LIFE HISTORY OF LAKE HERRING OF LAKE HURON 319 



first to the third year, inclusive, the — y- ratios rise during these years. In the fourth 

 year both ratios rise and thereafter vary in the same way. According to Molander, 



the y ratios indicate that the scales grow proportionally quicker than the body during 



L—50 

 the first three years of life, while the -^rr- ratios indicate that the scales grow 



proportionally more slowly than the body. The author believes that the trend of 

 the y fractions would not be altered by a change in the value 50. This, of course, 



is not true. For example, if we subtract 35 millimeters from the average length 



i-35 

 values of the whitefish of Table 13 we obtain y ratios, as follows: For the 53- 

 millimeter fish, 23.4; for the 269-millimeter fish, 40.7 — a rise in values occurs. But 

 if we deduct 10 millimeters instead of 35, then the ratios become 53+ and 43 + , 

 respectively — a decline in values occurs. 



An analysis shows that on the basis of Molander's method of studying body- 

 scale ratios the following relationships obtain: 



L—X '^ T 



If — y — remains constant with increased fish length, -y must decrease. 



If y decreases, -y must decrease. 



If y increases, -p. may decrease, remain constant, or increase, depending upon 

 the degree of relative slowness of scale growth. 



According to these relationships, if y decreases, as is the case in the lake herring, 

 then either the body and scale actually grow in proportion or the scale actually grows 

 faster or more slowly, proportionally, than the body. If -y remains constant or 



increases with age, the scales grow more slowly relatively than the body. The -y 



fractions do not then express the real growth relationship between body and scale. 



In the p;, ratios we study the length relationship between body and scale; in the 



i— 50 



— y— ratios we study the actual growth relationship. According to the first view 



we say, if the fish at the end of its second year of life has doubled the length reached 

 by it at the end of the first year, then the scale length at the end of the second year 

 must be twice that reached at the end of the first year if body and scale length are 

 to maintain a fixed relationship. The percentage of increase must be the same in 

 body and scale. According to the second view we say if the body growth during the 

 interval between scale formation and the end of the first year is doubled by the end 

 of the second year then the 2-year scale must be twice the size of the 1-year scale if 

 body and scale actually grow in proportion. But in this case the total length of the 



" X=leDgtb of fish at scale formation. 



