INDIRECT DETERMINATION OF THE WILTING COEFFICIENT. 71 



COMPARISON OF THE ACCURACY OF INDIRECT PHYSICAL METHODS FOR 

 DETERMINING THE WILTING COEFFICIENT. 



Since the numerical value of the ratio used in calculating the 

 wilting coefficient by indirect methods varies considerably according 

 to the method employed, it is necessary for purposes of comparison 

 to express the probable error in each case as a percentage of the ratio 

 which it affects. This comparison is given in the following table: 



Table XXIII. — Comparative accuracy of the ratios in the indirect methods for determining 



the wilting coefficient. 



Methods. 



Ratio. 



Probable error of mean 

 ratio. 



Absolute 

 value. 



Per cent 

 of ratio. 



Moisture equivalent 



1.84 



.68 



2.90 



1.00 



±0.013 

 ± .012 

 ± .06 

 ± .025 



±0.7 





±1.8 





±2.1 





±2.5 







The probable error of the mean ratio shows the degree of uncer- 

 tainty that is attached to the value given for the ratio. That is to 

 say, if the moisture-equivalent series were repeated, the chances are 

 even that the mean ratio would fall between 1.827 and 1.853. In 

 other words, in a soil having an observed moisture equivalent of 18.4 

 per cent the chances are even that in so far as the accuracy of the 

 ratio is concerned the wilting coefficient lies between 9.93 and 10.07. 

 This corresponds to an uncertainty of ±0.7 per cent in the value of 

 the wilting coefficient calculated by means of the ratio 1.84, as shown 

 in the last column of the table, in which the probable error of the 

 mean ratio is given, expressed as a percentage of the ratio itself. 

 This affords at once a means of comparing the accuracy of the 

 different methods. It will be seen that the probable error in calcu- 

 lating the wilting coefficient by the moisture-equivalent method is 

 about 0.7 per cent; by the hygroscopic-coefficient method 1.8 per 

 cent, or over twice as great; by the moisture-holding capacity 

 method over 2.1 per cent, or three times as great; and by the mechan- 

 ical-analysis method 2.5 per cent, or nearly four times as great. 



It should be clearly recognized that the formulas which have been 

 deduced will not necessarily give the correct calculated value of the 

 wilting coefficient within the limits of the probable error of the ratio. 

 The uncertainty regarding the value of the observed quantity (mois- 

 ture equivalent, hygroscopic coefficient, etc.) enters into the calcu- 

 lation of the wilting coefficient for any particular soil, in addition to 

 the uncertainty of the ratio. According to the formulas a linear 

 relation existed in each case and the observed departures are attrib- 



230 



