276 Part III. — Seventeenth Annual Report 



show the true meaning of this overlapping — i.e., to bring out the mean or 

 average of both sets, and allow the variations to dovetail into one another 

 on the one side or the other, or both. This Matthews did not attempt, 

 nor could he very well at that time, but what he did was to divide up the 

 grounds of variation into a number of small divisions, and arrange under 

 each division the number or percentage of individuals observed to have 

 this or that variation. 



An example may be given in order to show this. 



TABLE XXVI.,* 



Showing Percentage of Mature Herrings of Progressive Lengths 

 of Body, arranged according to Ratio of Position of Centre of 

 Anal Fin to Body-Length (less Head and Caudal Fin). 





Winter. 



Summer. 



Ratio of 

 Fin Position. 



•751 

 to 

 •762 



•763 

 to 

 •773 



•774 

 to 

 •784 



•785 

 to 

 •795 



•796 

 to 

 •806 



•807 

 to 

 •817 



•818 

 to 

 •828 



•829 

 to 

 •839 



•751 

 to 

 .762 



•763 

 to 

 •773 



•774 



to 

 •784 



■785 

 to 

 •795 



■7!t6 

 to 

 •806 



•807 



to 



•817 



•818 

 to 

 •828 



•829 

 to 

 •S39 



f 

 PS 



"o 

 A 



bt) 



a 



mm. 

 150 to 169 



% 



% 

 11-1 



% 

 5-6 



% 

 33*3 



% 

 33-3 



% 



11-1 



% 



5-6 



% 



X 



3-6 



% 

 10-7 



% 

 14-3 



% 

 21-4 



X 



32-1 



% 



10-7 



% 

 7-2 



% 



170 to 189 



2-9 



12-8 



32-8 



21-5 

 



25-7 



4-3 







•7 



4-2 



5'7 



19-0 



29-5 



22-5 



14-8 



3-5 



190 to 209 



1-4 



11-4 



24-3 



24-3 



25-7 



8-6 



2-9 



1-4 



•7 



1-4 



5-4 



15-6 



31-3 



26-5 



13-6 



5-5 



210 to 229 





10-8 



22-9 



22-9 



25'3 



14-4 



24 



1 2 









io-s 



39-1 



24-0 



19-6 



6-5 



230 to 249 





2-6 



13-2 



29-0 



31-6 



21-0 





2-6 







10-0 



io-o 



30-0 



20-0 



30-0 





Percentage of 

 all Lengths. 



•9 



97 



19-8 



26'2 



28-3 



11 9 



2-2 



10 



1-0 



3-3 



7-1 



15-4 



32-4 



207 



17-0 



3-1 



The reasoning by which Matthews reached his conclusions should also 

 be given, and as it is common for all the differences recorded, it can be 

 centred round the above example. First, objection was taken to 

 Heincke's earlier method of dividing up the variability into three classes, 

 which, legitimate in itself in order to display small differences, contains 

 the following possibility of error or flaw : — 



"We have," says Matthews, "in most of the characters a more or less 

 " common ground of variation — i.e., a region in which the character appears 

 "so commonly as to be entitled to the term normal,^ and an extreme of 

 "variation on one or both sides of this, and more or less great. By 

 " dividing the total variation into three equal divisions we perhaps in some 

 " cases include the normal in the first, in others in the second, or it may 

 "be in the third division. This would not necessarily be very confusing, 

 " but further, as in some of my cases, part of the normal cases would be 

 " included with one extreme of variation, part — probably an entirely 

 " different quantity — with another. If for facility in the investigation, so 

 "few artificial divisions of variation as three are used, they should be not 

 "equal in extent, but such as to cover a normal condition and an upper 

 " and lower extreme of variation, except where the variation is equally 

 "spread over the individuals." 



*Part II., Fifth Report of the Fishery Board for Scotland, p. 295, 1887. 

 t Italics are mine. 



