STATISTICAL AND ICHTHYOLOGICAL INVESTIGATIONS. 



173 



those suggested by Petersen,* was found only for the small individuals 

 from 7 to 14 cm. In other portions of the curve no distinct humps 

 were observed. 



The males proved more variable than the females in the number of 

 fin-rays. Table I. gives the indices of variability (Airy's error of mean 

 square a/^^) for each fin in both male and female. 



Table I., showing the Indices of variability of the number 



of fin-rays. 



Differences of age or sex corresponding to differences in the number 

 of fin-rays were not distinctly shown in the dorsal, anal, and ventral 

 fins. In both pectoral fins a slight increase of the numbers of rays 

 seems to occur with age {i.e. with increase of total length). 



Table II. gives the arithmetical mean values of the number of fin- 

 rays in six size groups of both sexes. Group I. contains individuals 

 below 10 cm. in total length ; group IL, from 10 to 14-9 cm., etc. ; 

 group VI., above 30 cm. (See page 174.) 



The variation is normal in three cases; in three (dorsal and both ventral 

 fins) it is skew, according to Pearson's Type IV. {Fhil. Trans. Roy. Soc., 

 Vol. 186 A.); in the dorsal, however, this skewness is only slight. The 

 correlation (according to Pearson's t formula) between the numbers of 

 fin-rays of the dorsal and anal fin is very high, r = 0*672. | This is 

 higher even than that of the pectoral fins, r = 0-588. The latter I find 

 to be less than in the symmetrical species mentioned below, in which 

 1 = 0-700 and 0720 respectively. The correlation of the ventral fins 

 is only 0-2085. 



* Report of the Danish Biol. Station, IV., 1893, "The Biology of our Flatfishes." 

 t Fhil. Trans. Roy. Soc, Vol. 187 A, p. 265. 



t Compare this with the corresponding values of the Acanthoptcrygians Acerina 

 ccrnua, Linn., r = 0-238, and Cotlus gobio, Linn., r = 0-300. 



M 2 



