12 POWER DISTRIBUTION FOR ELECTRIC RAILROADS. 
given terminal drop, the copper necessary for a wuni- 
formly distributed load is one-half that required for the 
same load concentrated at the end of the line. As the 
number of sections increases, too, the likelihood of ob- 
taining a disarrangement of load sufficient to disturb the 
terminal voltage much, decreases. The effect of a uni- 
form motion of all the loads on the terminal voltage is 
small. So long-as the schedule is uniform and is ad- 
hered to, the worst that can happen is a transformation 
of the system into half the original number of sections. 
Suppose in Fig. 6 all the load points of odd numbers to 
be moving to the right and all those of even number to 
the left, at uniform speed. Then after each point had 
moved half a section, there would be five sections each 
loaded with a pair of coincident loads. Applying (7) to 
the data of Fig. 6, E = 60, assuming the sections uniform. 
As, however, the first section would be but three-fourths 
the length of the others, the real loss would be 55 as 
before.* Another equal movement and the ten sections ap- 
pear in their original relation. Amnother and we have the 
five sections, but with an initial section one-fourth the 
length of the others and total loss of 45 volts. Next 
would come a ten-section arrangement, but with the first 
load at A, and E = 45, and so on. ‘The upshot is that 
while the terminal voltage oscillates through a range equal 
to the drop in the first section, the final effect on the aver- 
age drop of uniformly moving the loads is the same as load- 
ing each section at the middle point or increasing 7 in- 
definitely. Hence, in a line with uniformly spaced and uni- 
formly moving loads, we may assume 
[E—I} — 1 in (9):ahd write 
7 
  
I1 
(10) oo, = M%E 
2 
or, transposing, 
IT 
i 
2 E 
That is, the area of the line can be calculated for average