CHAPTER XIV.
INSTRUMENTS OF REFLECTION—OCTANT OR QUADRANT—REFLECTING CIRCLE—SEXTANT—PRINCIPLE—PARALLAX—CONSTRUCTION—EXAMINATION—ADJUSTMENT—ARTIFICIAL HORIZON—SOUNDING SEXTANT—BOX SEXTANT—SUPPLEMENTARY ARC—IMPROVEMENTS UPON THIS—OPTICAL SQUARE—OPTICAL CROSS—APOMECOMETER.
615.—The Octant or Quadrant measures angles within 90° by an arc of 45°. This instrument is generally termed an octant on the Continent from the space of the divisions; a quadrant by English-speaking races, from the extent of angles it takes. The idea of bringing the reflection of an object from a mirror in line with the direct sight line from another object, to measure the angle at the position of the observer subtended by the two objects, was originally proposed and worked out in a manner by Hooke,[38] and also by Newton.[39] Newton's invention was the more simple and important. This was communicated to Dr. Halley, then Astronomer Royal, but it was left unpublished until after his death, when it was found in Newton's own handwriting among Dr. Halley's papers.
Newton employed two mirrors to obtain the reflection of an object placed at any angle of less than 90° to the axis of the telescope or sight tube, to throw an image directly through the tube. One of these mirrors was placed at an angle of 45° to the axis of the telescope and covered half its field aperture, so that a direct image of an object could be received by the eye from the open uncovered part of the telescope at the same time as the reflected image of another object from the mirror. The second mirror was placed so as to throw its reflection into the mirror on the end of the telescope without giving any obstruction to the open aperture. This side mirror was fixed with the centre of its plane over the axis of a movable arm which read upon an arc the amount of its angular displacement to 90°. The mirrors were so arranged that their faces should be parallel to each other when the movable arm was placed at the zero of the arc. The graduation of the arc was of double the closeness of the ordinary arc reading, so that the angular positions of the two mirrors in relation to each other was indicated according to the following law:—
That the angle between two reflections in the same plane is equal to twice the inclination of the reflecting surfaces to each other.
616.—Hadley's Quadrant.—In Newton's quadrant the arc was brought most inconveniently in front of the face. By Hadley's arrangement the telescope or sight line is brought in a direction about parallel with the chord of the arc, producing the very convenient form of instrument now in use. This instrument was exhibited at the Royal Society, 13th May, 1731.[40] It was tried experimentally by the Astronomer Royal, August, 1732, in a yacht excursion, when readings were taken satisfactorily within a minute of arc.[41] It afterwards came into general use.
The quadrant was at first held to be sufficient for measuring the sun's altitude for obtaining latitude, but Hadley, as early as 1731, saw the advantage of extending the arc so as to be able to observe the opposite horizon if the direct one was obscured. It was also found that measuring the moon's angular distance from a star beyond 90° was serviceable in determining longitude. He therefore proposed by a duplicate system of reflections to extend the arc by what is termed a back sight to 220°. The means he suggested, which were commonly carried out in instruments of the period, were found to be too complicated for practice.[42] In the meantime the construction of these instruments, originally framed of a combination of wood, ivory, and metal, was much improved by making the frame entirely of metal. There were also great improvements made in the optical parts, by which the arc of 90° was extended. In 1757 Captain Campbell had an instrument constructed of metal of 60° of arc which therefore read to 120°. This instrument, with details of improvement, principally by Ramsden,[43] became the modern sextant.
617.—Reflecting Circle.—As soon as the success of the sextant was assured there appeared to be a general desire to complete the circle by reflections, many inventors thinking this would possess great advantages over the arc of 120°, and we find therefore no lack of inventions to this end, even by eminent men. Reflecting circles, as they are termed, that were of sufficient merit to come into limited use, were designed by Mayer, 1770; Borda, 1787; Mendoza, 1801; Hassler, 1824; Fayrer, 1830. Troughton's circle of about this period was no doubt the best instrument of the class.[44] We have also meritorious reflecting circles by Pistor and Martins, and by Amici.[45] Although these instruments were used at sea to a limited extent, particularly on foreign ships, they were also used on land, where indeed they were more manageable. As no further reference to these reflecting circles will be given, anyone interested in the matter may refer to the books mentioned in the notes, where very full particulars of their structure are given. It was felt necessary to mention the subject here, as the same ideas are constantly cropping up as assumed advantages where previous experience is forgotten. Reflecting instruments at sea are tedious to use when the angle to be taken exceeds that taken in by the eye without movement of the whole body. On land, when the angle exceeds 120°, a theodolite is better; but supplementary angles may be taken with the sextant conveniently on land, where the portability of the instrument is of great consideration. This will be again brought forward in discussing box sextants with supplementary arc.
618.—The Sextant, of the invention of which some particulars have just been given, is only used as a surveying instrument for the exploration of new countries, for which employment—it may be used with or without a tripod or stand—it is found to be a most convenient, light, and portable instrument for the traveller for ascertaining longitude, latitude, and time with the aid only of an artificial horizon. Triangulation may also be taken with it of terrestrial objects, even for the complete circle, by repetitions from station to station in angles within 120°. The same principles which are followed in the construction of the nautical sextant are followed also in the manufacture of two modified forms of this sextant which are used for surveying only, the sounding sextant and the box sextant. As the nautical sextant is most open to observation of its parts it will be more convenient to discuss the construction and general arrangements of this instrument first.