The Massachusetts Western Railroad may be divided into the four sections below (including the Boston and Worcester road).
| Length miles. | Maximum grade. | |
|---|---|---|
| Boston to Worcester, | 44 | 30 |
| Worcester to Springfield, | 54½ | 50 |
| Springfield to Pittsfield, | 52 | 83 |
| Pittsfield to Albany, | 49½ | 45 |
Assume the speed of freight trains as fifteen miles per hour, the resistance on a level will be 9.3 lbs., or for simplicity call it ten pounds per ton.
| The resistance due to a | 30 feet grade is | 13 | lbs. per ton. |
| The resistance due to a | 50 feet grade is | 21 | lbs. per ton. |
| The resistance due to a | 83 feet grade is | 35 | lbs. per ton. |
| The resistance due to a | 45 feet grade is | 19 | lbs. per ton. |
| And the value of r for a | 30 feet grade is | 13 10 | lbs. per ton. |
| And the value of r for a | 50 feet grade is | 21 10 | lbs. per ton. |
| And the value of r for a | 83 feet grade is | 35 10 | lbs. per ton. |
| And the value of r for a | 45 feet grade is | 19 10 | lbs. per ton. |
And the relative length of the several sections will be,
| Boston to Worcester, | 10 10 + 13 10 = | 23 10 of | 44 | = | 101 |
| Worcester to Springfield, | 31 10 of | 54½ | = | 169 | |
| Springfield to Pittsfield, | 45 10 of | 52 | = | 234 | |
| Pittsfield to Albany, | 29 10 of | 49½ | = | 144 | |
| And the sums, | 200 | 648 |
the equated distance being 3¼ times the actual length. This length assumes the resistance of the several sections to be for their whole length that given by their maximum grade. This might seem erroneous; but its correctness will be seen when it is remembered that the greatest load that can be taken over any section is limited by its maximum grade.
Now suppose that the engine employed is of the following dimensions (as it is very nearly).
| Cylinders | 16 × 20 inches, |
| Wheels | 54 inches. |
Assume the cylinder pressure 110 lbs., and the tractive power of the engine is 5,287 lbs.