SEA-FISHERIES LABORATORY. 



173 



expressed as percentages of the total catches : the distri- 

 butions for the various months can thus be compared, 

 and we are enabled to superpose curves plotted from the 

 relative frequencies, and to express the statistical constants 

 in the same units. The percentages of frequencies have 

 been integrated : that is, beginning with the greatest 

 length, the percentages have been added together, each to 

 the sum of all those referring to higher lengths, as in the 

 following Model Table. 



Mersey Estuary ; 13,343 Plaice caught in trawl-nets of 

 |-inch mesh. January, 1909-1913. 



Mean 



Actual 



Percentage 



Integrated 



length. 



frequency. 



frequency. 



frequency. 



4-5 



406 



2-97 (f x ) 



99-90 



5-5 



2,586 



19-38 (f 2 ) 



96-93 



6-5 



2,903 



21-76 (f 3 ) 



77-55 



7-5 



3,018 



22-62 (&c.) 



55-79 



8-5 



2,054 



15-39 



3317 



9-5 



896 



6-72 



17-78 



10-5 



435 



3-26 



11-06 



11-5 



415 



311 



7-80 



12-5 



214 



1-60 



4-69 



13-5 



173 



1-30 



3-09 



14-5 



96 



0-72 



1-79 



15-5 



75 



0-56 



107 



16-5 



27 



0-20 



0-51 



17-5 



25 



0-19 



0-31 



18-5 



7 



005 



0-12 



19-5 



6 



04 



007 



20-5 



1 



00 



003 



21-5 



2 



0-01 (&c.) 



0-03 (&c.) 



22-5 



3 



0-02 (f 19 ) 



0-02(f 21 +f a0 +f 19 ) 



23-5 







0-00 (f 20 ) 



0-00(f 20 +f 21 ) 



24-5 



1 



0-00 (f 21 ) 



0-00 (f 21 ) 



Totals 



13,343 



99-90 





This has been done for all the distributions in the Sum- 

 mary Tables, although the integrated frequencies are not 

 given there. A graph has also been drawn for each distri- 

 bution, both for the frequency series and the integral 



