THE ROYAL ARTILLERY INSTITUTION. 
503 
too steep for manoeuvring troops over, and may be depicted as impracticable 
ground. By giving the maximum amount of shade to the 45° incline 
instead of 90°, we shall have increased our powers of discrimination between 
that incline and the horizontal plane. 
The scale of shade is arranged to enable the draughtsman to shade the 
different slopes, on the horizontal hachure system, the hachures being drawn 
in directions coincident with the contours of a hill. Its use entails the 
necessity for contours to be run at certain vertical intervals, dependent upon 
the scale to which the plan is drawn. It is adapted to a scale of 6 inches to 
the mile, the vertical interval of the contours being 50 feet; but can also be 
used when the plan is drawn on any other scale—such as 1, 2, 3, 9, 12, 18, 
24, &c. inches to the mile—as long as the vertical interval of the contours is 
altered accordingly. 
If we refer to Big. 1 (which is drawn to nearly three times the original size of 
Eig. l. 
2 3 5 7 ]0 15° 20*25* 35- 
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the scale of shade), it will be seen that the shaded spaces marked 35°, 25°, &c. 
are each equal to the distance apart of the contours in plan, where the vertical 
interval is 50 feet and the drawing on a scale of 6 inches to the mile. Let 0 
be taken as centre, and OA (= 50 feet vertical interval of contours), as radius, 
a circle described, and angles of 35°, 25°, 20°, 15°, 10°, 7°, 5°, 3°, 2°, be 
laid off in the quadrant AOK, we shall have AB , AC, AD, &c., the co¬ 
tangents of these different angles of inclination to radius AO, and will be the 
distances apart in plan of contours, having a vertical interval of 50 feet; so 
that, if in possession of a plan drawn on a scale of 6 inches to the mile, and the 
contours run at vertical intervals of 50 feet, by means of the scale of shade the 
value of the different inclinations in degrees can be ascertained. Thus, if on 
applying the scale of shade (see Plate) to the plan, it is found that the 
interval between two adjacent contours is equal to the fifth shaded space 
on the scale of shade, the inclination at that spot will be 10°. 
These spaces, AB, A C, AD , &c. are then filled in with hachures, or strokes— 
these strokes being drawn thickest and closest together so as to give the 
greatest amount of shade for the slope of 35°, and becoming gradually finer 
and further apart as the incline approaches the 2°, the least inclination—and 
a gradation or scale of shade thus obtained. The number of hachures 
assigned to each inclination is purely arbitrary; the number adopted is 
supposed to distribute the light and shade in as even a progression as 
possible. 
It will be observed, beneath these shaded portions two vacant spaces 
exist; these spaces are each equal to the cotangent (to radius AO), for the 
different angles marked on them; from the top, therefore, of one shade to 
