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- 
sSpermae, 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 Valley Metaspermic Species. 
EASTERN. WESTERN. 
Typh'aceae. 
Typha latifolia................ Typha latifolia... ............ 
Sparga|niaceae. 
Sparganium simplex..........| Sparganium simplex.......... 
Sparganium androcladum..... Sparganium androcladum..... 
Sparganium eurycarpuM......)... eee eee eee ew ees 
Potamog etonaceae. 
Potamogeton natans........... Potamogeton natans.......... 
Potamogeton fluitans.......... Potamogeton fluitans......... 
Potamogeton amplifolius....... Potamogeton amplifolius..... 
Potamogeton perfoliatus. 0... bec ce cece eee eens 
Potamogeton heterophyllos....| Potamogeton heterophyllos. .. 
Potamogeton gramineus var. 
FLA shoal clea ad ois RGus Leva AR a eS aWemw weg eats a bee eee 
Potamogeton rutilus........... Potamogeton rutilus......... 
Potamogeton illinoenSis.......).. 6. cece ee ce cee ee etc e eens 
Potamogeton pectinatus....... | Potamogeton pectinatus...... 
Potamogeton pusillus.......... Potamogeton pusillus........ 
Potamogeton lucens........... | Potamogeton lucens.......... 
