II.—Graphical Methods in Field-Geology

Extract

In determining the actual position of strata from the appearances presented by their exposed edges in natural and artificial sections, certain mathematical problems are of constant occurrence. To a field-geologist who is not content with rough guesses founded on judgments by eye, the solution of these problems is a matter of importance, and methods have accordingly been given for some of those most frequently met with. These solutions take the form of (1.) trigonometrical formulæ, which can be applied only with the aid of trigonometrical and logarithmic tables; (2.) tables specially prepared from these formulæ for use in the field; (3.) graphical methods, requiring only a ruler, scale and protractor, which may be conveniently combined in one instrument. Of the first kind is the formula for deducing the true dip of strata from two apparent dips, given in Green's Geology (p. 341, 1st ed.), etc. Among special tables are those of Mr. Jukes for finding the apparent dip in any direction from the true dip, and for connecting the dip, thickness and depth of beds: these tables are given in the appendix to the Survey Memoir on the Geology of the South Staffordshire Coal-field, and reproduced in Jukes's “Manual of Geology.” Graphical methods have been used for finding the true dip from two apparent dips: a method partly graphical but requiring a table of cotangents is given in Phillips's “Treatise on Geology” (p. 298, 5th ed.), and also by the Rev. E. Hill (Geol. Mag. 1876, p. 334); a purely graphical method by Mr. W. H. Dalton (Geol. Mag. 1873, p. 332); and an approximate method by Mr. Penning (Geol. Mag. 1876, p. 236), reproduced in his “Field Geology.” As Prof. Green has pointed out (ib. p. 377), the last-named method is equivalent to taking the angle for its tangent, and so applicable only to small angles of dip. Mr. Dalton's solution (loc. cit. p. 334) of another question, to find the effect on strata already inclined of a second tilt in a new direction, is only an approximation, and cannot be applied if the dips are considerable. It is erroneously assumed that the inclination of the strata in a direction at right angles to that of the second tilt is unaltered by the tilting.