380 



FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



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4 5 6 7 8 9 10 



TOTAL LENGTH (INCHES) 



Figure 9. — Length-frequency distribution of Saginaw Bay yellow perch in 1929-30 (solid lines) 



and 1943-55 (short dashes). 



two periods the mesh size of the fishing gears 

 did not change appreciably, if at all, and thus 

 the effect of net selectivity could be excluded. 

 This change of length is reflected in the per- 

 centage of legal-sized fish (8i/ 2 inches) in the 

 two periods. In 1929-30 the legal-sized yellow 

 perch comprised 73.9 percent of the catch. In 

 1943—55 this percentage dropped to only 11.0 

 percent. 



LENGTH-WEIGHT RELATION 



The length-weight relationship of fish has 

 sometimes been described by the "cube law," 

 W = CL Z (where W = weight, C = a constant, 

 and L = length). This law, however, can be 

 applied only if the form and the specific gravity 

 of fish remain constant throughout life. These 

 requirements are so rarely met, that the more 

 general equation W = cL n (c and n are deter- 



mined empirically) is usually the more suitable 

 in the study of length-weight relationship. Hile 

 (1936) demonstrated that the exponent n can 

 vary widely (he showed values from 1.34 to 3.68 

 for various samples and stocks of ciscoes). Hile 

 (1936) and Le Cren (1951) discussed many of 

 the questions and controversies involved in the 

 application of this relationship. The cube rela- 

 tionship serves best in the study of "condition" 

 since the value of C, the condition factor, meas- 

 ures "plumpness" or degree of well-being regard- 

 less of the actual length-weight relationship. 

 Some have advocated the use of c in W — cl" in 

 the study of condition, but this application is be- 

 set with many difficulties (Hile 1936). 



The equation W = cL" was proved by several 

 authors to describe the general length-weight 

 relationship of yellow perch adequately (Hile 

 and Jobes, 1941 and 1942; Jobes 1952; and Le 

 Cren 1951 for the European perch). 



