8 Fishery Board for Scotland. 



15. Size of the eye. Greatest horizontal diameter of the eye- 

 bulb. 



16. Distance between the dorsal and ventral fins. 



17. Number of rays in the ventral fin. 



18. Number of vertebrae. The last vertebra counted is the first 

 vertebra that distinctly bends upwards. 



19. Number of vertebrae to the first haemal arch. 



20. Number of tail-vertebrae. 



21. Number of keel-scales between the ventral fin and the anus. 



22. Breadth of operculum. 



Complete sizes, with the exception of the total length, were 

 measured in a straight line by means of callipers. 



The greater errors are those of measurement, made, for example, 

 on fresh or spirit-preserved specimens. All the errors are large 

 when made on soft parts. 



Method of Treating the Measurements. 



All the measurements are expressed as percentages of certain 

 body-dimensions, e.g. total length, or lateral length of the head, or 

 the upper length of the skull (p. 80). 



The average size of each character is calculated for the group 

 of herrings examined. The average for the whole race is approxi- 

 mately deduced by the aid of the curve of probability. Two quantities 

 (the fluctuations of the mean) are obtained, between which the mean 

 for the race is supposed to lie. If the fluctuations of the mean 

 for a character in two shoals of herrings do not overlap, the character 

 is considered to be racially distinct in the two shoals. 



" The application of the method of combined characters to the 

 different herring-races which have been so far investigated yields 

 a sure natural system, which is sketched below" (p. lix.) Heincke 

 remarks that the system is only a provisional one. 



Heincke distinguished among the European herrings the following 

 ten groups, some of which consisted of more than one race : — 



1. Herrings of Iceland. 



2. Spring-herrings of Norway. 



3. Spring- and coast-herrings of the northern part of the North 

 Sea and of the Skagerak. 



4. Spring- and coast-herrings of the southern part of the North 

 Sea and west part of the Baltic including the Kattegat. 



4a. Spring-herrings of Kiigen. 



5. Autumn- or sea-herrings of the northern part of the North 

 Sea, including the Skagerak and Kattegat. Northern bank-herrings. 



6. Autumn- or sea-herrings of the southern part of the North 

 Sea. Southern bank-herrings. 



7. Autumn- or sea-herrings of the Baltic. Baltic bank-herrings. 



8. Spring-herrings of the eastern part of the Baltic. 



9. Herrings of the English Channel. 



10. Herrings of the White Sea. 



