00 VALUATION, DEPRECIATION AND THE RATE-BASE 
works originally must not be confounded with a replacement 
fund. The one may be necessary to pay for the works in the 
first instance, the other to maintain them for all time. T he 
annual contribution to the sinking fund is a partial payment 
for the original work. The contribution to a replacement fund, 
in the case of a plant which is to serve without time limit, is for 
the purpose of perpetuating the work, because in that case the 
replacement fund, as far as it will go or as far as it is required, 
will be used for making replacements. 
The Wisconsin R. R. Commission in the case of the Superior 
Commercial Club vs. Duluth Street Railway Co. (Wis. R. C. 
R., Vol. 11, pp. I to 21) elsewhere quoted makes clear the 
distinction between depreciation and amortization. Referring 
to depreciation the Commission in the matter of the Fennimore 
Mutual Water & Light Plant, in 1913 (Wis. R. C. R., Vol. 12, 
p. 209), warns against the confusion of the depreciation fund 
with the depreciation reserve. The “fund ” is actually created 
by setting a part of the income aside. The “reserve ” is merely 
a book account which designates the amount and character of 
various transactions bearing upon depreciation and replacement 
expenditures. 
Though it may be difficult to make satisfactory forecasts with 
reference to necessary reinvestments to replace discarded parts of 
a plant, the requirements for amortization, being based on cost, 
are usually readily determinable with some degree of precision. 
Application to Complex Plants. — Thus far, the plant is as- 
sumed to have been constructed and put into use all at once, 
and is of such a character that all its parts have the same life. 
The same principles will apply when a plant is made up of many 
elements or parts having various periods of usefulness. The 
amortization or the replacement annuity is, in such case, de- 
termined for each part and from the sum of the annuities thus 
ascertained the minimum earnings which will prevent loss are 
determined. 
Mathematical Determination of the Replacement Fund. — 
The following problem presents itself: In the case of a plant