216 ‘TRANSACTIONS LIVERPOOL BIOLOGICAL SOCIETY. 
numbers of fish belonging to two successive age-groups, 
and when few fish of other groups are present, a complex 
curve should result. The latter would be complex even if 
plotting the original data gave an apparently uni-modal 
curve. 
In making use of Professor Pearson’s methods for 
the representation of fish measurement series, we should, 
then, first of all separate the series into as many groups 
as there are distinct years of age among the fish caught. 
This would involve the dissection of every specimen 
measured 

an impracticable proceeding generally. But 
in many of the catches of plaice made in the Irish Sea 
one age-group is predominant, and in such cases it seems 
that a Pearsonian frequency formula may be applied 
without serious error. The graduated statistics thus 
obtained would be a better expression of the actual 
distribution than the rough data. Such a sample is 
represented by the catch of plaice treated on p. 218, 
where the age-group O is the predominant one. 
The following series of. measurements represents a 
catch where an entirely different method must be 
employed. 
The second and fourth column are graphed in the 
figure on p. 218. 
In ‘‘smoothing’’ a rough series of figures the 
method of finding the mean of every three successive 
groups is usually adopted, that is any _ value, 
y= ise aL ae 
This would graduate the series in respect of the errors 
of measurement, for it is likely that some fish which 
ought to belong to group z are placed in groups #—1 or 
z+1. But it would not take account of larger errors 
