TABLES 433 
In Tables 4 to 7, Chapter VL* the annual replacement re- 
quirement is noted for groups of numerous articles, all of the 
same probable life new. These tables cover the two cases of a 
plant which has attained its full growth and of a plant to which 
a uniform annual addition is being made. The annual replace- 
ment requirement is based on the probable annual number of 
failures. Similar tables can readily be prepared for other terms 
of usefulness than 5, 10 and 20 years covered by these tables 
and for any other hypothesis of the rate at which actual failures 
will take place. 
All figures noted in Tables 4 to 61 and in Table 31 are approx- 
imation figures derived from smoothed-out curves. They are, 
in fact, modifications of the values which were obtained as a 
result of the assumption already fully discussed that failures 
among any large group of articles will be greatest in number at 
or near the end of the probable life term, that practically no 
articles will survive twice the probable life term, and that there 
will be a uniform increase in the annual rate of failures from the 
beginning to the year of maximum number of failures and that 
the decrease in the number of annual failures will follow a similar 
law. 
To find the expectancy of any perishable article which has a 
probable life term new of # years, not covered by any of the 
subdivisions of the table here published, the ten-year life sub- 
division of Table 31 may be called to aid. 
Let e = the expectancy which is to be determined, 
m = the age of the article, 
n = the probable life new of the article, 
m’ = the relative age of an article whose probable life 
new was 10 vears such that 
;. 4] 130. 
ZL = mr (31) 
Let ¢’ = the relative expectancy at the age m’ of an article 
whose probable life new was 10 years. 
* Page 104 of “Valuation, Depreciation and the Rate-Base.” 
t See pages 112-114 of “Valuation, Depreciation and the Rate-Base.” 
AT 
=