latitude, the resulting error in azimuth will have opposite signs in forenoon and afternoon.

As the sun at any particular time, say 9 o'clock A. M., has a fixed height in the heavens on any particular day, if the dif ferent angles are properly set off on the instrument, and the line of collimation turned upon the sun, its image will at that time be accurately centered between the proper lines on the silver plate, and the line of sight will lie in the true meridian; but suppose an error of l' too much be made in setting off the declination, then we will have set our line of collimation too high for the position of the sun at 9 o'clock, and it will not, when the instrument is in the meridian at 9 o'clock, center properly between the lines, but obliquely above; consequently, if we have clamped the hour circle at 9 o'clock, we must wait some time for the sun to reach the height that we have set off on the instrument for it before it will be properly centered. If we do center the image at 9 o'clock, it will be by turning our instrument slightly from the position it should occupy, and our line of sight will not lie in the meridian, but to the west of it, if looking south, or east of it, if looking north, by 1'.85 for latitude 40°. In the afternoon the converse will be true.

Seventh. If the adjustments are not carefully attended to, the error in the bearing of a line may be much greater when taken by the solar attachment than is likely to be made by the needle when there is no local attraction.

When the sun is on the equator, September 22d and March 20th, the declination arm will be perpendicular to the polar axis, and the zero of vernier will coincide with zero of declination arc. From March 20th to September 22d, the sun being above the equator and consequently above the equatorial plane, its rays will pierce the equatorial plane from above, and the relative positions of the declination arm, equa torial plane, polar axis, and horizontal plane will be as in Figure 170a. From September 22d to March 20th, the sun being below the equator, its rays will pierce the equatorial

plane from below, and the relative positions of the declination arm, equatorial plane, polar axis, and horizontal plane will be as in Figure 1706. When the declination arc is graduated in but one direction from the zero of the scale, then it is necessary to have on each block a lens and silver plate, or, in other words, to have two lines of collimation; and it is necessary to revolve the declination arm from the position shown in Figure a, which is for north declination, to that shown in Figure 6, for south declination. If, however, the declination arc is graduated in both directions from the zero of the scale then but one line of collimation is necessary.

THE TIME OF DAY, when the meridian is known, may be approximately ascertained with the solar attachment by setting the telescope in the meridian, then setting off the co-latitude and approximate declination and bringing the image of the sun between the hour lines by moving the declination arm in hour angle only; then the index on the hour circle will show apparent time, which can be reduced to mean time. It is best ascertained, however, when the sun is on the meridian, the time thus given being that of apparent noon, which can be reduced to mean noon by adding or subtracting the equation of time, as the sun is slow or fast

CHAPTER XIII.

THE SEXTANT.

DESCRIPTION.-The Sextant (Fig. 178) is a hand instrument for measuring angles, up to 120°, subtended by any two objects, the angle being in the plane through the instrument and the two objects. It consists of the following parts-viz., a mirror I (Fig. 179) called the index glass, rigidly attached to a

movable arm A called the index arm, and a mirror H called the horizon glass, rigidly attached to the frame of the instrument. The lower half of the horizon glass is silvered while the upper half is clear. Both mirrors should be perpendicular to the plane of the graduated limb C.

The arc of the limb is about 65° or 70° long, graduated to degrees, half degrees, etc., each half degree being numbered as a whole degree so the reading will be the angle subtended by the objects. On the ex-P tremity of the index arm is a vernier V. Opposite the horizon glass is a telescope T. Colored glasses are provided for neutralizing the sun's rays, and a magnifying glass for reading the vernier.

FIG. 179.

THEORY.-The principle of its construction is that a ray of light reflected at two plane surfaces in a plane normal to both is deviated from its orignal direction through an angle double that made by the two reflecting surfaces. Thus a ray of light from S to T being reflected at I to H, and again reflected at H to T, the angle STH between the original direction ST and the direction after the second reflection HT is double the angle IVH between the mirrors. For, drawing the normals n, n, to the mirrors and representing the angles of incidence and reflection at I by i and at H by i', as in the figure, in the triangle ITH the exterior angle

2i=2i'+T, .. T=2i-2i', =2(i-i),

and in the triangle HVI the exterior angle

IHp=90°-i',
=HIV+V,
=(90°-i)+V,

.. V—(90°—¿')—(90°—i)—i—i'
.. T=2V.

Where Used.-The sextant (Fig. 178) is the one principally used at sea in observing the altitude of the sun and lunar distances, to determine the latitude and longitude, where the unstable position of the mariner excludes the use of almost all other instruments. On land it is one of the most

convenient, accurate, and generally useful instruments with which to obtain data for the solution of a variety of astronomical and other problems.

THE POCKET SEXTANT (Fig. 180) is the one most frequently used in recon

naissances, preliminary surveys and explorations.

FIGURE 180.

Description. It is, in construction, exactly like the larger one, except that the mirrors and colored glasses are enclosed in a cylindrical box 2 to 3 inches in diameter and 1 to 1 inches high, with suitable openings in the side for exposing the mirrors. The index arm is worked by a milledhead screw and revolves on top of the box on which is the limb. The vernier reads to 1 minute. The telescope, when not needed, may be taken out, and a slide having a small peephole may be pushed over the opening. The adjustments are made by means of a key in holes provided on top and on the side of the horizon glass. The cover is screwed on the bottom of the box, serving as a kind of handle in making observations. The pocket sextant is used the same as the larger one.

The advantages of the pocket sextant are its accuracy and portability. When one's exact position is not material it can be readily used on horseback, in a tree, or wherever it may be necessary to take an observation. It is not affected by magnetic disturbances like the compass needle.

The disadvantages are, that it cannot be generally used in traversing and other surveying operations, but is limited to measuring minor angles in triangulation, finding one's place on a map, and determining heights and distances.

ADJUSTMENTS.-1st adjustment: To make the index glass Test by setting the vernier at about the middle of the graduated arc,

perpendicular to the plane of the graduated arc.