Taking the same basis as the author, namely, 4.7 lb. per ton, rate of grade × 20, and weight on drivers, gives:
Hill A, 18.078%, remainder of division, 19.462%
Hill B, 20.068%, remainder of division, 21.279%
Hill C, 19.549%, remainder of division, 21.279%
It will be noted that the author uses the weight on the drivers as the criterion, but the tractive power is not directly as the weight on the drivers, some engines being over-cylindered, or under-cylindered; in the class of engines above mentioned the tractive power is 23.35% of the weight on the drivers.
The writer made a study of several dynamometer tests on Hill C. There is a grade of the same rate, about 1 mile long, near this hill, and a station near its foot, but there is sufficient level grade between this station and the foot of the hill to get a good start.
All the engines of the above class, loaded for Hill C, gained speed on the 1-mile grade, but began to fall below the theoretical speed at a point about 2-1/4 miles from the foot of the hill. This condition occurred when the trains stopped at the station and also when they passed it at a rate of some 16 or 18 miles per hour, the speed becoming less and less as the top of the hill was approached.
The writer concludes that the author might stretch his opinion as to using heavier rates of grade on shorter hills than 10 miles, and indeed his diagram seems to intimate as much, and that, for economical operation, the maximum rate of grade should be reduced after a length of about 2 miles has been reached, and more and more in proportion to the length of the hill, in order that the same rating could be applied all over a division.
This conclusion might be modified by local conditions, such as an important town where cars might be added to or taken from the train.
While it does not seem practicable to the writer to calculate what the reduction of rate of grade should be, a consensus of results of operation on different lengths of grade might give sufficient data to reach some conclusion on the matter.
The American Railway Engineering and Maintenance of Way Association has a Committee on "Railway Economics," which is studying such matters, but so far as the writer knows it has not given this question any consideration.
The writer hopes that the author will follow up this subject, and that other members will join, as a full discussion will no doubt bring some results on a question which seems to be highly important.