08 VALUATION, DEPRECIATION AND THE RATE-BASE 
tization and replacements should not be determined by the 
interest bearing sinking fund method based on original probable 
life but should be otherwise determined, as hereafter shown. 
When, in other words, opportunity is not given to accumu- 
late the 40 per cent of the invested capital (approximately), which, 
for ordinary periods of useful life of perishable properties, should 
in the course of time be in a replacement, depreciation or amor- 
tization fund, any amount estimated from amortization tables 
on the original full period of useful life will fall short of the 
real replacement requirement. 
Illustration of the Replacement Requirements. — Let it be 
assumed that a conduit, such as a cast-iron pipe, used for any 
purpose, has a length of 40 miles. Let it be also assumed that 
the pipe is not being further extended, that the life of this pipe 
is 40 years, no more and no less, and that it was constructed 
progressively, one mile each year. It took 4o years to install 
the pipe, and at the end of this time the first mile of pipe laid 
was ready for replacement —it had served its time. Each 
year thereafter, one mile of pipe has to be replaced, and the 
replacement at this rate will continue indefinitely. The annual 
replacement expenditure during the first 40 years is nothing, 
but, thereafter, it is the cost of installing one mile of pipe. If 
prices of labor and material have remained constant, and if 
conditions have otherwise remained as they were when the first 
mile of pipe was laid, then the annual replacement expenditure 
will be one-fortieth of the total amount invested in the pipe line. 
Provision for this replacement must be made if the pipe is to 
continue in service. If, now, the extension of the pipe pro- 
gresses beyond the go-year period at the same rate, before 
assumed, of one mile per year, there will be no changes in the 
annual replacement requirement during a second period of 40 
years, but at the end of this second period — at the end of 8o 
years — there will be 80 miles of pipe in service, and thereafter 
during the third go-year period there will have to be replaced 
annually 2 miles of pipe, or one-fortieth of 80 miles, or twice the 
amount of pipe extension per annum.