THE ROYAL ARTILLERY INSTITUTION. 
505 
the mile scale; if we refer to Fig. 3, it will be seen that it can be used for 
Fig. 3. 
5 10 MILE 
any scale which is either a measure or a multiple of the 6 inch scale, by 
simply altering the vertical interval of the contours, and thus obtaining 
horizontal equivalents corresponding to those marked on the scale of shade. 
In Fig. 3 we have three representations of the same slope (in section), on 
three different scales—viz. 12, 6, and 3 inches to the mile —BC the ver¬ 
tical interval between the contours (=50 feet), a the angle of inclination, and 
AB the distance apart of the contours in plan. Now, if the scale of shade 
was applied along the guiding line AB between the contours in each 
instance, we should have the inclination a represented—■ 
In the 6 inch plan by the true amount of shade, 
#12 « the shading would be too light, 
n 3 a a n dark. 
In the 12 inch representation, the base AB is double the base in the 
6 inch plan; in order, therefore, truly to depict the angle a, it would be 
necessary to bisect AB in B } and apply the scale of shade between A and B, 
and again between B and B. If the plan, therefore, is on a scale of 12 inches 
to the mile, the contours should be run at vertical intervals of 25 feet; we shall 
thus have horizontal equivalents corresponding with those marked off on 
the scale of shade, and consequently the different inclinations represented 
by the amount of shade assigned to them. In the 3 inch representation, 
the base or distance apart of contours in plan is evidently half that of the 
[vol. vi.] 6a 
