b. 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 deg. 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accounts were superseded by numerous later instances, including some of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.

Table 2 (in which the writer follows the author in assuming frictional
resistance at 4.7 lb. per 2,000 lb.) shows the cases giving the maximum
and minimum values of the quantity represented by the ordinates in the
author's diagram, namely, "Traction, in percentage of weight on
drivers."

It will be seen that the maximum percentage (16.1) is practically
identical with that found by the author (16) for grade lengths exceeding
17 miles.

Near the middle of the 34-mile distance there is a stretch of 1.51
miles, on which the average grade is only 5.93 ft. per mile (0.112%),
and this stretch divides the remaining distance into two practically
continuous grades, 19.39 and 13.13 miles long, respectively; but, as the
same loads are hauled over these two portions by the same engines, the
results are virtually identical, the maxima furnishing two more points
closely coinciding with the author's diagram.

TABLE 2.--TRACTIVE FORCE, CATAWISSA TO LOFTY.

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