ENVIRONMENT OF THE BOLL 95 



Further examination would destroy this conclusion, for 

 it would then be noticed that the two curves do not run 

 exactly counter to one another, but that there are occa- 

 sional minor rises and falls which are the same in both. 

 These might be due to two causes : either the hypothesis 

 of antagonistic development is wrong, and the general 

 antagonism of the two curves is mere accident; or the 

 methods by which these lengths and strengths are deter- 

 mined are not sufficiently accurate, and the minor rises 

 and falls are of no significance. 



Here comes in the utility of modern statistical methods ; 



by their aid we can give a numerical expression to the 



chances of inaccuracy for these points which 



Stafosfcca 1 compose the curves. It is not necessary to 

 Methods. 



go into details of the way in which these 



" measures of inaccuracy " are derived, but the result in 

 the case of these two curves is as follows : For any point 

 in the length curve the chances are even that it is not 

 more than 1 per cent, out of the position which it would 

 occupy were infinite pains and repetition used in its 

 exact determination, while it is highly improbable that 

 it should be more than 3 per cent, out of place. For the 

 curve of breaking strain the even chance is 1-5 per cent. ; 

 and extreme improbability at 5 per cent. 



We now take the rise in strength, which culminates on 

 August 9 (August 5 to 12); we find that the rise is 10 per 

 cent. If only August 5 and August 9 were available, this 

 difference might just be explicable by the summation of 

 two extremely improbable occurrences. There are, how- 

 ever, some eight days involved, all in regular sequence; 

 since the addition of each extra observation decreases 



