32 



In order to make comparisons easier the ratios ex- 

 pressing the distance of the dorsal fin from the tip of the 

 snout are divided into four groups each of which is 

 distinguished by a number : — 



1. AVhen the ratios varied from 2'08 to 2'17 



2. „ „ „ „ 2-18 to 2-27 



3. „ „ „ ,, 2'28 to 2'37 



4. „ „ „ „ 2-38 to 2-47 



In a similar manner each of the other ratios was divided 

 into four groups with the exception of the distance of the 

 aniis which was divided into five. To each of these groups 

 descriptive numbers or letters were applied, viz. : — 



In the first place it should be noted that the formulee 

 do not express what they are intended to, and that it is 

 quite possible that they can convey false impressions. 



For instance it is quite possible that two groups of 

 spring herring, to each of which Heincke's average 

 formula 2bII. applies, are really much more unlike one 

 another than one of them is unlike a group of autumn 

 herring to which Heincke's formula 2al. applies. 



This difference may theoretically be very great, as may 

 be seen on reference to the following table : — 



