cover or coincide with divisions on the arc, or the difference between a division on the arc 59 and one on the vernier is of a division of the arc; if, therefore, a division on the arc is 10', the difference will be of 10', or 10". Every sixth division of the vernier being distinguished by a figure denoting minutes, and the interval between each of these figures is divided into six parts of 10" each. Hence, to read off on a Sextant, we proceed thus:-First examine the divisions and sub-divisions on the arc, up to the line which stands before the index. We then move the microscope on the vernier and examine the numbered lines. If any one of these coincides in direction with the opposite one on the arc, the reading off to be added will be so many minutes; if not, we observe between which numbered lines the coincidence actually takes place, and then reckon the preceding minutes as numbered, and afterwards the sub-divisions of the vernier, as so many minutes or seconds. now suppose the index to stand between the second and third divisions from 40°. In reading off, first 40° 20' is noted on the arc, and then running the microscope farther on the arc, it is observed that a line on the vernier and Let us |