258 TRANSACTIONS LIVERPOOL BIOLOGICAL SOCIETY. 



Remarks. 



The mathematical investigation of these data can scarcely 

 be regarded as giving very satisfactory results ; many of them 

 are conflicting and in some cases one result completely annuls 

 another. The reasons may be sought in many directions, some 

 of which under present circumstances would be difficult to follow. 

 We might get more trustworthy results from weekly samples 

 of herrings and by dealing with them immediately. This, 

 however, would necessitate the abandonment of some other 

 equally important work during a very critical time in a marine 

 laboratory programme. Methods of measurement might be 

 improved and additional characters investigated, including the 

 counting of the vertebrae. 



The grouping of the data according to scale markings has 

 been considered. That is, instead of giving a range of per- 

 centages of T.cd. of any one character and lumping together 

 all the fish of a sample irrespective of their ages, as we have done 

 in the present report, the fish would be selected according to the 

 scale markings and each age group treated separately. This, 

 however, has the great disadvantage of reducing the present 

 data to many groups with much smaller frequencies and would 

 consequently necessitate much larger samples. The samples 

 would at least be homogeneous as far as age was concerned, and 

 any peculiarities due to a possible shifting of any character 

 might reasonably be expected to be confined to the particular 

 age group under consideration and to be evenly distributed 

 among the varying length frequencies. 



Our examination of scale markings of the various samples 

 considered reveals great heterogeneity as regards age. A sample 

 generally contains fish with from two to six scale rings. In 

 some cases one special ring group will predominate, in another 

 perhaps three groups will be equally represented and form the 

 bulk of the sample. 



