The zero of the horizontal circle represented the direction of Clausthal Church. The arithmetical mean of the results shows that the meridian formed an angle of 126° 18′ 51′′ with the direction of Clausthal Church. Observations made the next night gave exactly the same results. The same number of observations were made on the two following nights with the telescope inverted. The mean of all the results obtained during the four nights gave 126° 18′ 49′′. It must be noted that in these observations the stars employed were not first sighted and the angle of altitude then read. The vertical circle was clamped at a given division, and the star then brought on to the vertical wire of the telescope, and followed by means of the tangent screw of the upper plate until it also passed the horizontal wire.

If the theodolite is set up on a fixed point, and if the terrestrial object, the azimuth of which is determined, is also a secure point, a further marking-out of the meridian is not absolutely necessary. In the preceding case, however, it was thought advisable to mark out the meridian by means of a large square stone buried in the earth on a mountain in the vicinity. A hole drilled in the surface of this accurately in the meridian served for the reception of a signal staff.

The meridian may be determined during the daytime by sighting the upper edge of the sun before and after mid-day, a dark glass being placed before the objective of the telescope. A correction has, however, to be made on account of the obliquity of the ecliptic-a correction that is not taken into account in the shadow method. This method of determining the meridian is not to be recommended, as the astronomical almanacks required for making the correction are not always available. The crosswires, too, may be directed to a star with far greater precision than to the sun.

3. Determination of the Meridian by Means of the Pole-Star.Of the bright stars of the northern heavens, the nearest to the pole is the first star in the tail of the Little Bear, or the Polestar (a Ursa Minoris). It is a star of the second magnitude, and may easily be found by imagining a straight line to be drawn through the stars ẞ and a of the Great Bear, and continued for about five times the distance from ẞ to a, counting from a. These two stars are known as the pointers.

The meridian may be determined by observing the pole-star either when it is in the meridian, or when it is at its extreme elongation. The pole-star is not situated exactly at the north pole of the heavens, but is now about 1° 17′ from it. Twice in each sidereal day (23 hours 56 minutes) it is in the meridian.

A very simple method of determining the meridian of a place consists in sighting the pole-star, marked A in Fig. 15, when it

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Fig. 15.

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appears in the same vertical line with the star Alioth in the Great Bear (ε Ursa Majoris). This may be done by watching for the moment, when a suspended plumb-line will cover both stars. They will then be approximately in the meridian. The pole-star is exactly in the meridian about 17 minutes after it has been in the same vertical plane as Alioth.

The meridian may also be determined by observing the pole-star at its extreme elongation, that is, when it is at its greatest apparent angular distance east or west of the pole. At this instant, the horizontal projection of the apparent movement of the star alters its direction, and the motion of the star appears to cease for a short time. The greatest and least horizontal angles made by the pole-star with any given line when the star is at the greatest distances east and west of the pole, are observed and the mean of the angles taken. This will be the angle made by the given line with the meridian. This method is rarely practicable with an ordinary theodolite, as one of the observations must generally be made by daylight.

4. Determination of the Meridian by means of a Map.-For an approximative determination of the meridian, a large-scale map may be employed. The direction of the meridian is shown by joining the degrees of longitude marked at the top and bottom of the map. The angle formed by the meridian and some line easy to determine on the ground, is measured on the map. With the aid of this line, the angle is marked off on the ground. The approximation thus obtained is at most 15 minutes.

Setting-out the Meridian Line.-In every mining district it is very desirable that all difficulty in ascertaining the true meridian should be at once removed by the erection of two conspicuous objects placed exactly on a meridian line, to remain for permanent reference. T. Sopwith, writing in 1822, urged that it would be a work of enormous advantage to the prosperity of mining districts to have meridian lines carefully set-out at distances of 1 mile from each other, and tall posts placed on these meridian lines at every mile in length, the undulating surface of the country being truly reduced to a horizontal base, so that these posts or stations should indicate squares of exactly square mile.

1

The best method of permanently marking out the meridian is to insert, to a depth of 3 to 5 feet in the ground, a hard stone, 6 to 8 feet long and 2 feet square. The portion of the stone projecting from the ground is faced, and the top plane is made at right angles to the axis. To avoid as much as possible the action of frost, it is advisable to give the stone a good foundation and to fix it in cement. On the top of the stone a brass plate, a foot square, is fastened, so that it is exactly horizontal, and on this the direction of the meridian line is shown by a fine engraved line.

When the direction of the meridian is to be shown by two stones a distance apart, points must be marked on them exactly in the meridian. For this purpose, it is best to drill holes into which staves can be inserted.

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For practical purposes, a simple method of ascertaining the annual variation is to take the bearing of some remote permanent object, such as a church steeple, from a fixed point. bearing of this so-called line of orientation is recorded from year to year, the difference in the readings giving the annual variation.

This line is also of great value if several dials are used in the same mine. In consequence of small errors in the construction of the instruments, the bearing of one and the same line is found to vary when determined with different dials. By observing the line of orientation, the error of each dial may be determined, and applied as a constant correction to all subsequent readings.

Inclination of the Magnetic-Needle.-If a magnetic-needle is free to move vertically, it does not, at most places on the earth's surface, rest in a horizontal position, but inclines more or less from it. The angle between the needle and the horizontal line is called the dip or inclination of the needle, provided that the vertical plane in which the needle moves is the magnetic meridian of the place. The dip varies at different places; at the magnetic equator there is no dip, whilst at the magnetic poles the needle stands vertically.

The dip is not of great importance to mine-surveyors in Britain, as the needles of dials are carefully compensated when sold. Surveyors going abroad with an English dial should be provided with a small sliding balance for the needle, which may be adjusted when necessary, should the dip prove at all trouble

some.

Like the magnetic declination, the dip is subject to secular variations. The following are results of observations near London extending over a series of years :—

CHAPTER V.

SURVEYING WITH THE MAGNETIC-NEEDLE IN THE
PRESENCE OF IRON.

Influence of Iron Rails.-The method of surveying described in the preceding chapter cannot be used in mines where magnetic substances deflect the needle. On account of the increasing use of iron and steel in mines in the form of rails, props, &c., the number of mines in which the magnetic-needle is not affected is extremely small.

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Rails placed end to end on the ground become, in the course of time, permanently magnetised, and if a magnetic-needle is brought near the junction of two rails, it assumes a position parallel to the two rails. Some interesting experiments to determine the influence of iron rails on the magnetic-needle were made by Professor Combes of the Paris School of Mines. found that the nearer the direction of the rails approached that of the magnetic meridian the more highly polarised they became. The following deflections were observed when a miner's compass was brought near rails which were placed in the direction of the magnetic meridian :