Fig. 71.
It will be evident, on reflection, that when the cylindrical body stands parallel with the direction of the rays of light, as shown in [Fig. 68], the lightest part will be in the middle, and the shade will increase in intensity as it approaches the edges. The shading of the interior of a cylinder is, as we have already remarked when treating of shade lines, the converse of that of the exterior. This is shown in the sectional elevation, [Fig. 69]. When parallel with the direction of the rays of light, as in [Fig. 70], the internal shading is the same as the external. On bright circular surfaces, such as that of a circular saw, or the polished end of a shaft, the light is radiated from the centre, as shown in [Fig. 71]. This mode of shading is strictly in accordance with the appearance presented by such surfaces. It may be remarked here, that if, through inadvertence, any part should be made too dark, the error may be corrected by darkening all the other parts in a corresponding degree.
Fig. 72.
Shading Lines in Topographical Drawings.
—The shading lines put upon mechanical drawings are merely accessories used for purposes of embellishment. But in topographical drawings, shading lines are applied to give expression, and they constitute an essential element in the representation. We have shown how undulations of the ground, constituting hill and valley, are represented by contour lines. But it is obvious that these lines furnish information respecting the character of the surface only at those points through which they pass. Thus we are necessarily left in ignorance of the irregularities existing between any two successive contours. To supply this information which the contours fail to give, shading is resorted to. Another important object of hill shading is to represent the surface of the ground conventionally in a manner that will immediately afford an idea of its character without the aid of regular contours. The method adopted consists in employing lines varying in their thickness and in their intervals apart according to the slope of the ground to be represented. This method is based upon the principle of the horizontal contours, which is to give to the same vertical interval the same absolute amount of shade, whatever the inclination of the ground may be. The shading lines are used, as we have said, to fill in the features of the ground between contours already fixed; and to ensure accuracy and uniformity in the representation, a “scale of shade” is employed. The accompanying [Fig. 72] shows the standard scale of shade adopted by the Council of Military Education, and made use of for all the Government surveys. The second and the fifth columns of this scale show the spacing of the hachures and their thickness for different angles of slope, while the first and the last columns show the number of hachures to be interpolated between contours at every 25 feet vertical intervals, supposing the slope to be uniform. The slope is denoted both by the number of degrees in the angle it makes with the horizontal, and by a fraction showing the ratio of the vertical height to the base in a right-angled triangle, the hypothenuse of which is the slope in question.
The scale of shade is constructed for a horizontal scale of six inches to the mile, and the amount of shade has been chosen with a view of producing the best possible artistic effect. Of course, the most satisfactory results, both artistically and practically, will be obtained when the ground is delineated to this scale, but it can be readily applied to any other scale. For example, the horizontal interval for a slope of 1⁄20, corresponding to a vertical interval of 25 feet, will be 20 × 25 = 500 feet, which, on a scale of six inches to a mile, will be represented by a length equal to 500⁄5280 × 6 = 0·566 inches. In this case, therefore, supposing the slope of the ground to be uniform between two given contours 25 feet apart, we should represent it by means of the hachures shown opposite a slope of 1⁄20, continued over a space of 0·566 inch.
Fig. 73.