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perimentally. If means for finding one curve are available, any and the limiting length of a No. 28 B. W.A, steel wire, is about other required curve could probably be found by the same 10 feet. In the case of pillars whose neutral axes are conapparatus ; hence there was no need for analysis. Prof. Perry strained to be vertical both at top and bottom, the results show remarked that experiments could not be made on a machine that a definite ratio must exist between the bending monents before the machine was built ; whereas the E.M.F. curve could producing the constraints. -A paper on choking coils, by Prof. be predetermined from its design. By analysis, its current Perry, F.R.S., and a description of the uses of Rice's choking curves, when working under various conditions, could be found. coils for regulating the brilliancy of incandescent lamps, by Mr. Prof. Ayrton, referring to the, mnemonic character of the Hammer, were postponed until next meeting. modes of representation described by Dr. Thompson, suggested that the symbols in the author's book should be more mnemonic.

Linnean Society, March 3.-Prof. Stewart, President, in He himself was in the habit of using large letters for currents

the chair.—A letter was read from the Home Secretary, conveyand small ones for resistances : A and a for the armature, S and

ing the thanks of Her Majesty the Queen for the address of s for series, and Z and s for the shunt, currents and resistances,

condolence which had been forwarded on behalf of the Society respectively, and o and 6 for the series and shunt turns. He

on the death of H.R. H. the Duke of Clarence and Avondale. — also found the following “electromotive force” rule very con

The President announced the presentation by Sir Joseph Hooker venient. Draw three rectangular axes, OM, OF, and oE, as

to the Society of iwo medallion portraits of Sir James Ross and shown in Fig. 2. If, then, of represents the direction of the

i Dr. John Richardson, whose names are well known in connec

tion with Arctic exploration. The medallions were executed in 1843 by the late Bernhard Smith. A vote of thanks to the donor was passed unanimously.-Mr. Clement Reid exhibited a collection of fossil plants and seeds which he had found associated with the bones of Rhinoceros and other mammals in the neighbourhood of Selsea, and West Wittering. By means of diagrams Mr. Reid showed the exact position of the bed, and described the condition in which the various specimens were deposited. --On behalf of Mr. W. E. Beckwith, of Shrewsbury,

Mr. H. Seebohm exhibited a specimen of White's Thrush 0 →M

(Turdus varius) which had been shot near Shrewsbury on January 14 last. He pointed out that this species, which in

habits Eastern Asia, belongs to the sub-genus Oreocincla, an force (magnetic), om that of the motion, then oe shows the exclusively Eastern group of ground Thrushes, and is the only direction of the induced E.M.F. Dr. Thompson, in replying, one which is Palæarctic and migratory. It does not breed anysaid he thought Mr. Blakesley had misunderstood what had been where west of the Yenisei, and its occurrence in Europe is said, for no ambiguity existed. In describing the windings of accidental. Mr. Seebohm added that it had been met with armatures, difficulty arose from want of proper names for the twice in France, four times in Italy, three times in Belgium, various elements, and in his forthcoming work suitable names once or twice in Austria and Prussia, once in Norway, thirteen had been given. To Prof. Ayrton he pointed out that in his times in Heligoland (between 1827 and 1884), and about a book he (Dr. Thompson) had used mnemonic characters, for score of times in the British Islands, including three occurrences Ma, I's, and rm represented the resistances of armature, shunt, and in Ireland, and one in the extreme south of Scotland.-On series magnet coils respectively. The symbol I for current had behalf of Mr. A. Craig Christie, the Secretary exhibited some also been recommended for adoption by the Frankfort Com- specimens, as was supposed, of Lycopodium complanatum, col. mittee. He objected to Greek letters except for specific quanti- lected in Scotland, on which it was suggested that the plant ties, such as angles, specific inductive capacities, refractive might be regarded as British. In the opinion, however, of indices, &c. He appreciated the simplicity of Prof. Ayrton's Mr. James Groves, who had carefully examined the specimens, E.M.F. rule, bat thought it would be better to rotate oe and of and other botanists present, they were referable to L. alpinum. through a right angle about om, thus giving Fig. 3.-A paper on Mr. Groves pointed out the distinctive characters of both. Mr.

Carruthers was of opinion that L. complanatum had been met F

with in the south of England, but not within the last ten years. Mr. E. M. Holmes was under the impression he had seen it growing a few years ago near Stroud. -A paper was then read by Mr. A. D. Michael, on variations in the internal anatomy, and especially the genital organs, of the Gamasina, a typical sub-family of the Acari. In this paper the author gave the results of two years' research, including many hundreds of dissections and serial sections, with lengthy observations of

the living creatures. The comparison of variable organs was →M

worked out in numerous species, showing great specific differ

Four of the species were found to be previously undescribed, and for these the names Hemogamasus horridus, H. nidi, Lelaps oribaloides, and L. ligoniformis were proposed.

Royal Microscopical Society, February 17.-Dr. R. Braithwaite, President, in the chair.-Prof. F. Jeffrey Bell

said that he had, in accordance with the resolution passed E

at the last meeting, forwarded a copy of the message of condolence from the Society to the Prince of Wales, to General Sir

Dighton Probyn, and he had received the following letter of the flexure of long pillars under their own weight, by Prof. M. Dighton Probyn, Comptroller and Treasurer of the Household, is

acknowledgment :-Sandringham, Norfolk.-General Sir Fitzgerald, was read by Mr. Blakesley. The subject of upright desired to convey to the members of the Royal Microscopical pillars fixed at the base and free at the top is treated mathematically, the differential equation being integrated in two

Society' the heartfelt thanks of the Prince and Princess of

Wales for the Society's kind resolution, expressing sympathy series, involving ascending powers of the variable. Putting L for the ratio of length to diameter, the results, when applied to

for their Royal Highnesses in their deep affliction.- January 25,

1891.”—Mr. Watson exhibited and described a new vertical thin steel tubes and rods, for which Young's modulus is taken

camera for photomicrography designed upon the same lines as as 12,000 tons per square inch, show that the limiting height (in

that used by Dr. Van Heurck. The President then read his feet) of pillars which can stand without bending is given by annual address, postponed from the last meeting under the 15 X 106 for tubes ; and H = 7'5 X 106

for rods. If special circumstances then mentioned. The subject chosen was L

the impregnation and modes of reproduction in Ferns and L= 100, the maximum height of a tube is 1500 feet, the Mosses ; diagrams in illustration were exhibited and explained diameter being 15 feet. For wires, L may have larger values, and specimens were also shown under microscopes.-A cordia

ences.

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H =

of Mesmerism:

A.

P.

vote of thanks, proposed by the Rev. Canon Carr and seconded February 13-14, but less violent, were registered by the Parc by Prof. Groves, was given to the President for his valuable Saint-Maur instruments on March 6-7-On the magnetic address.- Mr. J. J. Vezey moved that the best thanks of storm of February 13-14, by M. H. Wild. A comparison of the Society be given to its officers, and also to the auditors the records made by instruments at Pawlowsk with those oband scrutineers for their services during the year.–The Presi- tained at Parc Saint-Maur shows that, although the recent magdent declared the motion to be carried by acclamation.-Prof. netic storm commenced at approximately the same time, the Bell thanked the Society on behalf of himself and the other variations at the two places were in the opposite directions. officers, at the same time calling attention to the special Other differences have been observed in the two records.-Qn services rendered by the Treasurer, Mr. Frank Crisp. — The the atmospheric, magnetic, and seismic disturbances of February following are the names of the members of the new Council, 1892, by M. Ch. V. Zenger. The author has marshalled facts who met for the first time at this meeting :-President: Dr. R. to show that magnetic storms, cyclones, snow-storms, discharges Braithwaite. Vice-Presidents : Mr. A. W. Bennett, Prof. J. W. of atmospheric electricity, earthquakes, and volcanic eruptions Groves, Mr. G. C. Karop, and Mr. A. D, Michael. Treasurer: occur simultaneously.--On three fossil human skeletons found Mr. Frank Crisp. Secretaries: Prof. F. Jeffrey Bell and the in the Baousse-Roussé grottos, in Italy, by M. Émile Rivière.. Rev. Dr. W. H. Dallinger. Ordinary members : Dr. Lionel S. Beale, Rev. E. Carr, Mr. James Glaisher, Dr. R. G. Hebb, Mr. E. M. Nelson, Mr. T. H. Powell, Prof. Urban Pritchard,

BOOKS RECEIVED. Mr. W. W. Reeves, Prof. C. Stewart, Mr. W. T. Suffolk, Mr.

Books.-Phases of Animal Life : R. Lydekker (Longmans).—Meteor

ological Observations made at the Adelaide Observatory, &c., during C. Tyler, and Mr. F. H. Ward.

the Year 1889 (Adelaide). -The_Rationale

Sinnett (Kegan Paul).- Zoological Record, 1890 (Gurney and Jackson).– PARIS.

Elements of Economics of Industry: Prof. A. Marshall (Macmillan). —

Elementary Mathematical Astronomy : C. W. C. Barlow and G. H. Bryan Academy of Sciences, March 7.-M. d'Abbadie in the

(Clive).-The Dietetic Value of Bread: J. Goodfellow (Macmillan).-Air chair. -Fermentation of blood, by MM. Berthelot and G.

and Water : Prof. V. B. Lewes (Methuen).- Le Climat de la Belgique,

1891: A. Lancaster (Bruxelles, Hayez) —Soils and Manures: Dr. J. M'H. André. The blood of cattle, defibrinated, was fermented for Munro (Cassell). -Longmans' Schol Geography for North America : G. 130 days in a water-bath at 35o. The paper contains an account G. Chisholm and C. H. Leete, and edition (Longmans). -Precious Stones of the products of the fermentation. It will be published in

and Gems: E. W. Streeter, 5th edition (Bell). - The Oak : Prof. H. M.

Ward (Kegan Paul). -The, Labrador Coast: Dr. A. S. Packard (Kegan greater detail in the Annales de Chimie et de Physique.- On the Paul). -Contribution à l'Étude de la Morphologie et du Developpement distribution in latitude of solar phenomena observed at the des Bactériacées : A. Billet (Dulau). -Bateaux et Navires : Marquis de Royal Observatory of the Roman College during the second Folin (Paris, Baillière). -Diseases of the Nose : Dr. G. Macdonald, and half of 1891, by M. P. Tacchini. (See Our Astronomical

edition (Watt). -Annals of the Royal Botanic Garden, Calcutta, vol. iii.

(Calcutta). -A Short Text-book or Inorganic Chemistry : Dr. H. Kolbe, Column.)-Phenomena observed at Kalocsa, on the large translated and edited by Dr. T. S. Humpidge, 3rd edition (Longmans). --group of spots of February 1892, by M. J. Fényi. A promin. Laboratory Practice: Dr. J. P. Cooke (Kegan Paul).- Catalogue of the ence, 124" high, was observed in the position 220°-230°, as the

Specimens illustrating the Osteology of Vertebrated Animals recent and

extinct, contained in the Museum of the Royal College of Surgeons of recent large spot.group was crossing the limb.-On the impossi: England, Part 3, Class Aves: Dr. R. B. Sharpe (Taylor and Francis). bility of certain movements, by MM. A. de Saint-Germain and L. Lecornu.—On the movement of a conical pendulum, by M. de Sparre.-On electro-capillary phenomena, by M. Alphonse

CONTENTS.

PAGE Berget.-On the co-existence of dielectric power and electro- Man in Nature, By J. G. G.

457 lytic conductivity, by M. E. Bouty. It appears from the ex. Fnrniture Woods .

459 periments described that the dielectric constant only varies Our Book Shelf:slightly under conditions which produce an enormous increase Dary : “ L'Électricité dans la Nature"

460 of conductivity. Thus, water and ice have sensibly the same Lock : "The First Book of Euclid's Elements.

-W. 460 dielectric constant, whilst the conductivity may vary from 1 to Bothamley : “ The Ilford Manual of Photography." 105 or 106.-On the thermal conductivity of crystalline bodies,

W..

4бо by M. Charles Soret.-Rule for finding the number and nature Hughes and Williams : The Advanced Class-book of accidentals of the gamut in a tone and a given mode, by M. of Modern Geography" Pierre Lefebvre.-On the density of aqueous solutions, by M. Letters to the Editor :Georges Charpy. The author concludes from his results that Carpenter on Eozoon.-Sir J. William Dawson, the variation of the density of a solution, as a sunction of the

C.M.G., F.R.S.

461 concentration, is a complex phenomenon, and cannot be used in The Samoan Hurricane. -Everett Hayden; H. studying the state of the dissolved body. There is no reason

F. B..

461 why the solution at which the maximum density is reached Phoronomy.-Dr. W. H. Besant, F.R.S. should be regarded as corresponding to a definité hydrate.

On the Terms “Centrisugal Force” and “Force of Compounds of gaseous ammonia with boron iodide and bromide, Inertia.”—George S. Carr

463 by M. A. Besson. Synthesis of the minerals crocoisite A Lecture Experiment in Surface Tension. (Illus. and phoenicite (phornicochroite), by. M. C. Luedeking.-On trated.)-E. D. Fridlander

463 the value of the primary alcoholic function, by M. de The Orientation of Ancient Monuments.-Rev. Forcrand.—On the production of quinine di-iodomethoxide

Fred. F. Grensted

464 from cupreîne, by MM. E. Grimaux and A. Arnaud. -A study The Nickel Heat-Engine. - Rev. Frederick J. of the velocity of decoin position of diazo-compounds by water,

Smith

464 by MM. P. Th. Muller and J. Hausser. The law according to The Limpet's Power of Adhesion.--Percy A. Aubin 464 which sulphanilic acid is decomposed is expressed by the for On the Variation of Latitude.- Robt. B. Hayward,

A mula C = log. nat. in which @ is the time, C a con

F.R.S.

465 A

Ornithology of the Sandwich Isles. By Prof. Alfred stant, A the total nitrogen that can be evolved, and x the Newton, F.R.S.

465 amount of nitrogen evolved. C is independent of the concen- Prof. Bunsen and the Chemical Society tration.— Action of capryl iodide on trimethylamine in aqueous

Notes

470 solution, in equimolecular proportions ; formation, when Our Astronomical Column:heated, of dimethylcaprylamine ; production in the cold Solar Investigations :

473 of caprylene, by MM. H. and A. Malbot.-New syn- New Double Star, 26 Auriga

473 thesis of tartaric acid, by M. P. Genvresse. (See Notes.) Rotation of Jupiter

473 On the pyloric secretion of the dog, by M. Ch. Contejean.- The New Star in Auriga

473 New rings or intercalary rings of nerve-ducts (tubes nerveux), The Lick Spectroscope

473 produced by the impregnation of silver, hy M. Benjamin A Bright Comet

473 Ségall.—On two new species of Streptothrix, Cohn, and Calculation of Trajectories of Elongated Projectiles. on the place of this genus in the classification, by MM. By Rev. F. Bashforth

473 C. Sauvageau and M. Radais. - History of the Garcinia Forthcoming Scientific Books

476 of the sub-group Xanthochymus, by M. J. Vesque.-On the Scientific Serials.

477 magnetic disturbance and the aurora borealis of March 6, Societies and Academies 1892, by M. Th. Moureaux. Disturbances similar to those of Books Received

480

460

462

- r

469

478 of the type

ΣαΣός

THURSDAY, MARCH 24, 1892.

Laplace, Lagrange, and Bezont. We find that Lagrange knew that the discriminant of a binary quantic of the second order is an invariant of the linear transformation.

He did not, however, express either the discriminant or THE HISTORY OF DETERMINANTS. the determinant of transformation in a determinant form. The Theory of Determinants in the Historical Order of The author critically examines the claim of Laplace to be its Development. Part 1. Determinants in General.

the discoverer of the expansion theorem. He finds that By Thomas Muir, M.A., LL.D., F.R.S.E. (London : although the case in which as many as possible of the Macmillan and Co., 1890.)

factors of the terms of the expansion are of the second THE *HE theory of determinants is in that borderland degree had already been given by Vandermonde, and

which separates the “pass” from the “honour” | Laplace himself did not give a statement of the rule student of pure mathematics. In elementary text-books

suited for general application, the claim can in the main the subject is rarely more than introduced for the purpose be upheld. Hindenburg (1784) and Rothe (1800) took of representing some result of geometry or analysis in a

up the subject in Germany, and between them constructed convenient, beautiful, and suggestive form. The essen

an elementary theory of permulations. Rothe, it is intial properties of a determinant are not set forth, but the teresting to observe, employed a graphical method which student is perhaps referred for further information to one

will remind the reader of Prof. Sylvester's modern conor other of the two excellent treatises which are already

structive theory of partitions. Gauss (1801) followed, and at our disposal in the English language, viz. those of then we come to the important papers of Binet (1811) Mr. Muir and of Mr. R. F. Scott. The value of the idea and Cauchy (1812). These memoirs establish the multithus given to a student of the shape and convenient use plication theorem in its full generalization. The method of a great analytical implement is beyond all question. adopted by Binet may be described as that of symmetric His imagination and curiosity are alike excited, and the

functions, which he uses freely. He employs identities “trick" possibly prevents his passage through life under the delusion that all mathematics are comprised within

Lab'd' = {axbxc + 2abc

baca - Lc Lab, the covers of the school-books. The honour student, as having reference to several systems of quantities. He a matter of course, reads some work on the subject, and was not, however, sufficiently acquainted with the theory is as surely enchanted. He cannot fail to recognize the of such functions; and was unable to supply rigid proofs power and beauty of the notation. He observes that the of the theorems in determinants which, from his point object of his study is constructive in its nature. He of view, rested upon these identities. Nowadays, the becomes convinced that pure mathematics is one of the identity in question will be recognized as the expression fine arts, and just as a beautiful picture gives pleasure to of an "elementary” symmetric function (single unitary, one who understands painting, just as a fine piece of and having three parts in its partition) by means of sculpture delights one who understands modelling, so he symmetric functions each of which is expressible symsees unfolded to his intellectual eye an exquisite example bolically by a partition composed of one tripartite part. of constructive art, which his previous mathematical read-The law of the coefficients, undivulged by Binet, is now ing has fitted him to understand and appreciate, and to perfectly well known. It is, in fact, an easy generalizaregard as a beautiful object of contemplation. The theory tion of the law by which, in the case of a single system of determinants is one of the most artistic subdivisions of quantities, the elementary symmetric functions are of mathematical science, and accordingly has never expressed as functions of the sums of powers of the wanted enthusiastic admirers. It is most gratifying to quantities. Cauchy at the same date (1812) introduced find such an authority as Mr. Muir devoting his leisure the idea of “fonctions symétriques alternées,” which led to its historical development. Any mathematician taking him to a new symbolic definition of a determinant and up this volume would anticipate a treat, and he would to many valuable results. Mr. Muir devotes several not be disappointed. In this first instalment the reader pages to an examination of Cauchy's title to share with is taken from Leibnitz (1693) to Cauchy (1841). Mr. Muir Binet the credit of the generalized multiplication theorem. assigns a chief place of honour to Vandermonde (1771), He gives his decision against Cauchy, and probably the who, in his “Mémoire sur l'Élimination” (Hist. de l'Acad. reader who closely follows the argument will find himself Roy. des Sciences), denoted a function formed from the in accord with the historian. Notwithstanding this concoefficients of a set of linear equations by a symbolism clusion, Cauchy's memoir is excellent in quality and which is at once recognized as a condensed form of the abundant in quantity; he “opened up a whole avenue of determinant matrix of the present day. He was the first fresh investigation, and one cannot but assign to him the to give a connected exposition of the theory, and to give place of highest honour among all the workers from 1693 the true fundamental properties of the new functions. to 1812." His notation, moreover, was exceedingly good, and much A retrospect is given of the period 1693-1812 accomsuperior to that adopted by some subsequent writers who panied by an interesting tabular record. As a means of overlooked or neglected his important work.

reference the work appears to be absolutely perfect. Vandermonde has also recently received justice, long Each new result as it appears is marked in Roman denied him, in other branches of analysis, and there is figures ; and if the same result be obtained differently, now no doubt that the value and originality of his work or be generalized by a subsequent investigator, the same entitle him to a place in the ranks of the mathematical Roman figure is employed, followed by an Arabic pioneers of his time. Up to the close of the eighteenth numeral. It is found that to this point nearly every century the most noteworthy additions were made by ! important advance is due to French mathematicians.

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During the second period (1813-1841) the chief names position held by the author, seem to call for more are Cauchy, Schweins, Jacobi, and Sylvester ; to these detailed notice of this work than is usually accorded to may be added Desnanot and Scherk, to whom fresh a new edition. departures, of less extent, are due. Schweins himself The “Anthropogenie," which was first published in may be said to have been discovered by Mr. Muir. 1874, is the third of the series of books in which Prof. This author (1825) deals with the subject under the title Haeckel has attempted to determine the laws governing " Theorie der Producte mit Versetzungen." He made a the form, structure, and mutual relations of living things, notable generalization described as the transformation of and to establish the general principles of biological an aggregate of products of pairs of determinants into science. The first of these, under the title “Generelle another aggregate of similar kind. He further discussed Morphologie," appeared in 1866, almost simultaneously special forms, and, it is clear, possessed a firm grasp of with the completion of Herbert Spencer's “ Principles of his subject.

Biology.” It is a comprehensive and ambitious work, The work of Jacobi and Sylvester, and the further' which, in its author's words, work of Cauchy will be more or less familiar to mathe- "constituted the first attempt to apply the general docmaticians. Germany has passed to the first place ; and trine of development to the whole range of organic the occurrence of Sylvester's name in the history marks morphology, : : . and to introduce the Darwinian a revival of learning in pure mathematics in England.

theory of descent into the systematic classification of The volume is remarkable for the study it presents in animals and plants, and to found a 'natural system'on nomenclature and notation. There is an extraordinary pedigrees for the various species of organisms."

the basis of genealogy; that is, to construct hypothetical variety in the symbolism. It is easy to observe the distinctive characters of French and German notation that it contains also the first systematic attempt to deal in are so marked at the present day. It is well known that

detail with the ancestry of man, as regards the groups of much lies in an appropriate notation. Every young

animals lower than mammals. This is, perhaps, the mathematician with a predilection for original work

most solid piece of work Prof. Haeckel has done ; it should read this book, to note the power of suitable contains much matter of great value, and discussions symbols, to grasp the reason of their power, and, above and speculations of extreme ingenuity and interest.

Later discoveries have rendered much of it obsolete, but all, to see what to avoid. The book also points a moral which is not far to seek.

it still remains the most important work of its kind ; and It would be easy to pick out many such phrases as,

but for its somewhat cumbersome terminology, would be

was acquainted with the writings of very few of his prede- widely read even now. The “ Natural History of Creacessors”; was unaware apparently of the existence of tion,” first published in 1868, goes over a good deal a theory of determinants"; "hasty, if not contemptuous,

of the same ground as the earlier work, but is written in disregard of historical research.” To this tendency to

a much more popular style, and aims at presenting in a

form suited to the general reader the main arguments on work on without proper attention to previous work is doubtless due in some measure the unfortunate multipli- detailed application of the theory to the principal groups

which the Darwinian theory is based, together with a cation of names and symbolisms which is so perplexing of animals, and an attempt to determine their mutual reand irritating to a reader. This failure to collaborate with others can only retard the progress of the science. lations and lines of descent. The “Anthropogenie,” the It is perfectly true that great original thinkers, like

book now before us, is a more elaborate application of Gauss, Cauchy, Jacobi, and Sylvester, may take liberties

the same principles to the special problem of the evolution of this kind ; and the fact of their doing so may even be beneficial to the subject, as resulting in memoirs of

In the new edition the general arrangement remains more unfettered originality. But this is not so in the much the same as before ; but, in order to include the case of lesser men. In taking leave of this fascinating results of more recent investigations, a great part of the history one can look forward to Part II. with sincere book has been re-written, and new chapters have been pleasure, which is not diminished by the knowledge that added on subjects that have attracted especial attention of the later developments have been largely due to our

late years, such as the Gastræa theory, the Colom theory, countrymen. We have yet to see Sylvester's most

and the nature and origin of segmentation. A large powerful investigations, and all Cayley's researches ;

number of new figures have been inserted, and the geneaand, finally, the successive steps by which the lofty logical tables, for which Prof. Haeckel has a special heights of the theory of matrices and the theory of fondness, have been greatly increased in number, and in multiple algebra (involving the generalization of quater

elaboration of detail. nions) have been attained.

The book, which is adapted rather for the general P. A. M.

reader than the scientific student, is written in an attrac

tive and popular style, and presents the main facts of THE EVOLUTION OF MAN.

vertebrate embryology in an intelligible and well illusAnthropogenie, oder Entwickelungsgeschichte des Men trated form. As might be expected from his former

schen. By Prof. Ernst Haeckel. Fourth Edition, re- writings, the main feature of Prof. Haeckel's work is a vised and enlarged. Pp. i.-xxvi. and 1-906. (Leipzig : detailed exposition and vigorous defence of what he has W. Engelmann, 1891.)

named “the fundamental law of biogenesis," better known HE importance of the subject-matter of the book, in this country as the recapitulation theory, according to

of man.

appearance of the former editions, and the pro ninent animal is a repetition of the ancestral or phylogenetic development of the species ; or, to put it more simply, it is not too much to say that our knowledge of the deveanimals in their development climb up their own genea- lopment of the human embryo, from a stage corresponding logical trees. This is now generally accepted by embryo- to a chick embryo at the cominencement of the second logists, but it has not always been so, and Haeckel day onwards, is as satisfactory, as complete, and as well reminds us, with justice, that he was one of the first to illustrated as that of any other mammal. realize and teach the doctrine.

For this great advance we are indebted almost entirely Prof. Haeckel has much to say on other points of to the labours of German embryologists, and notably to theoretical interest. He protests strongly against Weis- the splendid work of Prof. His. Prof. Haeckel has in mann's views with regard to heredity, pointing out that his volume many hard things to say of Prof. His, but is the very existence of germ-plasma is as yet a mere assump- indebted to him for the only really good figures of tion, and maintaining that acquired characters may be and human embryos which he gives, and would have mateare actually transmitted. He objects equally strongly to rially improved his book had he studied more carefully the views as to the widespread occurrence of degenera- the admirable descriptions of the Leipzig Professor. It tion, which were first put forward by Dr. Dohrn; and on is a matter for great regret that a book of 900 pages, the much-debated question of the origin of Vertebrates having for its title, “ Anthropogenie, oder Entwickelungshe sides with those who fully accept the evidence afforded | geschichte des Menschen,” should be allowed to appear by the anatomy and development of Amphioxus; he in which the account of the actual development of the admits the Vertebrate affinities of Balanoglossus, and human embryo is so inadequate or even erroneous. looks for the ancestors of Vertebrates among the un

A. M. M. segmented Turbellarian worms. As a controversialist Prof. Haeckel is impressive rather than convincing. He

OUR BOOK SHELF. hits hard and with effect, but prefers to counter rather than to parry the blows of his opponent. It is impos- | Philosophical Notes on Botanical Subjects. By E. sible to pass over without protest the terms in which he

Bonavia, M.D. With 160 Illustrations. 368 pages. writes—it must be admitted under provocation-of the

(London : Eyre and Spottiswoode, 1892.) opinions and work of other investigators.

DR. BONAVIA's philosophy is concerned with the evoluProf. Haeckel's fondness for genealogical trees, and

tion of vegetable organisms, and the gist of it is that all

land-plants have descended from sea-weeds. He sees his facility in constructing them, are well known and

modifications and traces developments not obvious to have been much criticized, perhaps a little unfairly. ordinary observers, and he is prepared for derisive critiAcceptance of the doctrine of evolution involves the cism. To quote from his preface :-" The fact is that, in recognition of a blood-relationship, near or remote,

this stage of existence, certain thoughts are often a great between any one animal and any other; and the only by day, they turn up by night, they turn up in the morn

worry. One often cannot get rid of them. They turn up true classification is one which places this fact in the

ing, and they haunt one at all times, and the only remedy forefront, and adopts it as the basis on which the

for mitigating this worry of civilization is to commit them scheme is to rest. Genealogical tables undoubtedly to paper. This done, there are several ways of disposing stimulate inquiry, and so long as it is realized that of your written thoughts. You can burn the papers they they are necessarily in great part tentative or pro

are written upon or otherwise destroy them, or you can visional, they probably will do more good than harm.

leave them in a drawer as a legacy to your heirs !

neither of these processes can you entirely give yourself It would be easy to take exception to many points in repose, then the most effective way of ridding yourself of Prof. Haeckel's numerous and elaborate pedigrees, but the worry of such thoughts is to have them published (if it will be generally admitted that they are instructive, any publisher will perform this kind office), and to see and often extremely suggestive, even though the con

them adversely criticized if anyone will even take so clusions may not meet with general acceptance.

much trouble." The least satisfactory part of the book is that which reached the acute stage, and he is so far relieved as to

As the book before us testifies, Dr. Bonavia's worry deals with human embryology. No attempt whatever is have found a publisher; but we do not propose to gratify made to explain the earlier stages of development; | him by adverse criticism. We prefer giving one short the special difficulties of the problem are absolutely extract from his sixteen“ general conclusions": ignored ; the human gastrula is spoken of in a confident

“Fifteenth :-The fig is obviously a further developway, as though such a stage really existed; and the ment of a conceptacle of a Fucus or other sea-weed.

And there is every reason to believe that the oil.glands accounts of the development of the several organs and

of the bark, leaves, and peel of the Citrus, and similar systems are too often taken from other animals. A glands in other plants, are mere remnants of sea-weed student who relied on Prof. Haeckel's descriptions would conceptacles-that is, persistent features turned to other obtain an entirely erroneous idea of the actual course of

W. B. H. development of the human embryo.

The Zoological Record for 1890. Edited by Frank E. Owing to the difficulty of obtaining material in proper Beddard. (London: Gurney and Jackson, 1892.) condition for microscopical examination, our acquaintance This is the twenty-seventh volume of the Record of with human embryology long remained imperfect; and Zoological Literature, and it has been prepared on the the descriptions in text books were largely based on our same plan as the volume published last year. First of knowledge of other Vertebrates, and illustrated by figures | all there is a list of works on general subjects, by J. A. from embryos of dogs, pigs, rabbits, or even chicken

Thomson. Then come the titles of writings on the foland dogfish. The time for all this is now past. During Bowdler Sharpe ; Reptilia, Batrachia, and Pisces, by

lowing :-Mammalia, by R. Lydekker; Aves, by R. the last ten years our knowledge has advanced wonder

G. A. Boulenger ; Tunicata, by W. A. Herdman ; Molfully ; and although the earliest stages are still unknown, / lusca, Brachiopoda, and Polyzoa, by P. C. Mitchell ;

If by

uses."

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