28 THE MEASUREMENT OF VARIATION. 



absolute measure of its variability, as Verschaeffelt,* 

 Brewster,f and others have done. He thinks that the 

 indices of variability alone may be of morphological 

 significance, for in this case, at least, they are obviously 

 independent of the mean values of the characters. 



How far Duncker's view is to be accepted can only 

 be determined by further enquiry. Doubtless it will 

 be found to hold good occasionally, but I think that the 

 great weight of evidence at present available, especially 

 as regards measurements of size and shape, rather than 

 those of numbers of organs, is in favour of the alterna- 

 tive hypothesis. 



The three indices of variability above referred to are 

 by no means numerically equivalent. They bear the 

 following relations to each other: 



Probable error, 1.000 Corresponding grades, 25. 0, 75. 



Arithmetic mean error, 1.183 " " 21. 2, 78. 8 



Error of mean square, 1.483 " " 16. 0, 84.0 



Thus the error of mean square is nearly half as large 

 again as the probable error, and therefore includes a 

 proportionately larger percentage of the deviations 

 from the mean within its limits. On the frequency 

 curve given a few pages back are drawn dotted line 

 ordinates A, A' and S, S', which enclose areas of the 

 variation polygon corresponding to these " mean error ? 

 and " error of mean square ? indices of variability. 

 The " probable error " index is in some ways the most 

 convenient of the three, as it is the smallest, and in- 

 cludes within its limits just half of all the variants. As 

 the error of mean square is held to be a more accurate 



*Ber. d. deutsch. bot. Ges., xii. p. 350. 

 f Loc. cit. 



