example, the needle has been known to be deflected to the extent of 60° from its proper bearing. Experience shows that certain eruptive rocks, notably those of a dark colour with a base of hornblende or augite, affect the needle in the same way as magnetite or magnetic pyrites. In districts composed of magnetic rocks, the dial cannot be employed, as is shown by observations made at Ammeberg in Sweden, where at equidistant points along a straight line, the following bearings were obtained :3° 5, 3° 4′, 3° 25', 3° 1′, 2° 73', and 2° 6'. To make a number of observations along a straight line is the best method of finding out if there is any local attraction affecting the needle. The influence of magnetic deposits on the compass has been utilised in Sweden and the United States in exploring for iron ore.

Surveying with the Dial in the presence of Iron.-With the general employment of iron rails in mines, the question arises to what extent may surveys be made with the ordinary dial without fear of deflections of the needle giving rise to error? As a matter of fact, the magnetic-needle may be used for the purpose of obtaining the true bearings of the traverse lines in places where attraction exists, provided that the mode of procedure is slightly modified. The method is based upon the fact that the deviation of a magnetic-needle remains the same, if the relative positions of the dial and the attracting object remain unaltered. All that is necessary is to note the back- and fore-bearing at each station, however much the magnetic-needle may be deflected. Then, if the needle is attracted on looking to the back object, it is attracted to precisely the same extent on looking forward, so that the difference of bearing of the two lines is unaltered. Consequently, if a correct bearing of any one line of the traverse can be obtained, an accurate survey may be made.

Dialling-Book. The best form of dialling-book to adopt is an ordinary account-book, the £, s., and d. columns serving for fathoms, feet, and inches. If the measurements are made in links, only one column is required. The date column of the account-book serves for the number of the draft. In the space between the date and money columns, two lines are ruled, giving three columns, which may be used for the back-bearing, the forebearing, and the calculated true bearing.

The method of booking a survey is shown by the following example of a closed traverse, surveyed in the presence of a very large amount of iron. The bearings and distances were as

follows:

The instrument was set up at B, where there was no attraction, and a back-bearing was taken. This was found to be 3° 36'. This bearing being correct, it was also entered as a fore-bearing at A. A fore-bearing was then taken at B; this was found to be 1° 36'. This also is correct, as there was no attraction when the back-bearing was taken, and the dial was not moved to take the fore-bearing. The instrument was then moved to C, and a back-bearing to B taken. This should have read 1° 36′, the correct fore-bearing from B to C. It was, however, found to be 5° 27', showing that the needle was considerably deflected from its true position. Back- and fore-bearings were taken at each of the following stations, and in each case the needle was found to be seriously deflected. Consequently, before the survey could be plotted, the correct bearings had to be calculated.

The bearings 3° 36′ and 1° 36′, being known to be correct, might be inserted in the correct-bearing column. The backbearing at C was found to be 5° 27′ instead of 1° 36′. It was therefore 3° 51' too great, and as the dial was not moved, the attraction remained the same, so that the fore-bearing at C was also 3° 51' too large. The correct fore-bearing at C, then, was 327° 44' 3° 51' = 323° 53'. The back-bearing at D, which should be the same as this, was found to be 319° 15', that is, 4° 38' too small. The fore-bearing taken at the same station under the influence of the same attraction must also have been 4° 38′ too small, so that its correct value is 224° 53′ + 4° 38′ : 229° 31'. The back-bearing at E should be identical with this. It was, however, found to be 202° 57', that is, 26° 34' too small. The fore-bearing at the same station must also be 26° 34' too

=

=

183° 18'.

small. Its correct value, then, is 156° 44′ + 26° 34′ This should be identical with the back-bearing at F, which was found to be 167° 48', or 15° 30′ too small. The fore-bearing at F is also 15° 30' too small, and its correct value is 165° 03′ + 15° 30′ 180° 33'. This should be identical with the backbearing at G, which was found to be 166° 15', or 14° 18' too small. The fore-bearing is also 14° 18′ too small, and therefore the correct bearing is 79° 48′ + 14° 18′ 94° 06'. This should be identical with the bearing at the last station, which was found to be 79° 34', or 14° 32′ too small. The fore-bearing at the same station is also 14° 32′ too small, and therefore its correct value is 349° 04′ + 14° 32′ = 363° 36', that is, 3° 36'. The last line of this traverse is identical with the first, so that the first and last bearings should be identical. Thus, in a closed traverse the surveyor is able to check the accuracy of his work.

The following page from the dialling-book at a metalliferous mine may be taken as an example for calculation :—

If the first and last bearings are not identical, and if the difference does not amount to more than a few minutes, the slight error, due possibly to the imperfections of the instrument employed, may be to a great extent eliminated by dividing the error by the number of station-lines, and adding the result to, or subtracting it from, each bearing. Thus, in the example given, if the observed fore-bearing at H had been 349° 00′ instead of 349° 04′, the final error would have been 4'. It would be assumed that no error occurred in reading the first bearing. The error in each bearing would consequently be about ', and the calculated bearings could have been corrected for this error by adding in each case, that is to say, 'to the calculated bearing of B, 1' to that of C, 1' to D, 2' to E, 21' to F, 3' to G, and 4' to H.

In applying this method to colliery and surface-surveys, it will be found advisable to book upwards in the usual manner, noting the back-observation (B.O.) at each station. A tabulated statement of the bearings may then be made, and the true bearings calculated.

Errors in Compass Surveys. In all cases where the dial is used for surveying in the presence of iron, the greatest care must be taken in making the observations; otherwise very serious errors may arise, especially in long traverses. This may be illustrated by an example.

In making a survey in the ordinary way with the dial, any error in the readings will cause the next draft to have a false position when plotted. Assuming that a survey is made between the points A and E, Fig. 16, and that the bearings are read

direct from the dial without error, the plan of the traverse will be correct, as shown by the line A B C D E in the figure. If, on the other hand, a mistake is made during the progress of the survey, and the bearing, NA B, of the line A B incorrectly determined to the extent of the angle BAB' or a, then the following drafts will have the same error. B' will be the end point of first draft when plotted, thus giving a lateral error of B B'. The other bearings of the traverse being correctly determined, on plotting, the lines B'C', C'D', D'E' will be obtained. These lines must be equal and parallel to the lines BC, CD, DE, and therefore BB' CC' DD' = EE'. In other words, the lateral error B B' caused by the

Fig. 16.

the

=

incorrect determination of the bearing of the line A B is carried uniformly throughout the traverse, whatever its length may be. The magnitude of this error is found by trigonometry to be

The magnitude of the error is entirely different when the dial is used as an angle-measurer in surveying over iron. Again, assuming that the bearing of the line A B has been incorrectly determined to the extent of the angle a, the angle N A B' having been read instead of the angle NAB, if now the dial is employed for measuring the angles, the bearing of the next line, BC, is obtained by adding or subtracting the exterior angle at B, according as the line B C is to the right or left of A B. The other bearings in the presence of iron may be assumed to have been correctly taken. The bearing of the line AB being incorrect, the bearing of the line BC will also be incorrect to the extent of the angle a. Each of the following bearings will be incorrect to the extent of the same angle, so that on plotting the calculated bearings, the line A B′ C" D" E" will be obtained. The error a thus affects the whole traverse from A to E, and increases in proportion to the distance apart of those points. The length from A to E being represented by L, the lateral error, E E" is equal to 2 L sin 2.

a

It is thus evident that a survey may be very inaccurate, when the angles are not correctly measured. In applying the method of surveying with the needle over iron, the surveyor should not fail to make a check-survey, or reverse course of dialling, selecting fresh points for his stations. Not only in this method, but in all other surveying operations, it is highly desirable that the mine-surveyor should adopt the practice of always checking and verifying every part of his work.