THURSDAY, MARCH 1, 1906. MATHEMATICAL ASTRONOMY. The Collected Mathematical Works of George William advance which their solution implies. The latter paper was the first which threw any real light upon the general problem of three bodies, and it is well worth notice how large a part arithmetic plays in its success. The analysis is pregnant in the extreme, but it is the actual calculation of a whole sequence of periodic orbits which a moon might occupy that gives it shape and name. If this memoir may be said to be the first significant word on the problem of three bodies, the former one, on the motion of the lunar perigee, seems to be almost the last word on a question that had outrun calculation from Newton's day to Delaunay's. It is doubtful whether the more determined effort to calculate this quantity was made by Newton or IT is a rare mind that can handle the cumbrous developments of practical astronomy and leave uppermost with a reader the impression of variety, ease, and polish; and curiosity will be felt as to the circumstances which have developed Hill's remarkable powers. From an interesting introduction to the present volume by M. Poincaré we learn that he spent three years at Rutgers College, New Jersey, by Delaunay, but though naturally the degrees of under a certain Dr. Strong. Dr. Strong "'était un homme de tradition, un laudator temporis acti; pour lui Euler était le Dieu des Mathématiques, et après lui la décadence avait commencé; il est vrai que c'est là un dieu que l'on peut adorer avec profit," and if it led Hill to the study of originals, we may overlook the depreciation of the moderns. From New Jersey he went to Cambridge to continue his studies at Harvard; very soon here, by a paper contributed for a prize to a mathematical miscellany, he attracted the notice of Runkle, the editor, who was Newcomb's predecessor at the office of the American Ephemeris. Hill became attached to the Ephemeris as computer, and remained in discharge of these duties for thirtytwo years. At first he worked at his own home, as was then the custom; but under Newcomb's management, and in order to complete his theory and tables of Jupiter and Saturn he lived for some years at Washington, incessantly absorbed in his task. "The only defect of his make-up of which I have reason to complain," Newcomb has written, "is the lack of the teaching faculty." In 1892 he withdrew to the little farm where his boyhood was passed, and where he still lives, asking nothing but the liberty to continue his labours. The present volume carries us up to 1881, and includes most, but by no means all, of his best known papers. The essay which attracted Runkle's notice is No. 3, 'On the Conformation of the Earth," and was written at the age of twenty-three. It is perhaps not of any permanent importance, yet it is marked by the clearness and the firm hand of his later writings and the same salutary determination that theory should give an account of itself arithmetically. It is natural to compare it with Stokes's memoir "On the Variation of Gravity," written some twelve years before, when he also was a young man, and the comparison shows strikingly how Stokes is the physicist and Hill the analyst. The two great memoirs by which Hill is best known are No. 29, "On the Part of the Motion of the Lunar Perigee which is a Function of the Mean Motions of the Sun and Moon," and No. 32, "Researches in the Lunar Theory." These writings have been greatly praised, but it seems impossible to praise them too highly, whether for their difficulties or the way these are overcome, or the greatness of the approximation they attained were very different, they of the methods employed. Hill first, with the smoothhad this in common, that they proved the inadequacy ness of a conjurer, gives form to the intractable equations, and then shows how the solution is contained in a certain transcendental equation, an infinite determinant. It affords striking evidence of Hill's power to contrast his treatment of this determinant with that of Adams, who followed a similar route, sed longo intervallo, as he said himself. The complexity arising from an infinite sequence of equations might seem to preclude any general conclusions from being beautiful manner to derive the eliminant in a transdrawn, but Hill uses this very feature in the most cendental form in the shape cos TC = a known quantity, and from this equation determines c, the required ratio. The secret of the success is now apparent. c is nearly equal to unity; hence it is very much easier to approximate to cos c, where we are in the neighbourhood of a stationary value, than to c directly; and though the difficulty recurs when we seek to find the arc wc from a cosine in the neighbourhood of its minimum, it is then an insignificant one, for we are past the true complexities of the problem.1 The remaining papers are naturally not of equal moment with these, but we may be grateful to the Carnegie Institution for making them accessible in the present collection. Several of them arose in connection with Hill's duties as Ephemeris, but even on such hackneyed subjects as computer to the eclipse computing and reduction of star places he has something good to say. . He is a true artist; nullum quod tetigit non ornavit. Of considerable general interest are No. 18, "Remarks on the Stability of Planetary Systems," and No. 14, "A Method of Computing Absolute Perturbations," which contains a rescension of Hansen. Even the smaller papers, like No. 22, "On the Solution of the Cubic and Biquadratic Equations," are usually marked by some analytical felicity that makes one wish that Hill had been able to bring his great powers to bear upon a material not so invariably intractable and overloaded with tradition, and limited in its problems, as practical astronomy. But if we feel that his hand 1 The point of this approximation is put somewhat incorrectly by M. Poincaré in bis introduction. the other hand, sedimentation rapidly takes place under the influence of gravity, and its rate is little influenced by the withdrawal of water or by the addition of electrolytes. The suspension may be reformed by purely mechanical means. (3) Alterations in the total energy of the system are frequently associated with the process of coagulation. These have been measured in several cases by means of the calorimeter. (4) Colloids in solutions are capable of undergoing reactions with one another, which closely simulate purely chemical reactions. The next section of the book deals with the classification of colloid solutions or hydrosols. The classi fications of the hydrosols have been based on two principles, namely, the size of the particles and the reversibility or irreversibility of the hydrosol (Hardy). On plate i. the author gives a graphic representation of a classification of colloids founded on these principles. The reversible colloids differ from the irreversible in not being readily coagulated by the addition of electrolytes. It is noteworthy that irreversible colloids may be partially protected from the coagulating action of electrolytes by the addition of a reversible colloid to their solutions. Great quantitative differences are found to exist in the extent of protection given by different reversible organic colloids to irreversible gold hydrosols. A brief account is first given of the nature and properties of colloid solutions or hydrosols. At the outset the author refers to the difficulty of giving a satisfactory definition of the term "solution." He adopts homogeneity as the most universal characteristic of solutions. The definition of homogeneity will naturally vary according to the delicacy of the methods employed to test it. By means of the method of ultramicroscopy devised by Zsigmondy and Siedentopf, the majority of colloid and even some crystalloid solutions can be shown to be optically heterogeneous. Every increase in the accuracy of the methods of examina-perties of irreversible colloid solutions occupies the tion would lead to a further limitation of the term "solution." In order to include the colloids Zsigmondy defines solutions as uniform distributions of solids in fluids, which are transparent to ordinary light, and not separable into their constituents by the action of gravity or by filtration. In order to gain a clearer idea of the nature of colloid solutions, it is necessary to find criteria for distinguishing such solutions from those of crystalloids on the one hand and from suspensions on the other. Zsigmondy only refers very briefly to the distinguishing characteristics of the former, as this subject has been previously treated by Bredig in his monograph on "Inorganic Ferments." He deals more fully with the properties of colloid solutions which distinguish them from suspensions. In this connection he mentions the following as the chief features distinguishing colloid solutions from suspensions : (1) The particles in colloid solutions are much smaller than in suspensions. In colloid solutions the average diameter of the particles varies from 5 to 20 μμ. This difference is, however, one only of degree. (2) Many colloids are capable of undergoing irreversible changes. Separation of a metal from its colloid solution may be readily brought about by the withdrawal of water or the addition of electrolytes. In this process the metal has undergone an irreversible alteration or coagulation. For the reformation of the colloid solution, chemical or electrical means must be employed. In the case of suspensions, on A historical account of the preparation and pro next section of the book. The author next gives an interesting account of the development of the method of ultramicroscopy by Siedentopf and himself. A full description is also given of the necessary apparatus and of the method of using it. The succeeding sections give details of the results of his own researches on gold hydrosols. By means of the ultramicroscope he was enabled to determine approximately the average size of the gold particles, their colour, and the rapidity of their movements both translatory and oscillatory. The limit of size determinable by the ultramicroscope appears to be about 6 μ in the case of gold hydrosols. Still smaller particles (amicrones) are also present in gold hydrosols. Their presence may be proved by the coagu lation of the hydrosols on the addition of electrolytes. An excellent summary is also given of the results obtained by other observers through examination of various colloid solutions by means of the ultramicroscope. Brief reference only is made to some points of great theoretical interest, namely, the causes of the stability of colloid solutions, and the mechanism of their formation. The book concludes with a short summary of what is known with regard to the products of coagulation of colloid solutions. The work as a whole is to be regarded as a valuable monograph indispensable for those interested in the ultramicroscope and its applications. J. A. MILROY. at The manual is issued by the Prehistoric Society of France, and has been written by several of its leading members. Taken in conjunction with the first Congress of the society, held in the autumn Périgueux, it indicates a widespread interest in the remote past as represented by flint implements, cave deposits, dolmens, and Gaulish burials. Of recent years, more and more emphasis has been laid on the need for systematic excavation as opposed to haphazard relic-hunting by amateurs; and this publication is intended, not only to assist the explorer in his search for records of the past, but also to render them accessible and self-explanatory when found. Private interest and personal feeling always stand in the way of corporate action in such investigations, but much would be gained if the advice contained in this manual were followed by the depredator, if only for his own ends. To put it on the lowest ground, relics accurately labelled and located gain enormously, not only in scientific, but also in market value; and if archæology is to justify its claim to be regarded as a science, scientific exploration must be the rule, and not the rare exception. The chapters are all much compressed, and none can be singled out as more important than another. There are instructions for all the ordinary branches of exploration in a most compact form; but in spite of the French tradition, we venture to think that the volume would have been even more practical if published in a light but stout binding. A handbook in a paper wrapper is hardly fit for use in the field. Attention may be directed to the method of hardening and preserving skeletons and other bones by means of silicate of potash, and to the practical advantages of the process advocated for preserving iron. This metal is the scourge of museum curators, and neither the soda nor paraffin treatment has proved altogether successful. The simpler, and apparently the more satisfactory, method is to allow the metal to dry for several hours after brushing in water, and then to heat it to a dull red; if allowed to cool slowly, the object should then be rust-proof, and the surface clean and firm. One of the most useful features of the manual is the table for computing the height of a subject from various bones of the skeleton; this method would no doubt greatly reduce the number of 7-feet skeletons found even in this. country. Another point on which emphasis is laid is the desirability of photographing dolmens, menhirs, and other antiquities of the kind precisely from the four cardinal points; picturesque views are dear to the ordinary photographer, but are of little value for purposes of comparison. On this to the point a caution should have been given as difference between the true and magnetic north, as accurate compass bearings of megalithic monuments may often prove of considerable importance. The student of prehistoric archæology in France and elsewhere will be glad to find the various classifications of the Stone age brought together, even if no attempt is made to coordinate them. The most important are those of Mortillet, Piette, Salmon, Boule, and Rutot, and in the last mentioned occurs (as occasionally elsewhere) the irritating term "Forest Cromer bed." Among the few cases where no scale is indicated for the illustrations is that of the Pressigny nucleus (Fig. 74); the extraordinary size of these flints ought surely to have been stated. Finally, it is somewhat of a shock to the orthodox to find the following item in the glossary at the end:-“ Bulbe de percussion.--Mot impropre (voir Conchoïde).' OUR BOOK SHELF. Smoke Abatement: a Manual for the Use of Manufacturers, Inspectors, Medical Officers of Health, Engineers, and Others. By William Nicholson. Pp. xiii+256. (London: Charles Griffin and Co., Ltd.) Price 6s. net. 66 THE author of this handbook is chief inspector to the Sheffield Corporation, and seems to have an extensive acquaintance with the various enactments that have been passed in this and other countries with a view to ameliorate one of the greatest nuisances of modern times, and devotes more than a third of the 250 pages the book contains to their recital. This is undoubtedly useful to those desiring to make themselves acquainted with the legal aspects of the case, but scarcely justifies the subtitle of a practical handbook, as the author's idea of the nature of smoke is of a most delightfully rudimentary character, and his power, therefore, of prescribing remedies necessarily limited. On searching the book for a clear definition of smoke and a description of the constituents that go to build it up, we find on p. 12 the following:- "Nature of the Nuisance-Smoke consists of minute particles of carbon together with a sticky tarry matter which settles and sticks to everything it comes in contact with. It is dirt. Lord Palmerston's definition of dirt from a health point of view is Matter in the wrong place,' and carbon or coal in the atmosphere is matter in the wrong place." One of the chief remedies suggested by Mr. Nicholson is that the Sanitary Institute should now deal with the question, and arrange for courses of lectures on the subjects of "Smoke and the Injury therefrom, ""The Causes of Smoke," and "The Practical Prevention of Smoke, after which examinations should be held, and "certificates of competency given to all who satisfy the examiners." The result of this is foreshadowed by the author as follows: "If such facilities were offered, hundreds of engineers and others would avail themselves of them, and would not rest satisfied until they had procured a smoke inspector's certificate, which would become as popular and as valuable as the sanitary inspector's certificate. Having obtained the certificate and possessing the theoretical as well as the practical knowledge, they would quickly be on the look-out for official appointments, and if there was an willingness on the part of the Local Authorities to appoint them, the necessary pressure to compel them to do so would be forthcoming.' un If Mr. Nicholson could induce the Sanitary Institute to add a lecture on "The Nature of Smoke " to the course he prescribes, and was to attend it, he would find the information of distinct advantage in dealing with "smoke abatement." The Preservation of Antiquities, a Handbook for Curators. Translated from the German of Dr. Friedrich Rathgen by Dr. G. A. Auden and Dr. H. A. Auden. Pp. xiv +176; with 48 figures in the text. (Cambridge: University Press, 1905.) Price 4s. 6d. net. DR. RATHGEN states in his preface to the German edition of this little book that it is intended to stimulate curators and others interested in the preservation of antiquities to make public their experiences in this branch of archæology. The first part deals with the changes brought about by the long-continued action of soil, moisture, and air on metals, glass, organic substances, limestone and clay; the materials of which "antiquities are most usually composed. This is a subject about which very little is known, one of the commonest cases, the "rusting of iron," being still a subject for argument and speculation among chemists. The author, therefore, is only able, as a rule, to state the effects produced by these natural agents, and in comparatively few cases can suggestions be made as to the modes by which these effects are brought about. In the second part, methods of cleansing recently disinterred antiquities of various kinds and of preserving them are given, and here the author, is able to quote largely and usefully from his own wide experience of this work. The translators have added to the English edition some notes of recent work and additional illustrations which are useful in elucidating various points in the text. The book should be useful not only to curators for reference, but should prove suggestive to all interested in the preservation of natural or artificial structures exposed to the action of air, soil, or moisture. Organography of Plants. By Dr. K. Goebel. Authorised English edition by Prof. I. Bayley Balfour. Part i., pp. xvi + 270. IOS. net. Part ii., pp. xiv+ 708. 21S. net. (Oxford: The Clarendon Press.) THE German edition of the " Organography ' has already been reviewed in NATURE (vols. lviii., p. 74, lxiii., p. 149, lxvi., p. 51), and it is unnecessary, therefore, to insist again on the importance of Prof. Goebel's book, both to botanists and to others who are interested in the development of plant life. The Clarendon Press is to be congratulated on having secured Prof. Bayley Balfour to undertake the responsibility of preparing the English edition, and his name on the title-page carries with it the assurance that the work has been well done. Moreover, his great knowledge of plants has enabled him to give that indefinable cast of originality and interest to the translation that one so often misses in presentations of this kind. The text is well broken up, by means of headlines and by the use of different founts of type, thus rendering the book more easy to use. The printing, and also the figures, are excellent, and there is a good index, both of illustrations and of subject-matter. Both the Clarendon Press and the editor have laid English-speaking botanists under obligation by the excellent production in our own language of this important work. J. B. F. Catalogue of the Madreporarian Corals in the British Museum (Natural History). Vol. v., The Family Poritidæ, ii., The Genus Porites, Part i., Porites of the Indo-Pacific Region. By Henry M. Bernard. Pp. vi+303+ XXXV plates. (London: The Trustees of the British Museum, 1905.) In the preparation of this important catalogue Mr. Bernard was confronted with the difficulty, experi enced by nearly all naturalists who have attempted to arrange corals in specific groups, that the characters afforded by the skeletal structures only are so variable that there is no possibility of accurately defining the limits of "species." This is a difficulty which is wont to grow rather than dwindle as our knowledge of specimens of a genus increases, and Porites being a common and widely distributed coral, represented in the museum by very many specimens from numerous localities, the difficulty presented itself in a particularly exaggerated form. But No one will deny that the binomial system when applied to such a genus is unsatisfactory, and it will probably remain so unless further investigation of the anatomy of the living polyps reveals some characters of better value for purposes of classification. the system adopted by Mr. Bernard, of abandoning the old specific names and giving the specimens a geographical label and a number, does not appear to offer a more satisfactory solution of the problem, and will not, probably, be generally approved. Unsatis factory as they may be, many of these specific names are of some value, and all of them of historical interest. To sweep them all away at a stroke is a drastic measure which cannot be recommended, either on the ground of science or expediency. But even if Mr. Bernard's system is disapproved, naturalists will undoubtedly agree in their tribute of thanks for the skill and patience he has displayed in building up this monumental work on the IndoPolynesian specimens of the genus. The detailed description of the specimens in the museum will be of value to those who may, in the future, be tempted to grapple with the species question in the genus; but a real and important contribution to knowledge is to be found in the concise statements concerning the morphology of the skeleton and the affinities of the genus. The catalogue is adequately illustrated. Microscopes and Accessories: How to Make and Use Them. Edited by Paul N. Hasluck. Pp. 160. (London: Cassell and Co., Ltd., 1905.) Price 15. net. WE are very doubtful whether the first portion of this book, dealing with the practical construction of a microscope by the amateur, will serve any useful purpose. Such an instrument, however well constructed. must almost inevitably fall far short of the perfection attained by the instrument makers, even if the amateur be a first-class mechanic, and efficient instruments may nowadays be picked up second-hand at ridiculously low prices. In the description of the tube, all that is said with regard to the attachment of the objective is that at the bottom (of the tube) a disc of brass is sweated on, the hole in its centre being } in, diameter. and chased with a fine thread; not a word about the standard screw now adopted by all makers. The latter portion of the book, dealing with the preparation and mounting of objects, is concise and to the point, but presents nothing novel in its treatment of the subject. R. T. HEWLETT. 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.] Cooperation between Scientific Libraries. THE note in NATURE (February 15, p. 372) on Dr. T. Muir's paper in the Proceedings of the Royal Society of Edinburgh directs attention to a difficulty which, as you rightly say, affects many others than the mathematicians of Scotland. You adduce, for example, Wales; but may I, without giving offence to the Principality, venture suggest that the metropolis itself has still better claims to dishonourable mention? to In the two sciences which chiefly appeal to me, geology and zoology, the difficulty mentioned by Dr. Muir has long presented itself forcibly, and there is a lengthy list of books that I have been trying to see in vain, some of them for more than five years. They are, so far as I can ascertain, in none of the many libraries of this city. Naturally, the remedy suggested by Dr. Muir long ago presented itself to me, and I have lost no opportunity of urging it in conversation and in print. In view of your own recognition of the importance of the subject, I venture to ask you to reprint for a wider public the following paragraph from a paper contributed to the Museums Journal for April, 1902. After alluding to the cooperation between American libraries in the matter of cataloguing, and to the specialisation among the libraries of Chicago, I wrote :— "The extraordinary difficulty that a student has, even in London, in seeing the literature of his subject-in fact, the impossibility, unless he is prepared to spend large sums of money on his private library-must have made many a one long for the day when the learned societies and other library authorities of London shall take this question of cooperation in hand. To what end is all this fuss about an international catalogue of scientific literature, with its elaborate mechanism and enormous expense, if, when the list of books is in his hands, it be still impossible for the student to refer to them? The amount of money annually spent by Government, through the libraries of the British Museum, the Education Department, the Patent Office, and the like, when joined with that spent by the great societies, such as the Royal, the Zoological, the Linnean, the Geographical, the Geological, with the College of Surgeons and other public bodies of like character, is surely enough, if properly administered, to buy the world's output of books each year; and far more than enough, if we remember that all publications of the United Kingdom go to the British Museum as a matter of course, and that the donation lists of many of these libraries are nearly as big as their purchase lists. If only the money could be pooled, and the purchases distributed according to some pre-arranged scheme among the various libraries; and if a joint catalogue were prepared, and kept up from month to month, showing not only the titles of books, periodicals, and papers, but the libraries in which they were to be found, then weary searching and fruitless wandering would no longer be the lot of the conscientious student. Even as things are, without so radical a reform as a redistribution of income, I feel sure that a conference of librarians, bent rather on furthering the interests of the reader than the pride of their own institutions, and armed with the necessary powers for cooperation, would soon lift London libraries out of the hopeless muddle that we now have to struggle with." I hope that now this subject has been taken up in your influential pages it will not be allowed to drop until those concerned have at least attempted the remedy. F. A. BATHER. much care, but has met with no more success in obtaining any positive result than he has in repeating a large number of M. Blondlot's own experiments, most of which he has essayed, in all cases with absolutely negative results, provided proper precautions were taken to avoid effects due to temperature and other extraneous causes of disturbance. According to M. Gutton's experiment, the effect of the n-rays that proceed from a Nernst electric lamp upon a spark in a primary circuit is to diminish the brilliancy of another spark electrically induced in a secondary circuit by the primary discharge. Here one would suppose that the degree of brilliancy of the secondary spark can only be matter of the amount of the electrical energy in the secondary circuit, but the writer finds that a very sensitive Duddell thermo-galvanometer, which would indicate a very small percentage of variation in the amount of this energy, shows no variation whatever. A. A. CAMPBELL SWINTON. 66 Victoria Street, London, S.W., February 20. a A 300-Year Climatic and Solar Cycle. Astro IN June, 1902, I made a few remarks on an apparent coincidence between sun-spot periods and longer periods of rainfall and famine in north China. Not being, in any sense, a meteorologist, I did not publish my conclusions except locally. In connection with a notice in the nomical Column" of NATURE, November 9 last (vol. lxxiii. p. 38), they are of sufficient general importance to recall them. The notice in NATURE is headed A 300-year Cycle in Solar Phenomena," and refers to a discussion in the Astrophysical Journal wherein Mr. H. W. Clough, of the Washington Weather Bureau, arrives at the conclusion that a 300-year cycle exists in solar and the allied terrestrial phenomena, and finds likewise an intermediate 36-year cycle, and supports both by a reference to various phenomena, such as aurora, periods of grape harvest, &c. In 1877 Mr. A. Hosie, H.M. Consul at Chengtu, published a paper in the Journal of the China Branch of the Royal Asiatic Society on droughts in China (new series, xii., 51), extracted from Chinese records. As the records included all China, south as well as north, the tables did not at first sight exhibit any apparent periodicity. Some years after, on making a careful division into north and south, I was struck with a remarkable period of about 300 years, which seemed to me marked clearly in north China as an especial era of drought and famine. As, however, there seemed no reason for founding a new period, for the intercalation of which there was as yet no accumulated evidence, I proceeded no further with the subject. Mr. Hosie's paper went from the year 620 to 1643, covering a period of 1023 years, and attached to it was another notice of sun-spots observed in China, also going back for some 1300 years. The latter table, on account of the want of any observation instruments, is, of course, very fragmentary, but at the time I deduced from it without reference to European observations, which I had not by me, a probable period of 99 maxima in the 1920 years covered, which seemingly gave a mean of 11.085 years, and which, produced to modern times, fell in sufficiently satisfactorily with the European records of the last century. Sir Norman Lockyer in 1901 had also published observations bearing on a climatic curve of about six sun-spot periods, and commenting on all these I made the following remarks, which are entirely confirmative of Mr. Clough's findings, although deduced from such entirely different authorities. "I now come to the long period or era which Mr. Hosie's records seem to require. The first of these calling for notice seems to cover the three sun-spot periods 664697, though this is not so well marked as the others. The second covers the similar period from the maximum in 963 to that in 996, when besides two years of drought in northern China, 961 and 962, we find no less than twentythree years oct of the thirty-three characterised by excessive droughts in one or more of the northern provinces. The third covers the periods 1262-1295, when, in addition to the antecedent year 1260, there are noted twenty-one years of drought in the same provinces. The fourth is included between the spot maxima of 1561 and 1594, and though not so marked as the second and third, yet ten years of |