18 BULLETIN 77, U. S. DEPARTMENT OF AGRICULTURE. 
The curves will show how much additional initial cost is warranted 
when a given increase in life due to the treatment under consideration 
is assumed and the initial cost and life for the existing conditions are 
known. The diagram also illustrates graphically, by the steepness 
of the curves, the great economy in prolonging the life of timbers 
that ordinarily last but a few years. 
To illustrate the use of the curves, assume that an operator wants 
to find out approximately what saving he would effect by carrying 
out some proposed scheme to lengthen the life of his timbers in cer- 
tain permanent openings. Assume that each timber set costs $6, 
including the expense of framing and setting. If its life is five years, 
its annual charge as shown by the curves is approximately $1.40, 
Let us next assume that the proposed treatment will double the fife; 
that is, give the timbers a service of 10 years. A further inspection 
of the curves at the line of 10 years' life shows that the same annual 
charge of $1.40 results from an initial cost of $10.50. In other words, 
the economy of a timber that costs $6 in place and lasts five years is the 
same as one that costs $10.50 and lasts 10 years; and, therefore, the 
proposed treatment would pay if the final cost of the treated timber 
was anything less than $10.50. If we assume the cost of the treat- 
ment to be $1.50 for each timber (making the total cost in place $7.50) 
the annual charge would be about $1. The cost of using treated tim- 
bers would increase the total cost of timbering each year until the 
period of the natural (untreated) life of the timbers (five years in 
this example) had been passed; after that time, however, there would 
be a period of very low total costs until it was necessary to replace 
the treated material. The economy shown in an annual charge of $1 
in comparison with $1.40 represents the average conditions due to a 
continuous maintenance. It means, expressed in another way, that 
the investment required to maintain the untreated timber perma- 
nently would be 828, and that the investment for the maintenance 
of the treated timber would be $20, under the conditions given in 
this example. 
