CH. IV] THE HOLLOW CURVE 35 



from Mexico to Rio de Janeiro or south of it, the smaller genera 

 over less districts. Siparuna has one species that covers the whole 

 South American area of the genus, some of intermediate areas, 

 and a great many of very small areas. Mollinedia, on the other 

 hand, though its total area is much the same, has only one species 

 that even ranges as far as from Rio de Janeiro to Monte Video; 

 most of its species are quite local, and over 95 per cent are so local 

 as to count as relics under the natural selection conceptions. Is it 

 a failure because of the small areas occupied by the individual 

 species, or a success because of their number, and the area 

 occupied by the genus as a whole? What is selection doing in 

 these two cases? And still more, what is it doing or going to do 

 with the rest of the family, where the genera contain 30, 25, 15, 

 15, 11, 7, 6, 5, 4, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 

 1, 1, 1 species respectively? One cannot draw a line in a curve like 

 this, to separate the sheep from the goats. Relics would not be 

 made in steadily diminishing numbers, nor would local adapta- 

 tion be neatly graduated like this. All families of reasonable size 

 show the same curve, as seen in fig. 2, which gives the fifteen 

 largest families of flowering plants. Close together though they 

 are, the curves never touch. When turned into logarithmic curves, 

 as in the next figures (3, 4), they all give approximations to 

 straight lines, i.e. they have the same mathematical form, and 

 must be the expression of some definite law which is behind 

 evolution and distribution, and does not agree with current 

 views about these subjects. Many distributional subjects show 

 the same form of curve, as may be seen in fig. 5, which shows 

 families of plants and animals, lists of endemics, floras, fossils, 

 and areas occupied, all mixed up. The curve shows in the names 

 in the telephone book, where the very common names are few, 

 the very uncommon many. It shows in the list of numbers of 

 hotels in towns in the advertisements in Bradshaw, where (in the 

 one examined) only London and Bournemouth had large num- 

 bers, while a great many had only one each, and there were a 

 few in the intermediate numbers. 



This similarity interested me very much, and I have lately 

 completed a study of the distribution in Canton Vaud (Switzer- 

 land), where I live, of the surnames of farmers, a class who move 

 about less than others. Vaud is about the size of Gloucestershire, 

 but divided into valleys often separated by very high mountains, 

 which make intercourse between the vallevs difficult. After a 

 day on the farm, a young man is not going to cross a high moun- 



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