18 POWER DISTRIBUTION FOR ELECTRIC RAILROADS. 
for a uniformly loaded line is the same as if the load were 
concentrated at the center. ‘The weight is proportional to 
the cross section multiplied by the length. In the circular 
distribution of Fig. 12, therefore, the area of the conduc- 
tors is proportional to §7, the radius of the circle, while 
their lengths equal7. Hence, the weight of copper for 
such a distribution is directly proportional to the product 
of these factors and equals & K 7. 
If, now, the system is fed from another point than O the 
center, such as A, the weight of copper will be propor- 
tional to the new moment of inertia, and, since this is made 
up of the sum of the terms mentioned, the copper will be 
doubled when d?=} 72, i. e. when d= {;—O. It will be mul- 
tipled by 3 when d?=r? and so on, rapidly increasing. 
The following table gives the relative weights of copper 
corresponding to a few values of W. 
W=1,d=0 
Ccgrai. 2, _‘7;” 
V2 
¢ =3, V\/g_ 
“« =4 7V2 
e 7’\/%? 
““ =, ry2 
In any sort of distribution the mechanical analogue 
furnishes a solution of the copper problem in the ways 
just indicated. 
Tt at once appears from these considerations that the 
cost of copper runs up with disastrous rapidity if the center 
of distribution is distant from the center of load. From 
the data given one can figure out readily the extra invest- 
ment in real estate that it will pay to make in order to put 
the station near the center of load. 
The facts set forth are a powerful argument for the 
economy of an alternating current distribution with high 
tension feeders, if such a system can be rendered available 
for ordinary railway work. The main objection to locating