is quite probable that the resistance assumed in the calculation
is far below the actual. Items 15 and 17 are both high. To account for
this, it is to be noted that this road has been recently completed,
regardless of cost in the matter of both track and rolling stock, and
doubtless represents the highest development of railroad practice. Its
rolling stock is all new, and is probably in better condition to offer
low resistance than it will ever be again, and there were no "foreign"
cars in the trains considered. The train resistance, therefore, may be
naturally assumed to be much less than that of roads hauling all classes
of cars, many of which are barely good enough to pass inspection. As the
grades are light in both cases, this feature of train resistance is
larger than in items including heavier grades. Attention should be
called to the fact that a line connecting the two points representing
these items on Fig. 1 would make only a small angle with the sketched
curve, and would be practically parallel to a similar line connecting
the points represented by Items 13 and 16. There is, therefore, an
agreement of ratios, which is all that needs consideration in this
discussion.

[Illustration: FIG. 1.--DIAGRAM SHOWING PERCENTAGE OF WEIGHT ON DRIVERS
WHICH IS UTILIZED IN TRACTION ON GRADES OF VARIOUS LENGTHS]

Wellington, in his monumental work on railway location, presents a table
of this character. The percentages of weight on the drivers which is
utilized in draft show the greatest irregularity. He does not give the
length of the grades considered, so that it is impossible to say how far
the introduction of this feature would have contributed to bring order
out of the chaos. In his discussion of the table he admits the
unsatisfactory character of the results, and finally decides on 25% as a
rough average, "very approximately the safe operating load in regular
service." He further states that a number of results, which he omits for
want of space, exceeds 33 per cent. The highest shown in Table 1 will be
found in Item 1 (0.06 mile, 0.066 grade), showing 33 per cent. There is
no momentum effect here, as the grade is a short incline extending down
to the river, and the start is necessarily a "dead" one. The reports of
Item 3, which shows 31%, and Item 5, which shows 27%, state specifically
that the locomotives will stop and start the loads given at any point on
the grade.

The results of a series of experiments reported b