180 VALUATION, DEPRECIATION AND THE RATE-BASE 
Theoretically there would be no accumulation in the replace- 
ment fund because in the case of numerous articles the annual 
demand on the fund would be offset by the replacement allowance. 
The simplicity of the Unlimited Life Method, as well as its 
advantage in requiring least earnings in the early years, appears 
from a comparison of such accounts as above presented. 
Before leaving this subject attention may be called to the 
fact that the balance which these figures show to be probable 
in a replacement fund under the Sinking Fund Method of pro- 
cedure and the amount of the amortization under the Equal 
Annual Payment Method do not agree with what would be 
found on the impossible hypothesis that all articles serve through- 
out their probable terms of usefulness and no longer. On this 
purely hypothetical assumption (see page 94) the fund should 
contain about 38 per cent of the cost of the depreciating articles 
after five years of operation (5 years probable life being here 
under consideration). 
If the various methods of procedure and fixed rules of account- 
ing are closely adhered to and a comparison of results be made 
at the end of the tenth year, numerous articles all having a 
probable life of 5 years being under consideration, the results in 
so far as the amount of amortization or the amount in the re- 
placement funds are concerned should be about as follows: 
On the hypothetical assumption of agreement 
between actual and probable life, and an 
amortization allowance estimated by com- 
pound interest methods, the original invest- 
ment should have been reduced by about. . 38 per cent 
By the Sinking Fund Method, if the replace- 
ment allowance continues during probable 
life, the amount in the replacement fund 
should be about........ . RT. ss per cent 
By the Sinking Fund Method, if the replace- 
ment allowance continues during the actual 
life, the amount in the replacement fund 
should be about... -.. hl leblesitt LL. 24 per cent