88 OLASSrPIOATION OF THE PUBLIC LANDS. 



best illustrated by giving a concrete case, such as is represented in 

 figure 5. 



On this map lines were drawn from the position of one measure- 

 ment to the position of each adjacent measurement and the thick- 

 ness was assumed to grade uniformly from one to each of the other 

 points. Valuation is then based on the average thickness thus found 

 for each forty that is being valued. If the measurements do not 

 show any regularity in the change of thickness, the Survey has 

 adopted a method of computing thickness that permits the thickness 

 of the coal under any tract' of land to be considered as less than the 

 average of the measurements, in order to favor the buyer, for the 

 reasons already stated. For while the coal is as likely to be above 

 the average as below and, mathematically, is more likely to be just 

 the average thickness than any other, yet a cautious buyer bargain- 

 ing for coal would always want to discount the probability a little, 

 as a matter of safety. If all the measurements on a bed indicate the 

 same thickness, that thickness may be safely taken as the thickness 

 of the coal under any land included by the measurements. If the 

 measurements vary but slightly from the average, the thickness un- 

 der the land where no measurements are obtained is not hkely to be 

 much below the average. If, however, the variation is large, the 

 coal in some places may be even thinner than the smallest measure- 

 ment ; yet to assume that the coal under all the land where no actual 

 measurements were made is as thin as the thinnest measurements 

 obtained would be overcautious. A more probable thickness is ob- 



SD 

 tained by multiplying the average of the measurements by (1 — „-), 



— o 



in which S is the sum of all the measurements and SD is the sum of the 

 numbers obtained by subtracting from the average each measurement 

 below it or subtracting the average from each measurement above 

 it. For example, if the measurements on a given bed in a certain 

 area are 4 feet, 5 feet, 7 feet, 3 feet, 4 feet, 8 feet, 5 feet, 2 feet, 4 feet, 

 2 feet, 6 feet, and 10 feet, the average of all the measurements is 

 5 feet; the sum of the measurements is 60 feet; the difference be- 

 tween the several measurements and the average 5 feet is 1 foot, 

 0, 2 feet, 2 feet, 1 foot, 3 feet, 0, 3 feet, 1 foot, 3 feet, 1 foot, 

 5 feet, which added together give 21 feet; so 21 feet divided by 60 

 has been called the " modulus of irregularity " and has been adopted 



21 

 as a factor of safety; 1 — — or 100 per cent — 35 per cent = 65 per 



cent ; 65 per cent of 5 feet = 3^ feet ; therefore 3 J feet is taken as a 

 safe average thidaiess on which to sell the coal — in other words, 

 the thickness which it is highly probable will be reached or exceeded 

 by the coal under any of the land within the area of the measure- 



