Sextant (the sixth part), an instrument used in nautical observations and in hydrographic and land surveying for measuring the angular distance between objects. Its principle and the manipulation of it, in its ordinary form, are explained in the article Quadrant, which instrument it has entirely superseded for observations at sea, partly on account of its greater portability, but mainly because of its capability of measuring a wider range of angles. For important land surveys a full circle is preferred, of which there are the following forms: 1. A simple reflecting circle, made by extending the arc of the sextant to a whole circumference and producing the index arm so that it can carry a vernier on each ex-tremity. Observations with this are free from the error of eccentricity, and in part from the accidental errors of graduation and of reading, since they are derived from the mean of two readings at opposite divisions of the arc. 2. The repeating reflecting circle, which differs from the first only in having its horizon glass and telescope fixed to the arm which revolves about the centre of the instrument, instead of permanently attached to the frame. By taking a sufficient number of cross bearings with this, errors of reading, eccentricity, and imperfect graduation are essentially eliminated.

In theory, therefore, the repeating circle is very nearly perfect, capable of eliminating its own errors. But as we cannot pretend to measure "what we cannot see," the refinement of the circle is really thrown away so long as an optical power is used so feeble as that of the telescope now employed; for in fact its results do not surpass those of the common sextant so much as was expected from its theoretical perfection. 3. The prismatic reflecting and repeating circles, which differ from the above only in substituting for the horizon glass a glass prism, which is fixed on the line of sight behind instead of in front of the index glass. The advantage of this arrangement is that angles of all magnitudes can then be measured. These are the transformations which the sextant has undergone to adapt it for the varied requirements of the practical astronomer and surveyor on land; but to satisfy the demands of the nautical astronomer and hydrographic surveyor, changes even more radical and varied have been made. To the navigator the sextant is invaluable; and in the special work of hydrography along a coast line, where the position of the boat or vessel is generally determined by observing from the boat, the sextant is the only available instrument of precision in use.

And yet in its ordinary form it has certain deficiencies which prevent its universality of application. This fails to measure the angles between 140° and 180°, and the hydrogra-phers of all countries have studied to remedy this defect, with varied success. M. Daussy, a very skilful French hydrographer, and Messrs. Piston and Martius, instrument makers of Berlin, have in different ways modified the form of the sextant so as to overcome this difficulty; but their instruments are embarrassing in their manipulation, especially when the objects are indistinct or the observation must be made from a boat continually disturbed by the action of the waves. Mr. T. J. Lowry of the United States coast survey has succeeded in removing this imperfection in the sextant, and has also made other improvements by which many other difficulties are overcome. The improved instruments are handled with the same facility as the old sextant, and are equally adapted to rough usage in a boat. By means of some additional glasses and certain improvements in the graduated arcs and verniers, the following objects are accomplished: any angle from 0° to 180° can be measured without inverting the instrument and while reflecting but one object; two angles, one to the right and the other to the left of an object, either angle being any number of degrees from 0 to 120, can be measured at the same instant.

By certain additions which are easily made to the ordinary sextant, Mr. Lowry makes the instrument capable of measuring two angles, one to the right and the other to the left of the central object, in quick succession, without previously estimating their relative magnitudes, or inverting the instrument or lengthening its arc. Lastly, by a modification of M. Daussy's improvement, Mr. Lowry makes the ordinary sextant capable of measuring an angle and giving an inter-range at the same instant, and also of fulfilling many other conditions which M. Daussy's will not.