THURSDAY, NOVEMBER 18, 1897.

THE MATHEMATICS USED IN CONNECTION WITH PHYSICS.

The Theory of Electricity and Magnetism; being Lectures on Mathematical Physics. By A. G. Webster, Assistant Professor of Physics, Clark University, Webster, Massachusetts. Pp. xii + 571. (London: Macmillan and Co., Ltd., 1897.)

THE

HE aim of the writer, according to the preface, in the preparation of this volume has been to present to the students the results of the Maxwellian theory as it stands at present, after the labours of Faraday, Maxwell, Helmholtz, Hertz, and Heaviside.

Prof. Webster is a somewhat young man of marked promise, whose contributions to the discussions in Section A of the British Association formed one of the features of the meeting of that section at Toronto this year, and the book shows that he is fully capable of appreciating the mathematical significance of physical facts. It is doubtful, however, whether a student would be able to appreciate the physical significance of the mathematical theory from reading it. Possibly the students of the Clark University, when listening to such lectures as are given in this treatise, have the physical meanings of the various mathematical processes explained to them. If not, they must possess an exceptional amount of ability to enable them to arrive at correct physical interpretations of the mathematical equations.

The first fifty-two pages of the book are occupied with a short summary of the principles of the vector calculus, the definitions of variables, functions, differential coefficients, definite integrals, line and surface integrals, something about the calculus of variations, &c. It is not quite obvious what is the object of giving this, since a student who was capable of following the book would understand the meaning of a differential coefficient before opening it; or if, on the other hand, he was ignorant of the differential and integral calculus, he would require far more detailed information than is given in these fifty-two pages before he could tackle triple integrals, vector differential operators, &c., which are used quite early in the book.

Is it correct to say that, "following the usage of the majority of writers, we shall denote

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brings us to p. 91, discusses the theory of functions of a complex variable with clearness and conciseness; and this section might with advantage have been extended, and some of the earlier portion of the book omitted.

Part i., which commences on p. 91, is on the "Theory of Newtonian Forces"; but forces as realities, and not merely letters which satisfy a number of equations, have not much existence in the chapter. Take, for example, d'Alembert's principle described on p. 107 This principle is in reality the result of an argument based on Newton's laws, and leads to a valuable set of equations in dynamics. The reader, however, is not told this, bat only that the analytical statement of d'Alembert's principle is given in Lagrange's equation of virtual velocities. This equation, Mr. Webster rightly states, involves all the internal forces, and so the student might not suspect that the essence of d'Alembert's principle was the elimination of these internal forces.

The rest of the Part i. is good, the subject of attractions being well and lucidly treated. Does not, however, the introduction of the n axes of the harmonic of the nth degree add unnecessary difficulty, and somewhat hide the beauty of harmonic analyses? For students who already possess a good knowledge of magnetism, the treatment of polarised distributions will be useful. Although the title of this book, as given on the cover, is "Electricity and Magnetism," it is not until p. 243, or nearly the middle of the book, that we come to the portion that deals specially with electricity. The statement of the general problem of electrostatics, as given at the beginning of $ 135, is insufficient since, as pointed out, any number of solutions could be given to it. The method, however, which is indicated for the solution of the problem is correct, and leads in a neat way to the conception of coefficients of induction from which the coefficients of potential are deduced.

§ 151, on Green's function, like much of the matter in the book, is divorced from its physical application, so that a student will hardly see the physical nature of the problem that Green set himself to solve, or the method by which he solved it. In fact, the author criticises Green's work as follows:-

"Reasoning depending on such physical facts was frequently made use of by Green, and while not legitimate for purposes of mathematical demonstration, is frequently of service to the physicist."

The discussion, however, of the application of conjugate functions is good.

It is not the custom in this country to call the conductor of a Wheatstone's bridge, in which the galvanometer is

this practice is followed in America either.

On page 357 the author defines μ as the inductivity of the medium, and explains that this becomes specific inductive capacity in the electric case, and permeability in the magnetic. This analogy is, of course, quite correct, but it is carried too far when the same letter μ is used for specific inductive capacity on some pages and for magnetic permeability on others. In considering the dimensions of the electrostatic and electromagnetic systems of units, the propagation of waves, &c., the beginner

might expect to find instead of which he finds μ; the meaning, however, of this does not seem to be given, and he is left to discover for himself that this stands for the specific inductive capacity for which μ has been previously employed.

We should prefer to say that the absolute dimensions of specific inductive capacity and of permeability were yet unknown rather than they were "arbitrary," and we do not agree with the statement that attempts to settle their absolute dimensions are evidently based upon misconceptions of the theory of dimensions.

on Mathematical Physics" may fitly contain explanations of the physical interpretations of the equations developed without running the risk of appearing to pander to the needs of the electrical contractor. W. E. A.

THE ELECTRICAL PHENOMENA OF NERVE. Lectures on Physiology. (First Series.) On Animal Electricity. By A. D. Waller, F.R.S., &c. Pp. viii +144. (London: Longmans, 1897.)

μ

The last chapter in Part ii., on the conduction in dielectrics, contains some interesting work, such as that on the effect of heterogeneity.

Part iii. deals with the electromagnetic field in a lucid and satisfactory manner. We feel somewhat divided in our judgment regarding Mr. Webster's inability to respond to Boltzmann's appeal that Maxwell's notation should be followed. It will undoubtedly be somewhat perplexing for the student to have to employ X, Y, Z for the components of electric field intensity when he reads this book, and for the components of a mechanical force when he is studying Maxwell's classical treatise. But Mr. Webster is an American, and the secret of the success of his countrymen lies in their having gone ahead instead of merely following precedent. Hence, whatever may be the wrench we feel at being torn away from our timehonoured notation, we must respect Mr. Webster's independence in employing what he considers a better one.

The book finishes with an excellent introduction to the theory of electromagnetic waves, which deals with the more important points of this subject in a clear and concise manner. The statement made on page 550, that the matter on the preceding seventeen pages applies only to a submarine cable of infinite length, should have come much earlier; for, on reading these pages, we certainly thought that the author was under the mistake of imagining that the treatment applied equally well to a finite cable.

On page 536 the author pokes fun at established authority by giving more than one reason why longdistance telephony has not existed in England, and on page 547 he sits in judgment on Mr. Heaviside in an equally humorous way, although in this case the fun is not intentional on the part of the author.

The book is on the whole distinctly good, and any one who has mastered it will possess a sound acquaintance with the most important parts of mathematical electricity. The absence of reference to experimental methods is, as stated in the preface, intentional, and, of course, no practical applications of electricity are referred to. But, even if this system has been followed as a protest against those who forget that the practice of to-day was the theory of yesterday, we would suggest that a course of "Lectures

published a series of lectures on the electrical properties of nerve, in which he tells us that his aim has been to give "an exposition of the principal data" relating to the subject. Such of these data as have been derived from his own experiments have been already made known by him in his published papers; but the physiological reader will find it much easier to appreciate their value, now that they are placed before him in connection with facts already known to him. A point of great scientific interest in Dr. Waller's work consists in the circumstance that he has adopted and strictly adhered to a uniform method of "testing" the physiological conditions of a nerve. The gratitude of the reader is further excited by the perspicuity with which the method itself and the first fruits of its application are described, as well as by a vividness of style which makes him feel as if he had been present at the demonstrations.

Dr. Waller's object is to prove that the phenomenon by which a separated nerve most strikingly shows its vitality-the negative variation of du Bo is Reymond— is also a measure and criterion of the physiological condition of the nerve. For this purpose he employs an automatic arrangement by which at regular intervals of a minute, the appropriate "stimulus" for producing this effect is applied to the nerve, at the same time that the electrical "response" made by the nerve is recorded photographically. The effect thus recorded-the negative variation just mentioned-is the diminution of the socalled nerve current, the amount of which diminution is indicated by the deflections of a galvanometer connected with the nerve in the usual way. Consequently, so long as the strength and duration of the stimulus (a succession of induction currents led through the nerve at a distance from the part under observation) remains constant, the perfect uniformity of the periodical deflection indicates that the state of the nerve is unaltered; and the effect of any other condition, as, e.g. acid or alkaline reaction, change of temperature, &c., manifests itself by augmenting or reducing the deflection. As evidence that the deflection itself is a "vital" one, that is, one belonging to the living nerve as such, it is shown that the transient loss of function which follows the action of the vapour of ether is accompanied by an equally transient disappearance of the normal electrical reaction of the nerve, and again, that the presence of carbon dioxide in the saturated atmosphere in which the nerve is placed for observation, even in the smallest quantity, augments in an equally remarkable way the power of the nerve to respond to stimulation.

In the third lecture Dr. Waller sets forth further interesting facts relating to the mode of action of carbonic acid gas, and compares it with the effects of repeated stimulation, drawing certain inferences as to the agency of this body in producing fatigue, which it would be out of place to criticise here.

The fifth and sixth lectures are devoted to the elucidation of certain changes in the electromotive properties of living nerve, to which half a century ago du Bois-Reymond applied the term electrotonus. Using the method of observing and recording the responses to periodical automatic stimulations already referred to, Dr. Waller demonstrates du Bois' extrapolar electrotonic currents in

way than before by Dr. Waller's excellent forms of experiment, his lucid description, and the admirable diagrams which make those descriptions easy to follow. J. B. S.

NOTES OF A NATURALIST AND

ANTIQUARY.

Memories of the Months; being pages from the Notebook of a Field Naturalist and Antiquary, to wit, Sir Herbert Maxwell, Bart., M.P. Crown 8vo. Pp. xii + 300. (London: Edward Arnold, 1897.)

correspondence with phenomena of the same kind observed in "core models" (ie. cylindrical conductors of which the cores are metallic, the sheaths soaked with solutions of electrolytes), and finally proves, as before, with the aid of ether vapour, that although these phenomena resemble those of physical polarisation so closely, they are, notwithstanding, dependent on a vital activity which the nerve loses and recovers again when for a few minutes put to sleep by the anaesthetic. In the last lecture Dr. Waller goes into the rather more recondite phenomena of "polarisation increment and decrement." His mode of exposition of this subject is so original that one begins to fear that he is about to demolish the interpretation of these phenomena which has been given by his distinguished predecessors in this field of investigation. Happily it is not so. When the time comes for explaining, the instructed reader is gratified to find that although the terms employed are peculiar and unusual, there is nothing abnormal about the doctrine. "Active tissue is zincative, resting tissue is zincable." Consequently in a living nerve through a certain bit of which a battery current is flowing, the anode is more zincable than the kathode; for the living substance of the nerve is at rest at the anode, awake at the kathode. But what does zincable mean? It is a word

which Dr. Waller proposes to introduce into scientific terminology because he cannot find an English equivalent for the German "leistungsfähig." Regarding the "Leistung" of a nerve to be chiefly electrical, its "Leistungsfähigkeit" is its capability of being aroused to electromotive action" (p. 83)—a property which he emphatically distinguishes from "excitability," rightly holding that this word ought only to be used to denote the facility with which a response is evoked.

Dr. Waller's explanation of the increment and decrement is that the diminished excitability which is the well-known effect of the anode during the flow of a voltaic current along a nerve, is necessarily associated with what he calls increased zincability. Hence if the nerve passes from the electrotonic into the excited state, those parts which are most zincable are most susceptible of excitatory change. The point which is thus enforced - that is, the association of increased capability with diminished promptitude to reaction-is a fundamental one in the physiology of all excitable tissues. There can be no doubt that in relation to the phenomena now in question, it has been brought out in a more striking

pleasure have their reaction. An increasing number of people are turning with interest to the study of natural history, and are willing to learn from those who can write about it. This is a hopeful sign to those who believe that the social health and physical standard of the nation depend in large measure on affection for country life, and that it would be an evil thing should field and flood cease to afford attractions for active minds. As Sir Herbert Maxwell truly remarks, no head is constructed to carry about an explanation of half the things noticed in the course of a single morning's walk ; but if notes are made at the moment of what attracts the eye, be it a landscape, a ruin, a battle-field, a flower, bird, or insect, recourse may be had at home to the information abundantly stored in books, and the significance of what seemed commonplace or trivial becomes evident at once. Without attempting to become a specialist himself, every one has at command the accumulated fruits of the labours of specialists.

Acting upon this conviction, it would appear that Sir Herbert Maxwell has long been in the habit of making wayside notes on a variety of subjects, and from time to time has amplified and published them for the benefit of others.

His method of presenting them to the reader is not very new, as will be perceived by those who are acquainted with the Rev. Robert Willmott's "Summer Time in the Country," Mr. Oswald Crawfurd's "Round the Calendar in Portugal," Prof. Miall's "Round the Year," and other books of a similar nature; and it might, perhaps, have been better to have arranged his miscellaneous and fragmentary notes under zoological, botanical, and antiquarian headings, instead of grouping them, as he has done, under the headings of the months to which more often than not they have no particular relation. This plan would have been more convenient to specialists as affording them the opportunity of at once finding all that relates to their own subject, instead of having to search for scattered notes through three hundred pages.

No one, however, who dips into this little volume will begrudge the time bestowed upon it, for whether he be in search of particular information on a given subject or not, he will perforce linger upon many a page wherein he will find both amusement and instruction.

What more amusing, for example, than the author's account (pp. 259-266), of the attempts made to decipher the inscription on the celebrated Ruthwell Cross, variously interpreted-and by experts too-as Runic

Old Norse, and Anglo-Saxon; or his explanation (p. 184) of the reason for keeping cattle in herds.

For instruction we may turn to such chapters as those on the "Revival of a primitive fauna," on "West coast meteorology," or on "Assisted vision." Some of the pleasantest reading is to be found in the pages which give the results of the author's out-of door observation. Here, for example, is a note on the enmity between bees and butterflies :

"All kinds of stonecrop possess peculiar attractions for bees and butterflies owing to their abundant secretion of honey. One of the tall growing kinds, Sedum spectabile, is by far the handsomest. It is the latest to flower, and its great, flat, rosy corymbs are irresistible to that splendid autumn butterfly, the Red Admiral. . . I have been watching a number of these robust insects busy on the large stonecrop-so busy as to allow me to use a lens on them. There were no less than sixteen Admirals at work on one group of Spectabile stonecrop. The honey bees, however, interfered with them, and it was curious to see how shrewdly a Red Admiral would sheer off at the approach of a bee of less than one-tenth of his own bulk. Now, how do butterflies learn to dread a bee? How do they know that bees are armed? It can hardly be by experience, for no butterfly could survive the stab of a bee's sting. It is part of the mystery enveloping the intelligence of animals not personally educated by their parents. . . . The phases of insect life-the egg abandoned by the parent, the stages of larva, pupa, and imago-seem specially calculated to interfere with hereditary knowledge, and to prohibit the communication of instruction. . . . This avoidance of bees by butterflies seems to be an instance of pure instinct.”

On another page, in the course of some remarks on the choice of food by animals, the author alludes to the fact that some creatures will thrive upon plants which to others are poisonous, and instances the case of the Spurge Hawk Moth (Deiliphila euphorbia), of which the caterpillar feeds exclusively on the Sea Spurge, although this plant secretes an acrid juice “so painfully poisonous that it is difficult to imagine a digestive apparatus competent to deal with it." He might have mentioned the still more curious case of the caterpillar of another moth, Deiopeia pulchella, which feeds on the virulent poison contained in the seed of the Esere or "Ordeal Bean" of Old Calabar (Physostigma venenosum), and is unaffected by it (cf. Dr. T. R. Fraser, Ann. Mag. Nat. Hist., May 1864).

We should like to know the authority for the statement (p. 141) that in the lines from the Midsummer

66

Night's Dream" (So doth the woodbine the sweet honeysuckle gently entwist), Woodbine means the Bittersweet or Deadly Nightshade. This interpretation appears to have the sanction of Dr. Prior in his Popular Names of British Plants," but is opposed to the view of Canon Ellacombe, who has made a special study of the "Plantlore of Shakespeare."

We have noted other passages on which criticism might be offered did space permit; but enough has perhaps been said to indicate the scope of the volume. While too much in the nature of a scrap-book to entitle it to praise as a literary effort, it has the merit of being distinctly entertaining, and of conveying in a light, pleasant style a variety of information on subjects of more or less interest.

OUR BOOK SHELF.

By

Notes on Micro-organisms Pathogenic to Man. Surgeon-Captain B. H. S. Leumann, Indian Medical Service. Pp. 96. (London: Longmans, Green, and Co., 1897.)

THIS Compact and well-written little volume does not make any pretensions to be a text-book in the ordinary sense of the word, and we should be sorry if the "students and practitioners" for whom it is intended should in their turn make any pretensions to a knowledge of the subject after its perusal. Indeed, students and practitioners "who have no opportunity of working at the subject themselves, or time to read a larger book," had better remember the old adage, a little learning is a dangerous thing. Bacteriology, unfortunately, suffers at the present time from the idea that it is essentially a popular science-that it is a subject well within the comprehension and well within the grasp of any one who chooses to hold out his hand for it. Thus we too frequently find it taken up by totally unqualified persons, and the results of their recondite researches serve to bring the whole domain of microbes into disrepute. We do not quarrel with Surgeon-Captain Leumann's little book, for it is clearly and concisely written, and makes every endeavour to be accurate and up to date; and of particular interest is the local colouring, if we may use such an expression, which characterises it in dealing with the most recent work in India on plague and cholera. We have no desire to depreciate these notes, but we do regret that the author encourages the practice of reading about bacteria instead of working at them in a class of professional men who ought certainly to be able to do something more substantial than talk about them. Bacteriology to be of any value must be studied in the laboratory; and without a practical acquaintance with micro-organisms, the latest and most exhaustive manual "made in Germany" will fail to do more than acquaint the reader with the superficial phraseology of the subject.

The Winter Meteorology of Egypt and its Influence on Disease. By H. E. Leigh Canney, M.D. (Lond.), &c. Pp. 72. (London: Ballière, Tindall, and Cox, 1897.) To people who, for health's sake, pass the winter in Egypt, and to practitioners who wish to know the climatic conditions of the various health resorts of the country, this book will be an invaluable possession. The volume comprises a paper read before the Royal Meteorological Society last December, and one read before the recent International Congress of Medicine at Moscow. The first of these papers contains the results of a series of meteorological observations made under precisely comparable conditions during three or four winters in Egypt. The stations at which observations were made were Cairo, Mena Honse, Helouan, Luxor, Assouan, Valley of the Tomb of the Kings, and the crest of the Libyan Hills. As self-recording thermometers and hair-hygrometers were used at each station, valuable data were obtained on the diurnal variation of temperature and humidity. It appears from the discussion of the observations that the climate of Egypt is influenced by the Libyan or Western Desert, the Mediterranean Sea, and the extent of cultivated land.

The second part of the treatise provides the medical profession with a valuable guide to the therapeutic influences of the climates of different health stations in Egypt. Practitioners who have not been able to visit the country will find this section most serviceable.

Appended to the volume are several clear and instructive diagrams showing, for the six months from November 1895 to April 1896, the temperature and relative humidity at various hours of the day at Helouan, Mena Honse,

Luxor, and Assouan; the drying power of the air at the temperature of the air; and the drying power of the air at the temperature of the body.

Les Fours Électriques et leurs Applications. Bv Ad. Minet. Pp. 178. (Paris: Gauthier-Villars et Fils; Masson et Cie.).

ALL thermo-electric effects in which electricity is the prime agent are regarded by the author as coming within the scope of the title of this book, the grounds being that all forms of apparatus for converting electrical energy into heat, come under the generic head of fours électriques. The book thus includes not only descriptions of electric furnaces in which temperatures approaching four thousand degrees are reached, but also of simple conductors and resistance coils raised a few degrees above the temperature of the atmosphere by the electric current. The first part of the volume is devoted to an account of the heating effects of electricity; it includes descriptions of the heat produced by a current passing through a metallic resistance, the maximum temperatures of conductors, and electric heating generally. The remaining three parts deal with the electric arc and arc carbons of various forms, electric furnaces and their applications, and carbide of calcium and acetylene. It will thus be seen that portions of the book are not exactly pertinent to the title, nevertheless they assist the reader to a clear understanding of electro-thermal phenomena. The section on electric furnaces is a concise account of the various forms of furnace devised for different purposes.

The book belongs to the Encyclopédie scientifique des Aide-Mémoire series edited by M. Léauté. Bibliography of X-Ray Literature and Research (18961897); being a Ready Reference Index to the Literature on the Subject of Röntgen or X-Rays. Edited by Charles E. S. Phillips. With an Historical Retrospect, and a chapter of "Practical Hints." Pp. xxxvii + 68. (London: The Electrician Printing and Publishing Co., Ltd.)

THE work before us gives, in a handy and succinct form, a good deal of information respecting the literature of X-rays. The subject proper of the volume is prefaced by a brief historical retrospect, in which, however, the average worker in physics will find little but what is already known to him, and a short chapter of practical hints intended to appeal more especially to physical students about to turn their attention to high vacua research." The main and most valuable portion of the book is the bibliography, and this should certainly prove of utility to investigators in this branch of science. The volume, so far as we have been able to test it, appears to have been compiled with great care, and certainly a mass of useful knowledge is here gathered together in a form easy of reference.

Die Meteoriten in Sammlungen und ihre Literatur, nebst einem Versuch den Tauschwert der Meteoriten zu bestimmen. Von Dr. E. A. Wülfing. Pp. xlvi + 460. (Tübingen: Laupp, 1897.)

THE author has sought information relative to the meteorite collections, public and private, from those in charge of them, and has collated and indexed the results in the form of an alphabetical list, giving for each preserved meteorite a statement of the date of fall or find, a list of the more important memoirs relating thereto, and the weights preserved in the various collections. The work has been carefully done, and will be very useful to collectors of these extra-terrestrial bodies. As regards the pecuniary values to be assigned to the meteorites, we are afraid that the dealers will eschew all such mathematical calculations as are suggested by the author, and will in each case get, as heretofore, what they can.

LETTERS TO THE EDITOR

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

Rediscovery of the Tile-fish ("Lopholatilus ").

I AM indebted to Dr. John Murray for drawing my attention to an error in the address which I had the honour of delivering before the Linnean Society on May 24. In referring to the discovery and subsequent remarkable disappearance of the Tilefish (Lopholatilus chameleonticeps), I stated that since the year in which the extraordinary mortality in this species had been observed (1882), “no specimen of the fish has ever been found." I must take an early opportunity of correcting this error, which I might have easily avoided by reading more carefully the concluding paragraphs of Goode and Beane's account of the Tile-fish in "Oceanic Ichthyology,” p. 288, from which I may be allowed to quote as follows: In the fall of 1892, Colonel Marshall McDonald, the Com.

missioner of Fisheries, made another attempt to discover the fish, and was successful, obtaining it from the following stations [five stations are enumerated, on which eight specimens were caught]. The Tile-fish then is restored to the list of existing species of our North Atlantic coast, and it is probable that in time it may attain to its former abundance. The temperature. investigations made by Colonel McDonald have been carefully discussed by him, and he is convinced that the destruction of Lopholatilus was due. entirely to climatic causes."

What these climatic causes are we learn from a report by Prof. William Libbey, jun.. published in the U.S. Fish Commission Report for 1893 (Washington, 1895, 8vo), p. 32; they consist in a variation of the relations of the Gulf Stream to the Labrador current, affecting the temperature of a certain area inhabited by the fish. A lowering of the temperature by the latter current is believed to have caused the sudden mortality, allow the fish to gradually reoccupy the depopulated area. whilst a subsequent invasion of warm Gulf Stream water would

Kew Gardens, November 14.

A. GÜNTHER.

The Exploration of the Air by Means of Kites. THE highest kite ascent, described in NATURE of October 7, was in turn exceeded here by more than 1800 feet on October 15, when excellent meteorological traces (of which a facsimile is enclosed) were brought down from a height of 11,086 feet above Blue Hill. The flight was effected with only four kites, and the ascent and descent occupied but four and a half hours. of elevation, the results agree with those already stated for the Excepting a more rapid decrease of temperature with increase previous high flight.

. I now desire to call attention to the fact that the deductions from our automatic records obtained with kites seem to confirm, in general, the conclusions reached by Messrs. Welsh and Glaisher from their observations in free balloons many years ago in England. For example, we find also that the most rapid decrease of temperature with height occurs usually in the lower mile of air during the daytime, and, even with no visible clouds that damp strata often exist in the dry air of the upper regions. A discussion by Mr. Clayton of more than one hundred meteorological records, obtained with kites since 1894, is now in the press, and will form an appendix to Part i. vol. xlii. of the Annals of the Astronomical Observatory of Harvard College.

A curious illustration of how identical methods sometimes may serve diametrically opposed investigations, is the application of the deep-sea sounding apparatus of Sir William Thomson (now Lord Kelvin) to bring down these aerial soundings. A. LAWRENCE ROTCH. Blue Hill Meteorological Observatory, November 1.

Lord Rayleigh's Proof of Van 't Hoff's Osmotic Theorem.

IN what follows I shall understand by "Van 't Hoff's Osmotic Theorem," the statement, that if P, V be the osmotic pressure and volume of unit mass of a solute, and p, v the gas-pressure and volume of the same mass of the same substance supposed gaseous at the same temperature, then pv = PV.