ELECTRIC DISTRIBUTION AND WIRING. 299 



considerations is proportional to the distance, /, and inversely pro- 

 portional to the voltage of delivery. 



Limitations of Kelvin 's law. The economic balance between 

 the loss of power in transmission wires and the cost of copper 

 was first pointed out by Lord Kelvin, and the condition expressed 

 by equation (46) is sometimes called Kelvin's law of economy.* 

 In the derivation of equation (46) it was assumed, first, that 

 the cost of poles, cross-arms and pins, and the cost of erection 

 of the pole line are the same whatever the size of the wire may 

 be, and second, that the cost of the wire is so much per pound. 

 The first assumption is approximately true only for wires of 

 moderate weight. For very heavy wires the supporting struc- 

 ture must be very strong and therefore expensive. The second 

 assumption is approximately true only for bare wires. For in- 

 sulated wires the cost per pound varies considerably with the size 

 of the wire. 



The sum of the three items : (a) Annual value of energy lost 

 in a line, reckoned on the basis of its cost per kilowatt-hour at 

 the switchboard ; (fc) Annual interest on the entire cost of the 

 line, and taxes ; (^) Annual cost of line depreciation and repairs, 

 makes the difference between the cost of the energy at the switch- 

 board and its cost delivered to a customer. 



121. Electric strength of line insulation as a factor in the deter- 

 mination of the size of wires. The two diagrams, A and B, 

 Fig. 169, represent in section 

 two lead-encased cables with 

 the same radial thickness of 

 insulating substance between 

 the central wire and the lead 

 sheath, and the fine radial lines 

 represent the lines of force of 



the electric field in the insulating medium for the same volt- 

 age between the wire and the lead -covering in each case. 



* A very complete discussion of Kelvin's law is given by Dr. F. A. C. Perrine in 

 his book entitled Conductors for Electrical Distribution (D. Van Nostrand, 1903), 

 pages 161-178. 



