180 TRANSACTIONS LIVERPOOL BIOLOGICAL SOCIETY. 



(1892-1906) was considered, that is, for instance, all the 

 average hourly hauls for January were added together, 

 and a new average, giving the number of fish caught per 

 hour's fishing for the month of January (1892-1900), was 

 thus obtained. Similarly, to find the yearly variation, 

 which was only possible in the case of the summer months, 

 owing to lack of data for the winter, an average hourly 

 catch for the six-monthly period, May to October, was 

 obtained in each year, and the variation of this average 

 from year to year was studied. Curves were drawn 

 through points corresponding to these averages, and since 

 it was found that these points were too irregularly dis- 

 tributed to give reliable results, they were modified in the 

 following manner: — The values representing the average 

 catches were arranged in chronological order, and the first 

 and last were taken as correct. For each of the other 

 monthly averages a new value was substituted, obtained as 

 follows : — The average catches for the month in question 

 and that immediately preceding and succeeding it were 

 added together and the sum divided by three. This is the 

 well-known statistical device of " taking three-monthly 

 averages monthly." In some cases the figures thus 

 obtained had to be again treated in the same way before 

 it was found possible to draw a really smooth curve 

 through the points, showing distinct maxima and minima. 

 The following figures, those for average catches of plaice 

 with the shrimp-trawl net, will serve to show the method. 

 Original Figures. First Smoothing. 



Jan 72 ... (taken as correct) ... 72 



Feb 93 ... 72 + ^ + 182 = 116 



Mar 182 ... 93 + *f + 9A = 123 



April 94 ... 182 + 9 * + 155 = 144 



May 155 &c. 



&c. 



