The delineation of parallel folds in structural sections, and the extraction therefrom of stratigraphic information, has generally been done with considerable personal interpretation. If profiles must be drawn, or sections measured, from structural observations used in pairs, this is unavoidable; but superior results may be obtained if more than two observations are simultaneously utilized.
The first section of this paper is an exposition of the method of evolute and involutes, which is applicable if three or more observations are available, lying in or close to a profile plane that is normal to the strike of a series of folded rocks. Parallel curves, which in certain sections represent the traces of parallel stratigraphic surfaces, are necessarily involutes that may be generated from one or more evolutes. It is more practical to derive an evolute, and to construct from it a set of parallel curves, than it is to draw such curves directly. Simple graphical methods are given for the construction of evolutes from different sets of structural data, and for the subsequent derivation of parallel curves. An examination of the resulting evolutes and involutes shows that most of them may be represented by the equation y = axn, if suitable values are assigned to the parameters a and n.
The second section of the paper is an exposition of methods that apply to the measurement of stratigraphic thickness, or other stratigraphic dimensions, if structural observations must be used in pairs. Four methods are discussed, which are known as the method of mean strikes and dips, the method of integrated trigonometric functions, the method of skew-line normals, and the method of integrated strikes and dips. The last named of these is a new method, which yields a mean value for the strike or dip, utilizing indirectly the concept of concentric arcs. A formula for mean dip (or mean strike) is derived, which has been computed for all values from 0° to 90°, at intervals of 5°. The results of this computation are given in a chart, which is used for the graphical computation of these values and for interpolation to less than 5°. The mean values of strike and dip that are thus obtained are substituted in any formula for stratigraphic dimensions that applies to a homoclinal sequence of rocks.
Under the topic of Errors and Differences, it is shown that the error resulting from the application of the method of evolute and involutes is small and is dependent mainly upon original errors in the determination of strike and dip. When observations are used in pairs, however, the resulting error may be much larger. If certain enumerated conditions are favorable, this error may be 10 per cent or less; but under unfavorable conditions, it may be 100 per cent or more.