181 



such would be expected to differ from big samples from the 

 same locality at another time— if the physical conditions had 

 changed. At all events it was necessary to test this. 



First of all we have taken all the herrings measured so far 

 and have (as a rule) taken them sample by sample and not 

 lumped them. The characters D, V, A, l.cp.l., and K2 only 

 are dealt with. A separate frequency distribution was made in 

 each case. In each case the independent variable is D, etc., 

 expressed as a percentage of T.cd. The classes of D, etc., 

 change by 0-25 %. In the tables " 50-25," " 50-50," " 50-75," 

 etc., must be read as " 50-25 to 50-49," " 50-50 to 50-74," " 50-75 

 to 50-99," etc. The dependent variable is, of course, the numbers 

 of cases of D, etc., falling within the classes 50-25 to 50-49, etc. 

 The conventional signs indicating the various characters 

 are as follows : — 



T. = Total length from tip of snout to the tip of the dorsal 

 lobe of the caudal fin. 



T.cd. = Total length to base of tail. 



D. = Length from tip of snout to beginning of dorsal fin. 



V. = Length from tip of snout to beginning of pelvic fins. 



A. — Length from tip of snout to anus. 



l.cp.l. = Lateral length of head. 



K2 = Number of keeled scales between anus and pelvic fins. 

 In order to investigate the matter further we have assumed 

 that all Manx herrings belong to the same " race." Thus the 

 samples of Jmie and September, 1920 (Table XII), for instance, 

 although they are rather different in respect of the distribution 

 of frequencies of values of D, are assumed to represent the 

 same " population " or " race." To what are the differences 

 due ? 



We assume they are due (1) to errors of measurement and 

 (2) to errors of random sampling. Errors of measurement are 

 then reduced somewhat by grouping the classes. Thus we 

 ta,ke, say, 50-00 to 50-49, 50-50 to 50-99, etc., instead of 50-00 



