ACTUAL AND PROBABLE LIFE 17 
procedure, even with the assumption of agreement between 
actual and probable life, this will not be the case. A full dis- 
cussion of this fact would be superfluous, but it is here stated 
as a caution against a possible erroneous assumption. * 
However, in view of the fact that the termination of service 
or failure of any article does not occur at the exact end of its 
probable life term, there would be no sense in attempting to 
establish the remaining probable life for group values unless 
hard and fast appraisal rules are laid down by those charged 
with the regulation of public utility rates coupled with adequate 
assurance that such rules will be adhered to. 
The Assumed Hypothesis of Failures. — It may be repeated 
that the foregoing Tables 4 to 7 are based on the hypothesis 
that failures of any group of articles of the same probable life 
will be most numerous near the end of the probable life term; 
that there will be a gradual uniform increase in the number of 
annual failures from the beginning to the end of this term; and 
that but few, if any, of the articles will have a life in excess of 
double that of the probable life of the article new. 
It may be repeated, too, that this hypothesis is not based on 
adequate experience, that it probably departs further from aver- 
age results than would be found under strict adherence to the 
law of probabilities, which is the basis of Table 1 3, and that it 
remains subject to modification as experience may determine. 
Until suitably modified, it offers, however, a better means of 
approximating remaining value of any article than is afforded 
when calculations are made from probable life tables without 
regard to the condition of the article at the time of the valuation. 
Failures and Expectancy according to the Law of Probability. — 
A study has been made, as already stated, to see where the law 
of probability would lead, and the result of the comparison will 
be of interest. 
* The remaining life of an equivalent single article, when computations are 
made by the Sinking Fund Compound Interest Methods, is noted in a paper in 
Transactions American Society of Civil Engineers, Vol. XXV, p. 836, with ex- 
amples on a 4 per cent interest basis. 
int