April i, 1922] 



NATURE 



413 



strongly to the tourmaline plates (except for some 

 special purposes dealing with naval artillery) on 

 account of the high colouring they give, either green 

 or pink, wliich, unfortunately, results in an inaccurate 

 rendering of the natural tints of objects and makes 

 ineffective one of the most striking advantages of 

 polarised light, the wonderful and delightful dis- 

 closure of true colours in far-distant objects. 



Although the choice and careful making of the 

 Benard-Jobin spar prisms cemented by a special 

 poppy-oil prepared by M. Duffieux (then my assistant) 

 to equip the Jules Huet prism-binoculars of the 

 French Navy gave unqualified satisfaction, I must 

 confess — and I did so in the introduction of my paper 

 — that I feel ver>' much inclined to consider a very 

 thin plate of herapaihite (sulphatoperiodide of quinine) 

 of a few square millimetres, having its crystallographic 

 directions quite uniform in the whole area covering the 

 ocular-ring, as the best of all polarising equipments, 

 I cannot say it is the most practical one, because 

 beautiful transparent and uniform herapathite plates 

 are not easily obtained. However, I sincerely hope 

 that my conclusion will please W. B. Herapath's 

 fellow-countrymen, particularly as quinine salts are 

 more easily obtained than Iceland spar. 



Nevertheless, I mentioned at the end of p. 230 of 

 my paper the old use of tourmaline spectacles to dis- 

 cover the fishes in deep water, and so on. Nihil sub 

 sole novum. The optical constructor to whose talents 

 I referred in my paper, without mentioning his name, 

 as having, when he was a young man in the 'eighties, 

 played a hoax on his fellow-anglers along the River 

 Mame with tourmaline spectacles forty years ago, is 

 now living in Grenoble. , His name is M. Ivan 

 Werlein, formerly well known and appreciated for liis 

 skilfulness by French physicists and crystallographers 

 when he was working in Paris. ^enri Benard. 



University of Bordeaux, February 8. 



Statistical Studies of Evolution. 



SiNXE Dr. Willis and Mr. Udny Yule in their reply 

 to my letter in Nature (March 2) have asked me to 

 explain the case of the New Zealand flora, I feel that 

 I should attempt to do so. 



The time taken for almost all animals and probably 

 many plants to spread to the boundaries of a con- 

 tinuous area of habitable environment is short com- 

 pared with geological time : witness the progress of 

 Elodea in this country since its introduction only 

 some sixty years ago. Surely, therefore, the majority 

 of species at any particular time have already reached 

 the boundaries of that area of habitable environment 

 to which they are isolated [e.g. the Marsupials of the 

 isolated Australian region). 



Now the Indo-Malayan flora of New Zealand has 

 arrived recently, geologically speaking, and has not 

 yet reached a state of equilibrium ; it is still spread- 

 ing, unlike the majority of species. As Dr. Willis 

 and Mr. Udny Yule showed clearly in their original 

 article, the distribution of a fauna or flora that 

 is still spreading will conform to the " Size and Area " 

 curve. I believe that not only a spreading fauna 

 or flora but also one which has reached the boundaries 

 of its habitable environment will conform to the ' ' Size 

 and Area " curve. 



The oldest endemic families of New Zealand 

 must have reached this state of equilibrium and, 

 on my theory, should conform to the " Size and Area " 

 curve. Perhaps Dr. Willis could tell me if they do 

 so in this or in a parallel case. 



C. A. F. Pantin. 



Christ's College, Cambridge, March 13. 



NO. 2735, VOL. 109] 



Mr. Pantin has not replied to our query as to why 

 neither the northern nor the southern group of plants 

 in New Zealand shows any increase of local species 

 when it reaches the region where the other group 

 shows its maximum of such forms. Why is one 

 group represented by its most widely ranging endemics 

 at the place where the other shows chiefly its endemics 

 of least range ? 



If the Indo-Malayan invasion is so young in New 

 Zealand, why do its members, though mostly trees, 

 show a rather greater average range than those of the 

 herbaceous southern invasion of plants of northern- 

 hemisphere type ? Though it is a long time since 

 Britain was cut off from the Continent, why have 

 227 of its 1548 species not yet reached a distribution 

 of more than 5 vice-counties out of 112, and why have 

 only another 229 reached one exceeding 100 ? 



All observation goes to show that dispersal of 

 introductions is rarely rapid, unless, as in Ceylon 

 or New Zealand, St. Helena or North America, man 

 has completely altered the conditions, and destroyed 

 or interfered with the societies that already existed. 

 A few cases like Elodea, chiefly water plants, are 

 known, and it is probable that the plant entered a 

 society that was very incomplete. No other intro- 

 duction has spread rapidly in England for centuries, 

 though when the Romans came here, and cut down 

 the forest, thus altering the conditions, many intro- 

 ductions were rapidly dispersed about the country. 



To suppose that species have mostly reached their 

 possible limit of dispersal is to return to a position 

 like that taken up by the advocates of special creation, 

 invoking incomprehensibility. Why should Coleus 

 barbatus be found through tropical Asia and Africa, 

 including the summit of Ritigala mountain in Ceylon, 

 while C. elongatus, differing only in the form of the 

 calyx and inflorescence, and a few minor points, is 

 confined to that summit ? Why should a species of 

 the New Zealand flora that reaches the outlying 

 islands range much further in New Zealand than a 

 species that does not ? Why should one that reaches 

 the Chathams range much further than one that 

 reaches the Aucklands or the Kermadecs ? Nothing 

 but Age and Area can even suggest an explanation 

 of such facts. 



No theory based upon natural selection will enable 

 one to make predictions about distribution, whereas 

 Age and Area has already been used successfully in 

 this way nearly a hundred times, and has increased 

 our knowledge of the subject. If we suppose that 

 dispersal is already completed there is little left to 

 investigate, and to explain the distribution of species 

 about the world (as opposed to purely local dispersal) 

 becomes a task that has been abandoned as hopeless 

 by leading authorities upon distribution. The fact 

 that Age and Area can be used for successful pre- 

 diction shows that it is probably correct, and it offers 

 an explanation incomparably simpler than does the 

 natural selection theory, and explains with ease facts 

 utterly incomprehensible to the latter, such as that 

 the Auckland Is. contain 45 per cent, of Monocotyle- 

 dons in their flora, the Chathams 31 per cent., and 

 the Kermadecs only 21 per cent. How can natural 

 selection explain the remarkable maps in Ann. Bot. 

 32, 1918, pp. 343 seq., and the curves on pp. 357, 360 ? 

 Mr. Pantin's theory seems to us to lend itself neither to 

 explanation nor to prediction. We feel compelled 

 again to emphasise that his supposition as to random 

 combinations of environmental limitations does not 

 appear to us to bear any relation to facts. Nor, if 

 it did accord with facts, can we agree that his con- 

 clusions would follow. 



J. C. Willis. 

 G. Udny Yule. 

 P 2 



