270 



from the assumption that a collection at a single place is rep- 

 resentative of a larger area — an assumption necessary if any 

 wide significance is to attach to the analysis of plankton data. 

 It has been a matter of observation that the quantities of plank- 

 ton taken at different places in a body of water, or even within 

 very narrow limits, are not equal in volume under similar 

 methods of collection. Thus, Apstein ('96) in eighty catches in 

 German lakes finds the average deviation from the means 

 to be 5.52 per cent, when the plankton is computed per square 

 meter of surface. Of the eighty catches 68 or 85 per cent, ex- 

 hibit a departure of less than 10 per cent, from the mean, and 

 only four have a departure in excess of 15 per cent. These de- 

 partures are derived from averages of comparable collections 

 on various dates and in several different lakes in groups of only 

 two to five, evidently from mid-lake waters, and hardly afford suf- 

 ficient data for an analysis of the conditions of distribution in 

 any given lake or in atypical lake, since on account of their small 

 number they do not throw any light on the effect of shore, tribu- 

 tary waters, vegetation, currents, or other factors of the environ- 

 ment. They indicate, however, the probable error of ±5.52 per 

 cent, in mid-lake collections, and seem hardly sufficient to sub- 

 stantiate fully the more general conclusion that "das Plankton 

 sehr gleichmassig in einern Seebecken vertheilt ist." Reighard 

 ('94) finds in the case of twenty-nine hauls that his results 

 "agree very well with that of Apstein." Of his twenty-nine 

 hauls, 26, or 90 per cent., have a "percentage of difference from 

 the average" which is less than 20. These percentages yield, 

 I find, an average of 9.7 per cent, to Apstein's 5.52 per cent. 

 Reighard does not, however, compute his "percentage of dif- 

 ference from the average" in the same manner as Apstein deter- 

 mines the "Abweichung von Mittel," the former using the vol- 

 ume of each catch as the basis for the determination of the per- 

 centage of difference from the average, while the latter 

 employs the average of the two or more catches for this base. 

 Obviously this slightly increases one half of Reighard's percent- 

 ages and decreases the other half, though it does not materi- 



