214 TRANSACTIONS LIVERPOOL BIOLOGICAL SOCIETY. 
(2) ‘“‘ Smoothing’ empiric curves. 
If the preceding tables of frequency distributions 
be examined, still better if the graphs be examined, it 
will be seen that the calculated values do not “‘ fit’’ 
very closely to the observed values. This is, indeed, 
not to be expected, since the observed values must 
necessarily deviate to either side of a mean; but it will 
be noticed that the areas of the two figures formed by 
plotting observed and calculated ordinates are not the 

; Es — 
&) 10 15) 
Fic. 3. 5,057 plaice from Mersey area, January, 1909. 
same. The difference is not due entirely to the roughness 
of the original data, for when the larger series are 
considered the difference in areas still is apparent. It 
may be due, to some extent, to the difficulty in making 
the statistical ‘‘ adjustments,’’ but this is not the only 
source of difference. There is no doubt that the 
statistical data are not homogeneous and that the 
roughness of the smaller distributions may conceal this; 
but that while the roughness may disappear in the larger 

