108 VALUATION, DEPRECIATION AND THE RATE-BASE 
And, again, the failures were estimated for each year on the 
assumption that they will occur according to the law of prob- 
abilities, coupled with the assumption that all failures will occur 
within a period twice as long as the probable life term. The 
results on this assumption will be again referred to. In so far 
as the results relating to replacement requirements obtained by 
the law of probabilities is concerned, it may be stated that 
these, while not at great variance with the adopted hypothesis, 
were yet too irregular in amount to warrant the use of the law 
of probabilities in place of the other more readily applied hy- 
pothesis. Either hypothesis of rates of failure may be used as 
a fair basis for approximation to actual conditions. There has 
appeared no good reason, therefore, for confining the study to 
the law of probabilities which after all would have to be applied 
with some such assumptions as made, of practically no survival 
beyond twice the probable life term and so per cent of all fail- 
ures within a period equal to four-tenths of the probable life 
term, or with other assumptions which would also be more or 
less of a conjectural nature. 
Tabular Illustration of Expectancy for 10,000 Articles. — In 
order to further consider the question of the expectancy of any 
article which is no longer new, let it be assumed that 10,000 
articles are installed at the same time and that all of these 
have the same probable life. Let the probable life term be 
divided into ten periods. Then according to the hypothesis re- 
lating to the annual failures, as already stated, there will be 100 
of these articles going out of use during the first period; 200 
in the second period; and so on to rocco in the tenth period; 
thereafter goo in the eleventh period; 8oo in the twelfth period, 
etc., and too in the nineteenth period. 
On this hypothesis results are readily found as shown in 
Table 3, in which years may be regarded as representing 
periods.