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great floods of the Seine; and thirty-one tables are appended at the end of the volume, giving the rainfall, discharges, and water-levels at different dates in various parts of the Seine basin, and eleven sets of graphic curves indicating the decrease in the discharges of the Seine, some of its tributaries, and certain sources, at different periods. Table xxiii., giving the rainfalls of the warm seasons, and the high floods of the following cold seasons, at the Austerlitz Bridge, Paris, and at Mantes, from 1874 to 1900, shows that none of these warm seasons in which the rainfall was below the mean of 14.88 inches, was followed by floods of the Seine rising higher than 14.44 feet on the gauge at Paris, and 19.72 feet at Mantes; and the eight cold seasons in which the Seine reached or exceeded 16.40 feet at Paris, and 21.06 feet at Mantes, were all preceded by warm seasons in which the rainfall exceeded the mean. Moreover, with the exception of 1890, when the warm season came between two very dry cold seasons, all the warm seasons having a rainfall above the average have been followed by floods of the Seine, attaining at least 10.17 feet at Paris and 16.40 feet at Mantes; whereas none of the fourteen warm seasons with a rainfall below the average was succeeded by floods in the next cold season, reaching the height attained in eight of the cold seasons preceded by warm seasons in which the rainfall exceeded the average,



Elements of the Differential and Integral Calculus. By William Anthony Granville, Ph.D., with the editorial cooperation of Percey F. Smith, Ph.D. Pp. xiv + 463. (Boston and London: Ginn and Co.) Price 10s. 6d.


HIS is a book the main object of which seems to be to enable the student to acquire a knowledge of the subject with little or no assistance from a teacher; and, after a very careful study of it, we are enabled to say that the work is admirably constructed for the purpose. There is a complete absence of the stilted formality which is usually supposed to be appropriate to a mathematical treatise. In foot-notes, and sometimes in the text, the student is given scores of useful hints and warnings against errors into which he would probably fall. Thus the work possesses a very high value for the student; and it will be found no less helpful to the teacher, for it contains a very large number of examples in every part of the subject, while it abounds in excellent diagrams.

The portion on the differential calculus occupies 285 pages, and terminates with 6 pages containing nothing but figures of all the curves more or less famous which present themselves in the subject, such as the conchoid of Nicomedes, the cycloid, the catenary, the cissoid of Diocles, the probability curve, various spirals, &c.

The work is very strictly logical in its method-here and there a little too much so, perhaps.

Thus in p. 97 the proof that the angle between the radius vector and the tangent to a curve has rde dr for its tangent is quite unnecessarily accurate, and

has involved an error in work, which, however, is a mere slip. The theorem of mean value is very well explained and used in the deduction of Taylor's theorem for the determination of the remainder, a little geometrical figure assisting the student to understand the nature of this remainder. (Correct, however, the errors in sign in the first equation of p. 169.)

The discussion of the convergency and divergency of series is very good, and a somewhat uninteresting subject is rendered simple and attractive. An incautious statement, however, is made with regard to an alternating series, p. 241, according to which if we stop at the nth term of such a series the error made is numerically less than the value of the (n+1)th term. Clearly this is not in general true if the alternating series is one in which the numerical values of the terms increase for a while and then diminish. For example, the series for sin x is an alternating one of this kind. If x=5, the numerical values do not begin to diminish until after the third term. The property asserted, and the proof in p. 226, must be applied to cases in which we stop after the greatest numerical term has been passed.

The theory of maxima and minima is well illustrated by examples taken from various branches of physics. Even at the risk of being a little hypercritical, we must, however, point out that the time taken by a ball to roll down a plane the base of which is of length a and the inclination of which is

is not 2a/g sin 24, as it is said to be in p. 128. for the simple reason that the acceleration of the centre of the ball (if the ball is solid and homogeneous) is not g sin, but 5/7 g sin . This fact is of importance in dynamics, and the matter should be set right.

The part of the book dealing with curves is very good, and, in particular, we would commend the

systematic manner in which (pp. 267, 268) the student is taught to trace a curve from its equation.

In the portion dealing with the integral calculus an exhaustive exposition of all the devices used in integrating functions is given. The reduction formulas to be applied to the binomial integral

xm(a+bx")Pdx are given in tabular form on p. 345,


and the student is told very properly that he should not memorise them. Instead of memorising them, he should apply a single simple rule which was given long ago by Hymers in his " Integral Calculus." This rule enables us to obtain, without an effort of memory, the exact formula appropriate to the reduction of any given binomial integral.

Besides areas and volumes (accompanied by excel. lent figures), polar moments of inertia of plane areas are dealt with. The author speaks of these as moments of inertia about "a point "-an expression which leaves something to be desired, since it is always an axis that is involved. What we always require in this connection in dynamics is the mean square of distance of a body from an axis, and we should look to writers on the calculus to emphasise this notion of a mean square of distance, instead of the "square of the radius of gyration," k2. The

student might easily learn to regard k as the distance of mean square, just as we speak of the velocity of mean square in a gas.

The book has a useful chapter on the simpler forms of differential equations, and concludes with a figure and description of the integraph for finding the area of a curve. It might well include a description of Amsler's planimeter, and show how it finds areas, positions of centres of gravity, and moments of inertia of plane figures; and, as to the proof of the theory of Amsler's planimeter, it need occupy no larger space than the area of a shilling, notwithstanding the length and complication of proofs which are usually given.

The author's attention may be directed to the following misprints-p. 44, note, Leibnitz was Gottfried, not Gottfreid; p. 206 (A), read f' for f; p. 216, ex. 15, read v2 for v; p. 225, line 5, read 223 for 225; p. 275, line 6, read P' for P; p. 374, line 1, read y for dy. GEORGE M. MINCHIN.


Manual of Serum Diagnosis. By O. Rostoski. Authorised translation by Charles Bolduan. Pp. vi+96. (New York: J. Wiley and Sons; London: Chapman and Hall, Ltd., 1904.) Price 1 dollar.


HIS small work forms a companion volume to that by Wasserman on "Hæmolysins and Cytotoxins," which has already been noticed in these columns. Each volume forms a monograph on some part of those newer developments of bacteriology which concern immunity and kindred subjects. The aim of the series is to provide simple yet comprehensive accounts of our present knowledge suitable for those who do not make a special study of the laboratory aspects of disease rather than exhaustive treatises adapted for special students. That the information is authoritative and trustworthy is vouched for by the list of authors, which includes some of the most distinguished names in contemporary bacteriology. Each volume is the work of one who has himself made important contributions to the study of the subject.

The present volume deals with the practical use of agglutinins, bacteriolysins, and precipitins in diagnosis. More than two-fifths of the whole is devoted to an account of the Widal reaction in enteric fever. This section is extremely good, and for it alone the book is well worth reading. The author points out very clearly that the "test is not to be regarded as more than the " first of the cardinal symptoms of typhoid. Some discredit has been cast on the value of the reaction, because clinicians have not always found that infallibility which is so often expected of the laboratory, but which can never be present in dealing with so variable a complex as living matter. Removed from the pedestal of a test" to the common ground of a "symptom," the phenomenon seems to have a better chance of receiving the appreciation which it deserves. There is an admirable account of the mixed and "group" agglutinations in typhoid and paratyphoid infections, and due notice is taken of the use of typhoid cultures which have been killed by the addition of formalin. These react

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practically as well as living cultures; and, though the increased time required to obtain a result and the slight loss of delicacy render the use of living cultures still desirable in the laboratory, the safety and convenience of the dead cultures place the "test within the personal practice of every not-too-busy practitioner. It is, however, strange to read (p. 13) that the use of an oil-immersion objective is necessary.

The author then considers briefly the agglutination phenomena found in tuberculosis, dysentery, and other diseases. Serum diagnosis of tubercle is considered to be of very doubtful value. Appropriate stress is laid on the fact that in many diseases (especially plague and cholera) agglutination, in comparison with other symptoms, is of very little use for the direct diagnosis of the disease, though of the greatest value in the identification of the isolated organism. This part of the book is, however, less satisfactory than the earlier sections. Indeed, the serum diagnosis of Malta fever is not mentioned, though the practical value of the phenomenon in the diagnosis of this variable and often very obscure disease has been demonstrated beyond question.

The book concludes with an account of the identification of blood stains by the precipitin test. Readers will find here a wise injunction to make sure that any given stain is blood before deciding whether it is of human or animal origin; the precipitin will not distinguish between the different tissues of the same species of animal in the same way as it will separate the same tissue from different species. .

In the translation several useful additions have been made; the last chapter, which attempts an impossibly precise and entirely arbitrary definition of the Widal reaction, might, however, well have been omitted.

A. E. B.

HISTORY OF PHARMACY. Geschichte der Pharmazie. By Hermann Schelenz. Pp. ix+934. (Berlin: (Berlin Julius Springer, 1904.)

Price 20 marks.


HE successful practice of pharmacy implies some acquaintance with plant chemistry and with that branch of economic botany known as materia medica. For this reason the history of pharmacy, although it appeals particularly to the pharmacist and the physician, presents also many points of interest to the chemist and the botanist. Herr Schelenz does not consider that the classes of readers here enumer

ated form a sufficiently wide circle for his purpose, and he states in the preface to this volume that he hopes also to interest the legislator, the antiquarian, and the philologist.

The book begins with a description of the conditions under which pharmacy was practised among the Jews. A summary of the political history of the nation is first given, and this is followed by sections dealing with Biblical and Talmudic references to the practice of pharmacy and the social condition, &c., of the practitioners of the art. The most interesting portion of this section is that describing the drugs employed by Jewish apothecaries. It is curious that so many of these are still in use at the present day;

for example, myrrh, Indian hemp, cassia (or cinnamon), coriander, colocynth, galls, almonds, galbanum, and storax are among those mentioned by the author. The Jews also appear to have made use to some extent of natural mineral waters and various medicated baths as remedial agents.

Similar accounts of the practice of pharmacy among the Phoenicians, Assyrians, Egyptians, Hindus, Persians, Greeks, Romans, and other peoples are given, and then this racial method of treatment is interrupted, and a chapter is inserted giving an account of the methods of the professors of magic, astrology, and alchemy in the Middle Ages, and showing how the practice of these secret arts gradually led to a knowledge of natural science.

Resuming his narrative after this digression, the author deals with pharmacy among the Copts and Syrians, the Arabs, and the Teutonic races, and brings it to the close of the eighteenth century with a short account of the condition of medicine and pharmacy in Italy, when the school of Salermo exercised a paramount influence on these arts. It was at this period that a definite separation of pharmacy from medicine first took place.

Each of the succeeding chapters deals with the progress made during a particular century, an outline of the additions to physical, chemical, and botanical sciences being first given, with short biographies of the more famous exponents of these sciences. The bearing of these discoveries on pharmaceutical methods is then outlined, and finally the legislation of the periods, the social and commercial conditions, and other matters in so far as they affected the practice of medicine and pharmacy are discussed. The book is evidently the outcome of much literary and antiquarian research on the part of its author, but it is unfortunate that more care was not exercised in selecting the material to be included. There is no reason why so much space should be taken up in recounting the political and religious histories of the various peoples. Similarly, the short and necessarily inadequate biographies of eminent men of science, which are scattered broadcast through the second half of the book, might well have been omitted, since they are already better done elsewhere. By omitting these and other not strictly relevant matters, the size of the volume could have been much reduced, and at the same time it would have been unnecessary for the author to write in the compressed, unreadable style which now characterises the book. As it is, the volume can only be regarded as a useful work of reference on the history of pharmacy and allied subjects, and to this purpose its index (26,000 entries) is well adapted. T. A. H.

OUR BOOK SHELF. Guide to the Gallery of Birds in the British Museum. Pp. iv+228; illustrated. (London: Printed by Order of the Trustees, 1905.) Price 2s. 6d. THIS handsome volume is a new departure in the matter of "guides," so far as the natural history branch of the museum is concerned, being larger in size, more fully illustrated, different in style, and (perhaps most important of all) higher in price than

those to any of the other sections. The text is, in fact, a concise synopsis of the leading groups of birds, with special reference to the specimens exhibited in the galleries. The plan of the synopsis necessarily follows the system adopted in the museum, and it would therefore be quite out of place to criticise that system on the present occasion. A similar remark applies to the fact of the illustrations (which are admirable of their kind) being taken from the stuffed specimens in the collection instead of from living birds the guide is to illustrate the collection, and therefore it is quite right and proper that the figures of the birds should be taken from those shown in the gallery. In addition to the general synopsis, there is a guide to the series of British nesting birds. That the general plan and execution are in the main excellent cannot be denied; whether it will suit the taste -and the purses of the public remains, however, to be seen.

When a new edition is called for, certain emendations may with advantage be made in the text. The most serious error we have detected is the statement (p. 11) that the largest Epyornis was probably not more than 7 feet in height, whereas there are actually limb-bones in the museum itself which are nearly of these dimensions; such an error implies a want of cooperation between the zoological and palæontological departments of the museum. Of less importance, although far more embarrassing to the public, is the discrepancy between the terminations of the orders" of ostrich-like birds in the list on p. 8 and those in the synopsis on that and the following pages. Again, we venture to think that the public will not be likely to understand the semi-scientific jargon frequently employed in the text. The expression, for instance, on p. 106, "the remarkable Australian forms constituting this order," would have been much better had the word "birds" been used in place of 'forms." Neither is the construction of the sentences in all cases so good as it might be, as witness the following (p. 64): The appendage opens under the tongue and is largest in the male, giving the bird a very peculiar appearance. Like its allies it is an expert diver . . . R. L.



Laboratory Manual of Organic Chemistry for Beginners. By Dr. A. F. Holleman. Translated by A. Jamieson Walker, Ph.D. Pp. xiv+78. (New York: John Wiley and Sons; London: Chapman and Hall, Ltd., 1904.) Price 4s. net.

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THE preparation and properties of a number of organic compounds are dealt with in short paragraphs manner reminding one of the text-books of qualitative analysis, which are now so universally condemned. But little attempt is made to indicate the quantities which should be used, and no emphasis whatever is laid on the importance of making organic preparations in a quantitative manner. We even doubt whether the beginner would attain the required result in performing many of the preparations described.

It will be a sad day for the future of organic chemistry if text-books such as Dr. Holleman's come into general use; it is indeed difficult to imagine anything more calculated to encourage scamping of laboratory work. A growing complaint of the chemical manufacturer abroad at the present time is that the university graduates from the large modern laboratories are ruined by the elaborate apparatus. ready-made reagents and other time-saving appli ances placed at their disposal, so that they are no longer themselves capable of facing practical problems properly or of making the best use of the ordinary technical appliances. The physical chemical epoch from which chemical science is now slowly recover

ing has caused it to be forgotten that for successful work in chemistry it is essential that the investigator be a highly skilled manipulator. It is too often found that the best student in the examination room is all but worthless when set to perform even the simplest piece of experimental work; good workers can only to trained by the most careful and thorough grounding in making pure chemical preparations and by being taught to appreciate the importance and necessity of even the minutest details in the process. As a glance at the modern chemical literature shows, it is precisely this attention to detail which is so conspicuous a feature in some of the best work.

We fear that the book under notice would not lead the student to attach importance either to accuracy of method or to thoroughness of detail; it seems a pity even that it should have been found worth while to translate it and so add another to the legion of text-books.

Metaphysik in der Psychiatrie. By Dr. P. Kronthal. Pp. 92. (Jena: Gustav Fischer, 1905.) Price 2.50 marks.


THIS costly little work is written to ventilate a grievance. It would appear that certain authorities on mental diseases, including Kräpelin and Binswanger, employ in their works such terms association, apperception, power of imagination, anger, and the like. These, according to our author, are metaphysical terms, and must be carefully excluded from Psychiatrie, which is a purely natural science. New sciences spring up like mushrooms nowadays, and it is a misfortune that those who specialise in one, or seek to exploit it, so rarely know with precision what is being done in others, even when these are most closely akin to their own darling pursuit. We fear that this writer hardly understands that the terms which he criticises are used every day in psychology with a minimum of metaphysical reference, and that he is almost bound, before he proceeds a step, to show due cause why the terminology of Psychiatrie should differ seriously from that accepted by ordinary psychology. In spite of his parade of footnotes and his references to such grand conceptions as that of Allbeseeltheit, it may be doubted if this writer is competent to discuss so general a question. At any rate, his present work does not impress one as being well arranged, clear, or convincing.

1 Text-book of Physiological Chemistry. By Charles E. Simon. Second edition. Pp. xx+500. (London: J. and A. Churchill, 1905.) Price 15s. net. ALTHOUGH Dr. Simon's book has reached a second edition, it is one which has been hitherto unknown on this side of the Atlantic. Dr. Simon's name is not associated with any researches in physiological chemistry, and there is nothing strikingly new or original in his book, either as regards subjectmatter or arrangement. The work has, however, many excellent features. It is clearly written, and is free from inaccuracies; the sections dealing with the proteids and their cleavage products are especially good, and fully abreast of the recent advances which have been made in this important and interesting branch of the subject.


The author is conversant with chemical technique, and his descriptions of analytical processes specially lucid. It is evident that he is a careful student of chemico-physiological literature, and more especially with that part of it which originates in Germany. This is frequently seen in the nomenclature he adopts. Thus he speaks of casein and paracasein instead of caseinogen and casein spectively as employed in most English books. Occasionally the adherence to German terms leads to


confusion; for instance, the two German words Eiweisskörper and Albumine are both translated as albumins.


The work is primarily intended for students, and therefore references to literature are omitted. desire to keep the book within a moderate compass has no doubt induced the author to leave out a consideration of many subjects which might well have been expected to find a place in it. Thus we find no reference to the important subject of immunity and its side issues, like the precipitin test for blood. The numerous investigations now in progress on the velocity of ferment action are passed over in silence. Physical chemistry has during the last decade made great progress, and many and important are its applications to physiology. Such questions as absorption, secretion, osmosis, gaseous exchanges, and electrical conductivity have all been made clearer by the work of the physical chemist; but there is no reference to any of such investigations.

The strangest and most important omissions, however, are the absence of any account of general metabolism, animal heat, and respiration.

Turning to the title-page, one searches in vain for the words vol. i., for the omitted material would easily fill a second volume of the same size. One cannot help thinking that, interesting and instructive as the book undoubtedly is, it cannot be expected to take its place as a favourite until the deficiencies alluded to are rectified.

Astronomy for Amateurs. By Camille Flammarion. Translated by Frances A. Welby. Pp. 340. (London: T. Fisher Unwin, 1905.) Price 6s. MUCH that is interesting to amateur astronomers may be found in this volume. The descriptions are often discursive, but the matter is there, and in a readable form providing the reader's leisure is not too limited.

After a general exhortation to his readers to study and contemplate the marvels of the sky, the author proceeds to a study of the constellations, the stars themselves, the sun, and then the planets. Next follows a chapter on comets, containing some interesting facts concerning the ancient ideas of these "glittering, swift-footed heralds of Immensity," and a brief account of comets in general and of a few in particular. Shooting stars are then dealt with, and in chapters viii., ix., and x. the earth, the moon, and eclipses are severally discussed. In chapter xi. the more elementary methods of determining stellar distances and masses are described, whilst the next, and last, chapter is devoted to a discussion of life universal and eternal. The book contains eighty-four illustrations-the relevance of some of which is open to question-and it will be read with both interest and profit by those whose previous acquaintance with astronomical truths has been slight.


[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.] Scientific Correspondence of the late Sir George Stokes. ARRANGEMENTS are in progress for the publication of a selection from Sir George Stokes's scientific correspondence. The letters addressed to him, which are now in my custody, show that there must be many from him to others, of permanent scientific value, to which I have not access. I shall therefore be glad if cwners of letters of substantial scientific interest will entrust them to me, to be treated with care and ultimately returned. J. LARMOR.

St. John's College, Cambridge, May 8.

The Transposition of Zoological Names.


I WISH to say how thoroughly I agree with Mr. Lydekker in his remarks on the unwisdom of transposing zoological names, and on the confusion caused by this objectionable practice. To the instances which he has mentioned I may add the following cases relating to two well known and familiar species of animals. Linnæus called the only European hare known to him Lepus timidus, and for many years that name was applied to the common brown hare of Central Europe, while the northern hare, which changes to white in winter, was known by Pallas's appropriate name, Lepus variabilis. This the nomenclature used by Blasius, by Bell in his " British Quadrupeds, " and in all the ordinary text-books of zoology. It was, however, pointed out some years ago, first, I believe, by Liljeborg, that the Lepus timidus of Linnæus had been based mainly upon the northern or variable hare, or that at all events Linnæus had confounded the two species together. In these circumstances obviously the best plan was to call the middle-European brown hare by its next given name, Lepus europeus, and this course has been adopted by most writers. But the advocates of unrestricted priority are not content with this, and insist upon calling the variable hare Lepus timidus, the consequence being that when that name is used it is impossible to know which of two perfectly distinct animals is intended by it.

Another still more objectionable transposition of two well known names has been lately suggested. Linnæus, in the twelfth edition of the "Systema Naturæ,' gave the name Turdus musicus to the song-thrush and that of Turdus iliacus to the redwing, and these familiar terms have been used by all writers for these well known birds respectively ever since. But about a year ago it was discovered by an ardent member of the new school of priority that in his tenth edition of the " Systema "Linnæus had unfortunately (by some error in his MS. or of his printer) attached the diagnosis of Turdus musicus to T. iliacus, and that of T. iliacus to T. musicus. It was admitted that Linnæus had corrected the mistake in his later edition of 1760, but even Linnæus could not be allowed to correct his own errors in the face of the inviolable law of priority." In future, therefore, it was maintained, the song-thrush must be called T. iliacus and the red wing T. musicus! This course has been actually adopted by a subsequent writer, but we may trust that it will not meet with general approval, and that the song-thrush and redwing will remain under the old names given to them by the father of scientific nomenclature in 1760, and used by every subsequent writer until 1904. P. L. SCLATER.

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Modern Algebra.

THE publication of Messrs. Grace and Young's treatise on algebra will direct attention to the importance and difficulty of the theory of the concomitants of ternary and quaternary quantics in connection with plane and solid geometry. There are one or two points on which I propose to make some remarks.

In the first place, canonical forms are sometimes deficient in generality, and this will be the case whenever the form is the analytical expression for some special property of an anautotomic curve. Of this defect the canonical form of a ternary cubic furnishes a striking example, for it is the analytical expression for the theorem that through each of the three real points of inflexion one real straight line can be drawn which passes through one pair of conjugate imaginary points of inflexion on an anautotomic cubic curve; and since autotomic cubics do not possess this property such curves cannot be represented by the canonical form.

In the next place, anautotomic curves are not by any means the most interesting species of curves, and to go through the process of calculating their concomitants, and then specialising them for some particular species of autotomic curves, is often very laborious. In the case of unicursal quartics, many interesting results might be obtained by calculating directly the concomitants of the quantic (By, ya, aß)2, and this would give results applicable to all unicursal quartics, except those which possess

the five compound singularities called the tacnode, the rhamphoid cusp, the oscnode, the tacnode cusp, and the triple point. Also, since an evectant is the tangential equation of a curve which is related in a special manner to the original one, an examination of the evectants of the above quantic would lead to interesting results concerning conics and other curves connected with trinodal quartics.

In this subject geometrical methods are a powerful assistance to pure analysis. For example, let U be a ternary cubic in (a, B, y); eliminate y by means of the equation 8=ky, and equate to zero the discriminant of the resulting cubic equation in a 8. This will give a sextic equation ▲ (k)=0, which determines the six tangents drawn from A to the curve. The condition that the curve U=0 should have a node is that the equation A(k)=0 should have a double root; hence the discriminant of this binary sextic is the discriminant of the original ternary cubic U. Many other examples of a similar kind could be mentioned, and we may observe that from the discriminant of a binary duodecimic, all the conditions that a quartic curve should possess point singularities may be obtained. April 28. A. B. BASSET.

Current Theories of the Consolidation of the Earth.

IN Lord Kelvin's philosophical and justly celebrated paper on the secular cooling of the earth (Thomson and Tait's "Nat. Phil., vol. i., part ii., Appendix D), the assumption is made that the earth was once a fiery molten mass, liquid throughout, or melted to a great depth all round. He cites Bischof's experiments showing that "melted granite, slate, and trachyte all contract by something about 20 per cent. in freezing," and continues:

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Hence, if, according to any relations whatever among the complicated physical circumstances concerned, freezing did really commence at the surface, either all round or in any part, before the whole globe had become solid, the solidified superficial layer must have broken up and sunk to the bottom, or to the centre, before it could have attained a sufficient thickness to rest stably on the lighter liquid below. It is quite clear, indeed, that if at any time. the earth were in the condition of a thin shell of, let us suppose, 50 feet or 100 feet thick of granite, enclosing a continuous melted mass of 20 per cent. less specific gravity in its upper parts, where the pressure is small, this condition cannot have lasted many minutes. The rigidity of a solid shell of superficial extent so vast in comparison with its thickness, must be as nothing, and the slightest disturbance would cause some part to bend down, crack, and allow the liquid to run over the whole solid. The crust itself would in consequence become shattered into fragments, which would all sink to the bottom, or meet in the centre and form a nucleus there if there is none to begin with."

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In adhering to these views, Lord Kelvin has been followed by Prof. G. H. Darwin (cf. "Tides and Kindred Phenomena of the Solar System, p. 257) and other eminent mathematicians; so that the theory that the earth consolidated by the building up of a solid nucleus through the sinking of portions of the crust of greater specific gravity is no doubt generally accepted by geologists and others interested in the physics of the earth.

Recent researches on the pressures within the planets (cf. Astronomische Nachrichten, No. 3992) have thrown great doubt on this mode of consolidation of the globe. The line of argument by which we reach this conclusion is a double one :

(1) It is shown that the effect of pressure in the highly heated fluid assumed to have constituted the molten earth would have been to dissolve the portions of the sinking crust before they attained any considerable depth.

(2) The increasing density of the fluid itself would have prevented sinking of the crust below one-tenth of the radius, so that a solid central nucleus could not have been built up in this way.

To see this clearly. let us suppose that the earth were a molten mass, and that a crust of rock several kilometres in area, and a considerable fraction of a kilometre in thickness, had formed, and begun to sink in the molten fluid

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