THEORY AND PRACTICE OF ENGINEERING.

Book II.

844

vane is fixed perpendicularly with a fine wire stretched across it, opposite to which is aprism : on applying the eye to the latter, and bisecting any object with the wire in thesight vane, the division on the card coinciding with the thread, and reflected to the eyeof the observer, will show the angle formed by the object with the meridian. The instru-ment must be carefully used when the observation is made, and the card must have free playon its centre, otherwise the results will not be true: each angle as taken should beregistered down, which is more simple than first taking one object at 15, and others at20, 30, and so on, where one is to be subtracted from the other before the angles betweenany two given points can be ascertained.

The Box or Pocket Sextant is used for laying out angles, and for filling in the detailsof a survey, where the theodolite is employed in setting out the long lines, and layingout the larger triangles : it is usually divided to 140° on a silver plate, although a greaterangle than 110° should not be taken with it: to the sight is attached a small telescope,which often requires time to arrange, and is inconvenient. To take plain sights, thereis an aperture opposite the half-silvered or horizon-glass, which answers the purposebetter. When an observation is made, take the sextant in the right hand, andapply the eye to the small aperture, looking through the unsilvered part of the horizon-glass to some object or station marked on the line. Then with the left hand, turn thescrew which carries the silver glass, until it reflects the object, the angle of whichis to be ascertained ; when these two objects are, as it were, in conjunction, viz. theobject viewed direct through the unsilvered glass, and the reflected object appearing as one,the desired angle will be given. The index or vernier being placed at zero, before thescrew, which turns the silver glass is moved, the object viewed direct and by reflection beingthe same, is a proof that the instrument is correct: should this not be the case, the defect ofthe instrument must be set right by means of two screws, one in the upper part, over thehorizon-glass, and the other at the side of it; these screws must be turned until the objectviewed direct and reflected appear, as they really are, one, the vernier standing at zero.There is attached to the vernier a small magnifying glass, which enables the angle whenrequired to be read off

The Sextant in maritime surveys is of great service, and in all situations where the theo-dolite cannot be placed on a firm footing, or where the angular distance between two bodiesin motion is required, it is of the greatest utility, and almost the only instrument usedat sea for taking the altitudes of objects, or the angles they make with one another ; whenemployed it is taken in the right hand, and its face placed in the plane of the two objects,the angular distance of which is required : when the altitude of an object is required, the in-strument is held vertically, and when oblique angles are to be measured, in an oblique plane.

The sextant is a modification of the quadrant, and seems to have been the invention ofNewton : the principle of its construction may be thus described. Let A, 15, be two mirrorsmoving on axes, parallel to each other, the second mirror, 15, beinghalf silvered, so that it admits the passage of rays of lightthrough half its area. Suppose a ray of light to pass from theobject C, and reflected on the mirror at A, and after a second re-flection from the half-silvered glass 15, enter the eye at E. Alsolet a second object D be seen by direct vision through the halt-silvered glass B : it is required the angle subtended at the eye Eby the objects C and D. Produce the plane of the mirrors untilthey intersect in F : «the angle A FB is equal to half the angleC E D. For producing AB to G, we have GBE = toBAC+ A E B. Then, as the angle of incidence is equal to the angleof reflection,

HBA = FBE = GBF: thereforeGBE = 2 GBF = BAE + AEB: but2 GBF = 2 B A F + 2 A F B : thereforeBAE+ AEB 2 BAF + 2 AFB.

But because CAI = 15 AF = FAE,

B A E = 2 B A F :taking equals trom equals, we have A E B, or C E D equal to 2 A F B.

When the two mirrors are parallel to each other, and the angle formed equal to zero, thedistant object seen by direct vision and its reflected image will seem to coincide.

In constructing the sextant, the arc is graduated to 10 minutes of a degree: these areagain subdivided into 10 seconds by the vernier, which moves round an arc, the axis of whichis at the centre of the circle : over this centre, and attached to the arm carrying the vernier,is placed a mirror, perpendicular to the plane of the instrument, which moves with the index.

The Index is adjusted by clamp as well as tangent screws : another half-silvered glass isattached to the frame, nearly opposite the first, with its plane perpendicular to the plane ofthe instrument, and the zero on the limb is so placed that the vernier indicates zero whenthese two mirrors are in a parallel position to each other: glasses of different tints are

c

Fig.10G9.