COMPARISON OF SURVEYED LINES.
56. The requisite data for an approximate comparison of lines are, the measured length, total rise, total fall.
| Let the length of line A be | 100 | miles, |
| Let the length of line B be | 90 | miles, |
| Whole rise on A | 2000 | feet, |
| Whole rise on B | 5100 | feet, |
| Whole fall on A | 1200 | feet, |
| Whole fall on B | 4300 | feet. |
Assume the number by which to equate, as ninety-six, and we shall have
| Line A. | |
| Ascending, 100 + 2000 96 = | 120.83 |
| Descending, 100 + 1200 96 = | 112.50 |
| Sum | 233.33 |
| Mean | 116.66 |
| Line B. | |
| Ascending, 90 + 5100 96 = | 143.13 |
| Descending, 90 + 4300 96 = | 134.80 |
| Sum | 276.93 |
| Mean | 138.46 |
| The mean equated length of A is | 116.66 |
| The measured length of A is | 100.00 |
| The difference | 16.66 |
| The mean equated length of B is | 138.46 |
| The measured length of B is | 90.00 |
| The difference | 48.46. |
The cost of construction being assumed as the actual length, and that of working as the equated length, we have the final approximate comparison thus:—
Assume the construction cost as $25,000 per mile, and the cost of maintenance $4,000 per mile, and we have
The line A to the line B as
100 × 25000 + 116.66 × 4000 × 100
6 = 10,277,333, is to
90 × 25000 + 138.46 × 4000 × 100
6 = 11,480,667;
or A is to B as 10.3 to 11.5 nearly, although the line A is ten miles longer than B.