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 jbhe 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- 



