known, subtract the former from the latter, the difference is the meridian angle of the first station-line. If the vernier angle exceeds the meridian angle, add 360° to the latter in order to enable the subtraction to be effected. The meridian angle of the first station-line thus obtained is added to each subsequent vernier angle, the sum in each case being the meridian angle of the line in question.

For example, the following angles were taken with the rack dial, the needle being thrown off except where true bearings were taken at E, looking back to D and forward to F:

At station E the angle and bearing are known. Consequently, to obtain the bearing of line A the angle 286° 00′ must be subtracted from the bearing 277° 09'. The latter being smaller than the former, 360° must be added, giving 360° + 277° 09′ = 637° 09'. This result less 286° 00′ is equal to 351° 09', the bearing of line A. The same result is obtained with line F. Thus,

(283° 09′+360°) - 292° - 351° 09′. The bearings of the other station-lines may be easily found by adding 351° 09′ to the observed angle in each case.

The work may be plotted, without any preliminary calculation, with the protractor and scale as if the survey had been made with the magnetic-needle. The protractor must, however, be graduated in the contrary direction to that required for a needle survey, if the dial is a left-handed one.

3. When the dial is numbered from the north from left to right, all calculation can be dispensed with; the angles being

read direct from the magnetic meridian.

The Davis dial is

graduated in this way. The horizontal circle of that instrument being also graduated from left to right, the bearings can be taken simultaneously with the loose needle and with the vernier, the latter acting as an automatic check on the former.

In making a survey in this way, select some disused road, where there is no iron present, and take its magnetic bearing from stations at the beginning and end. If there is no attraction, the two results will be identical. Then with the dial set up at the end station, clamp the vertical axis by tightening the collar attached to the ball and socket, unclamp the vernier-plate by slackening the clamping screw, and turn the sights by means of the rack and pinion screw, until the vernier reads exactly the same angle as the magnetic bearing just taken. This bearing is used as the basis of the subsequent determinations of the angles of the traverse. Clamp the vernier-plate, unclamp the vertical axis, and by means of the loose collar direct the sights to the lamp at the first station. If the readings obtained with the needle and the vernier are identical, the dial is in adjustment, and the whole of the underground workings may be surveyed from this base-line. In taking a fore-observation, the surveyor must turn the south side of the compass face towards himself, whilst in taking a back-observation, his eye must be at the north sight. The following is an example of a survey made by this system:-

The survey was commenced in a disused road, the bearing of which was found to be 30° 05'. The vernier reading was made to correspond with that angle. Then with the instrument set up at

A, a back-observation was taken to the lamp at the end of the disused road, the vernier remaining clamped at 30° 05'. The vertical axis of the dial was then clamped, the vernier-plate unclamped, and a forward-observation taken to B2. The vernier was found to read 315° 58'. Clamped at this angle, the dial was moved to B2, and the survey continued as before. The survey can be checked at any point by liberating the needle. If the vernier and needle readings differ, the amount of magnetic attraction is the difference between the two readings.

The dial being graduated from left to right, 90° indicates West, and 270° East. In plotting the survey a protractor graduated from right to left must consequently be used.

Surveying in Inclined Shafts.-The vernier-dial is of great value for surveying in inclined shafts containing iron pumps. The survey should be commenced in a level free from magnetic attraction. On the basis of the bearing thus determined, the survey is continued to the shaft.

Should the surveyor be called upon to determine the bearing of an inclined shaft, containing iron pumps, with a miner's dial unprovided with a vernier, he may perform the operation with a cross-staff, either a well-made brass instrument or an improvised one made by drawing two lines at right angles on a board, about 6 inches square and 1 inch thick. The lines must be cut half an inch deep with a fine saw. The instrument thus made is fixed

on a three-foot stand.

The cross-staff is set up in such a position that a candle in the shaft can be seen through one pair of sights. In the line of sight of the other pair, the dial is set up in the level out of the way of magnetic attraction. In this way, the candle in the shaft and the dial in the level form a right angle with the cross-staff. An assistant must now look through the sights of the dial to a candle held immediately above the cross-staff, and read the bearing indicated by the needle. Being exactly at right angles to this line, the bearing of the shaft may be at once determined. Thus, assuming that the needle reads 282°, if the underlie is northerly, the bearing of the shaft will be 12°; if southerly, 192°.

The

The Vernier Compass.-The vernier of the circumferenter may be used for reading the magnetic bearing. In this method of surveying, the compass-box is clamped with the needle lying upon the zero or north and south line marked on the dial. sights being then directed to the object, the bearing is read direct from the vernier to 3 minutes, or by estimation upon a superior instrument to 1 minute. This method is very expeditious, and gives most accurate results. At any point in the traverse, a fast-needle observation may be made without difficulty.

In working with the fast needle, it is advisable to invariably start with a loose magnetic bearing, and, if practicable, to close with one. Intermediate checks by the same means are desirable, but not essential. In this way, the needle lies upon the zero line at every set, except where local attraction prevails, of which the amount and direction are shown by the needle's deviation from that line. The result is that the traverse angles booked are also magnetic bearings.

In order to show grounds for confidence in this method, the details of an actual survey, made by Mr. W. F. Howard,* may be quoted. The survey was made between the Speedwell and

* Trans. N. Engl. Inst. M.E., vol. xx., 1870, p. 31.

Netherthorpe shafts at Staveley, with the intention of effecting a holing into the latter. The straight distance between the shafts, measured direct on the surface, was 31.13 chains, and the distance between the shafts by the underground roads was 35-43 chains, making the total circuit 66-56 chains, and requiring 16 sets underground. The foregoing is a copy of the survey notes.

The survey was made with a 5-inch Davis dial, divided to halfdegrees, with a vernier reading to 3 minutes.

In this instance, the magnetic bearing and the horizontal distance sought, from the face of the heading to the intended upcast shaft, was calculated to be N. 58° 38′ E., 190.5 links.

It

was then determined to drive direct into the shaft, and the draft was accordingly set out at the above bearing; and the holing proved this bearing and the calculated distance to be absolutely

correct.