To show the method of measuring very long distances we have to work with a very small scale to the foot, and in Fig. 94 I have divided the base _AB_ into eleven parts, each part representing 10 feet. First draw _AS_ and _BS_ to point of sight. From _A_ draw _AD_ to ¼ distance, and we obtain at 440 on line _BS_ four times the length of _AB_, or 110 feet × 4 = 440 feet. Again, taking the whole base and drawing a line from _S_ to 8th distance we obtain eight times 110 feet or 880 feet. If now we use the 16th distance we get sixteen times 110 feet, or 1,760 feet, one-third of a mile; by repeating this process, but by using the base at 1,760, which is the same length in perspective as _AB_, we obtain 3,520 feet, and then again using the base at 3,520 and proceeding in the same way we obtain 5,280 feet, or one mile to the archway. The flags show their heights at their respective distances from the base. By the scale at the side of the picture, _BO_, we can measure any height above or any depth below the perspective plane.
_Note_.--This figure (here much reduced) should be drawn large by the student, so that the numbering, &c., may be made more distinct. Indeed, many of the other figures should be copied large, and worked out with care, as lessons in perspective.
FURTHER ILLUSTRATION OF LONG DISTANCES AND EXTENDED VIEWS
An extended view is generally taken from an elevated position, so that the principal part of the landscape lies beneath the perspective plane, as already noted, and we shall presently treat of objects and figures on uneven ground. In the previous figure is shown how we can measure heights and depths to any extent. But when we turn to a drawing by Turner, such as the 'View from Richmond Hill', we feel that the only way to accomplish such perspective as this, is to go and draw it from nature, and even then to use our judgement, as he did, as to how much we may emphasize or even exaggerate certain features.
[Illustration: Fig. 95. Turner's View from Richmond Hill.]
Note in this view the foreground on which the principal figures stand is on a level with the perspective plane, while the river and surrounding park and woods are hundreds of feet below us and stretch away for miles into the distance. The contrasts obtained by this arrangement increase the illusion of space, and the figures in the foreground give as it were a standard of measurement, and by their contrast to the size of the trees show us how far away those trees are.