(195.) To determine the exact distances between the stars by direct observation is comparatively of little service; but in nautical astronomy the measurement of their distances from the moon, and of their altitudes, is of essential importance; and as the sextant requires no fixed support, but can be held in the hand, and used on ship-board, the utility of the instrument becomes at once obvious. For altitudes at sea, as no level, plumb-line, or artificial horizon can be used, the sea-offing affords the only resource; and the image of the star observed, seen by reflection, is brought to coincide with the boundary of the sea seen by direct rays. Thus the altitude above the sea-line is found; and this corrected for the dip of the horizon (art. 23.) gives the true altitude of the star. On land, an artificial horizon may be used (art. 173.), and the consideration of dip is rendered unnecessary. (196.) The adjustments of the sextant are simple. They consist in fixing the two reflectors, the one on the revolving radius C E, the other on the fixed one C B, so as to have their planes perpendicular to the plane of the circle, and parallel to each other, when the reading of the instrument is zero. This adjustment in the latter respect is of little moment, as its effect is to produce a constant error, whose amount is readily ascertained by bringing the two images of one and the same star or other distant object to coincidence; when the instrument ought to read zero, and if it does not, the angle which it does read is the zero correction and must be subtracted from all angles measured with the sextant. The former adjustments are essential to be maintained, and are performed by small screws, by whose aid either or both the glasses may be tilted a little one way or another until the direct and reflected images of a vertical line (a plumb-line) can be brought to coincidence over their whole extent, so as to form a single unbroken straight line, whatever be the position of the moveable arm, in the middle of the field of view of the telescope, whose axis is carefully adjusted by the optician to parallelism with the plane of the limb. In practice it is usual to leave only the reflector D on the fixed radius adjustable, that on the moveable being set to great nicety by the maker. In this case the best way of making the adjustment is to view a pair of lines crossing each other at right angles (one being horizontal the other vertical) through the telescope of the instrument, holding the plane of its limb vertical, then having brought the horizontal line and its reflected image to coincidence by the motion of the radius, the two images of the vertical arm must be brought to coincidence by tilting one way or other the fixed reflector D by means of an adjusting screw, with which every sextant is provided for that purpose. When both lines coincide in the centre of the field the adjustment is correct. (197.) The reflecting circle is an instrument destined for the same uses as the sextant, but more complete, the circle being entire, and the divisions carried all round. It is usually furnished with three verniers, so as to admit of three distinct readings off, by the average of which the error of graduation and of reading is reduced. This is altogether a very refined and elegant instrument. (198.) We must not conclude this part of our subject without mention of the "principle of repetition;" an invention of E P d the former, A ML, is absolutely fixed in the plane of the objects, and carries the graduations, and the latter is freely moveable on the axis. The telescope is attached permanently to the latter circle, and moves with it. An arm O a A carries the index, or vernier, which reads off the graduated limb of the fixed circle. This arm is provided with two clamps, by which it can be temporarily connected with either circle, and detached at pleasure. Suppose, now, the telescope directed to P. Clamp the index arm O A to the inner circle, and unclamp it from the outer, and read off. Then carry the telescope round to the other object Q. In so doing, the inner circle, and the index-arm which is clamped to it, will also be carried round, over an arc A B, on the graduated limb of the outer, equal to the angle POQ. Now clamp the index to the outer circle, and unclamp the inner, and read off: the difference of readings will of course measure the angle POQ; but the result will be liable to two sources of error-that of graduation and that of observation, both which it is our object to get rid of. To this end transfer the telescope back to P, without unclamping the arm from the outer circle; then, having made the bisection of P, clamp the arm to b, and unclamp it from B, and again transfer the telescope to Q, by which the arm will now be carried with it to C, over a second arc, B C, equal to the angle POQ. Now again read off; then will the difference between this reading and the original one measure twice the angle POQ, affected with both errors of observation, but only with the same error of graduation as before. Let this process be repeated as often as we please (suppose ten times); then will the final arc ABCD read off on the circle be ten times the required angle, affected by the joint errors of all the ten observations, but only by the same constant error of graduation, which depends on the initial and final readings off alone. Now the errors of observation, when numerous, tend to balance and destroy one another; so that, if sufficiently multiplied, their influence will disappear from the result. There remains, then, only the constant error of graduation, which comes to be divided in the final result by the number of observations, and is therefore diminished in its influence to one tenth of its possible amount, or to less if need be. The abstract beauty and advantage of this principle seem to be counterbalanced in practice by some unknown cause, which, probably, must be sought for in imperfect clamping. (199.) Micrometers are instruments (as the name im ports) for measuring, with great precision, small angles, not exceeding a few minutes, or at most a whole degree. They are very various in construction and principle, nearly all, however, depending on the exceeding delicacy with which space can be subdivided by the turns and parts of a turn of fine screws. Thus in the parallel wire micrometer, two parallel threads (spider's lines are generally used) stretched on sliding frames, one or both moveable by screws in a direction perpendicular to that of the threads, are placed in the common focus of the object and eye-glasses of a telescope, and brought by the motion of the screws C E D B exactly to cover the two extremities of the image of any small object seen in the telescope, as the diameter of a planet, &c., the angular distance between which it is required to measure. This done, the threads are closed up by turning one of the screws till they exactly cover each other, and the number of turns and parts of a turn required gives the interval of the threads, which must be converted into angular measure, either by actual calculation from the linear measure of the threads of the screw and the focal length of the object-glass, or experimentally, by measuring the image of a known object placed at a known distance (as a foot-rule at a hundred yards, &c.) and therefore subtending a known angle. (200.) The duplication of the image of an object by optical means furnishes a valuable and fertile resource in micrometry. Suppose by any optical contrivance the single image A of any object can be converted into two, exactly equal and similar, A B, at a distance from one another, dependent (by some mechanical movement) on the will of the observer, and in any required direction from one another. As these can, therefore, be made to approach to or recede from each other at pleasure, they may be brought in the first place to approach till they touch one another on one side, as at A C, and then being made by continuing the motion to cross and touch on the opposite side, as A D, it is evident that the quantity of movement required to produce the change from one contact to the other, if uniform, will measure the double diameter of the object A. (201.) Innumerable optical combinations may be devised to operate such duplication. The chief and most important (from its recent applications), is the heliometer, in which the image is divided by bisecting the object-glass of the telescope, and making its two halves, set in separate brass frames, slide laterally on each other, as AB, the motion being produced and measured by a screw. Each half, by the laws of optics, forms its own image (somewhat blurred, it is true, by diffraction *), in its own axis; and thus two equal and similar images are formed side by side in the focus of the eye-piece, which may be made to approach and recede by the motion of the screw, and thus afford the means of measurement as above described. B (202.) Double refraction through crystallized media affords another means of accomplishing the same end. Without going into the intricacies of this difficult branch of optics, it will suffice to state that objects viewed through certain crystals (as Iceland spar, or quartz) appear double, two images equally distinct being formed, whose angular distance from each other varies from nothing (or perfect coincidence), up to • This might be cured, though at an expense of light, by limiting each half to a circular space by diaphragms, as represented by the detted lines. |