282 TIKWS, &C. PHYSIOGNOMY OF PLANTS 



best able to resist the cold, Ferns predominate more over 

 other phanerogamia in Lapland than either in France or 

 Germany, notwithstanding the absolute inferiority of the 

 gross number of ferns indigenous to the northern zone, when 

 compared with other countries. These relations are, in 

 France and Germany, as -^ and y^, while in Lapland they 

 are as -Jj. These numerical relations (obtained by dividing 

 the sum total of all the phanerogamia of the different floras 

 by the species of each family) were published by me in 1817, 

 in my Prolegomena de distributione geographica Plantarum, 

 and corrected in accordance with the great works of Robert 

 Brown, in my Essay on the Distribution of Plants over the 

 earth's surface, which I subsequently wrote in French. These 

 relations, as we advance from the equator towards the poles, 

 necessarily vary from the ratios obtained by a comparison of 

 the absolute number of the different species belonging to each 

 family. We often see the value of the fractions increase by 

 the decrease of the denominator, whilst the absolute number 

 of the species is reduced. In the fractional method which I 

 have followed as the most applicable to questions relating to 

 the geography of plants, there are two variable quantities ; for 

 in passing from one isothermal line to another, we do not find 

 the sum total of the phanerogamia change in the same propor- 

 tion as the number of the species of one particular family. 



In proceeding from the consideration of these species to 

 that of the divisions established in the natural system accord- 

 ing to an ideal series of abstractions, we may direct our 

 attention to genera or races, to families, or even to still higher 

 classes of division. There are some genera, and even whole 

 families, which exclusively belong to certain zones ; not merely 

 because they can only thrive under a special combination of 

 climatic relations, but also because they first sprang up within 

 very circumscribed localities, and have been checked in their 

 migrations. The larger number of genera and families have, 

 however, their representatives in all regions of the earth, 

 and at all elevations. The earliest inquiries into the distri- 

 bution of vegetable forms had reference to genera alone, and 

 are to be found in the valuable work of Treviranus.* This 

 method is, however, less appropriate for yielding general 

 results, than that which compares the number of the species of 

 * Biologie, bd. ii. a. 47, 63, 83, 129. 



