Figs. 302, 303.—Diagram of supplementary arc sextant.
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677.—Theory of Supplementary Angles to the Sextant.—For the measurement of these angles we have to consider direct reflections only of two reflecting planes placed one above the other nearly in contact, so that the images projected from both planes may reach the eye superimposed. Let Fig. 302 II′ be the surface of a mirror (index glass) which is movable to any angle in relation to the face of the mirror SS′ (supplementary index). For demonstration of the principle these mirrors are shown in this diagram at 90° to each other; therefore coincident reflections will be at 90° + 90° = 180°. Let the lines FC and BC form a right line (180°); F fore sight and B back sight. An object at F would be reflected from the mirror II′ to the eye at E, the angles FCI and ECI′ being equal. Another object at B reflected from the face of the mirror SS′ would also reach the eye at E, the angles BCS′ and ECS′ being equal. And as the angles FCI and BCI′ are equal in crossing a right line, the line FCB must be also a right line (180°) which is indicated by the angle of coincidence of the two reflections to E. The positions of the reflections are shown as angular measurements upon the graduated arc.
678.—In Fig. 303 let SS′ remain as before, angle BCE will remain as shown in both figures. Move the index glass from the position II′ of Fig. 302 to the position JJ′ of Fig. 303, so that after this movement the eye at E would receive the image of an object at a new position F′ as reflected from the mirror JJ′, F′CJ and ECJ′ being equal. In this process, as the reflector JJ′ in the angle ICJ would have moved half the angle JCF, the record of this movement upon the index, which moves with JJ′, is at the same time double the true angular difference, as with the sextant proper fully described, the graduations being in both cases the same pro ratâ. The increase of angle is taken supplementary to the angle given by the first reflection, by addition to this angle in a direction right to left from the right line of the former sight EC; consequently this increase is read backward on the sextant, that is, right to left, and is indicated by the outer line of numerals.
679.—Manufacture.—The general structure of this instrument is nearly the same as the ordinary box sextant, except the parts just referred to. The supplementary index glass is an ordinary mirror similar to the index glass but of only ¼ inch in depth: it is mounted in the same way. Its adjustments are similar to the horizon glass in kind, but there are no exterior screws, this glass being permanently fixed by the maker. Opposite the supplementary index glass a wide window is cut through the rim of the case near the sole plate to take sight of the object at angles exceeding 120°, so that in this sextant two large windows are cut out opposite to each other. The diameter of this sextant is 3 inches; the exterior depth about 1-5/8 inches, that is, 1/8 inch deeper than the ordinary box sextant. It weighs about 20 oz. It is carried in a solid leather case with strap to pass over the shoulder.
680.—Examination and Adjustment.—Examination will be nearly the same as for the common box sextant. The most important point is that the readings taken within both arcs should be alike, assuming, which is necessary, that the part comprising the sextant proper is perfectly adjusted. Thus there is a 90° on both direct and reverse arcs. The 90° may be measured by any pair of objects on the direct arc, and afterwards compared by shifting the index to the 90°, on the supplementary arc. If no object be found at 90°, then 95° 30′ or any other quantity may be compared. It is also well to compare readings at or about 120° on both arcs. The 90° and 120° fall in the same position in the reading, and this checks any error in either. If the adjustment be not fairly perfect, the instrument should be returned to the maker. Indeed, this sextant would be better without any external means of adjustment, leaving these to be made by the optician in such a permanent form that they will not be liable to change. It is, as the plain box sextant, exceptionally protected from accident.
681.—In using this instrument the arc up to 120° is taken exactly as with the plain box sextant. Beyond 120° the sextant is shifted to take sight through the supplementary pin-hole, being particular to observe that the pinion is now turned the reverse way to increase the angle, and that the vernier reads for the supplementary arc right to left. It is in this reversing, if not carefully performed, that a little difficulty is experienced in using this instrument.
682.—Box Sextant, with Continuous Arc to 240°.—This instrument is an improvement by the author upon one originally designed by Mr. W. Franklin. The reading is taken continuously from the same sight-hole and by the same arc, and in a direct manner without any reversal for part of the arc. This sextant reads with certainty to 240°.
683.—In the construction of this sextant there are two horizon glasses superimposed one above the other and crossing each other, with faces which are adjustable for perpendicularity at an angle of 120°. The horizon glass is divided top from bottom by a clear band cut through it, as in the old form of back-sight nautical sextants. One of the wide glasses reflects into the upper, and the other into the lower mirror of the horizon glass. The pin-hole sight or the telescope is placed in the same position as in the plain box sextant described. The horizon glass is fixed and both the index mirrors adjust to angular positions, or one index glass only and the horizon glass is adjusted, this arrangement being optional. The arc is graduated as the plain box sextant, but it reads with two rows of figures from 0° to 120°, and from 120° to 240°, the 0° of the under line being under 120° of the upper. When the arc is set to zero the index glasses are in such a position that the direct vision and the reflection as seen in the upper mirror of the horizon glass are coincident for direct images, as at the zero of the plain sextant, but at this point the lower mirror of the horizon glass reflects to the eye an object at 120°. When the index is moved forward the angles continue onward, reflected from both glasses, so that the upper reads on 10°, 20°, 30°, etc., whereas the lower read 130°, 140°, 150°, etc.; so that if the objects desired to be triangulated are under 120° the coincidence is seen in the upper mirror, and if over this in the lower, the great distance of 120° apart of the angles preventing the risk of accidentally taking the one for the other. In the compact form of a box sextant this instrument embraces the uses of the ordinary reflecting circle of double the diameter, due to the entire circle graduation; and the range is sufficient, as beyond 240° the head materially interferes with observation. The size and weight of the instrument are generally but little over that of the plain box sextant. The adjustments are made permanently by the maker. The use of this instrument is fully inferred from the description given. The construction is shown in Fig. 304, E place of the eye with direct ray through the horizon glass H to O. The index glass I is that of the ordinary sextant, shown by dotted lines, throwing the image of an object at P to the upper horizon glass and thence to the eye at E. B is the fixed supplementary glass with its surface at 60° to the lower horizon glass at A. The sight lines from an object at Q are reflected from B to A and thence to E. A spring arrangement shown SS with a milled head underneath permits the lower glass A to be drawn down to convert the instrument into a simple box sextant.