84 



CLASSIFICATION' OF THE PUBLIC LANDS. 



The following table gives the derivation of the formula showing 

 the relation of the thickness to value of bed, uniform recovery being 

 assumed : 

 ■Taile showing derivation of fornyula for relation of thickness to value of bed. 



The JBrst column in the table gives the thickness of the bed in 

 feet ; the second the average cost of mining anthracite at these thick- 

 nesses, according to Chance (not including breakerage charges) ; 

 the third column, the computed relative cost for bituminous coal; 

 the fourth column, the approximate combination of the two; the 

 fifth column, the relative values of beds of the same quality of coa.1 

 of different thickness, obtained by dividing 100 by the cost, given in 

 column 4; the sixth column, the difference in feet between 10 and 

 the particular thickness given; the seventh column, the square of 

 the numbers in column 6; the eighth column, the result of sub- 

 tracting from 100 the square of the difference between 10 and the 

 thickness in feet. By comparing columns 5 and 8, column 8 is seen to 

 give a close approximation to the computed figures in column 5, and as 

 the figures in column 5 are by no means absolute and fixed the figures 

 in column 8 have been taken as fairly expressing the relative value of 

 different thicknesses of the same coal ; but this is found by subtracting 

 from 100 per cent a percentage equal to the square of the differ- 



ence between 10 and the thickness, or ^-^— 



100 (10-0' 



100 



'-(^y- 



The value per ton of a bed less than 10 feet thick of a given grade of 

 coal may therefore be found by multiplying the normal value per ton 



for a 10-foot bed of coal of that grade by (1-(^ ^^~^ Y). 



In valuing land by the acre-foot, however, an additional factor 

 must be considered, namely, that a larger recovery of coal per acre- 

 foot is possible from thin beds than from thick beds. This difference 

 offsets in a measure the rapid increase in mining cost with thinning 

 of beds. Thus 1,000 tons an acre-foot for a 10-foot bed and 1,200 



