GRAPHIC AND MECHANICAL COMPUTATION OF THICKNESS OF STRATA 



AND DISTANCE TO A STRATUM. 



By J. B. Mertie, Jr. 



INTRODUCTION. 



Two problems that ctJiistiintly confront the 

 stratigraphic and structural geologist are the 

 computation of the thickness of a geologic 

 section and the computation of distanc-e to a 

 stratum from some designated point at the 

 surface when the position of the outcrop of 

 that stratum is known. The solution of each 

 of these problems is divisible into throe parts — 

 a geometric solution, a trigonometric generali- 

 zation, and simplified methods of computation. 

 It is the piu'pose of the present paper to con- 

 sider these three phases of each of the two 

 problems above mentioned. 



Analyses of these two problems, so essen- 

 tially a part of the geologist's work, have 

 doubtless been previously made, but it is odd 

 that so little has been published on this sub- 

 ject, and particularly significant that most of 

 the published material has been of recent 

 origin. The obvious iivference is that we are 

 approaching a period in the development of 

 geologic science when accurate data will be 

 considered more and more essential to correct 

 stratigi-aphic interpretation; and the recent 

 interest shown in these and related problems 

 is an index of the general appreciation of this 

 fact by geologists. In other words, geology is 

 changing progressively from a qualitative to a 

 cpiantitative science, and older methods are 

 giving way to newer ones more adapted to 

 present needs. 



The only fault that may be found with the 

 material so far published on this subject lies 

 m its incompleteness. In some of the pub- 

 lished papers the wi'iters have not worked out 

 general formulas but have confined themselves 

 to the consideration of special cases, the solu- 

 tion of which, though useful, is not of universal 

 application. In other articles, in which univer- 

 sal solutions have been evolved, the treatment 

 is not well balanced because the above-men- 

 tioned thi'ee phases of each of the two main 



problems have not been considered adequately. 

 Thus, a geometric solution is of interest, but 

 if that alone comes within the scope of the arti- 

 cle its value will be impahed because no for- 

 mula is deduced, and the geologist will have 

 to repeat the solution for every individual set 

 of data. The trigonometric solution is of much 

 more value, but it will not be used by many 

 workers because it recjuu'es mathematical com- 

 putation. It is very desirable that gi-aphic or 

 mechanical methods be employed in the solu- 

 tion of all geologic formulas, first because in 

 using such methods no knowledge of trigo- 

 nometry is requu'ed, second because of the 

 saving in time they permit, and thu'd because 

 the resulting solutions are well within the Imiits 

 of accuracy imposed by the nature of geologic 

 observations. 



The principal publications known to the 

 wi-iter in which the problems of thickness of 

 strata and depth to a stratum are considered 

 are as follows: 



Hayes, C. W., Handbook of field geology, 1909. 



Roe, J. W., Application of descriptive geometry to 

 mining problems; .\m. Inst. Min. Eng. Trans., vol. 41, 

 pp. 512-533, 1911. 



Smith, W. S. T., Some graphic methods for the solution 

 of geologic problems: Econ. (ieology, vol. 9, No. 1, 1914. 



Palmer, H. S., Nomographic solutions of certain strati- 

 graphic measurements: Econ. Geology, vol. II, No. 1, 1916. 



Palmer, II. S., New graphic method for determining the 

 depth and thickness of strata and projection of dip: U. S. 

 Geol. Siu-vey Prof. Paper 120, pp. 123-128, 1919. 



In Hayes's Handbook trigonometric for- 

 mulas are derived, but only that special case 

 is considered where the field traverse is made 

 perpendicular to the strike of the beds. Both 

 Roe and Smith have made descriptive geometric 

 solutions, but neither derives formulas there- 

 from. In his fii-st article Palmer has derived 

 the general formula for the calculation of 

 thickness of strata and developed three-vaiiable 

 alinement charts for its graphic solution. In 

 his secontl article he has developed tliree-vari- 



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