COMPUTATION OF THICKNESS OF STRATA AND DISTANCE TO A STRATUM. 



41 



plane of reference, may be measured, thus deter- 

 mining the distance OL. The line LK drawn 

 parallel to S,T is the trace of the top of the 

 stratum upon the rrfei'ence plane. Draw a 

 line connecting and perpendicular to LK and 

 SjT. Such a line, EH, is the distance between 

 the traces of the outcrops of the base and top 

 of the stratum, upon the horizontal plane. 

 When 5 and EII are known the right triangle 

 HDE may be revolved 90° upward on EH as an 

 axis into the plane of reference and the thick- 

 ness of the stratum (DE or /) may bo measured. 



TRIGONOMETRIC FORMULA, 



The trigonometric solution from this con- 



t = s (sin a sin 5 cos a + cos 5 sin a) 



When the dip of the beds and the slope of the 

 hillside are in the same direction, the + in the 

 formula changes to — . The general formula 

 therefore is 



t = s (sin a sin b cos a ± eos 5 sin a) 



(1) 



GRAPHIC REPRESENTATION OF THE FORMULA. 

 GENERAL PRINCIPLE. 



Computations may be performed numer- 

 ically, graphically, mechanically, or by a com- 

 bination of methods. Numerical solutions 

 of formulas recjuire the use of logaritlimic 

 tables and are avoided when possible cliieflj- 

 because they require too much time. It is 

 highly desirable to represent formulas graph- 

 ically or to compute them by some mechanical 

 device based on a graphic representation of 

 the functions involved. If some one formula 

 is used a great deal, it should preferably be 

 represented graphically, thus saving much time 

 in computation and reducing greatly the lia- 

 bility of errors in the result. If a variety of 

 formulas are being used, it will perhaps be 

 found more convenient to {)erform the com- 



putations by means of some universal com- 

 puting machine, such as a slide rule. 



The formula for the thickness of a stratum, 

 as above given, is one that may be used re- 

 peatedly in certain kinds of stratigraphic work 

 or only occasionally in other kinds but cer- 

 tainly is of use to every stratigrapliic geologist. 

 There are several objections to the numerical 

 computation of this formula. First, too much 

 time is required; second, the use of figures 

 introduces a greater liability to error than a 

 graphic computation; and tliird, the accuracy 

 of the answer, if five-place logarithmic tables 

 are used, is much greater than the character of 

 the original data justifies. The matter of 

 needless accuracy is often overlooked by geol- 

 ogists, \\-\i\\ the result that meaningless figures 

 and incongruous results are sometimes pub- 

 lished. In general it is true that in formulas 

 used by geologists in the field and office some 

 one of the variables will depend on an obser- 

 vation of the strike or dip of rocks. The 

 answer to the formula should obviously be no 

 inxDre accurate than the least accurate of the 

 component variables. For example, it is very 

 doubtful whether determinations of strike or 

 clip can be made with an error of less than 1°. 

 But even if 1° represents the maximum prob- 

 able error in careful work, it must lie remem- 

 bei'ed that geologic strata do not by any means 

 have mathematically perfect surfaces. There- 

 fore an adtlitioiud possil)ility of error is inti'o- 

 duced in the liability of the measm-ed direction 

 of strike or dip of surface to change within a 

 comparatively short distance, thus vitiating 

 a most carefully made measui'emeut. Extreme 

 accuracy in computation of geologic formulas 

 is therefore neither needful nor desirable, and 

 giuphic methods should be used. 



The graphic representation of a formula is 

 commonly accomplished by means of Cartesian 

 coordmates, but this system has serious draw- 

 backs when equations of more than two varia- 

 bles are to be plotted. When equations of 

 tlu-ee variables must be represented, a system 

 of curves must be drawn and an awkward 

 interpellation used. For equations of more 

 than three variables Cartesian coordinates are 

 not suitable. The equation 



t = s (sm a sin 5 cos cr ± cos 5 sin a) 



comprises five vai'iables, namely, t, s, a, 8, and 

 cr. Equations of three variables are most easily 



