Note 14: — CATEGORIES

The imaginary interval we place between objects of different perspective effacement, can be expressed in terms of exact lateral measurement. This is done by developing and measuring the associative groups represented in the perspective group. Supposing we wish to get an exact definition of the perspective condition of a mountain relative to a certain station, we can, from that station, develop all the natural groups up to the mountain (walk over the ground) and measure the lateral intervals and masses disclosed. The total measurements will be a definition of the mountain's perspective distance in terms of true associative distance. That is what we mean by saying a mountain is ten miles off. It is not really ten miles off—it is not an inch off. But to render it tactually perfect we should have to expend an amount of energy equal to 17,600 times the energy required to move from one associative object to another a yard apart from it laterally. If we practise the mileage scale in conjunction with the perspective indications, we may acquire the art of expressing in miles, though not measured, the distance of objects estimated from purely perspective data, but few can do this with any near approach to exactness14.