HORIZONTAL OR TRAVERSE DIALLING.
Plane sailing in navigation, and horizontal dialling in mining, are nothing more than the practice of right-angled trigonometry, calling the hypothenuse the distance, the perpendicular the difference of latitude, the base the departure, and the angle opposite the base the course : consequently, any range of dialling, however complicated and ex tensive, may be reduced into a single triangle, the perpendicular of which will either be the east and west or north and south line, according to the main direction or bear ing of the work ; the hypothenuse will be the actual length of the dialling in a right line from the point of setting out to the termination ; the base will be the distance the termi nating point will fall right or left of the perpendicular ; and the angle made by the hypothenuse with the perpendicular will be the final course or direction of the work.
It therefore follows that the general practice of repeating or retracing a course of underground dialling on the surface may be avoided, and thereby the difficulties and dangers arising from obstructions, irregular ground, and the attraction of the magnet by iron, which always abounds in the vicinity of a mine, be done away.
What is said of Mercator's sailing may, in the chief respect, be applied to horizontal dialling, viz.: " It is the art of finding on a plane surface the motion of a ship upon any assigned course by the compass, which shall be true in latitude, longitude, and dis tance sailed." The first thing to be attended to is the statement of the work, or so placing the drafts that there may be no confusion in the operation, and that the perpendiculars and bases may fall on their proper sides.
In order to succeed in this essential matter, which may be considered the foundation of the work, note on which cardinal point the main direction of your dialling runs, whether east, west, north, or south, and reckon off your degrees right or left from that line : thus, if your dialling runs easterly or westerly, let the equator, or east and west line, be the point for numbering off your angles,—if northerly or southerly, the meri dian, or north and south line : consequently, this line will be the perpendicular of every triangle in the operation that comes within the sweep of half the circle, or 180° ; and should any of the drafts return beyond the north or south points, or exceed 90° right or left of the east point, then the angle must be counted from the west towards the north or south, as the draft may happen to incline.
This being done, it is evident that on a course of east and west dialling the bases north and bases south must be subtracted one from the other, and the remainder will be the departure or base-line, north or south as the dialling may have prevailed on this or that side; and if any of the drafts have gone westerly, then the perpendiculars west must be subtracted from the perpendiculars east, for the real length of the perpen dicular ; but if the dialling has prevailed most in a westerly direction, the perpen dicular will lie on that side : in short, as a matter of course, either for the difference of latitude, or rather difference of longitude in this case (the perpendicular), or for the departure (the base), the less number must be taken from the greater, and the differ ences will show the sides on which the operation lies.
This process must all be performed by the first table, where the hypothenuse is given, because in every case the actual measured line will be the longest side of the triangle; and after stating the work, as before directed, take out the numbers standing against the given angles in the table, and multiply them respectively by the length of the hypo thenuse, reduced into fathoms and parts (if any), and place them in their proper positions until the whole has been calculated ; then take the sum of the bases north and south one from the other, and the sum of the perpendiculars east and west one from the other ; the perpendicular remainders will show the east and west line, and the bases the distance the dialling has extended north or south of that line.
The work is now brought to that case where the difference of latitude and departure is given to find the course and distance, and in order to avoid the necessity of intro ducing extensive and intricate tables, used by navigators for this purpose, we shall have recourse to one simple act of instrumental operation, and, as two sides of the triangle are given, the thing may be quickly and safely performed: thus, draw the base the given length by a scale of equal parts, raise the perpendicular on one end of the base (and of course at right angles therewith), and mark off the given length, draw the hypothenuse, and the triangle will be complete ; then, by the same scale, measure the hypothenuse, and it will be the actual length of the dialling in a right line, from beginning to end; then, with a protractor or scale of chords, measure the angle oppo site the departure or base, and it will be the true course, bearing, or direction of the extreme points.
The degrees on the miner's compass are generally graduated from 1 to 360, and are figured towards the left hand: consequently, 90° stands at the west point, 180° at south, 270° at the east, and ends with 360° at the north; and when the same course is to be pursued,—that is, when the angles are to be taken and the drafts measured again,— there will be no necessity for finding the real direction of the line; for, as the sights are always fixed, the dialler need only be careful to observe that the needle stands at the same degree as in the original course: but, when the operation is to be plotted or trigonometrically proved, there will be a necessity for ascertaining the actual bearing of every draft in the work; and this may be done by the following rule:—