above alluded to, in which the subject is treated at considerable length. No one, however, knowing the method of surveying by the chain, as taught in the parish surveying, and the use of the theodolite, ought to devote much time in acquiring a method far inferior.

SUBTERRANEAN SURVEYING,

AS PRACTISED IN COAL PITS, MINES, ETC.

Subterranean surveys are generally performed by means of an improved circumferentor, furnished with a large compass and magnetic needle, as in the common circumferentor; and a limb with a vernier, as in the theodolite. Such an instrument enables the surveyor to take angles with greater precision than the common circumferentor in general use. Being supplied with this improved instrument, you place it on the spot from which you mean to commence your survey, and sending a man with a lighted candle to as remote a point as can be seen from the instrument, you take the bearing of the candle, and measure up to it; then note the bearing and distance in your book. You now remove the instrument to where the candle stood, and sending the man with the candle forward in the direction you desire, you take the bearing of the candle, as before, and measure up to it with the chain, and noting the bearing and distance in your book, remove the instrument to the spot where the candle stood, and repeat the operations until the entire is completed.

The principal objects of a subterranean survey are,

1st. To ascertain the proper places for sinking shafts, either for the convenience of raising the produce, or for the purpose of ventilating the mine.

2nd. To ascertain if the workings extend to an adjoining property.

3dly. It may be necessary to direct the mine towards another pit.

There may be other cases in which be other cases in which it would be necessary to trace the course and distance of the mine on the surface; but whatever case may arise, the work may be effected in the following manner :

Place the instrument as near the pit as may be deemed convenient, "so that when the fore-sight is put in the direction of the first bearing, you may, by looking backwards, cut exactly the centre of the pit; if it does not do so, the instrument is not placed in a proper position, which must be obtained by shifting the instrument to the right or left, until it is in the situation before mentioned." Having this found, measure the distance of the first bearing from the centre of the pit; then you remove your instrument to the end of your reckoning, and take the next bearing as noted in your mine-book, and the proper distance along this bearing; and thus proceed till all the bearings and distances are traced on the surface, which have been noted in your mine-book. It is sometimes very difficult to ascertain the first bearing on the surface, by this method; therefore the following is recommended. You place your instrument near the mouth of the pit, and take the first bearing and distance, as noted in the mine-book; and also, from the same spot, take the bearing and distance of the centre of the pit; then at the end of the measured

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distance, place your instrument, and set it to the same bearing as the centre of the pit had, from the point commenced from; measure also the same distance, on the last bearing, that had been measured from the commencing point to the centre of the pit; then at the end of this distance place your instrument, take the second bearing and distance from your book, and so proceed till all is completed. After having found the first bearing, it would be much better to use the theodolite in the remaining part of the survey.

PROP. 1.- To find the variation of the Compass.

Astronomy points out various ways of finding the variation of the compass.

1st. The variation may be found by means of the azimuth of any celestial object, which is an arc of the horizon, intercepted between the meridian of the place, and the vertical circle passing through the sun or star; and is equal to the angle at the zenith, formed by the said meridian and vertical circle.

The azimuth is found by the following rule :

As radius is to the tangent of the latitude, so is the tangent of the altitude of the sun or star, to the cosine of the azimuth, from the south, at the time of the equinox.

The magnetical azimuth is an arc of the horizon, contained between the magnetical meridian and the vertical circle of the object; or its apparent distance from the north or south point of the compass. This is found by observing the sun or star with an azimuth compass, when it is 10 or 15 degrees high, either before

or after noon. The difference between the computed and observed azimuth, is the variation. The variation may also be found from the amplitude of the sun or a star, which is an arc of the horizon, intercepted between the true east or west point, and the centre of the sun or a star, at its rising or setting. The amplitude is found by the following rule :

As the cosine of the latitude is to radius, so is the sine of the sun's or star's declination, to the sine of the amplitude.

Magnetical amplitude is an arc of the horizon, contained between the sun or a star, at its rising or setting, and the magnetical east or west point of the horizon, as pointed out by the azimuth compass. The difference between the observed and computed amplitude, is the variation of the needle.

In the latitude of Dublin, viz. 53, when the sun's declination is 23° 28', then

That is, the sun then rises or sets 41° 26' from the east or west point to the north or south, according as the declination is north or south. If the magnetic amplitude be observed by the compass to be 14° 11', then the difference is the variation west.

The same conclusion may be arrived at by taking two equal altitudes and azimuths of the sun. For the meaning of the astronomical terms here introduced, see the author's Epitome of Astronomy.

PROP. 2.-Given the area, and map of a survey, to find the scale to which the map was laid down.

Construct another map, exactly similar to the given one, to any scale you please; find its area: then say, as this area is the given area of the survey, so is the square of the scale to which this plan was laid down, to the square of the scale required; the square root of which will be the required scale.

The area of a survey is 48A. 3R. 10P., and the area of a similar plan, constructed to a scale of 3 chains, or 12 perches to the inch, is 12A. OR. 32 P.; required the scale to which the map was constructed.

48A. 3R. 10P. 7810 perches.

1952 7810 :: 9:36. Then 36-6 chains. Hence the map was laid down to a scale of 6 chains, or 24 perches, to one inch.

PROP. 3.-To cut off any required number of acres from a given survey, by one line drawn through it.

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Let it be required to cut off 56 acres, 3 roods, and 8 perches, from the piece of land ABDC, commencing from AB. Draw FE at right angles to AC, cutting off, as nearly as you could guess, A the required area. Survey the figure ABEF, and find the difference betwixt its contents and 56 acres, 3 roods, 8 perches. Multiply this difference by 2, and divide the product by the length of EF in chains, then

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