In this diagram the distances of carriage are represented along the horizontal line, A B; while the rate charged is laid off vertically. The distances A C and E B represent the constant terminal cost; while the steadily rising rates with increasing distance, due to movement expenses, are shown by the sloping dotted line C D. This chart at once demonstrates why under the very simplest physical conditions a straight mileage tariff is unscientific and unreasonable. For the constant terminal expense, spread evenly over the mileage traversed as the movement expenses grow, becomes progressively less and less in proportion to the total of the two, which constitutes the real rate. The longer the haul, the lower the ton-mile cost as a matter of necessity. As Chanute calculated on the New York Central a generation ago,[65] while the average cost per mile of hauling a ton ten miles was 4.062 cents, it descended progressively to less than one cent per mile for distances over five hundred miles. A common rule is that the rate rises as the square root of the distance, rather than in proportion to it. A hundred-mile haul represents a cost approximately only twice as great as one of twenty-five miles, instead of being four times as much. For thrice a given cost the haul may be increased nine times. The course of such a tariff with increasing distance would be represented by the parabolic curved lines on the preceding diagram.[66] The particular curve would depend upon the commodity and local physical conditions. In territory where movement expenses were heavy or operation difficult, the curve would obviously rise more rapidly. Such a mathematical tariff does not depart widely from the one traced by the heavy dotted line C D first described. The progressive decline of the per mile rate with increasing distance may be illustrated by the rough estimate of allowing two and one-half cents per hundred weight or fifty cents per ton for terminal cost, with one-half cent additional per mile for movement expenses. For a ten-mile haul this would cost fifty-five cents, or an average of 5.5 cents per mile. Were the distance 500 miles, the average cost would be only (50+250)/500 cents or 0.6 cents per ton mile. [Illustration: Diagram of Belgian Tariff Sheets.]