353 



f'vr- T. to which we can rely upon them for further instruction, can 

 ', . ' 5 estimated by a study of such exact experiments as have been 

 made at the experiment stations throughout this country and Europe. 

 Some ilhistrations of this matter are given by C. S. Plumb, under the 

 title of the " Fallacies of plat experimentation " (Agr. Sci., Vol. II, 

 p. 4), to which I will add the following remarks. Two sets of meas- 

 ures are taken from the results of the year 1887 at Geneva, N. Y. 

 The plats were arranged in two series, or two fields, but were in every 

 respect as much alike as possible and supposed to be identical. The 

 harvests from the respective plats were as follows : 



The individual differences between these 36 plats simply show that 

 the conditions were not so uniform as the author supposed ; in fact, 

 the regular gradations from the high numbers at the top of the column 

 to the low ones at the bottom show that there was a slight systematic 

 difference among the plats in each series. On the other hand, the 

 decided apparent differences between the two series, as well as between 

 the plats, is very largely of the nature of those differences that are 

 called accidental in the theory of exact measurements. Similar dif- 

 erences in a long series of observations of the temperature or the rain- 

 fall of any locality are spoken of not as accidental error but as the 

 variability of the climate, and these differences in the present case 

 may properly be treated as variability in the productive power of any 

 plat compared with the neighboring plat without for the moment 

 inquiring as to the cause of this variability. But the mathematical 

 theory of probabilities, or chance, or errors of observation, is equally 

 applicable to this question of variability due to unknown influences. 

 According to that theory we obtain the index of variability if we take 

 the difference betAvcen the average of a series and the individual num- 

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