A simplified form of the "Method of Tangents" (Coates, 1945) is considered to be the most direct and the most flexible method of deriving geometrical control from the observed dips in the construction of accurate geological sections. The method is first described as applied to equal-thickness projections of folds in competent beds.

The causes of steep-limb attenuation in folds of orogenic belts are then analyzed. Without regard to the complexities introduced by plastic flow of mobile beds, it is considered that the major factor producing attenuation in a layered sequence of competent and incompetent beds is the varying compaction of the incompetent members. The compaction is greatest where the beds are vertical, where the resistance of the competent members offers no protection to the incompetent layers. A force resolution shows that the compaction for any attitude of dip (k¹) can be calculated from the formula, k¹ = K (1 - Cos dip), where K is the compaction in vertical beds expressed as proportion of original stratigraphical thickness. The fold profile does not become identical in depth u til K = 100 per cent, but it is apparent that identical folding can be produced only by plastic flow. There is empirical evidence to support the deduction that compaction has a maximum value of about 50 per cent.

The writer proceeds to demonstrate that the compaction factor as computed from the versed cosine formula can be allowed for in section construction by moving the projected "boundary ray," which on equal-thickness projections bisects the angle of tangent intersection, progressively toward the steeper dip. The position of such "compensated boundary rays" is determined by thinning ratios computed from the versed cosine formula.

To eliminate elaborate graphical constructions, the positions of these rays have been calculated for all possible adjacent dips in 5° units, and for values of K ranging from K = 10 per cent, at 5 per cent intervals to K = 50 per cent.