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by taking into account the conductivity. If, however, we start with von Helmholtz's theory, and introduce a viscous term into the equations of motion of the matter, it will be found possible for the real part of μ2 to be negative, provided the free period of the matter vibrations lies between certain limits. We are thus able to construct a mechanical model of a medium which represents the action of metals upon ethereal waves, and which leads to the same formulæ for the amplitudes of the reflected waves as those given by Cauchy.-The contacts of systems of circles, by A. Larmor.-On a class of automorphic functions, by Prof. W. Burnside.-Note on the identity 4(x − 1)/(x − 1) YpZ2, by Prof. G. B. Mathews. On the classification of binodal quartic curves, by H. M. Jeffery, F. R. S.-Researches in the calculus of variations; discriminating conditions in isoperimetrical problems, by E. P. Culverwell.-Note on Clifford's paper "On syzygetic relations among the powers of linear quantics," by Prof. Cayley, F.R.S.-Note on finding the G points of a given circle with respect to a given triangle of reference, by J. Griffiths.

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Linnean Society, November 19.-Prof. Stewart, President, in the chair.-Mr. S. Jennings exhibited a collection of wild flowers made by him during a recent tour through the Rocky Mountains, California, and Mexico.-Prof. G. B. Howes exhibited some dissections of fish crania made by his pupil Mr. R. H. Burne, in which the parts of the skeleton were so displayed that they might be studied in relation to the rest of the head and to the leading cranial nerves.-Mr. E. F. Cooper exhibited specimens of a new variety of Potamogeton from Loughborough, lately described and figured by Mr. Alfred Fryer (Journ. Bot., October 1891).-Mr. A. W. Bennett exhibited and made remarks upon some specimens of Hydro. dictyon utriculatum, Roth. (H. reticulatum, De Toni), and some drawings of anomalous Cypripedium and Disa.-Mr. W. Carruthers, F.R. S., gave a graphic account of a recent visit to Sweden in search of original portraits of Linnæus, and detailed the results of his inquiries. His remarks were illustrated by an exhibition of engravings and photographs.-A paper was then read by Mr. Thomas Hick, on a new fossil plant from the Lower Coal-measures. An interesting discussion followed, in which Mr. Carruthers, Mr. G. Murray, Prof. F. O. Bower, Prof. Marshall Ward, and others took part.

PARIS.

Academy of Sciences, November 23.-M. Duchartre in the chair.-On some manuscripts with figures of historical interest relating to artillery and mechanical arts towards the end of the Middle Ages, by M. Berthelot. Some manuscripts from libraries at Munich, Venice, and Paris have been examined, and appear to be of interest as marking a stage in the development of applied sciences. A few of the medieval figures are reproduced : one represents a diver in his costume; two others show primitive cannon, and one a small-arm used in the fifteenth century.Preparation and properties of the phosphides of boron, by M. Henri Moissan. By the use of boron phosphoiodide, two boron phosphides may be obtained. The compound PB combines with HNO3, H2O with incandescence, and inflames in an atmosphere of chlorine in the cold. The compound PB is much more stable, and is not acted upon in the cold by these two reagents. On some variations of the glycolytic power of the blood, and on a new method of experimental production of diabetes, MM. R. Lépine and Barral.-M. A. Potier was elected a member of the Academy in the place of the late M. Edmond Becquerel.-Résumé of a verbal report on a note by Prince Tourquistanoff, entitled "Le Calendrier vérificateur," by M. Wolf.-Résumé of a verbal report on a note by M. de Cohorne, entitled "Le Régleur solaire," by M. Wolf.-Observations of the total eclipse of the moon of November 15, made at Bordeaux Observatory, by M. G. Rayet.-Remarks à propos of the observation of M. Rayet as to the possibility of photographing the moon during a total eclipse, by M. A. Gautier.-Remarks on M. Rayet's communication, by M. J. Janssen.-Researches on the motions of stars in the line of sight made with the Paris Observatory siderostat, by M. Deslandres. (For the last four communications, see Our Astronomical Column.)-Remark on a communication by M. Markoff relative to linear differential equations, by M. Painlevé.—On the flow of liquids in capillary | tubes, by M. Albert Colson. The influence of temperature on the rate of flow of viscous liquids is seen from the following comprison of the times in which 5 c.c. of glycerine passed through the tube :

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Temperatures 150° 250° 265° Duration of flow... 8h. 360s. 114s. 40'5s. The same tube passed 5 c.c. of water at 20° in 34 seconds. author divides the liquids he has experimented upon into two classes, distinguished by being perfectly and imperfectly mobile. Ethers and aldehydes are representatives of the former class, for they appear to obey Graham's law that the duration of flow, or rather the rate of diffusion, is inversely proportional to the in this square root of the density. The values found for ND class of liquids is practically constant. On the other hand, the liquids imparfaitement mobiles, such as alcohols and benzines, furnish irregular values.-Mechanical determination of the position of the atoms of hydrogen in organic compounds, by M. G. Hinrichs.-Aniline black in dyeing by the dry method, by M. A. Gautier.-On a codeïne violet, by M. P. Cazeneuve.-On the distribution of saccharine matters in the different parts of the edible Cèpe (Boletus edulis, Bull.), by M. Em. Bourquelot.-On the existence of veins of leucite in a Mont Dore basalt, by M. A. Lacroix. Leucite has not before been recognized in any of the volcanic rocks of the central plateau of France. The author fully describes the petrological characters of the specimens he has discovered, and also their peculiar mode of occurrence. — Earthquakes, submarine eruption, and elevation of land at Pantellaria, by M. A. Riccò. Earthquake shocks were felt at Pantellaria on October 14. On October 18, the sea to the westnorth-west of the island, at a distance of about 5 kilometres, was seen in violent commotion, and a band of land about 1 kilometre long appeared, from which were ejected masses of heated rock and vapour. On approaching the place of eruption, a large number of dead fishes were found, and it was seen that the band was composed of an immense number of black floating masses of rock colliding together with great noise, and vaporizing the water over which they passed. On October 23 the position of the erupted island was determined as lat. 36° 50' N., long. from Paris 9° 33′ E. The island was then about 200 metres long by 50 metres wide. The interior of some of the masses of rock was still hot enough to melt zinc.

CONTENTS.

Field Geology. By Prof. A. H. Green, F.R.S..
The Land of the Lamas
Science and Brewing

A Theory of Gravitation. By A. G. G.
Our Book Shelf:-

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THURSDAY, DECEMBER 10, 1891.

GERMAN TECHNOLOGY FOR ENGLISH
MANUFACTURERS.

A Theoretical and Practical Treatise on the Manufacture of Sulphuric Acid and Alkali. By George Lunge, Ph.D. Second Edition. Vol. I. Sulphuric Acid. (London: Gurney and Jackson, 1891.)

The Alkali-maker's Hand-book. By George Lunge, Ph.D., and F. Hurter, Ph.D. Second Edition. (London: Whittaker and Co., 1891.)

SULE

ULPHURIC acid plays a part, directly or indirectly, in every manufacturing industry of civilized countries. It has been said, indeed, that one could gauge the civilization of a country by the amount of oil of vitriol it consumes. It is satisfactory, therefore, to know that Great Britain produces annually nearly a million tons of this civilizing agent, or an amount but slightly less than that made by all the rest of the world.

It is, however, a remarkable and not very creditable fact that no English or Scotch man has been at any particular pains to give his fellow-men an adequate description of the details of manufacture of this civilizing agent. Of course a certain number of books of a kind have appeared; but it has been left to a German Professor to give us the first complete monograph on the subject. No one is more competent than Prof. Lunge to write authoritatively concerning the manufacture of sulphuric acid. For eleven years previous to his election to the Professorship of Technical Chemistry at the magnificently equipped Polytechnic School which the forethought and patriotism of the Swiss Government have caused to be erected at Zürich, Dr. Lunge was the manager of a large alkali-works in the north of England'; and he has added to the experience thus gained by numerous visits to the other alkali manufacturing districts of Great Britain, and to those of Belgium, France, Germany, and Austria. His work, however, is not wholly based on the results of personal observation; it reflects, in fact, the existing state of chemical literature on the subject, for practically every important memoir or communication, wherever published, bearing on the manufacture, properties, or uses of sulphuric acid, is referred to and judiciously criticized. Moreover, the author's position, as director of one of the most modern and in many respects one of the best-appointed laboratories in the world, gives him unique advantages in the compilation of such a work; for, surrounded as he is by a band of earnest and enthusiastic workers, eager to aid him in elucidating the theory of established chemical manufactures or in investigating the validity of new processes, he is able to throw light on many obscure reactions by the systematic researches which he initiates, and of which the results, so far as they relate to sulphuric acid or collateral matters, are set forth in this book. It has been frequently observed that, although iron and oil of vitriol are among the most important of our staple products, we know comparatively little of the many chemical reactions which are concerned in their formation. The remark has, however, lost much of its force within recent years, and more especially in the case of sulphuric acid. During the last few years the various changes occurring within

the leaden chamber have been more carefully traced, and much definite information has been gained as to the nature of the interactions which result in the production of oil of vitriol. For not a little of this information we are indebted to Prof. Lunge and his pupils.

The present edition of this work differs in many respects from its predecessor. The ten years which have elapsed since the appearance of the first edition have seen many important changes in the manufacture of acid and alkali ; and hence, with a view of bringing his treatise within reasonable compass, Prof. Lunge has been obliged to curtail much of the historical or merely retrospective portion of the work, and to omit matter which deals with views and theories which may now be considered obsolete. In spite of all this, the book has greatly increased in size, and nearly half the illustrations are new. A comparison of the two editions shows that every page has been carefully overhauled, and much fresh information is given, even on points which appeared to be settled and accepted. The present edition is remarkably free from press errors. We have only detected two : on p. 108, calcium "bisulphate," should read "bisulphite"; and on p. 899 we read that SO3 is formed when limestone is burnt in oxygen, especially at increased pressures; of course "limestone" is a lapsus calami for "brimstone."

"The Alkali-maker's Hand-book," as it is now called, has an accepted position in the laboratory literature of the chemical works of this country. The book owes its origin to a suggestion, made by Mr. Stroof, manager of the Griesheim Alkali Works, to the German Society of Alkali-makers, that a standard manual should be published, with a view of securing uniformity in analytical methods, tables of specific gravity, &c., to be employed by buyers and sellers for the valuation of chemicals, and by manufacturers for controlling and superintending their various processes, in order to avoid disagreements, and to secure exact comparison of results. A small committee of the Society was appointed, and Prof. Lunge was commissioned to collect and sift the materials for such a manual. The present work is the outcome of this action. The great danger of a book of this kind is that it is apt to get stereotyped, in the extended and figurative sense of that word; and that, owing to the natural conservatism of manufacturers, who are loth to disturb arrangements which are found to satisfy commercial necessities, there is the possibility that it may fail to reflect the state of quantitative analysis of the time. So long, however, as the work remains under the direction of Dr. Lunge and Dr. Hurter, there is very little chance of such a fate overtaking it. The present

edition gives abundant evidence that care is being taken to make the book a faithful record of the condition of contemporary quantitative analysis. The work is conveniently arranged and well printed. We would take exception, however, to the character of the illustrations: these compare most unfavourably with those in Dr. Lunge's larger work. Simple outline drawings, like that of the nitrometer on p. 113, would be far preferable to the ill-drawn, ill-cut, and ill-printed designs which disfigure the book. Much of the value of the book depends, of course, on the care and accuracy with which the tables of chemical contents are compiled. We do not regard,

however, the value 122 as the atomic weight of antimony, and we strongly protest against the continued use of 197 18 as the atomic weight of platinum. We are aware of the reasons which have led to the adoption of this value, but not even a " Potash Convention" has the right to play fast and loose with a stoichiometric constant to the extent of nearly 3 units from the truth. Similar tricks were played in the old days with the atomic weights of sodium and manganese for commercial purposes. Let the Potash Convention agree among themselves to adopt any correction they please on their analytical results with a view of rendering them more accurate; but they have no right to tamper with an atomic weight in order to compensate for the imperfections of their quantitative methods. For table 22, showing the volumes of water at different temperatures, we should have preferred to use the more accurate table of Rossetti, which gives the mean results of the observations of Kopp, Pierre, Despretz, Hagen, Matthiessen, Weidner, and Kremers, and thereby tends to eliminate errors due to the employment of a special method, such, for example, as the dilatometrical method. We may also point out that the table of solubilities of certain gases in water is not based on the most modern data. Bunsen's values for oxygen have been superseded by the more accurate numbers of Winckler, Dittmar, and Roscoe and Lunt, Sondén and Petterson; and the original statement, based apparently on the work of Carius, that hydrogen is equally soluble in water at all temperatures between o° and 20°, has been shown to be erroneous by Bohr and Bock and Timofejew.

There is a passage in the preface of Prof. Lunge's larger work which may serve to indicate the difference with which the scientific aspect of his business is regarded by the English and Continental chemical manufacturer. In presenting his book to English manufacturers, Dr. Lunge ventures to express the hope that they will not think it too "scientific." He counsels them not to despise the purely chemical detail which they will find in it. There is, it may be thought, a certain element of humour in these remarks. But Prof. Lunge is very much in earnest. He very well knows that we are still ruled by the rule of thumb in these things; the "practical man still dominates, and nothing but the inevitable adverse dividend will move him out of the way. To what consequences the neglect of a scientific treatment of a practical subject leads, Prof. Lunge illustrates from his personal experience. He tells us that he left his native country for Great Britain rather more than five-and-twenty years ago, because industrial chemistry was but little developed in Germany:

"The manufacture of sulphuric acid, soda-ash, and bleaching-powder was at that time quite insignificant in Germany, and not very considerable in France as compared with Great Britain; nor could the technical appliances, the yields, or even the purity of the products in the two former countries vie with those of the latter."

How different matters are now is notorious:-
:-

"The manufacture of chemicals has made enormous strides forward, both in quantity and quality, in France, and even more so in Germany. Many of the chemicals of these countries outstrip those of English works in purity; and their plant and their processes are frequently superior to those used in the majority of English works.

Everybody knows how this has come about. The foreign chemists and manufacturers have looked all round, not merely in their own countries, but wherever they could find improved methods and apparatus and upon the practical knowledge thus gained they have brought to bear the scientific training they had received at their Universities and Polytechnic schools. Thus they have already, in many fields formerly remunerative to British manufacturers, distanced the latter, immensely aided though these be by their long occupation of the ground, and by permanent natural advantages, such as cheapness of coal and freight, and their superior command of capital, &c.; and this is likely to go on to an increasing extent if many British chemical manufacturers decline to profit from a scientific study of their respective branches.'

No one who has had the opportunity of comparing German chemical works with those of this country can be blind to the truth of these remarks. In certain branches of manufacture we are now absolutely distanced by the Germans, and in branches, too, which by priority of start and by every natural advantage ought to have been our exclusive possession. In the case of some of these we can hardly hope to recover our lost ground. Attempts have not been wanting, but it has to be admitted that British pluck and British capital have been hopelessly beaten by German energy and German capital plus German foresight and enlightenment. In some of these industries we may still hope to have a part, but it can only be a secondary one; and if things go on as hitherto, we must be content to be as the hewers of wood and the drawers of water. As we sow so shall we reap; and as we have sown little, it is but little that we may expect to garner.

The development of industrial chemistry in Germany during the last twenty years, and especially in those branches which depend upon the higher and more recondite branches of the science, has been amazing. In the manufacture of organic products the Germans and Swiss practically command the markets of the world; nor is there the least indication that their monopoly in the case of such products as demand scientific training and skill will be or can be assailed by us at present.

"If

Some months ago the writer was required to inspect and report upon the best examples of modern chemical laboratories to be met with on the Continent, with special reference to the work of instruction in chemical research, and in the higher branches of chemical teaching. The advice he received was most significant, and illustrates very strikingly the attitude of the German chemical manufacturer towards the science of his business you want to see how organic chemistry should be worked at," said Prof. Kekulé, " go to some of our manufactories: The men whom we have they show us the way now. trained in our academic laboratories have bettered their instruction and teach their teachers." Precisely the same counsel was given by Prof. Victor Meyer: "Do you wish to see how chemical research can be organized? Then go to Ludwigshafen." And to Ludwigshafen we went. The mental impression of that spectacle of “organized research" on the banks of the Rhine will not soon be effaced. The sight, indeed, would constitute a useful object-lesson to the legislators who have sought to grapple with the subject of secondary education by handing it over to the country gentlemen. The very existence o

such gigantic concerns as Meister, Lucius, and Brüning, and the Badische Anilin und Soda Fabrik, with their thousands of workmen, their splendidly equipped laboratories, and their scores of well-trained investigators, the product of the most advanced chemical instruction that the most eminent teachers in the world can impart, is a sufficient indication of what "the scientific treatment of a practical subject" leads to.

Some days after his visit to Ludwigshafen, the writer met Prof. von Baeyer at Munich, and the talk was of Höchst and Ludwigshafen, and the influence which these and many such places must have on the industrial position of Germany. “And do you know to whom we owe all this?" asked Baeyer. There was but one answer: "To Liebig." "You are right. It is to Liebig and the Giessen laboratory." What the Augustinian cell at Wittenberg was to German theology, the little University laboratory was to German chemical science.

"The foundation of this school," says Hofmann, who was himself one of its products, "forms an epoch in the history of chemical science. It was here that experimental instruction, such as now prevails in our laboratories, received its earliest form and fashion; and if at the present moment we are proud of the magnificent temples raised to experimental science in all our [German] schools and Universities, let it never be forgotten

excess of the corresponding one for England and Wales." There is thus far evidence that diphtheria as a cause of death is increasing in the country as a whole, and that this increase is very conspicuous in our greatest urban community" (p. 5). It is significant that, "concurrently (pp. 80-81) with the diminution of enteric fever, owing to advance of knowledge in the principles of health, and with the resulting intelligent administration of our sanitary laws, we find that the diphtheria death-rate is increasing in our midst." "But it is, above all, in our large towns and cities that this enlightened sanitary policy has been most marked during the past twenty years; . . . and yet, whereas when, in the past, sanitary defects abounded in our large centres of population diphtheria was essentially a disease of rural districts, that disease is now invading our more cleanly towns and cities to an extent unknown in the annals of their more faulty past."

Now, what is this increase of diphtheria in general, and the "formidable" increase in the London mortality from diphtheria in particular, due to? Although Dr. Thorne abstains from supplying a direct answer to this question, an attentive reader, after perusal of the enormous body of facts which Dr. Thorne produces, will be in a position to draw his own conclusions. This increase is certainly not to be explained by the better recognition and more correct classification of the disease (in the earlier returns

that they all owe their origin to the prototype set up by of the Registrar-General certain forms of scarlatina, true

Liebig half a century ago.”

Bureaucracies, being human institutions, have occasionally been known to err, but that bureaucrat who-by recalling the two Prussian students who had dared to seek the instruction in Hesse-Darmstadt which they failed to get in their own State-raised the storm of indignation which found eloquent expression in the famous letters that roused Germany and Austria to a sense of what science could do for their material interests, has deserved a better fate than oblivion. T. E. THORPE.

DIPHTHERIA.

Diphtheria: its Natural History and Prevention. By R. Thorne Thorne, M.B., F.R.S., &c. (London: Macmillan and Co., 1891.)

THE

HE volume before us is a republication of the Milroy Lectures, delivered by Dr. Thorne Thorne before the Royal College of Physicians in London, 1891; and all must heartily congratulate the author on the ability with which he discusses a complex and vastly important subject, and at the same time must be grateful to him for having, by republication in a handsome form, made these lectures accessible to a larger public.

Diphtheria is an infectious disease which was known before the Christian era, and was fully recognized and well described by Bretonneau in 1821. In this country it has of late years undergone, both as to its diffusion and mortality, a remarkable increase. While in former years diphtheria was considered a purely "rural" disease, of late years its repeated occurrence in large towns has raised it to an urban" disease; so much so that, "while the metropolitan (death) rate (from diphtheria) for 1861– 70 was lower than that for the country generally, it exceeded it during the two next periods, and the rise which has taken place in the rate for 1881-89 is far in

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diphtheria, and certain non-diphtheritic forms of croup are not well distinguished, in the later returns the distinction is carefully carried out), nor can this increase, obviously, be due to any new condition as to soil, water, and air. Dr. Thorne passes in review, and illustrates by numerous examples, collected by the most competent sanitary officers and inspectors, and minutely described in the Reports of the Medical Officer of the Local Government Board, the various conditions that have been, or were suggested as having been, connected with the origin and spread of various diphtheria outbreaks in this country; and a careful perusal of the immense body of facts recorded in this volume must impress the reader, not only with the great caution with which Dr. Thorne draws his conclusions, but with the admirably impartial way in which he tells his story, and in which he pays due regard to every detail, be it for or against. The one fact which above all others stands out prominently, and which it behoves everyone connected with our present system of compulsory school attendance carefully to consider, is the unmistakable influence of "school attendance" on diphtheria. Not the fact that diphtheria spreads from a child affected with diphtheria to another child with which it is brought in contact, either at school or at play or otherwise-a fact only too well known and unfortunately often enough actually illustrated; but the fact that "school influence"-that is, an influence affecting children aggregated in a confined space-has an important bearing on the generation of true diphtheria. This "school influence' tends to foster, diffuse, and enhance the potency of diphtheria; and this, in part at least, by the aggregation of children suffering from that sore throat which commonly is prevalent antecedent to, and concurrently with, definite diphtheria" (p. 219). Dr. Thorne devotes a considerable portion of chapter iii. to the consideration and discussion of this important subject.

and brings forward evidence, collected by himself before and after 1878, and by a number of well-known health officers and co-workers (Mr. W. H. Power, Dr. David Page, Dr. Jacob, Dr. Bruce Low, and others), which conclusively proves and confirms Dr. Thorne's proposition, first enunciated by him in 1878. Over and over again has it been shown (chapter iii.) that, in schools frequented by children some of whom were affected with simple sore throat, outbreaks of true diphtheria have occurred, for the explanation of which no antecedent case of diphtheria, nor any of the generally assumed insanitary conditions, could be brought forward. It is on these grounds that Dr. Thorne justly insists on a continued and careful inspection of the throats of the children, and on immediate separation from school of any child affected with sore throat.

The part that milk plays in the dissemination of diphtheria is fully discussed, and illustrated by a number of epidemics that have been recorded in the Reports of the Medical Officer of the Local Government Board; and the important relation of diseases of the lower animals, particularly of cows and cats, is also described and illustrated by epidemics in chapter iv. Last, but not least, Dr. Thorne considers the question of prevention and isolation. By his office as Assistant Medical Officer of the Local Government Board, and from an experience extending over many years, he stands in the unique

position of the very best authority, whose conclusions and recommendations deserve carefully to be studied by managers and owners of schools, by hospital authorities, by sanitary officers and Boards of Health, by the owners of dairies, and by all those to whom the health of the community ought to be of paramount importance.

THE NEW YORK MATHEMATICAL SOCIETY.
Bulletin of the New York Mathematical Society, a
Historical and Critical Review of Mathematical
Science. Vol. I. No. 1, October 1891. (New York: for
the Society.)

WE

life insurance companies, and a number of other persons interested in higher mathematics. At present an extension of membership is in progress."

Then it goes on to say :

"The Society is about to undertake the publication of a periodical review of pure and applied mathematics. The idea is not to enter into any competition with the American Journal of Mathematics, the Annals of Mathematics, or any other similar journal, but it is proposed to publish, primarily, historical and critical articles, accounts of advances in different branches of mathematical science, and reviews of important new publications; also résumés of lectures before the Society, short contributions from members and correspondents, and general mathematical news and intelligence. periodical, if circulated extensively, will do much to incite an interest in mathematical studies, and to maintain the interest of those who, having pursued such studies, are now perhaps at a distance from others of like tastes and training. It will appeal to many that our mathematical journals do not reach."

Such a

We have allowed the Society to state its aims: these have been sanctioned by Profs. Newcomb, Woolsey Johnson, and Craig (associate editor of the American Journal of Mathematics). We wish the Society every success in their endeavour "to promote a long-needed spirit of active co-operation, and to establish a bond of "Octonary

union between American mathematicians."
The Bulletin contains an article on
Numeration," by Prof. Woolsey Johnson.
cluding paragraph is as follows:-

The con

"As there is no doubt that our ancestors originated the decimal system by counting on their fingers, we must, in view of the merits of the octonary system, feel profound regret that they should have perversely counted their thumbs, although Nature had differentiated them from the fingers sufficiently, she might have thought, to save the race from this error."

The rest of the number is taken up with reviews of several books, viz. "The Teaching of Elementary Geometry in German Schools" (review of Schotten's “Inhalt und Methode des planimetrischen Unterrichts," by Prof. Ziwet); Bertrand's "Calcul des Probabilités" (by Prof. Ellery Davis); Fine's "Number-System of Algebra" (by G. Eneström, of Stockholm); and notices of works on West African longitudes and South American longitudes (by the treasurer, H. Jacoby). There are several short notes and a translation of Picard's demonstration of

the general theorem upon the existence of integrals of ordinary differential equations (by the secretary, T. S. Fiske).

E have occasionally wondered that now the study of mathematics is so diligently and successfully prosecuted across the Stream, there was no Society to bring together all such persons as were willing "to encourage and maintain an active interest in mathematical science." The "Organization of the New York Mathematical Society" gives a list of 174 members, mostly Professors of Mathematics or Astronomy. The President is Mr. Emory McClintock, a Vice-President of the Actuarial Society of America, who is also a member of the London Mathematical Society, and a contributor of some excellent memoirs to the American Journal of Mathematics. The constitution embraces six articles, and there are ten by-laws. These are apparently founded upon the rules which have been drawn up for other similar Societies. The date of the pamphlet (ie. the "Organization, &c.," cited above) is June 1891. From a circular we gather that the Society has only recently Delagoa Bay: its Natives and Natural History. By inaugurated the present state of affairs, for this document

states :

"The New York Mathematical Society has consisted in the past of most of the professors and instructors of mathematics at the several Colleges situated in New York and the vicinity, the actuaries of a few of the larger

From this account it will be seen that there are no mathematical memoirs read before the Society in this part, but that such papers have been communicated we learn from the fact that three are printed in the current number of the American Journal of Mathematics, viz. one by C. Steinmetz (February 6, 1891), and two by the President (March 6, 1891).

OUR BOOK SHELF.

Rosa Monteiro. With Twenty Original Illustrations after the Author's Sketches and from the Natural Objects by A. B. and C. E. Woodward. (London: George Philip and Son, 1891.) BOTANISTS and zoologists alike will remember the services rendered to science by the late J. J. Monteiro,

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