STATISTICS OF METASPERMAE. 



655 



the final differences, numerical and percentage, are produced 

 rather by the unequal entry of species regarding the pre- 

 ponderant range, of which there is little question, while those 

 which are entered as both north and south, as both east and 

 west, or as all four, by adding to two columns equally do not 

 alter the general averages In this way I have thought to give 

 a more accurate account of the range of Minnesota valley Meta- 

 spermae, outside of the valley, than by any effort to strike a 

 ratio of preponderance for every species and variety. The 

 areas have been drawn on a map, in most cases, before their de- 

 scription was attempted. The limiting lines for the areas were 

 derived from the range-descriptions compiled for each species 

 in the body of the list. It cannot but be apparent how numer- 

 ous and insidious are the opportunities for error in this list. 

 To test the probable range of error the writer has, at considera- 

 ble intervals, compiled the table three different times. The 

 three tables were different, but the average range of variation 

 from the mean, for all statistics was but 1.88 per cent., so it is 

 believed that the table, as finally presented, is of approximate 

 accuracy. 



of Minnesota Yalley Metaspermic Species. 



Potamogeton illinoensis ! 



Potamogeton pectinatus I Potamogeton pectinatus 



Potamogeton pusillus ' Potamogeton pusillus . . , 



Potamogeton lucens ' Potamogeton lucens 



