514 TRANSACTIONS LIVERPOOL BIOLOGICAL SOCIETY. 



the most common, it will be necessary here to emphasise 

 its great defects and almost worthlessness for quantitative 

 work when not supplemented by the other. Suppose that 

 one has a certain plankton catch obtained by a vertical 

 haul of the net through 40 fathoms, that the catch has 

 been estimated, and according as the various forms ate 

 relatively frequent or rare, they have been designated 

 with letters as above described in the tables. Now we 

 will assume that a second catch taken in another place 

 from the same depth has all the organisms present in 

 the same relative proportions as in the first, but in double 

 or treble the quantity. This would make no difference 

 whatever in the tables, the relative frequencies si ill 

 remain the same, even though a form which is represented 

 by " rare " in both catches may be present two, three, 

 or four times as many in one catch as in the other. 

 Thus the tables could not be directly comparable for 

 quantitative purposes. We have, however, assumed here 

 that the constitution of both catches was identical — 

 a thing of almost impossible occurrence. Let us assume 

 now that the constitution varies, and that three catches 

 are taken (an example given by Apstein), as one makes 

 a voyage out from the coast, and that these are estimated 

 by both methods. By counting, the first is found to 

 contain 50,000 Ceratium fusus and great masses of the 

 diatom Seeletonema. In the second catch, taken further 

 out, there are still 50,000 C. fusus, but the diatoms have 

 disappeared. At the third station C. fusus still remains 

 at about the same number, but Ceratium macroceros, up 

 till now rare in the catches, appears rather abundantly. 

 Now, an investigator who simply estimated the relative 

 frequency of these organisms would state that C. fusus 

 was very rare in the first catch (since they were over- 

 shadowed by the great masses of diatoms), common in 



