9218 TRANSACTIONS LIVERPOOL BIOLOGICAL SOCIETY. 
occurring frequencies are summed so that any value of 
y in column 3 is given by 
a being the end of the series. By working in this way 
we approximate to the value of the definite integral 
between any value of 2 and the end of the curve; but 
the increments 6x are not very small (1 cm. in the 
example). 
200 
seine LH 
2) | 
K 
ALIN 
pak alll LLL a 
Fic. 4. A catch of 2,228 plaice from Red Wharf Bay, November, 1910. 

The graph of the figures in column 3 can now be 
plotted with considerable accuracy, and if some 
mechanical means of drawing the curve be adopted, a 
fine clear line may be drawn, and there is no doubt, as 
