271 



ally affect the average of all of them. Apstein's method of 

 stating the ± error in terms of departure from the mean is, it 

 seems to me, to be preferred to the "percentages of difference" 

 which Reighard uses. 



In all instances but one Reighard averages but two collec- 

 tions, made at some one of fourteen points of collection in Lake 

 St. Clair. His percentages of difference, therefore, refer only 

 to these individual points of collection and not to the lake as a 

 whole. His collections were all made within an interval of ten 

 days, and it is probable that the results can be used to deter- 

 mine the departure from the mean in the lake as a whole. 

 This he has not done, though he concludes from these percent- 

 ages of differences of the pairs of collections that "the plankton is 

 dist rib tiled over Lake St. Clair with great uniformity." In the 

 case of Apstein's data the sets of collections are scattered over 

 several seasons and represent a number of lakes, and range in 

 number from two to five in each test. 



It is obvious that conclusions as to the uniformity of distri- 

 bution of the plankton in the lake as a whole should be based 

 upon a comparison of all catches with their average, and are 

 best expressed in terms of departure from their mean, employ- 

 ing the mean as a base and expressing the deviation in percent- 

 ages whose average will constitute the mathematical expres- 

 sion of the variation in distribution or the ± error of the method. 

 For reasons above stated, this method cannot be applied to Ap- 

 stein's data as a whole, though it is the one he uses for indi- 

 vidual lakes or tests. 



Applying this method to the data of Reighard's ('94, p. 33 ) 

 table, as in the accompanying tabulation, I find that the aver- 

 age departure from the mean is ±31.8 per cent., with a range of 

 +111.5 to- 57. 5, — a total of 169 per cent, — on the basis of the 

 amount of plankton per square meter of surface ; and ±28.8 with 

 a range of +91 .3 to —55.4, — a total of 146.7 per cent., — on a basis of 

 plankton per cubic meter of water — a deviation much greater 

 than that expressed by Reighard's method. This deviation 

 is much greater than that found byApstein ('96), and it re- 



