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grow older. Neither of these conditions obtain. There are neither 18 dorsal rays 

 nor 13 anal rays represented in the second year specimens; and in the first year 

 specimens 17 dorsal rays are not represented. In the dorsal spines where the 

 difference is most pronounced we have in the first year specimens the exact 

 duplicate of that of the third year specimens, while the second year specimens 

 are quite different. The scales in the lateral line present the same difficulty. 



Annual Variation. — The explanation that seems to meet all the conditions 

 most satisfactory is that the species varies with the varying conditions of successive 

 years. 



The difference in the dorsal spines of the different ages accounts thus for the 

 abnormality of the curve for the dorsal spines of all the Turkey Lake specimens, 

 Fig. 4. The 600 specimens for which the curve is constructed is a composite lot 

 of three age varieties. 



This conclusion, however, should be held with some reservation. It will be 

 noticed that nearly all the curves of Figs. 7, 8 and 9 are abnormal curves, which 

 may possibly be due to the presence of local races in the lake. While this may 

 possibly be the case, it is not at all probable, because, in the first place, the 

 curve constructed for the dorsal spines of 100 specimens of three year olds, 

 taken within a distance of 100 yards along the shores where the conditions were 

 undoubtedly uniform, gave a curve identical with that for all the three year 

 olds. In the second place, the second and third year specimens are found in 

 about equal abundance together, and since these were promiscuously preserved it 

 is altogether probable that from any given locality, an equal number of each age 

 was taken. 



The sex has been determined in all, and a summary shows that the sexes do 

 not differ in the characters entering into the above considerations. 



