bject to material
modifications in the presence of a larger array of data, therefore,
material assistance in reaching practical conclusions can be given by
the presentation of additional data.

DISCUSSION

C. D. PURDON, M. AM. SOC. C. E. (by letter).--Some years ago the writer,
in making studies for grade revision, found that the tractive power of a
locomotive up grade becomes less as the length of the grade increases,
and in some unknown proportion. This was a practical confirmation of the
saying of locomotive engineers, that the engine "got tired" on long
grades. On a well-known Western railroad, with which the writer is
familiar, experiments were made for the purpose of rating its
locomotives. The locomotives were first divided into classes according
to their tractive power, this being calculated by the usual rule, with
factors of size of cylinders, boiler pressure, and diameter of drivers,
also by taking one-fourth of the weight on the drivers, and using the
lesser of the two results as the tractive power.

Locomotives of different classes, and hauling known loads, were run over
a freight division, the cars being weighed for the purpose; thus the
maximum load which could be handled over a division, or different parts
of a division, was ascertained, and this proportion of tonnage to
tractive power was used in rating all classes.

Of course, this method was not mathematically accurate, as the condition
of track, the weather, and the personal equation of the locomotive
engineers all had an effect, but, later, when correcting the rating by
tests with dynamometers, it was found that the results were fairly
practical.

There were three hills where the rate of grade was the same as the rest
of the division, but where the length was much in excess of other grades
of the same rate.

Designating these hills as _A_, _B_, and _C_, the lengths are,
respectively, 2.44, 3.57, and 4.41 miles. There were no other grades of
the same rate exceeding 1 mile.

In one class of freight engines, 10-wheel Brooks, the weight of the
engine was 197,900 lb.; tender, 132,800 lb.; weight on drivers, 142,600
lb.; boiler pressure, 200 lb.; and tractive power of cylinders, 33,300
lb.

On Hill _A_ these engines are rated at 865 tons, as compared with 945 on
other parts of the division. As the engine weighs 165 tons and the
caboose 15 tons, 180 tons should be added, making the figures, 1,045 and
1,125 tons. Thus the length of the gra