CH. XIV] GENERAL DISCUSSION 173 



conditions, with nothing special to which to be specifically 

 adapted. The life in moving water, and the loss of proper polarity 

 of the plant (p. 20), are common to all. Yet there are about forty 

 genera with many species. The most reasonable explanation is 

 that evolution must go on, with or without adaptational reason, 

 and is not necessarily a matter of local adaptation. All are com- 

 pelled to "adapt" themselves more or less to the action of the 

 permanent force that acts upon them, which cannot be escaped in 

 any way. 



The author's work with endemic plants, which has occupied 

 many years, also showed that the old (and still more or less 

 current) view, that they are relics of previous vegetation, had no 

 sound basis. Under the Darwinian theory, there had to be found 

 somewhere some at least of the species that had been defeated in 

 the struggle for existence and were dying out. The harmless 

 endemics just came in conveniently to fill this position, but while 

 there are undoubtedly many relics in regions that were cooled in 

 the glacial periods, one cannot suppose this of most of the local 

 species of warmer climates. 



As one result of this work, the writer discovered the "hollow 

 curve" of distribution (chap, iv) that shows in plants and 

 animals, and in many other cases, such as surnames, and even in 

 inanimate objects (cf. p. 35). It shows well in areal distribution, 

 many species of any genus occurring on small areas, few on large. 

 It shows still better in the distribution of the genera in a family 

 by the numbers of species that they contain. On the average, 

 from which there is but small variation, with reasonable numbers, 

 about 38 per cent of genera have only one species, 12 per cent 

 two, and 7 per cent three. The curve turns the corner between 

 three and five, and tapers away in a long tail, and the larger the 

 family the more accurately does it follow the curve. When plotted, 

 as 38 + 7 make more than twice twelve, the curve has the dip in 

 the middle that gives it its name (fig. on p. 36). When plotted in 

 logarithms, the curves form close approximations to straight 

 lines, showing that all have the same mathematical form, and 

 have appeared as the result of the same law, working upon all. 

 The mathematical treatment of the subject will be found in Yule's 

 paper (75), the introduction to which should be read by all in- 

 terested in evolution. The general law, as he showed, that imme- 

 diately governed it was that at the end of certain intervals, 

 probably very variable in length, a genus became two, and both, 

 as a rule, survived. The parent genus of the two was not neces- 



