52 OUGHT THE MEAN OF SEVERAL 



the weight of bulbs differed by 2 tons 7 cwt., or one-fourth of 

 the whole gross weight of the crop. 



When differences so wide as those observed in the numerous 

 cases cited in the present section are likely to be met with, it is 

 quite clear that the result of no single trial can be regarded as 

 an indication of the exact or absolute effect of a given substance 

 upon a given crop in a given soil. Two or more experiments 

 must in each case be made, if any trustworthy or useful deter- 

 minations are to be obtained. Other illustrations of this posi- 

 tion will find a place in the subsequent sections. 



8. Ought the mean of the natural produce of different parts 

 of a field to be taken as the standard with which to compare 

 the produce of experimental manured portions f 



'But in what way are the results of the two or more experi- 

 ments we may make to be regarded ? Are we to take the 

 mean or average result of the whole, and to consider this as an 

 expression of the absolute natural productiveness of the land 

 where nothing is applied to it, or of the absolute effect of this 

 or that substance which we may have laid on ? Or are the 

 results of the several experiments of each kind to be compared 

 each with each, and the absolute effects to be deduced according 

 to some other method. For example, 



Suppose three several portions of a field of wheat to yield, 

 without manure, at the rate of 18, 21, and 24 bushels of grain 

 respectively, the mean being 21 bushels and that a fourth por- 

 tion, to which a certain manure is applied, yields also at the 

 rate of 24 bushels, are we to compare this last result of 24 

 bushels with the mean 21, and infer that the substance applied 

 increased the crop by 3 bushels ; with the number 18, and 

 infer that it had increased it by 6 bushels; or with the number 

 24, and say that the application had done no good at all ? In 

 such a case as this, the reader will, I think, agree with me that 

 no conclusion can be drawn as to the effect of the substance 

 applied, inasmuch as the crop it produces is not greater than 

 one portion of the field had produced without any application. 



This reasonable conclusion has an important bearing upon 

 the value to be attached to many series of otherwise praise- 



