144 



BULLETIN OF THE BUREAU OF FISHERIES. 



As a measure of the closeness of the relation between weight and length, we have 

 determined " the coefficient of correlation r, which is the index of relation between two 

 variables, such that the amount of variation in one is a measure of the amount of varia- 

 tion in the other. Using length as the type and weight as the array, the correlation table 

 (fig. 2) was constructed. In each square is given the number of specimens which fall 

 within the weight group and length group indicated. From this arrangement of the 

 data the coefficient of correlation is found to be r = 0.952, with a probable error of ± 

 0.0032. Remembering that unity represents a theoretically perfect correlation, it is 

 apparent that this coefficient indicates an extremely high correlated variability. 



RI'X.'VTIOX OF BODY MEASUREMENTS TO TOTAL LENGTH. 



With a view to discovering the relation between the dimensions of the external parts 

 of the fish and its total length, a series of measurements was taken on 123 of the 390 

 specimens used in the work discussed above. Of these, 80 were females and 43 males. 



Flc. 3. — Showing parts of fish measured fur comparisons plotted in figure 4. 



Referring to the diagram, figure 3, the measurements, in addition to total length and 

 weight, were: 



1. Standard length, from tip of snout to end of last caudal vertebra. 



2. Head length, AB, from tip of snout to end of opercular bone, i. e., excluding 

 the opercular flap. 



3. Body length, BD, from the end of the opercular bone to a point on the lateral 

 line immediately below the posterior limit of the base of the soft dorsal lin. 



4. Tail length, DE. 



5. Body width, taken at the point C on the line AE, immediately below the origin 

 of the spinous dorsal. 



6. Depth, GF, from the origin of the anal lin, G, to F, on a line perpendicular to 

 the long axis of the fish. 



For the depth measurement, j^ specimens were examined; of these 49 were females 

 and 24 males. * 



o Davenport, Charles B.: Statistical methods, with special reference to biological variation, ch. 4, New York, 1904. 

 b As shown above, and also by the plots in figure 4, sex is a negligible factor in a discussion of this data. 



