LIMITS OF NATURAL VARIATION. 73 



b Corn, as much as 5 or 6 bushels sometimes , or more gene- 

 rally 5 per cent may be regarded as a natural difference. 

 Eesults not differing more than 5 per cent may, in the absence 

 of other proof, be regarded as identical. 



c Hay, as much as 10 per cent, in the absence of satisfactory 

 experiment, can scarcely be considered as too wide a limit for 

 the natural differences in this crop. 



Now, suppose the results of a series of single comparative 

 field experiments to be laid before us, and that on inspecting 

 them we find that, in comparison with that portion to which 

 nothing has been applied, the produce of the other differs in 

 excess or defect no more than 5 or 10 per cent according to the 

 crop ; then, in regard to that series of experiments, we ought 

 to decide that no safe conclusions can be drawn from it, as to 

 the absolute effect of this or that substance in the given circum- 

 stances. There may be a probability that some of the sub- 

 stances employed have produced an effect, but that probability 

 ought to lead us not to form or adopt an opinion, but to make 

 new experiments on the subject. 



If the differences exceed this natural limit of variation, then 

 a positive conclusion to the extent of that excess may be drawn 

 from the comparative results. 



From published experiments I might select many illustrations 

 of this position. I shall confine myself to two taken from a 

 table of the results of twenty-three experiments upon turnips, 

 by Mr Lawes, made in 1843.* 



a In these trials, the portion to which no manure was 

 applied, yielded 4 tons 3' cwt. of bulbs, which only weighed 

 half-a-pound each on an average. In all the twenty-two other 

 experiments, the produce of bulbs varied from 8 to 12 J tons, 

 and the bulbs weighed each on an average upwards of a pound. 

 The conclusion, therefore, in this case is a safe one, though the 

 experiments be only single, that every one of the substances 

 employed did, under the circumstances, possess a large fertilising 

 power. But 



b Of the twenty-three results reported in this table, ten 

 vary between 10 and 11 tons of bulbs per acre. Differing not 



* Journal of the Royal Agricultural Society, yiii., p. 503. 



