132 TRANSACTIONS LIVERPOOL BIOLOGICAL SOCIETY. 



unnatural reluctance of the Fishery Officers to mis- 

 apprehend their instructions that large samples of the 

 iish caught by them should be sent to the laboratories 

 periodically. The modal lengths tabulated on p. 138 have 

 been determined by integration of the original frequency 

 series, as in the case of the other tables. As a rule there 

 is little difficulty in estimating very approximately the 

 position of the modal frequency. When the curves arc 

 drawn it is often apparent that one or other of the 

 extremities is unrepresented in the series, but this may 

 affect very little the value of the mode. As a rule, when 

 •JO to 50 fish of any of the Age- Groups are examined, 

 the mode can be ascertained. It is sometimes impossible 

 to determine the modal length of Groups I and II in the 

 same catch, the latter consisting predominantly of fish 

 of the same year; and as a rule it is impossible to 

 ascertain the length of plaice of Age-Group III except in 

 one or two of the Lancashire fishing grounds. Plaice of 

 more than three 3'ears of age are not allowed to inhabit 

 the shallow waters oil' the coasts of Lancashire and North 

 Wales in very great numbers. 



It would be a result of very great value if one could 

 determine the law of variation in growth, so that a 

 theoretical frequency-curve could be substituted for the 

 observed distribution. Unfortunately this has not been 

 possible. In order to determine the equation of the curve 

 which the observations would fit with least improbability, 

 a very large number of plaice would have to be examined, 

 and one would have to collect the fish under conditions 

 which would ensure the homogenity of the material ; thai 

 is, they must be' caught at the same time of year, and on 

 the same place, so as to avoid the influence produced by 

 migrations; and the catches would have to be made b\ 

 means of trawl nets of different meshes. For just as no 



