186 VALUATION, DEPRECIATION AND THE RATE-BASE
The total required earnings appear largest for the Unlimited
Life Method for the reason that the required earnings in the
early years of the plant’s life are supposed to have been low.
When rates are to be fixed for a public service property which
is long established, concerning which past records are unreliable,
 but which is legitimate, rendering a necessary service and
entitled to fair income, the question as to which method of
procedure should be adopted presents itself.
Let it be supposed that the records indicate a fairly normal
development and growth with some years of inadequate earnings
and no conclusive evidence that any part of the invested capital
has been repaid, but that worn-out parts have been renewed as
necessary and that the service rendered has been satisfactory.
In this assumed case the application of the various methods
of procedure will theoretically produce results as shown in Table
14. If any of the methods except the Unlimited Life Method
be adopted, recourse will probably be had to an addition of
large values for intangible elements in order that no injustice
may be done to the owner of the property. In most cases the
Unlimited Life Method will be indicated as most nearly equitable.
 This will be yet more apparent when the effect of the
non-agreement of actual with probable life upon the application
of the various methods of procedure is taken into account.
The comparison of results by the methods of procedure which
have been under discussion has been visualized, for the special
case of a single item which cost $100, in a diagram, Fig. 2.
It has been assumed in the preparation of this diagram that in
the application of the Unlimited Life Method to a single article
the replacement requirement will be anticipated and will be
estimated by the compound interest Sinking Fund Method. In
the practical application of this method a close approximation
of the replacement requirements is not essential because no part
of the replacement increment goes to the repayment of capital.
This entire increment remains in the replacement account and
will be subject to being decreased or increased from time to
time as this account shows to be necessary.