td PROCERDINGS OF TttE 



brought tlie scientific collections to Esquimaiilt in Oclober. 

 Stefansson organised a new searcli-party after this, by sledge 

 across Uanks Land, and later explored Parry Islands, discov(M'iiig 

 coal in Melville Island. The entire party wintero-d on J3arter 

 Island, 11)10-17; t'urtiier investigations followed, and the 

 expedition reached Nome in August, 1917. 



Tlie results were surveys of coasts hitherto unmapped, much 

 geologic material gathered, many fossils, implements used by 

 Esquimaux, with specimens of zoology and botany in quantity; 

 these records are now in com-se of publication. A series of lantern- 

 slides closed the communication. 



The next communication was " Somt? Statistics of Evolution 

 and Geographical Distribution in Plants and Animals and their 

 Significance," by J. C. Willis, M.A., Sc.D., F.R.S., and Gr. Fdny 

 Yule, C.B.E., M.A., F.R.S. 



At the Meeting of the Society on 18th November, 1920, there 

 were shown four closely parallel curves illustrating the per- 

 centages of genera belonging to families in order of size, taking 

 tlie same groups of (10) families for the world, and for various 

 sections of it, including finally the Avhole of the islands, to which 

 there were 15S2 genera confined. These curves are shown in the 

 'Annals of Botany,' xxxv. (1921) p. 510, and illustrate clearly 

 what may be termed the "hollow curve" of distribution, or 

 curve concave on upper side. The appearance of the curve 

 obtained bv plotting series of numbers like this is something as if 

 one bad taken a strong steel spring and tried to double it into the 

 angle of a brick wall. 



This " hollow curve pattern *' of distribution was first noticed 

 in 1912, in the flora of Ceylon, when working it up for the first 

 paper on "Age and Area." It reappeared in 1916 in the curve 

 of distribution of the endemics of New Zealand, which showed a 

 verv large proportion of the species in the class which included 

 only those of extremely limited area, with a ra|)id tapering off to 

 the large areas. It showed still more clearly in the endemics of 

 the Hawaiian Islands, where 47 per cent, of the species occurred 

 on one island only, and 20 per cent, on two (there are 7 chief 

 islands). It came out with complete regularity in every case of 

 distribution that was investigated, whether of endemic species or 

 of non-endemic. 



At the same time, investigation of areas showed clearK' that, 

 besides "Age and Area," the twin principle which may be called 

 " Size and Space" was also \alid. 



The hollow curve seems to be an almost universal feature, not 

 only of the geographical distribution, but of the evolution, of 

 plants and animals. The form of the distribution for sizes of 

 genera might be such that the logarithm of the lunnber of genera 

 plotted to t)ie logarithm of the number of species would give a 

 straight line. This law is found to hold fairly closely up to genera 

 of 30-40 species. 



