40 



.SHORTER CONTRIBUTIONS TO GENERAL tiEOLOGY, 1021. 



al)le alinement charts for the sohition of both 

 thickness and depth of beds, but only in the 

 phme perpendicular to the strike of the for- 

 mation. The present paper is devoted to four 

 topics, as follows: 



1. The graphic and numerical solution of the 

 prol)lem of thickness of strata and the con- 

 struction of a five-variable alinement chart for 

 the graphic solution of the general formula. 



2. The graphic and numerical solution of 

 the problem of distance to a stratum, and the 

 construction of a five-variable alinement chart 

 for the graphic solution of the general formula 

 for depth to a stratum. 



3. The construction of a chart for the graphic 

 solution of a right triangle, to be used in con- 

 junction with the two charts above mentioned. 



4. The construction of a trigonometric com- 

 puter for the graphic solution uf all trigono- 

 metric formulas that may be used in geologic 



field work. 



THICKNESS OF STRATA. 



OUTLINE. 



It is rec[uired to find the thickness of geo- 

 logic strata lying between two known points, 

 when the following data are given; 



1. The horizontal and vertical location of 

 two points, which may be considered the begin- 

 ning and end points of a traverse. 



Figure 2. — Geometric representation of the tliieknpss of a stratum when the dip of the stratum and the rela- 

 tive positions of a point on the upper surface of the stratum and another on the lower siu-face are given. 



2. The azimuth tingle l)etween the strike 

 of the rocks and ;i line joining the two points. 



3. The dip of the rocks. 



In connection with No. I , ;uiy two of tlit^ fol- 

 lowing metisurements will sulhce: (n) .\ngle of 

 slope between the two stations, (7*) difference 



in elevation between the two stations, (c) slope 

 distance between the two stations, id) hori- 

 zontal distance between the two stations. 

 Therefore four sets of data are given, and these 

 together with the answer (thiclviiess of strata) 

 will necessarily produce a trigonometric equa- 

 tion of five variables. 



GEOMETRIC CONSTRUCTION. 



In the first publictition by P.almer, previously 

 mentioned, the genertd formula for this ])rob- 

 lem is derived. A (Ufferent solution using 

 descriptive geometry, from which the formula 

 is derived, is here used. It is well known that 

 two cases re((uiring this formula exist — (1) 

 where the di]) of the beds and the slope of the 

 hillside sire in opposite directions, which is the 

 more usutil condition; and (2) where the dip 

 of the l)eds ;ind the angle of slope of the hillside 

 arc in the same direction. The solution for the 

 first of these cases is here given. 



In figure 2, let AB be a horizontal reference 

 plane which jiasses through the station Sj. 

 Let s be the slope ilistance between the two 

 stations Si and S, (traverseil distance), h the 

 horizontal distance between the t\vt> stations, 

 (' the ditl'erence in elevation between the two 

 stations, and a the angle of slope of the hillside. 

 Let a be the azimuth angle of the traverse, or 



angle between the di- 

 rection of traverse and 

 the strike of the forma- 

 tion, and let 8 be the 

 angle of dip of the rocks. 

 It will be assumed that 

 s and a are given. By 

 revolving the right, tri- 

 angle SiS,0 from its 

 vertical position down- 

 ward 90° on OS as an 

 axis into the plane of 

 reference, r and h may 

 also be measm'ed. 



Let S,T be the strike 

 of the beds. It will also 

 be the trace of the base 

 of the stratum to be 

 measured upon the reference plane. Through 

 O, the lioiizontal projection of S., upon the 

 reference plane, draw OM parallel to S,T. Lay 

 off ON = OS, = f. Then, r and 8 being known, 

 the right triangle NOL, which has been re- 

 volved downward 90° on OL as an axis into the 



