ANNOTATIONS AND ADDITIONS. 297 



merely tells how many of the species of one and the same family 

 are indigenous in each country or each quarter of the world. 

 The results of this method are on the whole more exact, because 

 they are obtained by the careful study of single families without the 

 necessity of being acquainted with the whole number of the phane- 

 rogamse belonging to each country. The most varied forms of 

 Ferns, for example, are found between the tropics ; it is there, in 

 the tempered heat of moist and shaded places in mountainous 

 islands, that each genus presents the largest number of species : this 

 variety of species in each genus diminishes in passing from the tro- 

 pical to the temperate zone, and decreases still farther in approaching 

 nearer to the pole. Nevertheless, as in the cold zone in Lapland, 

 for example those plants succeed best which can best resist the cold, 

 so the species of Ferns, although the absolute number is less than in 

 France or Germany, are yet relatively more numerous than in those 

 countries; i. e. their number bears a greater proportion to the sum 

 total of all the phsenerogamous plants of the country. These propor- 

 tions or ratios, given as above mentioned by quotients, are in France 

 and Germany ^ and ^\, and in Lapland J T . I published numeri- 

 cal ratios of this kind (i. e. the entire quantity of phaenogamous 

 plants in each of the different Floras divided by the number of 

 species in each family) in my Prolegomenis de distributione geo- 

 graphica Plantarum, in 1817; and in the Memoir on the distribution 

 of plants over the Earth's surface, subsequently -published in the 

 French language, I corrected my previously published numbers by 

 Robert Brown's great works. In advancing from the Equator to the 

 Poles, the ratios taken in this manner vary considerably from the 

 numbers which would be obtained from a comparison of the absolute 

 number of species belonging to each family. We often find the 

 value of the fraction increase by the decrease of the denominator, 

 while yet the absolute number of species has diminished. ,In the 

 method by fractions, which I have followed as more instructive in 

 reference to the geography of plants, there are two variables ; for in 

 proceeding from one isothermal line, or one zone of equal tempera- 

 ture, to another, we do not see the sum total of all the phanero- 

 gamae change in the same proportion as does the number of species 

 belonging to a particular family. 



