864 



SCIENCE. 



[N. S. Vol. XII. No. 310. 



ify the distribution of the mammals in such 

 a way that without paleontological re- 

 searches it would be impossible to recog- 

 nize the origin of the different faunal ele- 

 ments, the fresh- water faunas have resisted 

 almost unchanged all modifications in the 

 configuration of the continent. 



The fresh-water fauna is not only older 

 but also much more conservative than the 

 distribution of the mammals. One of the 

 most striking examples of this is given by 

 the history of Africa. While the character- 

 istic mammals are Neogene immigrants and 

 Lydekker proceeds quite correctly in mak- 

 ing Africa an annex only of the Holarctic 

 region, thus establishing his Arctogsea, with 

 relatiori to the fresh-water fauna, Africa is 

 a part of South America, somewhat modi- 

 fied by the Neogene invasion of Cyprinid 

 fishes. If as regards mammals Africa be- 

 longs to Arctogsea, with relation to the 

 fresh-water fauna it belongs to the Arch- 

 helenic region. 



This example demonstrates the absurdity 

 of the present system of construction of zoogeo- 

 graphical regions and maps. We caii construct 

 maps of the different classes and orders but not 

 at all of the animal kingdom, because the geolog- 

 ical history of the different groups is quite differ- 

 ent. When Osborn says that it is one prob- 

 lem ' to connect living distribution with 

 distribution of past time,' he says only what 

 had been the leading idea of Wallace and 

 of Eugler in their eminent works on zoo- 

 and phytogeography, but when he continues 

 ' and to propose a system which will be in 

 harmony with both sets of facts,' he pro- 

 poses a problem just as contradictory as 

 would be the construction of descriptions 

 and figures referring at the same time to 

 egg, larva, nympha and imago of an insect. 

 The works on ' zoogeography ' are almost 

 exclusive]}' discussions of the distribution 

 of mammals and birds, and the few words 

 spent on other classes are only ornamental 

 supplements. A wrong method cannot give 



valid results. For the exploration of the 

 zoogeographical relations and regions of the 

 beginning of the Tertiary and of the pre- 

 ceding Mesozoic epoch it is necessary to 

 study and to discuss the more ancient classes 

 and, as I have insisted for ten years, prin- 

 cipally the fresh-water fauna. 



H. VON Iheeing. 

 Sio Paulo, July 20, 1900. 



A HISTORY OF THE DEVELOPMENT OF THE 

 QUANTITATIVE STUDY OF VARIATION.* 



The quantitative study of variation has 

 for its object the investigation of evolution 

 by exact, quantitative methods. The study 

 demands a mathematical method as well as a 

 biological subject matter ; consequently the 

 development of the science has proceeded 

 along two main lines — the one biological 

 and the other mathematical. Accordingly, 

 the history of the development of the quan- 

 titative method involves a consideration of 

 both the study of variation and the elabo- 

 ration of the necessary method. 



The fact of variation has been recognized 

 since man began to think and to appreciate 

 that in stature, color and mental capacity 

 his fellow-men are diverse. The way for 

 quantitative studies in biology was paved 

 by the mathematical studies on the varia- 

 tion of measurements which engineers and 

 astronomers found it necessary to make for 

 their own purposes. These mathematical 

 studies led to the discovery and elaboration 

 of the law of error by Gauss and others — 

 and this law is the corner-stone of the 

 quantitative biological studies. 



The application of the law of error to 

 organic variation was, apparently, first 

 made by an anthropological statistician, of 

 the early part of the century, named Que- 

 telet. In his book, entitled ' Lettres a Son 

 Altesse Koyale le Due de Saxe-Coburg et 



* Being part of the report of the Committee of the 

 American Aasooiation for the Advancement of Sci- 

 ence on the Quantitative Study of Variation. 



