614 METASPERMAE OF THE MINNESOTA VALLEY. 
In the third place, it must be noted that the possible over- 
sights and errors in collection of plants and their subse- 
quent determination, or errors in compilation of herbarium 
data, or overlooked errors in printing, or the failure to set 
down each group of data properly in preparing the manuscript, 
might all influence the statistical results which are about to be 
presented. Together with all these errors comes the chance 
of mistake in printing the statistics themselves, by omissions 
or by alterations, in going through the press. It is apparent, 
therefore, that the air of mathematical exactness presented by 
the figures of a tabulation is, to some extent, deceptive. 
On the other hand, these chances of error thus stated in 
detail must not be overestimated. In spite of them all it is 
quite probable that every statistical entry will be sufficiently 
exact to serve as the basis of a generalisation concerning the 
distribution of Metaspermae in the valley of the Minnesota. 
Errors tend mutually to correct each other, and under the law 
of averages the results of a series of calculations vary little 
one way or the other. If it be discovered, for example, that 
of all the species indigenous to the region studied, 55.6 per 
cent. are of distinctively northern range, in North America, 
while 76.1 per cent. are distinctively southern in their range 
there is absolutely no question that the Minnesota valley Meta 
spermae are distinctively southern rather than northern in their 
distributional characters. 
Thus it happens that the preparation of statistical tables is 
of real value in so far as they serve to group together facts 
that may be used for generalisation. The percentages them- 
selves may be somewhat inexact, but the ratios between differ- 
ent percentages and the general comparative result will hardly 
be affected by the minor errors. 
Point of view of statistical compilations. The compiler 
has brought together such statistics regarding families, gen- 
era and species as have seemed to him fitted best to indicate 
the distributional and physiognomic characters of the meta- 
spermic population of the Minnesota valley. Unfortunately 
there are not lists of plants of other drainage-basins in North 
America with which comparisons would be instructive. Such 
comparative statistics are therefore omitted and an effort has 
been made rather to determine characters by an analytic pro- 
cess than synthetically to bring together results of comparison 
between the Minnesota valley and other districts. The inade- 
quacy, from a scientific point of view, of comparing the Min- 
