purposes of a theodolite when furnished with external graduated limb and verniers, while it is lighter and cheaper.

Sextant. For description and adjustments of sextant, see Chapter X., page 331.

Box Sextant. This is a very handy instrument for approximate measurement of angles, and as made by Stanley, is shown in Fig. 62. It consists of a circular brass box 3 or 3 in. in diameter, and about 1 in. deep. It is protected by a lid or cap which is screwed on the top when not in use, and is also screwed on to the bottom to serve as a handle when using the instrument. It may be used either with or without the telescope T, which for convenience in carrying is fixed by the screw s so that it may be unfastened when not in use. In the upper part of

M.

the instrument there is an arc of a circle A usually about 70° in extent and divided into 140°. The angle is read off by the vernier v and the microscope м. Opposite the slit for the eye or telescope T and inside the box there is a mirror having its upper half only silvered, so as to allow of one of the two objects between which the angle is to be measured to be seen directly through an opening in the side of the box beside this mirror. This mirror is called the horizon glass, and is fixed perpendicular to the plane of the instrument. The other side of the box opposite the side of the instrument shown in the figure is left open, and there is placed there inside the box another movable mirror which moves on the same axis as the vernier arm v. This mirror is called the index glass, and it and the vernier v are both moved simultaneously by the screw B which is connected to a rack and pinion

arrangement inside the box. When the two mirrors are parallel to each other the vernier should read zero. The angle actually read on the divided arc is the inclination of the two mirrors to each other. As shown below, this angle is half the actual angle between the two objects, and the arc of 70° is therefore divided into 140°. This is a source of error, as of course any error of observation is doubled. The vernier reads to 1 minute.

2nd Ranging Rod

Silvered

Unsilvered

Use of Box Sextant.-To use the instrument sight directly on one of the objects through the opening opposite the lower unsilvered half of the fixed mirror, and then rotate the other mirror by means of the screw B until the second object is seen reflected in the upper silvered half of the fixed mirror directly over the first object as seen through the lower unsilvered half as shown in Fig. 63. The

1st Ranging Rod

Fig. 63. Observing with Box
Sextant.

angle between the two objects is then to be read off by means of the vernier.

6

9

A

d

a

Theory of the Sextant. The principle on which the instrument is based is as follows:-"If there are two plane mirrors whose reflecting planes make a given angle with each other, and a ray of light in a plane perpendicular to the planes of both mirrors is reflected from both successively, its direction after the second reflection makes with its original direction an angle which is twice the angle made by the mirrors with each other." That this is so may be proved as follows:-In Fig. 64, let A be the fixed or horizon

Fig. 64.-Theory of the Sextant.

mirror, and в the movable or index mirror. Then arl is the line of sight, and the first object is viewed directly through the

aperture in the box and the lower unsilvered half of the fixed mirror A. The second object is reflected at c from the movable mirror B on to the fixed mirror A at b and thence to the eye at a, the mirror B being rotated until the reflection at bis in the line of sight ar1. The mirrors being in this position, the angle actually measured is the angle bec between the two mirrors. It is now to be shown that this angle is equal to half the actual angle r1ar2 between the two objects r1 and r2.

In the triangle bra the exterior angle cbr1 = sum of interior angles = bca + bac.

Therefore cbr1 - bca = bac

(1)

But cbr1 = 2cbf, because cbf = dbe, and dbe =fbr1, therefore cbf=

fbr1, or cbr1 = 2cbf. .

(2)

Similarly bea = 2bce, because bce = r2cg, and r2cg=dca, therefore bce=dca, or bca = 2bce.

(3)

Therefore substituting in (1) the values of cbr1 and bea given by (2) and (3), we get 2cbf - 2bce = bac.

(4)

That is, in the triangle cbe twice the exterior angle chƒ minus twice the interior angle bce is equal to bac.

But twice the exterior angle of a triangle minus twice one of the interior angles is equal to twice the other interior angle, which in this case is bec or 2cbf - 2bce = 2bec; but from (4), 2cbf - 2bce = bac. Therefore 2bec = bac=r1ar2, or bec=r1ar2.

Measuring Angles with Box Sextant when Ground is not Level.-In using the box sextant, unless the two objects between which the angle is measured are on a level with the eye, the angle observed will not be measured in a horizontal plane. As it is the horizontal projection of the angle that is required, we may observe this by placing two ranging rods in line with the objects so that these ranging rods are as nearly as possible on a level with the eye. The angle between the ranging rods may then be taken. If the ground does not permit of this, then the actual angle may be measured and afterwards reduced to its horizontal projection by the proper formula (see Chapter X., page 337).

Prismatic Compass.-This instrument is much used for rough surveys, and is especially useful for a rough traverse. Fig. 65 shows the instrument as made by Messrs T. Cooke & Sons. It consists of a compass card fixed to a magnetic needle in the

same manner as the ordinary ship's compass.

At A there is a

prism and a vertical slit for the eye, and at в there is an upright

A

D

B

with vertical hair for sighting upon the end of the line whose bearing is required. c is a mirror which slides up and down the upright B, and may be set at any angle so as to reflect the sun or other object at a considerable altitude. Upon placing the eye at the slit at a and directing the vertical hair in в upon any object, the magnetic bearing is simultaneously seen reflected in the prism at A, and is thus read off at once. The instrument may be used either mounted on the light tripod as shown in the figure or held in the hand. When not in use, the sight and mirror at B, as also the prism at A, are folded down, and the whole may be compactly packed in a leather case. For surveying in the details. in jungle or dense forest where traversing is the only method available, the prismatic is extensively used. It is best to use the prismatic on the tripod, as the needle comes to rest quicker and the work is altogether more satisfactory. A good pocket prismatic is shown in Fig. 232, page 408, Chapter XI.

Fig. 65.-Prismatic Compass.

Pocket Compass. No surveyor should go abroad to survey in undeveloped country without an ordinary pocket compass. In working through jungle and dense forest it will be found useful,

and should always be carried. In case of accident it will prevent one from losing one's way, besides being useful even for making a rough traverse upon occasion. The best kind is one protected in a case similar to the hunting case of a watch.

Plane Table. This instrument is much used by native surveyors on Government work in India for surveying detail. The plane table as made by Stanley is shown in Fig. 66. It consists of a drawing board varying in size from about 16 x 13 in. to 26 x 22 in., mounted on a tripod. A sheet of drawing paper is stretched on the board, on which is placed the "alidade," which may have either plain sights or a telescope as shown.

There

is also shown in the figure a trough compass attached to the alidade, and a level is attached to the telescope. In its plainest form the alidade is simply a metal rule with bevelled edge, having plain sights at its ends. A trough compass and a spirit level are then carried separately, and laid on the table when required. The table is attached to the tripod by a butterfly nut, and there are usually three levelling screws for levelling it up. The best form has also two rollers underneath worked by a ratchet motion for rolling and unrolling a continuous roll of paper and keeping it stretched tightly. One of the chief advantages of the plane table is that the work is plotted at once in the field, but its usefulness is greatly impaired in a wet climate, as it is of course impossible to work with it in wet or even showery weather.