To find the proportion of black to white in the foregoing scale for any given slope:--Subtract the given inclination from 45° for a denominator, and put the given inclination for a numerator. In the scale, as drawn in the figure, the variations are by 5°; but it is obvious that a scale may be drawn in the same manner to mark smaller variations, if thought desirable.
In applying this method in the United States’ Coast Survey, it was remarked that “this scale of shade does not represent slopes greater than 45°, thereby limiting the graphic capabilities and effect of the map. It also makes the slopes too dark as they approach the inclination of 45°, and does not well represent slopes of less than 5°, which latter it is often desirable and necessary to express distinctly.” The following modification was therefore made:--
-----------------+------------- |Proportion of Slope. +------+------ |Black.|White. -----------------+------+------ 2¹⁄₂° or 2³⁄₄° | 1 | 10 5° „ 6° | 2 | 9 10° „ 11° | 3 | 8 15° „ 16° | 4 | 7 25° „ 26° | 5 | 6 35° | 6 | 5 45° | 7 | 4 60° | 8 | 3 75° | 9 | 2 -----------------+------+------
By this scale, the slighter slopes are represented distinctly. For slopes less than 16°, the shades are darker than in Lehmann’s scale; this makes their difference more noticeable. Above 25° the shades are lighter.
A further modification, which for ordinary purposes possesses the advantages of simplicity and facility of application, has been made in England, and very generally adopted. This modification consists in fixing with accuracy only three proportions of black to white for three medium slopes, as follows:--
-------+------------- |Proportion of Slope.+------+------ |Black.|White. -------+------+------ Level | .. | all 15° | 1 | 2 22¹⁄₂° | 1 | 1 30° | 2 | 1 45° | all | .. -------+------+------
A scale of shade may at once be constructed from this Table, by assuming the thickness of the shading line for the medium slope of 22¹⁄₂°, which thickness must be suited to the scale, and to the degree of fineness and finish it is intended to give the drawing. Generally, if the lines have such a relation to the scale of the drawing as to present a well-connected appearance, it will be found that fewer shading lines and a rather coarse texture will conduce more to clearness of expression than a finer texture, which tends to produce a dryness of style. In shading to this scale, it should be applied to the drawing wherever the slope corresponds to one of the three on the scale. Intermediate slopes are indicated by graduating the thickness of the shading lines. In all cases a good deal must be left to correctness of eye and skill of hand.