APPRAISAL OF FlRR DAMAGK 37 



facts warrant ; but it is a much simpler process and more in keeping with the 

 purpose for which the formula is intended if one standard figure for all types 

 in a region is used. 



2. The resulting values for each age class are prorated to the different species 

 in accordance with their present relative commercial values. 



If these values were used directly in the formula they would give 

 values that are too high and make necessary the use of a reducing 

 factor. This factor must be dependent on the relative commercial 

 values and should place each value dependent on the others. It is ob- 

 tained by dividing the number of relative commercial values by their 

 sum, and is shown in the following formula by the expression of 



J- — This is a partial weighted average of the relative commercial 

 SR 



values. Under this condition, if one of the relative commercial values 



N 

 is changed, then the value of -^^ is changed, which of course directlv 



affects all values that may be computed. This then becomes a reducing 

 factor which is dependent on the relative commercial values. 



For example, if the relative commercial values of several species are 

 5, 3, 2, and i, this gives four relative values, which may be represented 

 by "N". Their sum is equal to ii, which may be represented by SR, 



where R represents each of the values, 5, 3, 2, or i. Then ^- is equal 



SR 



to -t. 



II 



The formula as proposed, with the above-mentioned modifications, is 

 as follows : 



V = RJ^[c(r.op..)(a)+ ^^"^P"-^m 

 Where * SR L i.op— i J ) 



V = Value per acre for any species or age class. 



R == Relative commercial values of the various species. 



In applying the formula to northern Idaho and Montana these have 

 been assumed as follows : 



White pine 5 



Yellow pine, cedar, and spruce 3 



Larch and Douglas fir 2 



Lodgepole pine i 



"R" is here equal to 5, 3, 2, or i, depending upon the species under consideration. 



N = Number of relative values, or 4. 

 SR^Sum of relative values, or 11. 



C = Average cost of planting, or $5. 



P^ Interest rate of 3 per cent. 



m = Average age of stand destroyed. 



