258 University of California Publications in Agricultural Sciences [Vol.3 



frequently been used in making up a composite sample. It is assumed 

 for the time being that the amount of nitrate actually found in a 

 composite sample is that expressed by the mean of any given number 

 of samples. All the calculations have been made upon the samples 

 reported in the tables below just as if these were the only samples 

 taken from the area, as would be done if such a number of samples 

 were used in an independent investigation. In this case, however, we 

 have a much larger number of samples to check the accuracy of the 

 results obtained with the fewer number. Table 9 gives the amounts 

 of nitrate found in ten surface samples, numbered from forty-two to 



fifty-one, inclusive. It will be noted that these samples are taken in 

 a straight line (see fig. 1), while the sixteen samples are taken indis- 

 criminately over the area. Considering the residual nitrate alone, it 

 is seen that the mean of the ten samples is 0.30 milligrams above the 

 mean of the total number of samples. Further, the probable error of 

 the mean is increased from ± .05 milligram to ± .17 milligram or. in 

 terms of the probable error, the chances are about 3 to 1 that the 

 difference between the two results is a significant one.* The coefficients 

 of variabilitv are very nearly the same in the two instances. 



* The probable error of the differences between two results is calculated from 

 the formula: 



Probable error of difference = * / E ' + E ' 



\r, 



2 



