Surveying and Levelling Instruments, Theoretically and Practically Described. / For construction, qualities, selection, preservation, adjustments, and uses; with other apparatus and appliances used by civil engineers and surveyors in the field.

by William Ford Stanley

Fig. 284.—Principles of reflection of the sextant.

Larger image

624.—The above scheme, Fig. 284, is taken from Captain Magnaghi's admirable work before mentioned, which gives a very clear geometrical demonstration of the value of angular positions in compound reflection. A ray of light SR directed to a plane mirror R is reflected therefrom to a plane mirror R′, following a plane of reflection perpendicular to the intersection of the two mirrors. The direction R′T of the ray reflected by the second mirror falls into the same plane of reflection, and makes with the direction SA of the incident ray an angle double that which is comprised between the two mirrors.

The two planes of reflection SAB and ABT unite in one because they both contain the line AB and the normal BP to the mirror R′.

In prolonging the normals of the mirrors to their point of intersection P we find that—

BTS = BAS - ABT;

but as ½ BAS - ½ ABT = BPA = BDA,

therefore BTS = 2 BDA.

625.—The mirrors being placed in the position shown in the figure, if we look through a telescope whose visual axis is placed in the line ET, with its objective to the mirror R′, we see in the centre of the field of view the image of the object S reflected consecutively by the mirrors R and R′. We also see in the telescope whether the mirror R′ is only a certain height above the plane of reflection, so as to permit half of the object-glass to receive the rays coming from the point E situated in the prolongation of the line TB, also the image of E which is necessarily coincident with that of S, because the rays by which each image is formed enter the telescope in the same direction BT. Therefore when the images of the two objects E and S appear superimposed or coincident in the middle of the field of view, we have an index given that the mirrors form an angle with each other which is half that which is made at the point T from the same objects, and when one is known the other is easily deduced.

626.—Nautical Sextant.—The ordinary construction of this instrument, Fig. 285, consists of a cast gun-metal frame, forming approximately in outline a segment of a circular disc AA″ including within its extreme radii about 155°.