Dip Chart

Discussion of the paper of HOWLAND BANCROFT, presented at the Salt Lake meeting, August, 1914, and printed in Bulletin No. 91, July, 1914, pp. 1767 to 1769. THEODORE SIMONS, Butte, Mont. (communication to the Secretary*). -While preparing maps and models for use in mining litigations the writer was frequently confronted with the problem referred to in Mr. Bancroft's paper. His chart gives the apparent angle of dip with which a vein should be plotted on a vertical section not at right angles to the strike of the vein. For a quick determination of this apparent angle the writer has used an exceedingly simple graphical method, which he believes may prove helpful to engineers engaged in practical work. It is submitted, not as a criticism of Mr. Bancroft's paper, but as a means of solving the same problem when no chart is available and when calculations would consume too much time. The writer's method requires merely a few lines marked off on a piece of tracing cloth, as shown in Fig. 1: Draw line be on any convenient scale. At b erect a perpendicular, ba. By means of a protractor cut off on ba a number of angles within the probable range of variation of dip, so that a line connecting a and c, for instance, forms an angle of 60° with be, etc. With b as a center and be as a radius, draw a circle through c. This completes the tool for solving the problem. Fig. 2 represents the line of strike of the vein and db the trace of the vertical plane on which the vein is to be plotted with the apparent angle of dip. A° is the angle which this plane makes with the strike. Fig. 3 shows the application of the method: Place line cb of tracing over line db of Fig. 2 and move fore and back until line of strike becomes tangent to the circle. Connect d with the point (a) that marks the true angle of dip as found by measurement in the mine (60° in the case illustrated). The angle adb is the apparent angle of dip (C°) to be used in the vertical section. Proof.-As stated in Mr. Bancroft's paper, the apparent angle of dip is: tan C° = sin A° tan B° (1)