always been that Venus in March of that year was invisible, while she ought to be a morning star in Pisces, which she was twelve months later. But it was pointed out six years ago that Dante very likely took the position of Venus from a perpetual Almanac compiled by a Jew. In the Hebrew original all the cycles begin in 1301, while in the Latin translations they begin in 1300, except those of Venus and the sun, which begin with 1301. It is therefore quite possible that Dante took the places of Venus for 1301, believing them to be for 1300, and Angelitti's tempting theory must therefore be abandoned, to the regret of the author of the present work, in which we cordially join.

Darwin have no reason to feel ashamed. The truth is that, though in art there must be nationality, science has become absolutely international : the observation made by a Dane to-day is checked by a Japanese to-morrow, and an American then carries it a step further.

J. L. E. D.

Biogeographie. Unter Redaktion von R. Hertwig und R. v. Wettstein. Pp. ix +620. (Leipzig and Berlin B. G. Teubner, 1914.) Price 12 marks.

“T°

O no nation, except the German," says General von Bernhardi, "has it been given to enjoy in its inner self that which is given to mankind as a whole. We often see in other nations a greater intensity of specialised ability, but never the same capacity for generalisation and absorption." That is the German way of expressing the German capacity for organisation and compilation, which, when it produces works such as that of which the present volume is a portion, performs a valuable service to the intellectual world. The whole work, "Die Kultur der Gegenwart," purports to be a systematic survey of modern culture on a historical basis, portraying the fundamental achievements of the diverse centres of civilisation in their relation to the whole as it exists now or promises to be developed hereafter. The division allotted to the organic natural sciences comprises four volumes, of which this is logically the last. Volume ii., the only other as yet issued, was reviewed by us in April, 1914 (vol. xciii., p. 107).

In view of the claim mentioned above, it is interesting to note that the contributors are not all German, for besides R. Hertwig, L. Plate, A. Brauer, A. Engler, and K. Heider, there are the Austrians, R. v. Wettstein and O. Abel, the Dutchman, W. J. Jongmans, and the Dane, J. E. V. Boas. It is, moreover, pleasing to observe that these authorities do not neglect the workers in other countries, but, by the lists of leading books which they furnish, prove that in this department, at all events, all nations take their share, and that the fellow-countrymen of

beyond or even away from him; but these last years show an unmistakable return to the views of the great British naturalist."

The articles on geographical distribution by Profs. Brauer and Engler, on palæontology by Profs. Abel and Jongmans, on the classification and phylogeny of plants by Prof. von Wettstein, and on the phylogenies of invertebrate and vertebrate animals by Profs. Heider and Boas, may be open to criticism in details, but afford on the whole admirable digests, made interesting by the fact that the distinguished authors have taken their own lines on disputed questions. It is, however, the chapter by Prof. L. Plate on the principles of taxonomy with special reference to the classification of animals that fills the most urgently felt want. The mere description of new species, as carried out by too many writers, is far from being good systematic work, or even scientific work at all. But the true systematist has perpetually to exercise his mind with the most complicated problems of his science, cannot venture to eschew metaphysics, and has even to rival the poet in his use of the imagination. All systematists who would understand their own task should read Dr. Plate's illuminating review of modern methods and ideas. F. A. B.

(1) THE

HERE is always an interest, and often no little instruction, to be derived from a study of the science and religion of ancient civilisations, especially when considered in their inter-relations. One of the newest of sciences, anthropology, appears to be rooted in the earliest strata of thought, as, for instance, among the natives of Central Australia. Greek speculation upon the origin and development of mankind was not limited to fairy-tales of the Golden Age type. From Herodotus onward their best minds had a very shrewd idea of the real process, such as we have come to see it. Lucretius repeated, with original observations of his own, the anthropological theories of Epicurus. But these are the culmination of Greek scientific thought in this direction. They were foreshadowed by Aeschylus and Herodotus, and developed later. It seems that the Greeks, who certainly had considerable opportunities, thanks to their trade, travel, and warfare, collected a considerable body of data relating to savage and barbarous peoples in the west, the east, and the south. There was, of course, another school, the Platonic; it was true then, as ever since, that a man is born either an Aristotelian or a Platonist.

Then, too, as now, the Platonist

built upon teleology. Mr. Sikes has done well to collect every statement in Greek literature that throws light on the scientific ideas of that "most quick-witted and curious of human races," concerning the origin and development of their own species. It should be read by all anthropologists, whether their Greek is "less 39 or more.

(2) But the Greek mind was more interested in the problems of cosmic and ultimate metaphysics, and the issues waged between Determinists and Creationists, or whatever the two fundamental types of mind be termed. These issues seem destined to be eternal. So Dr. Paul Carus, following up his interesting propaganda of many years, writes some notes upon representative quotations from exponents of both sides. "Mechanicalism" and teleology are first contrasted. The "contributions," as they may be called, to his volume include some very interesting expressions of opinion, especially Mark Twain's philosophy and La Mettrie's famous exposition of man NO. 2353, VOL. 94]

as

a

361

machine." It is curious that La Mettrie, when persecuted for his opinions, found refuge in Prussia and received a pension from Frederick the Great.

In another chapter Prof. W. B. Smith's eloconclusion that "it is a false antagonism between quent article from the Monist works up to the the causative and the teleological conceptions of the universe." Dr. Carus's text is that "nothing moves, nothing stirs nor happens that does not act in agreement with the laws of motion, and there is no harm in it that man's activity takes place in perfect agreement with mechanical laws. A man's a man for a' that!" As for the ancient using Ezekiel's metaphor, "There are not two and modern puzzle-dualism or monism-he says, things, the spirit and the wheels, but there is one reality." "Both spirit and machine are one, and the universal dominance of the laws of form determining the detailed uniformities of motion, commonly called mechanics, is by no means a depressing or melancholy thought. The laws of itself." form are the very means in which spirit reveals

(3) That versatile writer, Prof. de Lanessan, has written a critical history of the relations between these two modes of thought. He considers that evolutionary determinism (transformisme) and animistic supernaturalism (créationisme) are ultimately the only possible theories of the uni

verse.

the

interesting is the fact that practically all subsequent educational reformers have been the intellectual heirs of the French iconoclast, such as Pestalozzi, Fellenberg, Froebel, Herbart, and Montessori. While giving prominence to the evolution of education in America, Prof. Graves does not neglect this or other countries, and his account of the German experiments at Neuhof, Königsberg, and Keilhan is detailed. He has an interesting chapter on the introduction in recent years of scientific subjects into curricula, and another on the application of psychological results to the methods of education. The book includes an excellent selected bibliography, very useful in view of the enormous literature of the subject.

(5) The series of scientific and mathematical handbooks edited by Dr. Norrenberg is an encyclopædia for teachers. The fifth volume, on methods of instruction in natural history, by Prof. Schoenichen, of Posen, contains more than six hundred pages, crammed with detailed advice and facts. The author attempts, with success, to cover the whole ground of zoology, botany, and biology generally as an educational subject, and from the teacher's point of view. From psychological pedagogy to gardens and vivaria, he omits nothing that can come into the ken of the schoolmaster. Courses are laid down for the various classes in the Gymnasium, the Real-gymnasium, and the Real and Oberrealschule. The suggestions about methods of drawing, and those on excursions and collecting are excellent. A notable feature is the description of models, their manufacture and use.

Fas est et ab hoste doceri; the book is a triumph of method. A. E. CRAWLEY.

OUR BOOKSHELF,

The Rubber Industry in Brazil and the Orient. By C. E. Akers. Pp. xv+320. (London: Methuen and Co., Ltd., 1914.) 6s. net.

MR. AKERS contrasts in this book the unscientific, and unbusinesslike, rubber-collecting industry of Brazil with the rubber-planting enterprises of the British and Dutch East Indies, which are conducted on more or less scientific lines and with the commercial skill and acumen which distinguishes the two peoples concerned with these East Indian Colonies.

Compared with their competitors in the East, the rubber producers in Brazil have one great advantage their trees are mature and in their natural habitat. This advantage is believed to account for the general opinion that Brazilian Para rubber is better than the plantation article from the East Indies. Many competent judges maintain that this advantage that this advantage is illusory, and that properly-prepared East Indian plantation rubber, from well-established

trees of fair age, is just as good as "fine hard Para," and that the premium obtained by the latter in the markets is the result of conservative

prejudice on the part of manufacturers. However that may be, the advantage, supposing it is real. is bound to disappear, in view of the increasing age of the plantations in Ceylon and Malaya, and the untiring efforts of the planters there to improve and unify their methods of preparation.

In all other respects, such as cost and efficiency of labour, good administration and government, business skill and foresight, and last, but not least, the realisation of the necessity for scientific and technical research, the advantages lie with the East Indian producers, and Mr. Akers makes it clear that unless there is a drastic change in the conditions of working in Brazil, the rubber industry there is bound to disappear in the face of the competition of the East Indian plantations.

Mr. Akers probably records little that is new to rubber planters, but his book is none the less interesting on that account, and it can be cordially

recommended to all who are interested in the development of this great industry, in which British enterprise and technical skill have played so large a part.

The Beginner's Garden Book: a Text-book for the Upper Grammar Grades. By A. French. Pp. viii+ 402. (New York: The Macmillan Company: London: Macmillan and Co., Ltd., 1914.) Price 4s. 6d. net.

THERE is always much to learn from an American teacher of a rural subject. The science may be superficial, yet he manages to get his students to think about their work and to find reasons for the way in which the work is done. This book is a case in point. It takes the form of an address by a teacher of school gardening to boys engaged in the cultivation of school gardens. The American origin of the book little interferes with its use in this country. The English is almost free from Americanisms, and the cultivation of all our more commonly grown vegetables and flowers is described. The treatment of fruit culture and bastard trenching is inadequate, and grafting and budding are not even mentioned, but, on the other hand, several matters are dealt with that do not often find a place in gardening manuals. chapters on the saving of seed and on gardening under glass are excellent. A good deal of gardening can be learnt by merely looking at the numerous illustrations.

The

An Introduction to Geology. By C. I. Gardiner. Pp. xiv +186. (London: G. Bell and Sons, Ltd., 1914.) Price 2s. 6d.

MR. GARDINER is well known as a field-observer, and has added largely, both by himself and with Prof. S. H. Reynolds, to our knowledge of Silurian areas. He now attracts others to his favourite studies by a clearly written introduction to geology, which will be of especial interest to dwellers in the English midlands. General principles are supported by more detail than is usual in elementary works, and this method carries convic

tion as to the reality of the facts described. For instance, both a map and a photograph are given of Churchdown, the conspicuous outlier that rises above the Lias plain near Gloucester; while the description of the successive layers in the Victoria Cave furnishes an impressive picture of the history of British man. The statement of the loss of land along the Yorkshire coast demonstrates the effectiveness of forces now in action, and two successive views are given of the destruction of a chalk headland near Swanage.

The illustrations are practically all new, including a fine view into Lulworth Cove, taken from the hill at its west end. The printers have twice gone astray on the difficulties of Rhynchonella (pp. 60 and 79), and a bracket needs extension on p. xi to include the Cainozoic systems; but the mode of production shows how generously publishers are prepared to meet the demand for readable works on nature-study. G. A. J. C.

Catalogue of the Ungulate Mammals in the British Museum (Natural History). Vol. iii. Artiodactyla, Families Bovidæ, Subfamilies Epycerotinæ to Tragelaphina (Pala, Siaga, Gazelles, Oryx Group, Bushbucks, Kudus, Elands, etc.), Antilocaprida (Prongbuck), and Giraffidae (Giraffes and Okapi). By R. Lydekker, assisted by G. Blaine. Pp. xv+283. (London: British Museum (Natural History), 1914.) Price 7s. 6d. THE third volume of the British Museum catalogue of Ungulates completes the account of the antelopes (saiga, gazelles, oryx group, bushbucks, kudus, elands, etc.) and deals also with prongbucks and giraffes. Like its predecessors it is a fine piece of work with terse descriptions and scholarly synonymy. Its usefulness has been notably increased by the inclusion of fifty excellent figures, mostly of heads. As a work of reference it will be of great value and interest to those who have collected trophies of this sort. The prongbuck, the position of which has been the subject of discussion, is ranked by Mr. Lydekker as the only living representative of a separate family, Antilocaprida. Another interesting type, the Okapi, represents a genus along with the giraffe in the family Giraffidæ. Among the many other interesting forms may be mentioned, Ammodorcas, pyceros (the Pala), the Saiga, and the Chiru.

LETTERS TO THE EDITOR. [The Editor does not hold himself responsible for Neither opinions expressed by his correspondents. can he undertake to return, or to correspond with the writers of, rejected manuscripts intended for this or any other part of NATURE. No notice is taken of anonymous communications.]

The Age of a Herring.

To my doubts as to the truth of Dr. Hjort's theories of the herring's age, Dr. Hjort and Mr. Einar Lea have now replied (NATURE, November 5) by recapitulating their main arguments. I can do little more than reiterate my own unaltered incredulity. My position is simply this, that a theory has been put forward which seems to me, a priori,

extremely improbable, and that the statistical data on which it is based are, to my mind, not strong enough to support it. The large assertion that the Norwegian spring herring have consisted, in preponderating or overwhelming proportion, year by year from 1908 to 1913, of fish spawned in 1904, is based (so far as I can discover) on only nineteen samples, or little more than two a year, averaging somewhat above 300 herring each. Dr. Hjort and Mr. Lea have no difficulty in showing that their 1913 herring, grouped according to scale-rings or alleged years of growth, form a curve which is a bad fit to a probability curve; but they do not remind us that this so-called sample is no sample at all, but is a conglomeration of three separate samples from far-distant localities. Dr. Hjort's full data have not been published, so far as I know, for the years since 1909; let us try to discover how, for the year 1908, he arrives at the figure 34-8, which he gives (cf. NATURE, August 27, p. 672) as the percentage proportion, in the entire stock of Norwegian spring herring, of fish spawned (according to the evidence of their scalerings) in 1904. I find that this determination was based on two samples only,' from different localities, one consisting of 881 fish, the other of 549. In the former sample the percentage of 1904 fish is given as 159, in the latter as 65.2. The former determination, by Mr. K. Dahl, seems a little shaky for an independent determination of a part of the same sample, by Mr. Einar Lea, gave the alternative value of 10-2. But be that as it may, I find that Dr. Hjort's result is obtained by the simple method of adding together the two samples, one of 881 fish showing 15.9 per cent., the other of 549 fish showing 65-2 per cent., and so the resulting mean value of 34-8 per cent., decimal and all, is straightway arrived at. It does not need the eye of a mathematician to see that, in a problem of biological statistics, such a method of calculation is inadequate; and that it neither proves nor even renders probable the conclusion drawn from it, namely, that four-ringed herring (whatever those four rings may mean) constituted 34-8 per cent. of all the spring herring in Norway, in the year in question. D'ARCY W. THOMPSON.

The Cross X as a Symbol for Multiplication. HISTORIANS of mathematics attribute the first use of the cross as a symbol for multiplication to William Oughtred ("Clavis Mathematicae," London, 1631). See W. W. R. Ball's "Short Account of the History of Mathematics," fifth edition, 1912, p. 239; M. Cantor's "Geschichte der Mathematik," Bd. ii., 1892, p. 658; J. Tropfke's “Geschichte der Elementar Mathematik," Bd. i., 1902, p. 135. In some places, as, for instance, in Oughtred's "Circles of Proportion" (London, 1632, p. 38), the two bars of the cross are not quite straight, giving the symbol the appearance of the small letter x. In some of John Wallis's writings, as, for example, his " Elenchus geometriae Hobbianae," etc. (Oxford, 1655, P. 23), the symbol is not the usual cross, but is plainly the capital letter X turned on its side. In a paper by Lord Viscount Brouncker in the Philosophical Transactions (vol. ii., 1668, p. 646), the capital letter X occurs regularly as the symbol for multiplication. These and similar cases lead to the inference that the cross and the letter x were considered practically one and the same symbol for multiplication.

In this connection we desire to point out that the small letter x, and also the capital letter X, occur as symbols for multiplication before Oughtred (1631) in 1 Hjort, "Rapports et Procès-Verbaux, vol. xx., p. 29. (Copenhagen, 1914.) 2 Public. de Circonstance," No. 53, p. 94. (1910.)