the point, for this Case 10, up to the author's curve, instead of his 6
lb. per 2,000 lb., a frictional resistance of 66 lb. per 2,000 lb. would
be required, a resistance just equal to the gravity resistance on the
3.3% grade, making a total resistance of 132 lb. per 2,000 lb.

While this 66 lb. per ton is very high, it is perhaps not too high for
the known conditions, as above described. For modern rolling stock, Mr.
A. K. Shurtleff gives the formula:[D]

Frictional resistance, on tangent, }
in pounds per 2,000 pounds } = 1 + 90 ÷ C,

where _C_ = weight of car and load, in tons of 2,000 lb. This would
give, for 4,400-lb. (2.2-ton) cars, a frictional resistance of 42 lb.
per 2,000 lb.; and, on the usual assumption of 0.8 lb. per 2,000 lb. for
each degree of curvature, the 12.75° curves of this line would give 10
lb. per ton additional, making a total of 52 lb. per 2,000 lb. over and
above grade resistance, under modern conditions.

In the 9th to 17th editions of Trautwine (1885-1900), these early
accounts were superseded by numerous later instances, including some of
those quoted by the author.

In the 18th and 19th editions (1902-1909) are given data respecting
performances on the Catawissa Branch of the Reading (Shamokin Division)
in 1898-1901. These give the maximum and minimum loads hauled up a
nearly continuous grade of 31.47 ft. per mile (0.59%) from Catawissa to
Lofty (34.03 miles) by engines of different classes, with different
helpers and without helpers.