y Mr. A. C. Dennis in
his paper, "Virtual Grades for Freight Trains," previously referred to,
indicate a utilization of somewhat more than 23%, decreasing with the
speed.

All this indicates that the general failure of locomotives to utilize
more than from 16 to 18% on long grades, as shown by Table 1, can only
be due to the failure of the boilers to supply the necessary steam.
While the higher percentage shown for the shorter grades may be ascribed
largely to momentum present when the foot of the grade is reached, the
energy due to stored heat is responsible for a large portion of it.

When a locomotive has been standing still, or running with the steam
consumption materially below the production, the pressure accumulates
until it reaches the point at which the safety valve is "set." This
means that the entire machine is heated to a temperature sufficient to
maintain this pressure in the boiler. When the steam consumption begins
to exceed the production, this temperature is reduced to a point where
the consumption and production balance.

The heat represented by this difference in temperature has passed into
the steam used, thus adding to the energy supplied by the combustion
going on in the furnace. The engines, therefore, are able to do
considerably more work during the time the pressure is falling than they
can do after the fall has ceased.

The curve in Fig. 1 would indicate that the energy derived from the two
sources just discussed is practically dissipated at 15 miles, though the
position of the points representing Items 16, 18, 19, 20, and 21 would
indicate that this takes place more frequently between 10 and 12 miles.
From this point onward the performance depends on the efficiency of the
steam production, which does not appear to be able to utilize more than
16% of the weight on the drivers. The diagrams presented by Mr. Dennis
in his paper on virtual grades, and by John A. Fulton, M. Am. Soc.
C. E., in his discussion of that paper, indicate that similar results
would be shown were they extended to include the distance named.

From this it would appear that a locomotive is capable of hauling a
larger train on grades less than 10 miles in length than on longer
grades, and that, even when unexpectedly stopped, it is capable of
starting again as soon as the steam pressure is sufficiently built up.
Conversely, it should be practicable to use a higher rate of ascent on
shorter grades on any given line without