208 TRANSACTIONS LIVEEPOOL BIOLOGICAL SOCIETY. 



subject the results obtained to rigid statistical analysis, 

 with due consideration of the errors involved, the crude 

 results of experiments have questionable value. 



The graph of Age-Group I in Fig. 4 has, therefore, 

 been constructed from plaice examined in 1913. These 

 fish were caught by means of both shrimp-trawl and fish 

 trawl nets, that is, nets of |-inch and 6-inch meshes, and 

 the number caught in the smaller net was about double 

 that taken in the larger mesh net. It is obvious that this 

 combination of nets does take plaice of every length con- 

 tained on the ground sampled, but it is doubtful whether 

 the proportion of each (say) 5 cm. range of lengths caught 

 is truly representative of the proportions of fish at those 

 lengths actually living on the sea bottom. If the fre- 

 quencies actually obtained be integrated, and the results 

 then plotted, we obtain a curve which shows very clearly 

 two modes, one at about 12'5 cms., and the other at about 

 18 cms. It is very unlikely that such a distribution is 

 a natural one : if it were, we should have to conclude that 

 we were not dealing with a homogeneous population, but 

 with one consisting of two " races," that is, with one race 

 of plaice which had a modal length of 12*5 cms. at the end 

 of the second year of life, and another which had a modal 

 length of 18 cms. — a condition which is very unlikely. 

 If, however, we " smooth" these integrated frequencies, 

 that is, draw a curve as evenly as possible near to all the 

 points, but still a curve which will give only a single 

 point of inflexion, we obtain a modal length for the group 

 of about 15 cms., and this is the curve which is shown in 

 Fig. 4. 



There is little doubt that the series for Group is a 

 reliable one, and that the curve for this group given in 

 Fig. 4 really represents the naturally occurring popu- 

 lation. It shows that at the end of the yearly season of 



