Horizontal Distribution — Swarms. 367 



einmal an einer Stelle einige tausend Menschen zusammenstro- 

 men, so wird dadurch die Bewohnung noch nicht ungleichmassig. ,x 

 (Hensen, '95, p. 172.). 



I have placed at the head of this section Hensen's words 

 which seem to me to express with great clearness and 

 wisdom the general truth regarding the still disputed question 

 of the uniformity of the distribution of plankton animals. On no 

 question relating to the plankton are opinions so widely at vari- 

 ance, yet no question is more fundamental to the value of numer- 

 ical work in investigation. For example, Wesenberg-Lund says 

 ('96, p. 153) that plankton animals occur "saa godt som altid i 

 Svaerme. " On the other hand Apstein says: ('96, p. 64) "Es 

 ist bis jetzt nicht ein einziger wohl verbuergter Schwarm beo- 

 bachtet worden. " Thus in the same year opinions diametrically 

 opposed are expressed, each based upon investigation. Under 

 these circumstances the result of my work extending over two 

 and a half years, including some 400 catches, each of which con- 

 tained from 3 to 12 species, may contribute something to the 

 discussion. 



It is not easy to define what is meant by a "swarm. " No 

 student of the plankton expects to find the plants and ani- 

 mals distributed with absolute uniformity, and it is impossible 

 to state the degree of variation in distribution which will en- 

 title us to say that the species in question occurs in swarms. I 

 agree with Apstein ('96, p. 53) that two- to fourfold variations 

 are not to be counted as swarms. Apstein computes the actual dis- 

 tance of individuals of Diaptomus when the numbers are about 

 198,000 and 540,000 per square meter, and finds in the first case 

 the average distance would be 2.2 mm. and in the second 1.36 

 mm. He rightly states that such a difference in distance does 

 not justify the name of swarm. Most will agree, I think, that 

 a ten-fold difference in numbers will justify the statement that 

 such species occur in swarms. Certainly animals whose number 

 differ to that extent are very irregularly distributed, and if 

 they were found in large numbers in compact areas, and the 

 space between these areas was thinly populated, it would not, 

 be unfair to say that the species appears in swarms. 



In general, there is no evidence of swarms in my observations,. 



