« PrejšnjaNaprej »
composed." The bearing of these facts on the question of vegetal coverings in the earlier periods is briefly discussed. Observations on organic rocks, and on the distribution and development of the fauna and flora, lead up to the subject of historical geology, which the authors propose to deal with in another volume. H. B. W.
MACHINERY FOR HANDLING RAW
The Mechanical Handling of Material. By G. F. Zimmer. Pp. xii+521; illustrated. (London: Crosby Lockwood and Son, 1905.) Price 25s. net. N the preface Mr. Zimmer says that he has been for twenty years professionally engaged in this branch of engineering, and he was recently induced to put together in the form of a treatise-the first in English on the subject-the mass of notes he had gradually accumulated. The importance of the subject is emphasised in the introduction by a few suggestive figures as to the amount of raw materials which has to be dealt with annually, and it may be noted that the wages of an ordinary labourer are equivalent to the interest on 1000l. of capital.
The question of the continuous handling of material is treated in the first section of the book; special prominence is given to elevators for the conveyance of corn and flour, and to the important problem of the supply of coke. ore, &c., to the top of blast furnaces; illustrations are given of the latest American furnace hoists. The system of band conveying, due to the inventive skill of Mr. Lyster, engineer to the Liverpool Docks, and the automatic throw-off carriage for such conveyors, also due to Mr. Lyster, are described in detail. Vibrating trough conveyors-the latest type of such machinery, and especially useful with any material which would deteriorate in rough treatment -are then dealt with. Tightening gears, power required, and speed of travel in the different types of convevors are discussed in a special chapter, thus facilitating reference and comparison. The various types of pneumatic elevators, including the successful Duckham system for loading grain which has been extensively used, are next treated. This section of the book is concluded by a series of descriptions, in every case with illustrations, of conveyors which have been designed for special purposes, such as timber conveyors, hot coke conveyors for gas works, and casting machines for use with large blast furnaces.
The intermittent handling of material, mainly by endless chains and ropes, including the many systems of aërial cable-ways, forms the second section of Mr. Zimmer's book. One of the examples selected to illustrate the use of aërial ropeways is that used during the building of the new Beachy Head Lighthouse, and full credit is given to Messrs. Bullivant for the ingenious way in which the many practical difficulties were overcome. We may mention that it is to this system of aërial ropeway that the rapid completion of that remarkable bridge which will convey the Rhodesian railways over the great gorge of the Zambesi, almost within a stone's throw of the
famous falls, is due; it not only facilitated the erection of the bridge, but it also enabled the permanent way and rolling stock for the northern continuation of the railway line to be transported to the north bank of the gorge long before the bridge itself was completed. The interesting question of the coaling of ships at sea, a subject of special interest in view of the recent voyage of the famous Baltic Fleet to the East, forms the conclusion to this section.
The third section of the book is devoted to unloading and loading appliances. The discharging of vessels in docks, and the discharging of railway trucks-work requiring so much labour-have been fertile subjects of invention, and a large number of systems of grab-elevators and self-emptying trucks are described. In view of the enormous weight of coal annually shipped at the various coal shipping centres, no branch of the mechanical handling of material has received more attention than that of coal tips for loading colliers, and the chapter which treats of coal tips is a most complete and valuable one. In the last section of the book a number of miscellaneous devices, which the author has found it impossible to group under any of the previous divisions, are described, such as the automatic weighing of material, the coaling of railway engines, &c. Large flour and silo warehouses form an essential feature in the mechanical handling of raw materials such as grain and seed, and a couple of chapters, illustrated with the help of a number of plates, are given up to a detailed account of the main features of their design.
The book will be indispensable to all engineering firms, consulting engineers, and architects who have to deal with this important question either in the way of designing machinery or of erecting warehouses, and it is, though highly technical, a book which will appeal to the general reader anxious to obtain some slight knowledge of the latest advance in the mechanical handling and transport of the immense quantities of raw materials used daily in our industrial life. T. H. B.
THE BUTTERFLIES OF INDIA. The Fauna of British India, including Ceylon and Burma. Published under the authority of the Secretary of State for India in Council. Edited by W. T. Blanford. Butterflies. Vol. i. By Lieut.Colonel C. T. Bingham. Pp. xxii+511; Figs. 94: Plates 10. (London Taylor and Francis, 1905.) Price 20s.
NINETY years ago, when Kirby and Spence pub
lished the first volume of their "Introduction to Entomology," they considered it necessary to devote a whole letter, filling many pages, to refuting popular prejudices against the frivolity and uselessness of the study of entomology; and, no doubt, at that period butterfly-collecting was looked upon as a very silly, childish pursuit; while less than 200 years before, in the time of Charles II., a serious attempt was made to set aside the will of a certain Lady Glanvil, on the ground of insanity, as shown by her fondness for collecting butterflies.
Now, however, instead of butterfly-collecting being ridiculed, it has become almost necessary to discourage it in England in order to prevent the total extermination of all our rare and local species, while abroad it is pursued with enthusiasm by travellers and colonials, some of them belonging to the highest social circles. Again, during the last fifty years, so much light has been thrown on various scientific problems by the study of butterflies that eminent professors are ready to devote a great portion of their lives to such investigations.
Of late years, many Indian officers and civilians have taken up the collection and study of the butterflies of our Indian Empire, which are probably better known at the present time than those of any other part of the world outside Europe, except North America and South Africa. But there exists no complete work on the subject suitable for the use of students. Mr. F. Moore's great works on the butterflies of Ceylon and India are very bulky and costly, and the latter is still in progress, while the regretted death of L. de Nicéville left the work commenced by himself and Col. Marshall, and subsequently carried on by de Nicéville only, complete only as regards the earlier families. Lieut.Colonel Bingham, a retired Indian officer, who has collected insects assiduously in many parts of India, Burma, &c., and who has already published two volumes on Hymenoptera in the present series, "The Fauna of British India," has been wisely chosen to supply the existing want of a manual of Indian butterflies, and with his previous practical experience behind. him, and with sufficient leisure, and access to the collections and library of the Natural History Museum at South Kensington at his disposal, the work could not have been placed in better or more competent hands.
It is expected that three volumes will be required to deal adequately with the subject. Six families are admitted by the author, of which the first two, Nymphalidæ and Nemeobidæ, are discussed in the first volume. The arrangement of the work is similar to that which has been used in previous volumes of this series dealing with insects, which are already well known to all entomologists. The introduction, necessarily brief, contains remarks on classification, metamorphoses and structure, with text-illustrations of the larva and pupa of Vanessa, the head and body of Argynnis and Charaxes, and a very useful selection of figures of labial palpi, antennæ, neuration of wings, and legs. It is worthy of special remark that the author expressly discards the term "species" as liable to mislead, and uses "form" instead, as less objectionable.
Four hundred and seventy-nine species are described in vol. i., belonging to the Nymphalidae (with six subfamilies, Danainæ, Satyrinæ, Acræinæ, Libytheinæ, Morphinæ, and Nymphalina), and Nemeobida (five genera only).
The text illustrations are excellent, and among the more interesting ones we may note Figs. 13 and 14, on p. 40, showing the variations in shape and markings of the forewings of seven specimens of Euploea klugii, Moore, and Fig. 94, on p. 501, of Stiboges nymphidia,
Butl., showing its remarkable resemblance to a species of the well-known tropical American genus Nymphidium.
Ten full-page plates (half-figures only) are added, drawn by Mr. Horace Knight and lithographed by the three-colour process by Messrs. Hentschel, and these alone are sufficient to give some idea to outsiders of the variety and beauty of the butterflies of India. If we take the butterflies of Great Britain at 70, those of Europe at 300, and those of British India, within the limits of the present work, at 1500, we shall have a fairly accurate idea of the proportions borne to each other by these three faunas.
In outlying districts, no doubt, many species still remain to be added to the Indian butterfly fauna, but apart from this, nothing is yet known of the transformations, habits, &c., of a great proportion of the insects, which will be sufficient to occupy the attention of numerous observers for many years. The metamorphoses of each butterfly, so far as yet known, are briefly noticed by Lieut.-Colonel Bingham, but it is only occasionally that he has been able to offer his readers any information of this description.
THE STATE AND AGRICULTURE. The State and Agriculture in Hungary. By Dr. Ignatius Darányi, translated by A. A. György. Pp. xxii+264. (London: Macmillan and Co., Ltd., 1905.) Price 5s. net.
HERE are two fundamentally opposite theories of the duties of a public department dealing with a great industry such as the Board of Agriculture in this country-the one that its function is to foster the industry, the other that it is simply concerned in registering the progress and administering such legislative enactments as may be necessary from time to time.
Our English public offices have all grown up on the latter model, and the Board of Agriculture, which is always being abused for not doing this or that to improve the position of farmers, might legitimately answer that it was never designed to offer any such help to the agriculturist. Of course, the official apologists of the Board cannot put forward such a view nakedly; their plan is rather to divert the unreasonable attack by a show of activity.
To take a concrete case; the Board of Agriculture endeavours to eradicate swine fever-that it recognises as a proper function, true police work for agriculture -but supposing it should be urged to do something to improve the breed of pigs kept in England by introducing new breeds or by distributing boars of the right type in the backward districts, it would probably meet the demand by issuing a leaflet on "points be aimed at in pig-breeding." The English method is cheap; it is also supposed to be bracing; and the English farmer, being subjected to the Stateaided and bounty-fed competition of all other agricultural countries in the only open market, his own, is supposed to be in special need of a bracing régime.
So when people ask why the Board of Agriculture does not educate like France, or investigate like
Germany, or introduce new crops and new industries like the United States, or organise its workers like Hungary, the Board has one sufficient and final answer in the fact that such has never been the English theory of the function of a public office.
In the book before us we have an account of the
policy of a man who took a different point of view, and created, perhaps, the most paternal ministry of agriculture in the world. Dr. Ignatius Darányi was Minister of Agriculture for seven years (1896-1903) in Hungary, and during his tenure of office he built up an extraordinary system of agricultural education, investigation, and organisation in Hungary. It would be impossible in the limits at our disposal to discuss either the means adopted or the results that have accrued; roughly speaking, Dr. Darányi's method in any industry was to make a start with a State-owned farm or garden, forest or mill, as the case might be. Here proceeded the investigations necessary to establish the conditions requisite for success, and from this centre issued the teachers who carried the new methods to the cultivators. The State then stepped in again, sometimes to lend the cultivator the money necessary for the fresh start, or to organise a Cooperative society to enable him to realise the full advantage of the newer methods. Thus, by leaps and bounds, the whole character and quality Hungarian agriculture has been changed. The reader will find the process set out fully with a wealth of statistical detail in Dr. Darányi's book, which takes the form of a kind of valedictory report on quitting office. It has been excellently translated by Mr. György, who, knowing so well the conditions prevailing in England, adds a preface discussing the value and limits of State interference in such matters. It is a wonderful record; to the English reader, particularly if he be a farmer, it seems difficult to believe that so much can be done for the industry, and also that the distance of a few hundred miles should render impossible in this country methods that have proved so practicable and so fruitful for the Hungarian agriculturist.
OUR BOOK SHELF.
The Treatment of Diseases of the Eye. By Dr.
DR. VICTOR HANKE, the writer of this little book, is principal assistant to Prof. Fuchs in Vienna, and the methods of this famous clinique are those which are here given to a wider public. It naturally follows that it is characterised throughout by a practical sanity which has been sadly lacking in some books on similar subjects which have recently been thought worthy of translation. The author has no special hobby-horse on which to ride to mental destruction. His treatment throughout is practical, scientific in the best sense of the word, what we may call for lack of a more fitting adjective, commonsensical. There is no rash advocacy of new and untried methods of treatment simply because of their novelty. Consequently, it is a book which can be thoroughly recommended to all practitioners of the art of medicine. Reliance on it will not lead to dis
for the methods thoroughly modern and sound.
A careful reading reveals practically no ground for adverse criticism, and many points for active commendation. The warning against the indiscriminate use of cocaine is one that should be unnecessary to any practising ophthalmic surgeon, and yet we have only recently seen prescriptions for lotions and drops given to patients for frequent use containing cocaine. 66 The immoderate use of cocaine. . . is not only unnecessary but actually harmful to the corneal epithelium"; and again, "Cocaine should in general not be used, for on the one hand its action is only transitory, while on the other it has an injurious influence on the corneal epithelium; moreover the dilatation which follows the temporary contraction of the vessels is harmful."
It would be easy to point out many places in which good results can be obtained by methods of treatment other than those recommended, but as the book does not in any way pretend to be exhaustive, and as the methods given are thoroughly sound, it would be So. We doubt, however, the hypercfitical to do advisability of the use of adrenalin in severe inflammatory glaucoma, even if only given to facilitate the operation. Macallan, in a paper in the Ophthalmic Hospital reports some two or three years ago, pointed out the dangers of this drug in glaucoma, and its tendency to set up the hæmorrhagic form.
The chapter on the various forms of inflammation of the cornea and their treatment is quite the most valuable in the book, and generally the earlier chapters dealing with the external diseases of the eye are fuller than the later chapters. The reason of this is that the author does not pretend to give descrip "considerable skill and tions of operations where only experience can command success," and in diseases of the deeper parts of the eye the advice of the ophthalmic surgeon is more likely to be called for, and this book is not intended for him. In conclusion, we can only reiterate what we have already stated, that students of medicine will find this a thoroughly safe guide in the treatment of diseases of the eye. Die Stellung Gassendis zu Deskartes. By Dr. Hermann Schneider. Pp. 67. (Leipzig: Dürr'sche GASSENDI AND DESCARTES were contemporaries and Buchhandlung, 1904.) Price 1.50 marks. fellow-countrymen, but the relation between them is mainly one of contrast. Gassendi was of peasant origin, a writer encyclopædic in his range, an Epicurus redivivus with all Epicurus's distrust of mathematics and all his belief in a material soul, a sceptic who was yet content to remain in the ranks of the Catholic priesthood, his face ever turned to the past whether in philosophy or religion. On the other side there is Descartes, a noble by birth, a student principally of the human understanding, something of a Platonist. with the Platonist's reverence for mathematics and numbers, a dualist who fixed a great gulf between mind and body and between man and the lower animals, an uncompromising doubter of everything but his own doubt and all that is implied by the capacity to doubt, the exponent of cogito, ergo sumin a word, the representative of the distinctively modern tendencies, which mean in religion Protestantism, in science mathematical physics, in philosophy Kantianism new and old. Only in so far as modern thought inclines to atomism and materialism-and how much that is the author points out in his closing paragraph-do we find that its sympathies lie with Gassendi rather than with Descartes.
These contrasts, extended into a detailed discussion of some of the writers' most important works and particularly of their views on psychology, physics, and
ethics, are well brought out by this author. His book may be heartily recommended to students of the period described.
1 Text-book of Physics, Heat. By Prof. J. H. Poynting, Sc. D., F.R.S., and Prof. J. J. Thomson, M.A., F.R.S. Pp. xvi+ 354. (London: C. Griffin and Co., Ltd., 1904.) Price 158.
THE third volume of this well known text-book more than sustains the standard set by its predecessors. The volumes on sound and properties of matter have already appeared. The volumes on light and on electricity and magnetism we hope may follow at a somewhat shorter interval than has intervened between the first three volumes of the series. It is hardly necessary to say that the work is well up to date, and extremely clear and exact throughout, and that it is as complete as it would be possible to make such a text-book within the limits which the authors have laid down for the scope of their work. Among the more original features which should be valuable to the student as filling gaps which are noticeable in -imilar text-books, we observe that a useful chapter is included on the subject of circulation and convection, with illustrations from meteorology and ventilation. The treatment of the important subject of radiation, especially in relation to temperature and thermodynamics, is unusually complete and clear, and presents in a simple, connected form a number of most important results which the student would have difficulty in finding elsewhere. The experimental
spirit is maintained throughout the work in such a manner that the student will feel that he is learning from a practical master of the subject, and will unconsciously imbibe something of the attitude of mind of the original investigator. H. L. C.
The Oxford Atlas of the British Colonies. Part i. British Africa. Seventeen maps. (Oxford Geographical Institute: William Stanford and Co., Ltd., n.d.) Price 2s. 6d. net.
THE first thirteen plates consist of coloured maps, and the remaining four are outlines intended for use as "test" maps or for other class purposes. The first map shows a hemisphere in which Cape Colony occupies the centre, and it is possible from it to see at once the relation of South Africa to the other continents. Map ii. is a political map of the world drawn in accordance with Mollweides's equal area projection, and the student will notice at a glance the apparent distortion in shape, though the relative sizes of land areas in different parts of the map are correctly shown. In addition to meteorological charts. the atlas includes physical and political maps of Africa, and maps of Cape Colony, Natal and Zululand, the Transvaal and Orange River Colony, Rhodesia, and of West, East, and Central Africa. High Temperature Measurements. By H. Le Chatelier and O. Boudouard. Authorised translation and additions by Dr. G. K. Burgess. Second edition. Pp. xv+341. (New York: John Wiley and Sons; London: Chapman and Hall, Ltd., 1904.) 12s. 6d. net.
Is preparing the present edition it was found necessary to make a large number of additions, and the book now gives a useful summary of what is known about pyrometry. The advances in optical pyrometry during the last few years are recognised by the Authors, and a useful chapter on the laws of radiation has been inserted. A number of pyrometers are described, but the discussion of the principles involved is in general more adequate than the description of instruments. No mention is made of some of the best of these in use in this country.
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.]
A Comparison between Two Theories of Radiation. ON two occasions (NATURE, May 18 and July 13) Lord Rayleigh has asked for a critical comparison of two. theories of radiation, the one developed by Prof. Planck (Drude's Annalen, i. p. 69, and iv. p. 553) and the other by myself, following the dynamical principles laid down by Maxwell and Lord Rayleigh. It is with the greatest hesitation that I venture to express my disagreement with some points in the work of so distinguished a physicist as Prof. Planck, but Lord Rayleigh's second demand for a comparison of the two methods leads me to offer the following remarks, which would not otherwise have been published, on the theory of Prof. Planck.
Early in his second paper, Planck introduces the conception of the " entropy of a single resonator "S. There are supposed to be N resonators having a total entropy S, = NS, and Sx is supposed to be given by S、 = k log W+ constant, where W is the probability that the N resonators shall be as they are. Without discussing the legitimacy of assigning entropy to a single resonator, we may at present suppose S defined by S=k/N log W + cons.
The function W, as at present defined, seems to me to have no meaning. Planck (in common, I know, with many other physicists) speaks of the probability of an event, without specifying the basis according to which the probability is measured. This conception of probability seems to me an inexact conception, and as such to have no place in mathematical analysis. For instance, a mathematician has no right, quâ mathematician, to speak of the probability that a tree shall be between six and seven feet in height unless he at the same time specifies from what trees the tree in question is to be selected, and how. If this is not so, may I ask, "What is the probability that a tree shall be between six and seven feet high?
When Prof. Planck calculates the probability function W, he in effect assumes that a priori equal small ranges of energy are equally probable. Thus he tacitly introduces as the basis of his probability calculations an ensemble of systems of resonators such that the number of systems in which the energy of any given resonator lies between E and E+dE is proportional simply to dE. This, of course, he has a right to do, only he must continue to measure probability according to this same basis.
The systems of resonators are in motion, their motion being governed by the laws of dynamics. Will they, as the motion progresses, retain the statistical property which has been the cause of their introduction, namely, that the number of systems in which the energy of any given resonator lies between E and E+ dE is proportional simply to dE? It is easily found, by the method explained in my Dynamical Theory of Gases (S211), that in general they will not; the probability function W is not simply a function of the coordinates of the system. Prof. Planck's position is as though he had attempted to calculate the probability that a tree should be between six and seven feet high, taking as his basis of calculation an enclosure of growing trees, and assuming the probability to be a function only of the quantities six and seven feet. His ensemble of systems has not yet reached a statistical steady state.
Prof. Planck supposes his function S to possess the property of the entropy function, so that 1/T=dS/dU, where T is the temperature. Combining this with Planck's calculation of S, we find (1)
1/T=k/e log (1 + €/U)
matter how many degrees of freedom the resonator possesses, or what the form of its potential energy. Indeed, according to this argument, equation (2) is proved for any dynamical system, e.g. the molecules of a gas.
It is, however, known that equation (2), with Planck's meaning of k, is true if, and only if, the energy of each dynamical system is expressible as the sum of two squares. It can, indeed, be shown directly that this latter condition is exactly the condition that Prof. Planck's assumed basis of probability calculations shall be a legitimate basis, i.e. shall be independent of the time. Happily, this condition of the energy being a sum of two squares may be supposed to be satisfied by Planck's resonators, so that we may regard equation (1) as true for such resonators. The equation has, however, no physical meaning, owing to the presence of the arbitrary small quantity e, and can acquire a physical meaning only by putting e=0. It then leads merely to equation (2), which can be obtained much more readily from the theorem of equipartition.
Taking udy to be the law of radiation, where is the reciprocal of the period of vibration, Planck introduces from his first paper the equation
which agrees with my own result. Planck arrives at equation (3) by the help of his assumption of "näturliche Strahlung, but I believe it will be found that this "assumption is capable of immediate proof by the methods of statistical mechanics. Except for this, and the other differences already stated, the way in which expression (5) has been reached in the present letter is identical, as regards underlying physical conceptions, with the way in which it has been obtained by Lord Rayleigh and myself.
Planck does not reach expression (5) at all, as he does not pass from equation (1) to equation (2). Instead of putting =0, he puts ehv, where h is a constant, and this leads at once to his well known law of radiation. It will now be clear why Planck's formula reduces to my own when For taking = is the same thing as taking
yo, or e=0.
This law is obtained by Wien from thermodynamical considerations on the supposition that the energy of the ether is in statistical equilibrium with that of matter at a uniform temperature. The method of statistical mechanics, however, enables us to go further and determine the form of the function f(T/v); it is found to be Smk T/v), so that Wien's law (6) reduces to the law given by expression (4). In other words, Wien's law directs us take = hv, but leaves h indeterminate, whereas statistical mechanics gives us the further information that the true value of h is h=o. Indeed, this is sufficiently obvious from general principles. The only way of eliminating the arbitrary quantity e is by taking e=0, and this is the same as h=o.
the value of h is left indeterminate; on putting h=o, the value assigned to it by statistical mechanics, we arrive at once at the law (5).
The similarities and differences of Planck's method and my own may perhaps be best summed up by saying that the methods of both are in effect the methods of statistical mechanics and of the theorem of equipartition of energy, but that I carry the method further than Planck, since Planck stops short of the step of putting h=0. I venture to express the opinion that it is not legitimate to stop short at this point, as the hypotheses upon which Planck has worked lead to the relation h=0 as a necessary consequence.
Of course, I am aware that Planck's law is in good agreement with experiment if h is given a value different from zero, while my own law, obtained by putting h=o, cannot possibly agree with experiment. This does not alter my belief that the value ho is the only value which it is possible to take, my view being that the supposition that the energy of the ether is in equilibrium with that of matter is utterly erroneous in the case of ether vibrations of short wave-length under experimental conditions. J. H. JEANS.
On the Spontaneous Action of Radium on Gelatin Media.
SINCE my communication to NATURE on the subject of the experiments in which I have been for some time past engaged, my attention has been directed to the fact that M. B. Dubois, in a speech at Lyons last November, stated that he had obtained some microscopic bodies by the action of radium salts on gelatin bouillon which had been rendered " but in what manner it is not stated. aseptic,
I write to direct attention to the fact, as also to add that M. Dubois's experiments were quite unknown to me. Moreover, the theory that some elementary form of life, far simpler than any hitherto observed, might exist and perhaps be brought about artificially by "molecular and atomic groupings and the groupings of electrons "in virtue of some inherent property of the atoms of such substances as radium-was pointed out in my article on the "Radio-activity of Matter in the Monthly Review, carrying out to verify this view have been for a long time November, 1903, whilst the experiments which I have been known in Cambridge.
Although I did not make a speech on the subject, I demonstrated the growths to many people at the Cavendish and Pathological laboratories early in the Michaelmas Term last year.
confirmation, and much delay was also caused in taking So momentous a result as it seemed required careful the opinions of various men of science before I ventured to write to you upon the subject.
That M. Dubois's experiments have been made quite independently I do not entertain the slightest doubt.
Some critics have suggested that these forms I have observed may be identified with the curious bodies obtained by Quincke, Lehmann, Schenck, Leduc and others in recent times, and by Rainey and Crosse more than half a century ago; but I do not think, at least so far as I can at present judge, that there is sufficient reason for so classifying them together. They seem to me to have little in common except, perhaps, the scale of being to which as microscopic forms they happen to belong. JOHN BUTLER BURKE
The Problem of the Random Walk. CAN any of your readers refer me to a work wherein I should find a solution of the following problem, or failing the knowledge of any existing solution provide me with an original one? I should be extremely grateful for aid in the matter.
A man starts from a point O and walks yards in a straight line; he then turns through any angle whatever and walks another 1 yards in a second straight line. He repeats this process n times. I require the probability that after these n stretches he is at a distance between r+dr from his starting point, O.
The problem is one of considerable interest, but I have only succeeded in obtaining an integrated solution for tuo stretches. I think, however, that a solution ought to be found, if only in the form of a series in powers of 1 ", when n is large. KARL PEARSON.
The Gables, East Ilsley, Berks.
British Archæology and Philistinism.
Ar the end of the second week in July two contracted skeletons were found in a nurseryman's grounds near the famous British camp at Leagrave, Luton. Both were greatly contracted; one, on its right side, had both arms straight down, one under the body the other above; the other skeleton lay upon its left side, with the left hand