the plan is plotted is a large one, the measurements will be plotted more accurately; but any errors made in marking off the bearings from the protractor will be increased. In making a plan, the surveyor first plots the skeleton outline as shown in Fig. 99. When satisfied with that, he rules in the details as shown in Fig. 100; this gives the width of the gate-roads, strait-work, banks, and, if desired, the position of overcasts, stoppings, and other ventilating arrangements, though these are not usually shown on the working plan, but are put on another plan kept especially for ventilation, the arrangements for which, except in the case of permanent overcasts and some of the stoppings and separation doors, are liable to continual alteration. Ogle's Protractor.-Where it is possible to fix the paper on to a drawing-board and to use a T-square, the protractor shown in Fig. 100A can be advantageously employed. It consists of an outer frame, a, with a true edge to work on the T-square; inside this frame is a graduated ring, b, capable of being rotated; and inside this is another ring, c, also free to rotate. To use the protractor, the N and S marks on the ring b are placed parallel with the meridian line on the plan, and the ring is then clamped; the required bearing can then be set off by moving the inner ring c to the required angle. Trigonometrical Plotting.1-The mechanical errors of plotting may be altogether eliminated by adopting a system of trigonometrical computation, by which the latitude and longitude of every station in the mine are found, and recorded in a surveybook. The positions on the plan may be sketched in by hand or put on by scale, according to circumstances, and the distance between any two parts of the plan may be calculated from the information contained in the survey-book, and also the bearing of any proposed new road between any two places on the survey. To facilitate the drawing of the plan, it is made on paper ruled in squares, thus forming lines of latitude and longitude. In France it is a common thing to have the plan made upon a number of separate pieces of paper or cardboard, each piece say about 2 feet square; these can be pieced together, as shown in Fig. 101, as required. In England, however, the practice is almost universal of having the whole of the survey on one large piece of paper. If the size of this becomes unwieldy, the plan is divided into several districts; in this case a smaller scale plan is used, containing the whole of the mine for occasional reference, so that the engineer may see at a glance the relative positions of different parts of the mine, whilst using the large scale plan for details. The trigonometrical system of computation, where used in England, is generally used for checking some main stations when, owing to particular circumstances, greater accuracy than usual is necessary. The system, however, of ascertaining the latitude and longitude of every station has many advantages, especially where the area under one management covers a large extent of country, and in fixing the boundaries between different concerns. Wherever there is a Government survey the lines of latitude and longitude shown on the Ordnance maps should be adopted, the measurement to the shaft being taken from three or four of the nearest station marks. A short but excellent treatise on this subject, entitled, "Practice in Underground Surveying, etc.," by the late Mr. W. F. Howard, A.I.C.E., of Chesterfield, is contained in the Proceedings of the North of England Institute, vol. xx., and in the Chesterfield and Derbyshire Institute, April 13, 1878. This method of plotting is applicable equally to surface and underground surveying. It is usual, in England, to calculate the position of every station in links and to two decimal places. If the calculations are properly checked, there can be no error, and the relative positions of any two places on the surface, or any two underground places, or of one place on the surface and another place underground, can be stated to two decimal places of a link for distance, and with equal accuracy for bearing, always supposing, of course, that the measurements taken in the survey and the angles observed are perfectly accurate. By this system, therefore, the errors of plotting are entirely eliminated. On reference to Fig. 102 the method of computation will be explained. Five points on the survey are A, B, C, D, and E, of which A is the beginning. The bearing AB is N. 50° W., the length 850 links; the bearing BC is N. 33° 20′ W., and the length 731; the bearing CD is N. 41° 35′ 20′′ E., and the distance 762-2; and the bearing DE, S. 38° 30′ E., and the distance 280. If we assume that the point A is the point of origin, and has 0° longitude and 0° latitude, what are the positions of B, C, D, and E? In ordinary technical parlance in England it is usual to speak of distances measured from longitude to longitude as "departures," and of distances measured from latitude to latitude as "latitudes." In France the geographical terminology is maintained, and the distances measured from longitude to longitude are referred to as "longitudes;" but as in English books the word "departure" is constantly substituted for "longitude," the student must understand that they are convertible terms: the "latitude" means the distance measured N. or S. along the meridian, and the "departure" means the distance measured E. or W. at right angles to the meridian. To ascertain the latitude and longitude of B, the distance AB may be regarded as the radius of a circle of which a portion is shown, xyz; the meridian line AM is drawn through another radial line, and from B a perpendicular is let fall on to the meridian at s. The line Bs is the departure of the line AB, or distance measured between lines of longitude, and is the sine of the angle at A to radius AB. The line As is classed under the title of latitudes, and is the distance from latitude to latitude of the line AB, which is the cosine of the angle at A |