4 Journal of Agricultural Research voi.xiii.no. i 



were all made in connection with the growth of but one crop (alfalfa), 

 and as the time of observation after irrigation was made as nearly as 

 possible the same, it is believed that the results are comparable. The 

 acre-inch equivalents of the percentages before and after irrigation for 

 each acre-foot of soil were calculated by using equation 2, deduced on 

 page 3. The volume weights (Vw) used represent the density of the 

 soil in place, except in a few cases as noted. In order to facilitate com- 

 parison with quantities of water applied in irrigation, and also with the 

 total pore space of the soil, the quantities of moisture found before and 

 after irrigation are presented in terms of acre-inches per acre-foot of soil. 



PRECISION OF RESULTS 



The precision of the results presented in this paper is dependent upon 

 the following independent factors: (i) The accuracy of the moisture 

 determinations, (2) the accuracy of the volume weight determinations, 

 (3) the accuracy of the water measurements, and (4) the uniformity of 

 lateral distribution of the irrigation water. 



Factors i and 2 determine the precision of the absolute quantities of 

 water retained by the soil, but the accuracy of the percentages of water 

 accounted for depends upon all of the above factors. By use of 

 Peter's formula * probable-error (p. e.) determinations for each foot of 

 soil in 57 sets of six observations indicate average probable-error values 

 for single observations (r) of ± 1.32 and ± 1.52 per cent of moisture before 

 and after irrigation, respectively. The probable error of the mean of 

 n determinations {ro) calculated from the relation : 



r 

 ■yjn 

 indicates for the average number of borings per field or plot in which 

 w=36 average probable-error values of ±0.22, and ±0.25; for a type of 

 soil n averages 114 and the probable-error values are = ± o. 1 2 and ± 0.14, 

 respectively, from which the probable error of the difference in moisture 

 content before and after irrigation = ±0.18 per cent of moisture. 



By using i .40 as a mean volume weight, ± o. 1 8 per cent of moisture is 

 equivalent to db 0.03 acre-inch of water per acre-foot of soil. The average 

 probable error of the volume-weight determinations (±0.01) equivalent 

 to -I- 0.002 acre-inch of water per acre-foot of soil is too small to be sig- 

 nificant. Hence, the average probable error of the increase in water 

 due to irrigation = ±0.03 acre-inch for each acre-foot of soil. Upon 

 this basis the chances are only i to i that increases of 0.03 inch for each 

 foot of soil as given in the averages for the various types are due to the 



2V 

 ' r— 0.8453 X I—. — == where r=the probable error of a single observation; 

 V«(w— i) 



fo=-o.84S3X — ; ro=the probable error of the arithmetic mean of n observations; 



21/= the sum of the residuals without regard to sign; 

 n^the number of observations. 



