where _T__{_r_}, _T__{_a_} and _T__{_b_} represent the tonnage originating on the sectors of radius _r_, _a_ and _b_ respectively. For the first mile, _a_ = 1, _b_ = 0. _H_ = _T__{_r_} - ¹⁄₃(_T__{_a_}). For the eighth mile, _a_ = 8, _b_ = 7. _H_ = _T__{_r_} - _T__{8} + ²³⁄₄₅(_T__{8} - _T__{7}) THEORETICAL AVERAGE TONNAGE OF SIX UNIFORMLY DISTRIBUTED MARKET ROADS[180] -----+-----+-------------------------------------------------------- | | UNIFORM YIELD PER ACRE OF | +-----------------+------------------+------------------- | | One-tenth Ton | One-fourth Ton | One-half Ton | +-----+-----------+------+-----------+------+------------ | | |Tons Hauled| |Tons Hauled| |Tons Hauled | | | per day | | per day | | per day | |Total+-----+-----+ Total+-----+-----+ Total+------+----- Maxi-|Aver-|Tons |Over |Over | Tons |Over |Over | Tons | Over |Over mum | age | per | 1st |8th | per |1st | 8th | per | 1st |8th Haul| Haul|Year |Mile |Mile | Year |Mile |Mile | Year | Mile |Mile -----+-----+-----+-----+-----+------+-----+-----+------+------+----- 1 | 0.67| 33 | 0.07| | 84| 0.17| | 168| 0.34| 2 | 1.33| 134 | 0.40| | 335| 1.00| | 670| 2.01| 3 | 2.00| 302 | 0.96| | 754| 2.40| | 1,508| 4.80| 4 | 2.67| 536 | 1.74| | 1,340| 4.36| | 2,681| 8.71| 5 | 3.33| 838 | 2.75| | 2,094| 6.87| | 4,189| 13.74| | | | | | | | | | | 6 | 4.00|1206 | 3.98| | 3,016| 9.95| | 6,031| 19.90| 7 | 4.67|1642 | 5.43| | 4,106|13.58| | 8,211| 27.15| 8 | 5.33|2145 | 7.11| 0.85| 5,362|17.76| 2.13|10,724| 35.52| 4.25 9 | 6.00|2714 | 9.00| 2.75| 6,786|22.51| 6.88|13,572| 45.02|13.75 10 | 6.67|3351 | 4.13| 4.87| 8,378|27.82|12.18|16,756| 55.63|24.35 | | | | | | | | | | 11 | 7.33|4056 |13.47| 7.22|10,138|33.68|18.05|20,279| 67.35|36.10 12 | 8.00|4826 |16.04| 9.79|12,064|40.10|24.48|24,128| 80.20|48.95 13 | 8.67|5663 |18.83|12.58|14,158|47.08|31.45|28,316| 94.15|62.90 14 | 9.33|6568 |21.85|15.59|16,420|54.63|38.98|32,840|109.25|77.95 15 |10.00|7540 |25.09|18.83|18,850|62.73|47.08|37,700|125.45|94.15 -----+-----+-----+-----+-----+------+-----+-----+------+------+----- The table shows the theoretical average tonnage on each of six uniformly distributed radial roads. It is taken from Bulletin 136, U. S. Department of Agriculture. Since roads do not run in practice in this manner the results can only be used for comparison in confirming estimates.