332 



NATURE 



[Feb. 15, 1877 



sexes and undergone modifications suited to their separate 

 requirements, have again returned to their primitive state 

 of sexual proximity, and commenced a totally different 

 series of modifications destined to counteract the evil 

 effects of that proximity. A much more simple hypothesis 

 would be that Conifers separated from the parent stock 

 before the (development of floral envelopes, the higher 

 Dicotyledons before the separation of the sexes." 



The anemophilous fertilisation of the arborescent plants 

 of cool countries is perhaps rather a climatic adaptation 

 than a survival of a primitive condition, while the cases, of 

 which many have been recorded, in which diclinous plants 

 have produced hermaphrodite flowers — such as the papaw 

 and pitcher-plant in the Glasnevin Botanic Garden de- 

 scribed by Dr. Moore — would be easily explicable as the 

 results of atavism, i.e., of reversion to a former her- 

 maphrodite condition. On the other hand Mr. Darwin's 

 suggestion (p. 410) that " if very simple male and female 

 flowers on the same stock each consisting of a single 

 stamen or pistil, were brought close together and sur- 

 rounded by a common envelope, in nearly the same 

 manner as with the florets of the Composites, we should 

 have an hermaphrodite flower," offers very considerable 

 morphological difficulties. As a further argument that 

 the flower originates like the fructification of Selngiiiella, 

 by the sexual specialisation of adjacent lateral appendages, 

 one may point out that the early stages in the develop- 

 ment of macrospores and microspores are indistinguish- 

 able, while in flowering plants there is a reminiscence of 

 this in the case of ovules occasionally being polleniferous. 



Difficult as it is to resist discussing the suggestions 

 which everywhere present themselves in this most inte- 

 resting book, the limits of a review compel me to stop. I 

 will merely point out that here, as in so many cases, 

 investigations undertaken from a purely scientific point 

 of view are not without their practical utility. The pre- 

 cise conditions which Mr. Darwin has ascertained as 

 sufficient to fix in a fleeting variety any particular quality, 

 will be of the last importance in the hands of cultivators. 



Just two centuries before the date of this book Sir 

 Thomas Millington, at Oxford (1676), laid the foundation 

 of this branch of investigation by assigning to pollen on 

 theoretical grounds its hitherto unknown function. This 

 it only remained for Bobart, in the Oxford Physick Gar- 

 den, to experimentally verify (1681). Science is the pro- 

 perty of no nation, nevertheless one may feel some pride 

 that the first and the last of the capital discoveries that 

 have been made in respect to plant fertilisation belong to 

 Englishmen. W. T. Thiselton Dyer 



OUR BOOK SHELF 



Bulletin des Sciences Mathematiques et Astronomiqtces. 

 Tome dixieme. Mars-Juin, 1876. (Paris : Gauthier- 

 Villars.) 



We have no mathematical publication in this country 

 covering quite the same ground as this admirable Bulletin. 

 Indeed we hardly think such a journal could survive the 

 issue of half-a-dozen numbers here. The late Mr, T. T. 

 Wilkinson, in an interesting series of notices of " Mathe- 

 matical Periodicals," points out that such periodicals have 

 " formed a distinguishing feature in our scientific litera- 

 ture for upwards of a century and a half," and quotes a 

 remark of Prof. Playfair {Ediiib. Rev., vol. xi.) to the 

 effect that "a certain degree of mathematical science, 

 and, indeed, no inconsiderable degree, is, perhaps, more 



widely diffused in England than in any other country of 

 the world," These observations have reference principally 

 to such journals as the Lady's and Gentleman^ s Diary. 



A very limited circulation, we fear, rewards the editors 

 of the Quarterly Journal of Mathematics and the Mes- 

 senger of Mathematics. Nor do we think the state of 

 things would be greatly altered if such a publication as 

 the one before us were started here. The division is 

 mostly a triple one — a review, or reviews, of new mathe- 

 matical works, followed by an analysis of the contents of 

 current mathematical publications, occasionally supple- 

 mented by an original paper. 



In the March number we have a long account of Dr. 

 Lindemann's edition of Clebsch's "Vorlesungen iiber 

 Geometrie" (ersten Bandes erster Theil), a review of 

 Rear-Admiral Sands's " Astronomical and Meteorologi- 

 cal Observations" (1871, 1872), an analysis of Dr. Giin- 

 ther's " Lehrbuch der Determinanten — Theorie fiir Stu- 

 dirende." We have also in this and the other numbers 

 descriptions of the contents of Bellavitis' Rivista di 

 Giornali, Catalan and Mansion's Nouvelle Correspond- 

 ance Mathematique, Mathematische Annate n, Giornale 

 di Matematiche, Monatsberichte, and like periodicals. 

 Just noticing the interesting discovery that the Gaus- 

 sian logarithms (logarithmes d'addition et de sous- 

 traction) were first treated of by Leonelli (Avril No,, 

 p. 164), his work having been translated into German in 

 1806, and Gauss having published his table in Zach's 

 Monatliche Correspondenz in 18 12, we pass on to two 

 notices of mathematical histories. M, E, Hoefer's " His- 

 toire des Mathdmatiques, depuis leurs Origines jusq'au 

 Commencement du XIX° Si^cle"(Mars No.), comes in 

 for strong condemnation. At the end of the critique we 

 read " nous terminerons cette analyse en cxprimant le 

 d^sir de voir bientot paraitre dans notre langue un 

 ouvrage sur I'histoire des mathematiques, ecrit par un 

 mathdmaticien avec tout le soin que rdciame une tache 

 aussi difficile, et s'adressant, non a tout le ?nonde, mais k 

 ceux qui ont interdt k connaitre cette histoire et que 

 leurs dtudes mettent a meme de la comprendre." The 

 importance of Hankel's " Zur Geschichte der Mathematik 

 im Alterthum und Mittelalter" in the eyes of the editor 

 may be gathered from the fact that the notice of it takes 

 up thirty-four pages out of the forty-eight. Judging by 

 the extracts and comments the work is one oi much 

 research, originality, and interest. "Tel est le rdsumd 

 bien incomplet du remarquable volume dont nous avons 

 cherchd k rendre compte. Nous espdrons que ce que 

 nous venons de dire suffira pour engager tous ceux qui 

 s'intdressent k la science k lire le livre de Hankel, et pour 

 en faire ddsirer une traduction dans notre langue." Is it 

 too much to hope that now we have living amongst us a 

 mathematician whose " great historical treatises are so 

 suggestive of research and so full of its spirit " this country 

 will produce a work to rival M. Hankel's ? If it is too 

 much to expect then we hope some one will do for us 

 what the writer in the Bulletin, desires for liis own 

 country. 



LETTERS TO THE EDITOR 



[The Editor does not hold himself responsible for opinions expressed 

 by his correspondents. Neither can he undertake to return, 

 or to correspond with the writers of, rejected manuscripts. 

 No notice is taken of anonymous co?>imunications.'\ 



The Obsidian Cutlers of Melos 



During a tour in Greece in the past summer I obtained a 

 small number of stone implements chiefly from the Island of 

 Kythera (cerigo) and the Isthmus of Corinth, consisting of 

 a few corn-crushers or pounders, and some celts. The latter are 

 particularly clumsy and very thick in seclion, and are usually a 

 beach or torrent pebble of suitable form ground to a cutting 

 edge, and sometimes roughened by pecking at the other extre- 

 mity, as if to afford a firmer grasp for the hand. Their shape 



