This formulation assumes simple, perfect correlation between body length 

 and scale length, with a regression having its origin at zero. It was found, 

 however, that the assumption is no more valid for pilchards than for many- 

 other fishes studied. The scales are not formed until the fish has reached 

 a length of 3 to U centimeters. For a time thereafter, until the body be- 

 comes fully scaled, the gi'owth rate of the scales is rapid in relation to 

 that of the body; then it decelerates, until at length the slope of the re- 

 gression, b, becomes constant. This. occurs nelov* the minimum length of 

 fish found in our samples. Hence, for the material used in this study, 

 the relation of scale length to body length may be expressed by a simple 

 straight line regression of the type y = a + bx, and Lea' 3 formula (1) must 

 be modified to: 



fn ^ in 



S F + a 



(3) 



For calculating a, the regression of scale length on body length was 

 plotted separately for each of four year classes, those of 1936 to 1939, 

 to Tihich specimens had been allocated by scale studies. 



The values of a and b were as follows : 



Year Class a b 



1936 -2.2378 .7326 



1937 0.8U6U .7285 



1938 -20.3317 .8U05 



1939 2.081U .72UO 



Significance of differences, in terms, of P= (according to Fisher's t 

 test) is as follows: 



5 .o5r.io 



In regression of scale length on body length, year classes 1936, 1937, 

 and 1939 did not vary from each other beyond the range of random errorj but 

 year class I938 differed significantly from each of the other three, both 

 as to a and b. 



y That is, the probability that if an additional pair of samples be drawn 

 from the same population, they would differ as much by chance as the two 

 under comparison, or more. 



109 



