open space, and adjusted for observation before the star reaches its greatest apparent eastern or western departure, or elongation. The star should be continuously observed with the clamps tightened, until the motion round the vertical axis be found to cease. Then the star will be at its greatest elongation on that side of the meridian. The verniers on the horizonal limb should then be carefully read, and the reading entered. Again, when the star is approaching its greatest elongation on the opposite part of its apparent circular path, the upper plate of the horizontal limb should be unclamped, and the telescope directed to the star. The upper plate should be again clamped, and the star continuously observed by operating with the slow-motion screws to the vertical limb and the upper plate of the horizontal limb, until motion round the vertical axis be again found to cease; then the star will be at its greatest elongation on this side of the meridian. The horizontal limb should be again read, and the reading entered. As the elongations are equal, the upper plate should be unclamped, and after being reclamped for half the recorded angle passed over, the vernier should be made to read this angle; then will the vertical limb be adjusted in the plane of the meridian, which plane may be now traced on the ground for the survey or other purposes.

The meridian line may be approximately determined without the aid of a theodolite, or other angular instrument, as follows:

A flag-pole, or pole, should be erected on elevated ground, and a small lighted taper fitted on the top of it, when a circumpolar fixed star shall be approaching closely its greatest elongation from the meridian. The eye, at a low and remote station, should be brought into the line of the star and lighted taper produced by observing when

the centre of the flame of the latter covers the star. The eye should be in the rear of a suspended card with a sight-hole (which may be raised, lowered, or moved laterally at pleasure), when the eye, lighted taper, and star are in the same line, and when the lateral motion of the sight-hole card shall be found to cease. The star will then be at its greatest elongation. The position of the sighthole in the card should be referred to the ground with a plummet, and the point so found marked with an arrow. The taper should be extinguished, and refitted to its former elevated position. When the star shall be approaching its greatest elongation on the opposite side of the meridian, the taper should be again lighted, and the position of the sight-hole for the star's greatest elongation determined and marked as above.

W

Fig. 62.

n

In the diagram (fig. 62) m is the position of the lighted taper, W and E the greatest elongations of the star, a the position of the sight-hole point for the elongation E, and a' its position for the elongation W. From m the lines ma and ma' should be measured through the points a a' and made equal, so that ma a' shall be an isosceles triangle. The base a a' should be measured and bisected in s. The line ms will be a meridian line. For determining the meridian by a circumpolar star, the star should be visible to the naked eye for fully twelve hours.

a

m

S

If the sun be visible, the meridian line may be approximately determined in the daytime, as follows:

:

A truly straight pole a (fig. 63) should be set up vertical, so that it may be easily made to revolve. To the pole a an inclined arm tm should be fixed, so that

its prolongation may intersect the surface of still water at a lower level. To the lower end of the inclined arm a sight-vane and wire mv should be fixed, so that the sight-wire may be in the vertical plane tmv. At ta sight-hole card should be fitted, to have the diameter of the sight-hole in the same vertical plane. At m dark glasses should be fitted perpendicular to the inclined arm, to moderate the reflected rays of the sun. In the forenoon the sight-vane should be kept directed towards the sun S until the sun's reflected image s" be bisected by the line of the top angle surface of the inclined arm, which also bisects the sight-hole. Then, without disturbing the arm, the vertical plane of the reflected ray should be traced at a distant point c by means of the

sight-vane wire. In like manner the line a s'c' should be determined for the equal altitude of the sun in the afternoon. Now from a the distances a b, a b', on the lines a c, a c' should be measured and made equal, so

that a bb' will be an isosceles triangle. The base bb' should be measured and bisected in the point s, which will be a point in the meridian of a. The line as will therefore be the meridian line required.

The trace of the meridian may be accurately determined in the day time as follows:-The sun's altitude should be taken with a theodolite about four hours before apparent noon, and the clamped horizontal limb read for the altitude. The sun's declination for the day should be taken from the Nautical Almanac, and the declination for the time found by proportionality. From this data the altitude for the afternoon observation may be also found without serious error. The vertical limb of the theodolite should be clamped at the computed altitude, and, in the afternoon, at the approximate time for the altitude the sun's course should be followed (without disturbing the lower plate of the horizontal limb, which should remain clamped) until the altitude be reached and the sun properly observed. Then the horizontal limb should be read, the upper plate unclamped, and the vernier adjusted to the bisection of the angle passed over. This will adjust the vertical limb in the plane of the meridian. From the station of the theodolite, the meridian may be traced on this angle, and other angles may be measured to connect the meridian line with the lines of a survey, or with lines for other purposes.

LONGITUDE. BY LUNAR DISTANCES.

For finding the longitude by lunar distances, the angles of altitudes of the sun, or star, and moon, and their distance apart, should be measured with sextants, with the least appreciable lapse of time. These readings and the day and time of observation should be noted.

e

Fig. 64.

A

b

Let mh,sh' (fig. 64) be the observed altitude of the moon and sun, or of the moon and a known star; also let A be the zenith, HH the horizon, and eq the equator; on the earth's axis, and sm the measured lunar distance. The observed altitudes should be corrected for refraction,

TR

m

H

h

parallax, &c., to find the true altitudes m'h, s'h', and their respective zenith distances m' A, s′ A.

Now in the spherical triangle Ams the three sides a b c are given, and therefore half their sum s is given. From these data the angle A may be computed from the formula

In the spherical triangle Am's' the two sides b'c', and the contained angle A are given to find m's', or a'.

By the aid of an auxiliary arc or angle, a' may be found as follows. Let be the auxiliary angle. Then

This gives the correct lunar distance by means of the cosines.

The lunar distances are given in the Nautical Almanac for intervals of three hours, mean Greenwich time. If