1/10th scale.

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This Instrument has been designed to meet the requirements of Students and others who find the need of a Barometer which will give exact readings, and cost but a moderate sum.

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The construction is on that of the well-known" Fortin" principle. The level of the cistern mercury is reducible to zero, in exactly the same manner as in the more expensive forms.

The diameter of the mercurial column is 25 inch, and affords a bold, well-defined reading. The scales, by means of the double vernier, are capable of being read to or inch and 1 millimetre. It is mounted on a wellpolished, solid mahogany board, with plates for attachment to wall, opal glass reflectors for reading off, and screws for vertical adjustment.

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Price, complete, mounted as illustrated,

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or may be had with one scale (either inches or millimetres), and with thermometer on other scale, at same price.

NATURE says:-" Provides an accurate instrument at a moderate cost.'

FULL SIZE STANDARD BAROMETER of same design, bore o'5" diameter, inches and millimeter scales, verniers reading to o'oo2 inch and o'r m/m, on polished mahogany board with brackets and opal glass reflectors, £7 10 0

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THE MATHEMATICS OF NAVAL STRATEGY AND TACTICS.

Manuel Pratique de Cinematique navale et maritime. By Captain Leon Vidal. Pp. viii+171. (Paris: Gauthier-Villars, 1905.) Price 7.50 francs.

TH

HIS book was undertaken by the author in accordance with instructions from the Minister of Marine issued seven years ago. Captain Vidal was directed to collect in a single volume the numerous essays on mathematical naval tactics contributed by various authors, French and foreign, and scattered over many publications. Officers of the French Navy were asked officially to give all possible assistance to the compiler, and many of them have done so. The laborious task has been admirably performed, various problems dealt with have been classified, and those relating to similar subjects have been grouped in distinct chapters. Captain Vidal has drawn largely upon work done by other officers, and acknowledges the fact. He is an enthusiast on the subject and has supplemented theorems due to others by much original work, extending or completing his scheme. Solutions alone are given and detailed demonstrations are avoided, so that the volume is compressed within narrow limits in proportion to the range and variety of subjects dealt with. In order to facilitate the practical use of his book by naval officers, elaborate numerical tables have been calculated by which readers can construct diagrams representing particular cases that may require to be dealt with either during naval manœuvres or in warlike operations. Numerous illustrations are introduced, and the descriptions are brief and clear throughout. Captain Vidal had to examine and collate an enormous mass of material produced during the last thirty years, and it is not surprising, therefore, that he has been so long engaged on the book. French naval officers and professors have done most in this field, but foreign authorities have also been laid under contribution, and the volume will probably long remain the chief book of reference on its special subject.

The science of naval cinematics, says the author, "consists in the study of the movements of vessels considered ordinarily as moving points, but in many instances it also takes account of their length and gyration, as well as their powers." For the most part, in the strategical theorems dealt with it has been assumed that ships may be treated as particles, the influence of length and turning-power being neglected. Further, it is generally assumed that movements take place in a calm and tideless sea. tain corrections are suggested subsequently in order to make allowance for wind, wave, and current, but these sections are very brief, besides being incomplete in treatment, as is indeed unavoidable from the nature of the case. The turning-powers of steamships are but lightly touched, although they are most important in tactical manoeuvres either for single ships or squadrons.

Cer

It is well known that the mathematical training of French naval officers is more extensive than that given to officers in the Royal Navy, and Captain Vidal is exceptionally well equipped in this respect, even among French officers. The book is indeed mainly a collection of geometrical theorems, in two dimensions, bearing upon the movements of ships or squadrons performed under certain assumed conditions. Many of these theorems can have little practical value, but not a few have been made the basis of modern French naval manœuvres. The fundamental idea is that when the course of a ship departs from a straight line it may be assumed to follow a logarithmic spiral. Captain Vidal enumerates the principal properties of that curve, and gives tables for estimating the lengths of arcs and chords, the values of tangents at different points, and other useful items. He takes special cases for spirals described about a fixed point, or about a point in the rectilineal course of another moving body, so as to examine the relative positions, from instant to instant, of two vessels or two squadrons. Theorems attaching to the well-known "curves of search " employed by ships when scouting, or endeavouring to detect the position of an enemy who attempts either to arrive at or depart from some fixed point, are discussed at length. In another chapter theorems dealing with the movements of two vessels such as may take place in singleship actions are grouped and discussed fully. In a third chapter the most effective methods of concentration for scattered ships belonging to a fleet sent out for purposes of observation and scouting are dealt with. In another section the "lines of observation " to be patrolled by ships of a fleet, and the organisation required in order that an enemy cannot pass through the line without detection, are discussed. The influences of currents in rivers on the movements of vessels and the effect of wind and sea are also briefly investigated.

Captain Vidal writes fully as much as a mathematician as a naval officer. In his opinion the study of mathematics is both necessary and beneficial to all naval officers, whose duty he considers it to be to lay down conditions for programmes of ship-construction. Consequently he urges that officers should understand the work of the engineer and the trend of industrial progress if they are to give good advice and be the corps directeur of a modern fleet. Naval officers must, in his opinion, "make, in war, the synthesis of actual forces and guide them in producing the desired effects." To ensure success in this high mission the study of naval cinematics is essential, in Captain Vidal's judgment, since every advance in that science "enables one to foresee more clearly the results of movements of ships and to employ new combinations with intelligence." There is much force in this contention, but the class of work dealt with by Captain Vidal could be undertaken only by the élite of officers in the Royal Navy. His treatment would be over the heads of average naval men, and it is not likely to assist them in their daily work. The fact that the standard of mathematical attainment by average officers in our naval service is not so high

as in the French Navy may reduce the number of English readers of the book. But, happily, we possess many naval officers fully competent to take their place in scientific discussions of naval strategy and tactics. They will find much that is suggestive in Captain Vidal's book, and may be trusted to appreciate its investigations properly as well as to deduce therefrom rules for guidance, which will assist brother officers not so well instructed as themselves in the practical application of the theorems which Captain Vidal has collected. Shortly stated, the volume is better suited for the student than for the average naval officer, but it deserves a place in the professional libraries of all modern fleets.

W. H. WHITE.

THE CORRESPONDENCE OF HUYGENS. Euvres complètes de Christiaan Huygens. Publiées par la Société Hollandaise des Sciences. Tome dixième. Correspondance 1691-1695. Pp. 816. (Nijhoff: La Haye, 1905.)

THIS

HIS volume completes the publication of the scientific and miscellaneous letters of Huygens, the ten volumes comprising in all twenty-nine hundred letters and memoranda. There is, perhaps, not so much variety in the contents of the present volume as in those of previous ones, and the great majority of the letters of interest written during the last five years of Huygens's life have been published before, but they have now in many cases been further illustrated by the addition of rough notes from the books of adversaria of the author.

The correspondence with Leibnitz, which had been resumed in 1688 after a long interruption, went on regularly during the years 1691-5, dealing partly with pure mathematics, partly with the theory of universal gravitation. It shows that Huygens never became reconciled to the use of the differential calculus, but continued to prefer geometrical methods. In 1691 he acknowledges the utility of the calculus, and says that he has made some progress in it; yet in the very last letter to Leibnitz (of December 27, 1694) Huygens remarks that the new method ne me demeure pas présente à l'esprit quand j'ai discontinué longtemps à m'y exercer." But the numerous letters and notes on the quadrature of curves, especially of the folium of Descartes, exchanged between Marquis de l'Hospital and Huygens show that the latter's power of dealing with geometrical problems was as vigorous as ever. He also continued to correspond with Fatio de Duillier, whose letters foreshadow the accusation of plagiarism which he launched against Leibnitz in 1699, as he from 1691 repeatedly assured Huygens that Newton was the discoverer of the differential calculus, and that it would not be pleasant for Leibnitz if Newton's letters to him were published. Huygens, who continued to think the new calculus unnecessary, did not omit to tell Leibnitz that, according to Fatio, Newton knew more of the inverse problem of tangents than Fatio and Leibnitz did; to which Leibnitz quietly replied that everybody had his own ways of proceeding, and perhaps he

knew of some which Newton had not yet perceived. Fatio several times mentioned in his letters that he intended to publish a new edition of the "Principia," as Newton had declined to do it himself, and proposed to expand it into a folio volume, which he flattered himself would be more easily understood than Newton's quarto.

With Leibnitz, Huygens also exchanged ideas about the nature and cause of gravitation. In 1692 Leibnitz remarked that a vortex like that assumed by Descartes is necessary to explain why the earth's axis remains parallel to itself, while the fact that all planets and satellites move in the same direction also points to their being carried along by some fluid matter. He rejects the idea of Cassini, that the orbit of a planet is not an ellipse, but a Cassinian oval, since no physical reason had been given for this hypothesis. The spherical shape of a drop of water, the fall of a body to the earth, and the motion of the planets are all, according to Leibnitz, caused by the "materia ambiens." Huygens, on the other hand, thinks that the sphericity of a drop is more likely caused by the rapid motion of some matter which circulates inside, and as to the planets he fails to see why we should assume the existence of vortices when Newton had

proved that the law of inverse squares "with the centrifugal force" produces the ellipses of Kepler. He also makes other objections to the theory of Descartes, particularly to the small spheres of the second element which revolve round the accumulated first element (the sun), and are supposed to have been formed by the corners of the original matter being rubbed off; for if this matter offered any resistance to this rubbing, what should limit the resistance, and if there were none, what should prevent the total destruction of the particles? The vortex which should preserve the parallelism of the earth's axis is incompatible with the motion of the same matter in all directions which should produce gravitation; an objection to which Leibnitz could only reply that we have two such independent circulations here on the earth, causing gravity and magnetism. acknowledges that vortices are a convenient means Huygens of explaining the common direction of planetary motions, but the constant eccentricity of a planet and the variable velocity in the orbit cannot be accounted for by the theory.

In this connection it is most interesting to read some notes written by Huygens to the well known "Vie de Monsieur Descartes," published anonymously by A. Baillet in 1691. According to Huygens, Descartes was very successful in getting his conjectures and fictions accepted as truth. just as novels may be taken for real history; but, on the other hand, he dealt with tangible things, and not with mere words as earlier philosophers had done. Bacon did not understand mathematics and was wanting in penetration as regards physics, being unable even to conceive the possibility of the earth's motion, which he mocked as an absurdity. Galileo had enough of mental power and mathematical knowledge to make progress in physical science, and he was the first to make discoveries as to the nature of motion, although

he left very much to be done. He did not pretend to explain the cause of all natural phenomena, nor had he the vanity to want to be the head of a sect; he was too modest and too great a lover of truth for that. But Descartes wanted to pass for the author of a new philosophy which could take the place of the Aristotelian, and he stuck to what he had once proposed though it was often very wrong. He has done a good deal of harm to the progress of philosophy, for those who believe in him imagine that they know the cause of everything; they waste time in sustaining the doctrines of their master, and do not work to penetrate the real reasons of the great number of phenomena as to which Descartes has only propounded idle fancies. A severe judgment, but not an undeserved one as regards the tenacity with which the followers of the Cartesian philosophy clung to the vortex theory, though it hardly accounted for any of the phenomena of planetary motion.

Probably owing to the infirmities of old age, Huygens during the period covered by this volume did not do any astronomical work, though he wrote to his brother Constantyn in 1693 that he had got a tube made for a 45-feet object glass, chiefly to show the moon and planets to persons of quality who could not manage a tubeless telescope, which was pointed to an object by cords. His interest in the use of pendulum clocks at sea was unabated, and there are several short letters on this subject. As the results of repeated trials were not favourable, Huygens endeavoured to find other means of realising isochronic motion, not subject to disturbance from the rolling of a ship, and designed several forms of balance of which a full account is to appear among his hitherto unpublished works.

The

There are fewer allusions to current political and other events in this volume than in the previous ones, but naturally the anti-Copernican action of the University of Louvain in 1691 is not passed over. faculty of arts suspended Prof. van Welden for three years for asserting that the earth was one of the planets. He wrote to Huygens to beg for the intercession of Constantyn Huygens or of King William, but they do not appear to have done anything for him. During the last years of his life, Huygens wrote his well known little book "Cosmotheoros," which was not published until 1698, three years after the death of its author. J. L. E. D.

sidered independently of the various affections in which they are encountered. The second portion is devoted to the study of the individual psychoses.

The volume is rather unevenly divided; some subjects are fully dealt with, but the description of others is somewhat meagre. The chapter on ætiology is very good, and this important problem is thoroughly reviewed. We cannot agree with the author in his conclusion that heart disease is common in the insane, and Strecker's figures as to the prevalency of this malady in German asylums, viz. 61.7 per cent for men and 42.7 per cent. for women, would not coincide with similar statistics obtained from English asylums.

In the chapter on general symptomatology the subject of hallucinations and their causation is briefly but well described. Throughout the volume it is very noticeable that purely psychological matters are dealt with in greater detail than other subjects of equal, if not of greater, interest to the practical physician. For example, the pages on treatment are undoubtedly the weakest in the book. Very little space is devoted to this important subject, and the reader is left very much in the dark as to the management of cases of mental disorder.

The author has evidently had the usual difficulty in finding a good classification of insanity. He states that in the absence of one that is founded upon a pathological anatomy basis he has chosen "the most practical, the most convenient, and the one which in nosis and institute the treatment." We quite agree any given case would enable us to establish the progthat he has made the best choice in selecting Kraepelin's classification as the basis for his own scheme.

The first chapter in the second part is reserved for the consideration of the "infectious psychoses," of which the following are briefly reviewed :-febrile delirium, infectious delirium, and hydrophobia.

Under the heading of "Psychoses of Exhaustion," the author describes conditions of primary mental confusion and acute delirium. Toxic psychoses are divided into two divisions, (a) acute, (b) chronic, morphinomania and cocainomania being included in the second class. Dr. de Fursac recommends that, when possible, the rapid method of withdrawal of morphia should be employed in the treatment of morphinism, as he prefers this to the sudden and gradual methods sometimes employed.

The "autointoxication psychoses" include uræmia, the polyneuritic psychosis or Korsakoff's disease, dementia præcox, and general paresis. After thoroughly considering the relationship of syphilis to general paresis, the author states that "at the present time we have no conclusive evidence either for or against the syphilitic origin of general paresis."

66

The next chapters are devoted to the description of "psychoses dependent upon so-called organic cerebral affections," and psychoses of involution." The latter include "affective melancholia" and "senile dementia." We do not like the term "affective melancholia"; it seems redundant, for clearly all forms of depression must be affective. Further, the author uses the term in a new sense, which causes

confusion. The chapter on senile dementia is distinctly good and very instructive.

a

well-determined

Under "psychoses without etiology, which are apparently based upon a morbid predisposition," are found manic-depressive insanity, paranoia, and constitutional psychopathic conditions, such as mental instability, sexual perversions and inversions and obsessions. Paranoia is very briefly described under the title of "Reasoning Insanity." We strongly disagree with the author in his use of this term; it is by no means a good one, and is, in addition, confusing, since other writers have used it as designating the maniacal stage of manic-depressive insanity.

Epilepsy and hysteria are described under the heading of "Psychoses Based on Neuroses," and the concluding chapter is devoted to the consideration of the arrest of mental development.

The book is well translated, and the index is carefully compiled. This manual undoubtedly has its merits, but, as we have already stated, it will scarcely appeal to the practitioner, as the description of treatment is somewhat meagre, and the student will find the subject-matter almost too condensed. In any future edition the author will do well to correct these defects, for by so doing he will render his book a useful manual on psychiatry.

OUR BOOK SHELF.

Experiments with Plants. By Dr. W. J. V. Osterhout. Pp. x+492; illustrated. (New York: The Macmillan Company; London: Macmillan and Co., Ltd., 1905.) Price 5s. net.

THE author defines his aims in the following words (p. 7):-" The numerous questions which young people ask about plants are best answered by themselves. . . . To put them in the way of doing this so far as possible is the object of this book." In accordance with this plan, the apparatus used is of a rough and home-made description, constructed of fruit jars, lamp chimneys, clothes' pegs, india-rubber bands, and sealing-wax. Much ingenuity is shown in the design of apparatus so put together. Whether a sufficient degree of stability is always obtainable may perhaps be questioned, but from the author's point of view the advantages of his method certainly outweigh any such shortcomings. One great merit in the book is the insistence on the necessity of control experiments, which are especially needful with rough methods. The book is divided into chapters headed "The Work of Roots "-of leaves, of stems, &c.ending up with a chapter on Making New Kinds of Plants," which is a statement of what breeders and experimenters on variability have done rather than instructions for the making of such experiments.

The author very properly recommends common plants for use; but why students of botany should be confined to such names as "Kentucky Coffee Tree," "Dusty Miller," Live Forever," "Switch Plant," it is difficult to say. Occasionally we find the scientific name, and in this way we learn that a "Wandering Jew" is a Tradescantia.

Most of the experiments are clearly described, but we have been puzzled over some of them. For instance (p. 191), the method of answering the question, "Does the leaf decompose carbon dioxide?" seems to us to involve passing a lighted candle under

water into a jar of air. Here and elsewhere in the book the author neglects simple and striking methods. It is important that the student should be convinced that oxygen is given off by green leaves in light. The above-mentioned experiment is not satisfactory, whereas Engelmann's blood method is both simple and convincing. Again, the well-known plan of counting the bubbles given off by submerged plants in light, though not free from errors, gives useful comparative data for the study of assimilation. In the same way we think that more fundamental experiments should have been given under the heading of "Stomata." Stahl's cobalt method, which is merely mentioned in a note, can be used by the most elementary of students to demonstrate important facts.

In spite of some faults, the book will be found of value to anyone compelled to give a course of physiological botany under conditions which preclude the use of ordinary laboratory fittings.

Conversations on Chemistry. Part i. General Chemistry. By W. Ostwald. Authorised translation by Elizabeth Catherine Ramsay. Pp. v+250. (New York: John Wiley and Sons; London: Chapman and Hall, Ltd., 1905.) Price 6s. 6d. net. THE German original of this book has already received sympathetic notice in NATURE, and in connection with the translation now before us it is necessary to add little more than that Miss Ramsay has done her work with much skill, and has made the dialogue not less natural and vivacious than it is in the original. It is impossible to read the book without a feeling of refreshment and amusement, or without admiration of the ingenuity and resource of its philosophical author. It seems hardly fair to say that we have here a revival of Dr. Brewer or Mrs. Marcet. There are two striking differences between the old and the new dialogues. In the first place neither master nor pupil in Prof. Ostwald's book is endowed with that austere and depressing piety of mind which, to the unregenerate, provided perhaps the most afflicting feature of the older works. In the second place Prof. Ostwald's book shows a masterly treatment not only of the real difficulties of chemistry in itself, but a perfect appreciation of the pitfalls that beset the pupil in the early stages of learning. It is difficult to suppose that any teacher will fail to find something useful or to gain some valuable hints from reading the book, and on this ground it must be warmly recommended.

It would, however, be a misfortune if a teacher constrained his teaching to the exact course of the dialogue, and, of course, it would be worse still if he set so many pages as a lesson to be learned by the pupil. The real usefulness of the book will probably lie in the example it affords of the life that may be imparted to teaching when, on the one hand, the pupil is allowed a fair chance of thinking out things for himself and a full opportunity of frankly saying what he thinks, and when, on the other hand, the teacher takes the part of a guide, philosopher, and friend who has a soul above dictionaries and examination papers. A. S.

Mathematical Recreations and Essays. By W. W. Rouse Ball. Fourth edition. Pp. xvi+402. (London: Macmillan and Co., Ltd., 1905.) Price 75. net.

THIS edition differs from the third by containing chapters on the history of the mathematical tripos at Cambridge, Mersenne's numbers, and cryptography and ciphers, besides descriptions of some mathematical recreations previously omitted. The book has thus become more miscellaneous in character, but the additions fit in very well, and are all entertaining. Mr. Ball writes with enjoyment of his subject, and