Gr. W. KuHINSUN AND W. E. LlOYD 151 



Thus if /( borings are made and one determination made on each 

 boring the probable error of the average is 



± -'^ , ^^ or , . 



For example, in the case of P2O5 in Field A, 9 borings separately 

 analysed and averaged would give a probable error of 



13-4 



± — 77- = ± 4 ■40 per cent. 



If n borings are made and a composite sample obtained by mixing, 



the held error will be reduced to '^ , but the laboratory error will still 



be present, so that if 9 borings from Field B were mixed, the error of 

 one analysis would be 



13 -9 - 

 2-52 + { — - ) , or ± 5-05 per cent. 



Where the field error is large in comparison with the laboratory 

 error not much additional accuracy is obtained by analysing the borings 

 separately. Also, however many borings are taken and mixed, it is 

 not possible to reduce the final error to less than the laboratory error; 

 and it is also somewhat difficult to ensure the satisfactory mixing of 

 a very large number of borings. 



Performing more than one analysis on a composite sample will 

 serve to reduce the laboratory error, and consequently the final error of 

 result. 



If the field error for chemical analyses be taken as ± 10 per cent. 

 and that for the mechanical analyses as ± 5 per cent., we shall probably 

 not err on the side of minimising errors, since no field is sampled for 

 survey purposes unless it aj^pears fairly uniform. As is mentioned 

 above. Field A would not be considered uniform enough for survey 

 purposes. 



The following table shows the probable error of final result for 

 different numbers of borings and for single and duphcate analyses of 

 the mixed sample. The probable errors are calculated on the assump- 

 tion that the final probable error is etjual to the square root of the sum 

 of the squares of the separate probable errors. Thus the probable 

 error of an average of two determinations on a composite sample of 

 5 borings is in the case of mechanical analyses equal to 



*V (5) ^(■'^^' = ± 2-8 per cent., 



5_^2 



Journ. of Agric. Sci. vn H 



