THE MEASUREMENT OF VARIATION. 27 



results on the variability of the fin rays of certain fishes 

 in terms both of the mean error and the error of mean 

 square. Again, from data obtained by Petersen, Bum- 

 pus, Weldon, and himself, Duncker * has calculated 

 the error of mean square, and obtained the following 

 values for the number of fin rays in certain fishes : 



DORSAL FIN ANAL FIN 



Me Me 



Pleuronectes flesus, Baltic, 39.46 1.4838 



" North Sea, 41.56 1.7739 



Plymouth, 61.72 2.3895 43.61 1.6026 



americanus, 65.06 2.4467 48.62 1.8188 



Rhombus maximus, 62.98 2.2533 45.86 1.6792 



And the following for the number of rostral teeth: 



DORSAL FIN ANAL FIN 



M. e M. e 



Palcemonetea varians, 4.3137 .8627 1.6948 .4799 



vulgaris, 8.2819 .8145 2.9781 .4477 



These results show that though the average values of a 

 character may differ considerably even in the local races 

 of the same species, yet the indices of variability 

 may remain fairly constant, not only in these, but also 

 in different species, and perhaps even in different 

 genera and families. Thus the two species of Palce- 

 monetes vary by respectively 92.0 per cent, and 75.7 

 per cent, in the number of rostral teeth in their dorsal 

 and anal fins, but by only 5.9 per cent, and 7.2 per cent, 

 in their indices of variability. Arguing from these 

 data, Duncker f concludes that one has no right to ac- 

 cept the " coefficient of variation ' ' of an organ as the 



*Nat. Science, xv. p. 328, 1899. 

 f Amer. Nat., xxxiv. p. 621, 1900. 



