16 POWER DISTRIBUTION FOR ELECTRIC RAILROADS. 
gravity. Hence we may represent the above case by 
A B Tig: o 1f cbe the normal load of each section, 
then a load of 10 ¢ will be concentrated at C while a load 
of 2¢is at D. Hence, following out the principle of 
center of gravity, the system requires for a fixed value of 
terminal drop the same extra area of copper as if the 
whole load, 12¢, were concentrated at E, a point chosen 
&0 that 2 ¢/'= 10 ¢/. 'The same result is reached in many 
cases more simply by figuring the normal uniform load 
as if concentrated at C, and then treating the load 2cat 
D as if it were on a separate line, as in computing branches. 
This is the best procedure when grades and other extra 
loads are superimposed on normal and regular traffic. 
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FIG. IO. FIG. II. 
But the principle of center of gravity has another 
and a broader application. 
In any case of scattered load the center of gravity of 
the system is the proper point from which to distribute 
the power, at least in so far as this point gives the mini- 
mum weight of copper for a given loss. For instance, 
in the line of Fig. g, E is the point from which the power 
should be supplied, whether direct from a generator or 
from a feeder, if A’ B’ is but a single part of a large 
system. ‘The center of gravity of two points on a line is 
found by the ordinary balancing principle, as in Fig. 9. 
The center of gravity of any number of points in a plane 
is found by an extension of exactly the same method, as 
shown in Fig. 10. Let there be, for example, five load