LIFE HISTORY OF LAKE HERRING OF LAKE HURON 



377 



in weight), then many herring can spawn twice and a greater number can spawn at 

 least once, thus insuring the perpetuation of the species, provided tlie number of 

 spawners is not reduced below the number required for the maintenance of the species. 



RELATIONSHIP BETWEEN LENGTH AND WEIGHT 



"In similar solid figures the surface increases as the square, and the volume as 

 the cube, of the linear dimensions. * =n * And, taking L to represent any 

 linear dimension, we may write the general equations in the form 



SaU, VaU, 

 ovS = k.U, and V^IKU; 

 V 

 and^oZ." (Thompson, 1917, p. 16.) 



Assuming that weight (TV) is proportional to volume, the formula becomes 

 W'=]c.U, in which the constant Ic must be determined empirically. The formula is 

 valid for any species on the assumption that its form and specific gravity do not 

 change materially. Weight being known, length may be determined by the use of 

 this formula, or vice versa. It has been applied to species of fish and Mollusca. 

 (See Crozier, 1914; Crozier and Hecht, 1914; Hecht, 1916; Jarvi, 1920; Weymouth, 

 1918, 1923; Corbett, 1922.) 



Table 44. — Value of k in formula W = k.L', based on length and weight averages of different age 

 groups, shown separately for male and female lake herring of various lengths 



Table 45. — Value of k in formula W = k.L^ for lake herring of various lengths and without reference 



to sex, age, or year classes 



