69 



2.18 and 2.27, 3 between 2.28 and 2.37 and 4 when it is be- 

 tween 2.38 and 2.47. In the same way for the indices of the 

 abdominal fin the letters a, b, c en d are used ; for the anal 

 aperture five cases are distinguished and these are represeuted by 

 the ciphers O, I, II, III & IV. Finally the letters A, B, C and D 

 show to which category the fish is to be reckoned as far as the 

 length of the anal fin is concerned. The great advantage of ap- 

 plying this method is evident : with four letters and ciphers a 

 formula is composed, which fills the place of a description, and 

 enables us to compare numerous specimens with one another, 

 almost at first sight , and with mathematical precision. 



In the first place 200 fuU-grown Zuiderzee-herrings caught in 

 various months of the year were selected at hap-hazard and in- 

 vestigated. The result was that of the 320 matheraatically com- 

 patible combinations forty five were found represented under 

 these 200 fishes. When we neglect 21 lormulae which occurred 

 once, in the remaining 179 tishes altogether we only observe 24 

 combinations ; these , however , are not represented equally , as 

 may be seen from the followiug record. 



Though only 200 fuU-grown herrings were investigated , the 

 coraparatively great analogy of their formulae compels us, I think, 

 to acknowledge, that this number was not quite insignificant, at 

 least as far as the four peculiar traits which were investigated 

 are concerned. Comparing these formulae with those established 



