CLASSIFICATION OF MINERAL LANDS. 91 



the reduced value of the thin beds, the sum of the thicknesses of the 

 beds does not exceed 10 feet. If the total thickness of the coal under 

 a tract "of land, after reduction for thin beds -and for partings, is 

 more than 10 feet, the total value of the coal is computed by the 

 formula previously given for computing the value of thick beds. 



REDUCTION FOB DEPTH. 



It has been pointed out that the determination of the depth to 

 which a coal may be profitably mined is a problem involving the 

 consideration of diminishing profits. If a coal that is being mined 

 near the surface is yielding a net profit of 25 cents a ton and if the 

 cost of mining it increases 1 cent a ton for every 100 feet of increase 

 in depth (purely an assumption), it is evident that the profits 

 will disappear when the mine has reached a depth of 2,500 feet, so 

 that the coal becomes unminable at a reasonable profit at some point 

 of less depth, say 2,000 feet. Obviously anything that increases the 

 profits — such as a gain in quality — will increase the depth of profit- 

 able mining, and anything that decreases the profits — such as an in- 

 crease in the cost of mining — will decrease the depth of profitable 

 mining. 



If depth limits are assumed for coals of different grades and differ- 

 ent thicknesses, it may also be assumed that the cost of mining in- 

 creases uniformly with increase of depth, though it is strongly sus- 

 pected that the cost of mining increases at an accelerating rate as 

 the depth increases, but as sufficient data to prove this are not avail- 

 able a uniform rate of increase has been assumed. 



If a certain coal has a normal value at any depth within 500 feet 

 of the surface its value has been assumed to reach zero at 

 its depth limit, and its price has been decreased uniformly from a 

 point where it goes below the 500- foot depth down to its depth limit. 

 If, for example, a bed has a value of $60 an acre at the depth of 500 

 feet and its depth limit is 2,500 feet, and if it reaches its depth limit 

 3 miles beyond the point where it lies at a depth of 600 feet, its dip 

 remaining constant, it loses a value of $60 in crossing twelve 40-acre 

 tracts, or $5 for each forty. The successive forties underlain by this 

 coal would therefore be valued at $55, $50, $45, $40, $35, $30, $25, and 

 thence to the depth limit at $20. 



Ordinarily the depth of a bed does not increase uniformly to its 

 limit, but its steepest pitch or dip is at its outcrop and its dip grad- 

 ually lessens toward the center of the basin in which it lies. Its 

 depth at all places is indicated on the field sheets by contour lines 

 representing uniform elevations above sea level. From these contour 

 lines it is possible to compute the average depth of the bed under 

 any 40-acre tract, and, the rate of diminishing value having been 



