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composed.” The bearing of these facts on the ques- famous falls, is due; it not only facilitated the erection tion of vegetal coverings in the earlier periods is of the bridge, but it also enabled the permanent way briefly discussed. Observations on organic rocks, and and rolling stock for the northern continuation of the on the distribution and development of the fauna and railway line to be transported to the north bank of flora, lead up to the subject of historical geology, the gorge long before the bridge itself was completed. which the authors propose to deal with in another The interesting question of the coaling of ships at volume.

H. B. W. 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. MACHINERY FOR HANDLING RAW

The third section of the book is devoted to unloadMATERIAL.

ing and loading appliances. The discharging of The Mechanical Handling of Material. By G. F. vessels in docks, and the discharging of railway

Zimmer. Pp. xii + 521; illustrated. (London : trucks-work requiring so much labour-have been

Crosby Lockwood and Son, 1905.) Price 255. net. fertile subjects of invention, and a large number of
IN
N the preface Mr. Zimmer says that he has been systems of grab-elevators and self-emptying trucks

for twenty years professionally engaged in this are described. In view of the enormous weight of branch of engineering, and he was recently induced coal annually shipped at the various coal shipping to put together in the form of a treatise—the first in centres, no branch of the mechanical handling of English on the subject-the mass of notes he had material has received more attention than that of gradually accumulated. The importance of the sub- coal tips for loading colliers, and the chapter which ject is emphasised in the introduction by a few treats of coal tips is a most complete and valuable suggestive figures as to the amount of raw materials one. In the last section of the book a number of which has to be dealt with annually, and it may be miscellaneous devices, which the author has found it noted that the wages of an ordinary labourer are impossible to group under any of the previous equivalent to the interest on 1000l, of capital.

divisions, are described, such as the automatic weighThe question of the continuous handling of material ing of material, the coaling of railway engines, &c. is treated in the first section of the book; special Large flour and silo warehouses form an essential prominence is given to elevators for the conveyance

feature in the mechanical handling of raw materials of corn and flour, and to the important problem of the such as grain and seed, and a couple of chapters, supply of coke. ore, &c., to the top of blast furnaces; illustrated with the help of a number of plates, are illustrations are given of the latest American furnace given up to a detailed account of the main features hoists. The system of band conveying, due to the of their design. inventive skill of Mr. Lyster, engineer to the Liver

The book will be indispensable to all engineering pool Docks, and the automatic throw-off carriage for firms, consulting engineers, and architects who have such conveyors, also due to Mr. Lyster, are described

to deal with this important question either in the way in detail. Vibrating trough conveyors—the latest type of designing machinery or of erecting warehouses, of such machinery, and especially useful with any

and it is, though highly technical, a book which will material which would deteriorate in rough treatment appeal to the general reader anxious to obtain some -are then dealt with. Tightening gears, power re

slight knowledge of the latest advance in the quired, and speed of travel in the different types of mechanical handling and transport of the immense convevors are discussed in a special chapter, thus quantities of raw materials used daily in our industrial facilitating reference and comparison. The various

life.

T. H. B. types of pneumatic elevators, including the successful Duckham system for loading grain which has been

THE BUTTERFLIES OF INDIA. extensively used, are next treated. This section of The Fauna of British India, including Ceylon and the book is concluded by a series of descriptions, in Burma. Published under the authority of the every case with illustrations, of conveyors which have Secretary of State for India in Council. Edited by been designed for special purposes, such as timber W. T. Blanford. Butterflies. Vol. i. By Lieut.. conveyors, hot coke conveyors for gas works, and Colonel C. T. Bingham. Pp. xxii+511; Figs. 94: casting machines for use with large blast furnaces. Plates 10. (London: Taylor and Francis, 1903.) The intermittent handling of material, mainly by

Price 20s. endless chains and ropes, including the many systems INETY years ago, when Kirby and Spence pubof aërial cable-ways, forms the second section of Mr. lished the first volume of their “ Introduction to Zimmer's book. One of the examples selected to Entomology,” they considered it necessary to devote illustrate the use of aërial ropeways is that used a whole letter, filling many pages, to refuting popular during the building of the new Beachy Head Light- prejudices against the frivolity and uselessness of the house, and full credit is given to Messrs. Bullivant study of entomology; and, no doubt, at that period for the ingenious way in which the many practical butterfly-collecting was looked upon as a very silly, difficulties were overcome. We may mention that it childish pursuit; while less than 200 years before, in is to this system of aërial ropeway that the rapid the time of Charles II., a serious attempt was made to completion of that remarkable bridge which will set aside the will of a certain Lady Glanvil, on the convev the Rhodesian railways over the great gorge ground of insanity, as shown by her fondness for colof the Zambesi, almost within a stone's throw of the lecting butterflies.

Now, however, instead of butterfly-collecting being Butl., showing its remarkable resemblance to a species ridiculed, it has become almost necessary to discourage of the well-known tropical American genus Nymphit in England in order to prevent the total extermina- idium. tion of all our rare and local species, while abroad it Ten full-page plates (half-figures only) are added, is pursued with enthusiasm by travellers and colonials, drawn by Mr. Horace Knight and lithographed some of them belonging to the highest social circles. by the three-colour process by Messrs. Hentschel, and Again, during the last fifty years, so much light has these alone are sufficient to give some idea to outsiders been thrown on various scientific problems by the study of the variety and beauty of the butterflies of India. of butterflies that eminent professors are ready to de- If we take the butterflies of Great Britain at 70, those vote a great portion of their lives to such investiga- of Europe at 300, and those of British India, within the tions.

limits of the present work, at 1500, we shall have a Of late years, many Indian officers and civilians have fairly accurate idea of the proportions borne to each taken up the collection and study of the butterflies of other by these three faunas. our Indian Empire, which are probably better known In outlying districts, no doubt, many species still at the present time than those of any other part of the remain to be added to the Indian butterfly fauna, but world outside Europe, except North America and South apart from this, nothing is yet known of the transAfrica. But there exists no complete work on the sub- formations, habits, &c., of a great proportion of the ject suitable for the use of students. Mr. F. Moore's insects, which will be sufficient to occupy the attengreat works on the butterflies of Ceylon and India tion of numerous observers for many years. The are very bulky and costly, and the latter is still in pro- metamorphoses of each butterfly, so far as yet known, gress, while the regretted death of L. de Nicéville left are briefly noticed by Lieut.-Colonel Bingham, but the work commenced by himself and Col. Marshall, it is only occasionally that he has been able to offer and subsequently carried on by de Nicéville only, his readers any information of this description. complete only as regards the earlier families. Lieut.Colonel Bingham, a retired Indian officer, who has

THE STATE AND AGRICULTURE. collected insects assiduously in many parts of India,

The State and Agriculture in Hungary. By Dr. Burma, &c., and who has already published two volumes on Hymenoptera in the present series, “ The

Ignatius Darányi, translated by A. György. Fauna of British India,” has been wisely chosen to

Pp. xxii + 264. (London: Macmillan and Co.,

Ltd., 1905.) Price 5s. net. supply the existing want of a manual of Indian butterfies, and with his previous practical experience behind THERE are two fundamentally opposite theories him, and with sufficient leisure, and access to the col

of the duties of a public department dealing lections and library of the Natural History Museum

with a great industry such as the Board of Agriculture at South Kensington at his disposal, the work could in this country—the one that its function is to foster not have been placed in better or more competent the industry, the other that it is simply concerned in hands.

registering the progress and administering such legisIt is expected that three volumes will be required to

lative enactments as may be necessary from time to deal adequately with the subject. Six families are time. admitted by the author, of which the first two, Nymph

Our English public offices have all grown up on alidæ and Nemeobidæ, are discussed in the first the latter model, and the Board of Agriculture, which volume. The arrangement of the work is similar to is always being abused for not doing this or that to that which has been used in previous volumes of this improve the position of farmers, might legitimately series dealing with insects, which are already well answer that it was never designed to offer any such known to all entomologists. The introduction, neces- help to the agriculturist. Of course, the official sarily brief, contains remarks on classification, meta-apologists of the Board cannot put forward such a morphoses and structure, with text-illustrations of the view nakedly; their plan is rather to divert the unlarva and pupa of Vanessa, the head and body of reasonable attack by a show of activity. Argynnis and Charaxes, and a very useful selection of To take a concrete case; the Board of Agriculture figures of labial palpi, antennæ, neuration of wings, endeavours to eradicate swine fever—that it recognises

It is worthy of special remark that the as a proper function, true police work for agriculture author expressly discards the term “ species” as --but supposing it should be urged to do something liable to mislead, and uses “ form " instead, as less to improve the breed of pigs kept in England by inobjectionable.

troducing new breeds or by distributing boars of the Four hundred and seventy-nine species are described right type in the backward districts, it would probin vol. i., belonging to the Nymphalidæ (with six sub-ably meet the demand by issuing a leaflet on “ points families, Danainæ, Satyrinæ, Acræinæ, Libytheinæ, to be aimed at in pig-breeding.” The English Morphina, and Nymphalina), and Nemeobidæ (five method is cheap; it is also supposed to be bracing; genera only).

and the English farmer, being subjected to the StateThe text illustrations are excellent, and among the aided and bounty-fed competition of all other agrimore interesting ones we may note Figs. 13 and 14, on cultural countries in the only open market, his own, P. 40, showing the variations in shape and markings is supposed to be in special need of a bracing régime. of the forewings of seven specimens of Euploea klugii, So when people ask why the Board of Agriculture Moure, and Fig. 94, on p. 301, of Stiboges nymphidia, ! does not educate like France, or investigate like

and legs.

Germany, or introduce new crops and new industries appointment, for the methods advocated are like the United States, or organise its workers like

thoroughly modern and sound. Hungary, the Board has one sufficient and final

A careful reading reveals practically no ground for

adverse criticism, and many points for active comanswer in the fact that such has never been the

mendation. The warning against the indiscriminate English theory of the function of a public office.

use of cocaine is one that should be unnecessary to In the book before us we have an account of the any practising ophthalmic surgeon, and yet we have policy of a man who took a different point of view, only recently seen prescriptions for lotions and drops and created, perhaps, the most paternal ministry of

given to patients for frequent use containing cocaine.

“ The immoderate use of cocaine ... is not only agriculture in the world. Dr. Ignatius Darányi was

unnecessary but actually harmful to the corneal Minister of Agriculture for seven years (1896–1903) in

epithelium”; and again, “Cocaine should in general Hungary, and during his tenure of office he built up | not be used, for on the one hand its action is only an extraordinary system of agricultural education, in transitory, while on the other it has an injurious investigation, and organisation in Hungary. It would

fluence on the corneal epithelium; moreover the be impossible in the limits at our disposal to discuss

dilatation which follows the temporary contraction of

the vessels is harmful.”. either the means adopted or the results that have

It would be easy to point out many places in which accrued; roughly speaking, Dr. Darányi's method in | good results can be obtained by methods of treatment any industry was to make a start with a State-owned other than those recommended, but as the book does farm or garden, forest or mill, as the case might be. not in any way pretend to be exhaustive, and as the Here proceeded the investigations necessary to estab

| methods given are thoroughly sound, it would be

hypercritical to do so. We doubt, however, the lish the conditions requisite for success, and from this

advisability of the use of adrenalin in severe inflamcentre issued the teachers who carried the new

matory glaucoma, even if only given to facilitate the methods to the cultivators. The State then stepped operation. Macallan, in a paper in the Ophthalmic in again, sometimes to lend the cultivator the money | Hospital reports some two or three years ago, pointed necessary for the fresh start, or to organise a co-out the dangers of this drug in glaucoma, and its operative society to enable him to realise the full

tendency to set up the hæmorrhagic form. advantage of the newer methods. Thus, by leaps

The chapter on the various forms of inflammation

of the cornea and their treatment is quite the most and bounds, the whole character and quality of

valuable in the book, and generally the earlier Hungarian agriculture has been changed. The reader chapters dealing with the external diseases of the eve will find the process set out fully with a wealth of are fuller than the later chapters. The reason of this statistical detail in Dr. Darányi's book, which takes is that the author does not pretend to give descripthe form of a kind of valedictory report on quitting

tions of operations where only " considerable skill and

experience can command success," and in diseases of office. It has been excellently translated by Mr.

the deeper parts of the eye the advice of the György, who, knowing so well the conditions pre

ophthalmic surgeon is more likely to be called for, vailing in England, adds a preface discussing the and this book is not intended for him. In conclusion, value and limits of State interference in such matters. we can only reiterate what we have already stated, It is a wonderful record; to the English reader, par that students of medicine will find this a thoroughly ticularly if he be a farmer, it seems difficult to believe

safe guide in the treatment of diseases of the eye. that so much can be done for the industry, and also

Die Stellung Gassendis zu Deskartes, By Dr. Her. that the distance of a few hundred miles should render

mann Schneider. Pp. 67. (Leipzig: Dürr'sche

Buchhandlung, 1904.) Price 1.30 marks. impossible in this country methods that have proved

GASSENDI AND DESCARTES were contemporaries and so practicable and so fruitful for the Hungarian

fellow-countrymen, but the relation between them is agriculturist.

mainly one of contrast. Gassendi was of peasant

origin, a writer encyclopædic in his range, an Epicurus OUR BOOK SHELF.

redivivus with all Epicurus's distrust of mathematics

and all his belief in a material soul, a sceptic who was The Treatment of Diseases of the Eye. By Dr.

yet content to remain in the ranks of the Catholic Victor Hanke. Translated by J. Herbert Parsons,

priesthood, his face ever turned to the past whether in F.R.C.S., and George Coats, M.D., F.R.C.S.

| philosophy or religion. On the other side there is Pp. vi+222. (London: Hodder and Stoughton,

Descartes, a noble by birth, a student principally of 1905.) Price 3s. 6d. net.

the human understanding, something of a Platonist. Dr. VICTOR HANKE, the writer of this little book,

with the Platonist's reverence for mathematics and is principal assistant to Prof. Fuchs in Vienna,

numbers, a dualist who fixed a great gulf between and the methods of this famous clinique are

mind and body and between man and the lower those which are here given to a wider public. It

animals, an uncompromising doubter of everything naturally follows that it is characterised throughout but his own doubt and all that is implied by the by a practical sanity which has been sadly lacking in capacity to doubt, the exponent of cogito, ergo sumsome books on similar subjects which have recently in a word, the representative of the distinctively modern been thought worthy of translation. The author has tendencies, which mean in religion Protestantism, in no special hobby-horse on which to ride to mental science mathematical physics, in philosophy kandestruction. His treatment throughout is practical, tianism new and old. Only in so far as modern scientific in the best sense of the word, what we may thought inclines to atomism and materialism-and call for lack of a more fitting adjective, common- | how much that is the author points out in his closing sensical. There is no rash advocacy of new and un- paragraph-do we find that its sympathies lie with tried methods of treatment simply because of their Gassendi rather than with Descartes. novelty. Consequently, it is a book which can be These contrasts, extended into a detailed discussion thoroughly recommended to all practitioners of the of some of the writers' most important works and art of medicine. Reliance on it will not lead to dis- / particularly of their views on psychology, physics, and

His

of an

rthics, are well brought out by this author.

LETTERS TO THE EDITOR. book may be heartily recommended to students of

[The Editor does not hold himself responsible for opinions the period described.

expressed by his correspondents. Neither can he undertake | Text-book of Physics, Heat. By Prof. J. H. to return, or to correspond with the writers of, rejected Poynting, Sc.D., F.R.S., and Prof. J. J. Thomson, manuscripts intended for this or any other part of NATURE, M.A., F.R.S. Pp. xvi + 354. (London : C. Griffin

No notice is taken of anonymous communications. ] and Co., Ltd., 1904.) Price 155.

A Comparison between Two Theories of Radiation. THE third volume of this well known text-book more than sustains the standard set by its predecessors.

On two occasions (NATURE, May 18 and July 13) Lord

Rayleigh has asked for a critical comparison of two. The volumes on sound and properties of matter have

theories of radiation, the one developed by Prof. Planck. already appeared. The volumes on light and on

(Drude's Annalen, i. p. 69, and iv. p. 553) and the other plectricity and magnetism we hope may follow at a

by myself, following the dynamical principles laid down somewhat shorter interval than has intervened by Maxwell and Lord Rayleigh. It is with the greatest between the first three volumes of the series. It is hesitation that I venture to express my disagreement with nardly necessary to say that the work is well up to some points in the work of so distinguished a physicist as dite, and extremely clear and exact throughout, and

Prof. Planck, but Lord Rayleigh's second demand for a that it is as complete as it would be possible to make comparison of the two methods leads me to offer the followuch a text-book within the limits which the authois ing remarks, which would not otherwise have been pubhave laid down for the scope of their work. Among lished, on the theory of Prof. Planck. the more original features which should be valuable

Early in his second paper, Planck introduces the conception of the

entropy of a single resonator " S. There in the student as filling gaps which are noticeable in

are supposed to be N resonators having a total entropy similar text-books, we observe that a useful chapter Sy=NS, and Sy is supposed to be given by Sy = k is included on the subject of circulation and convec-log W+constant, where W is the “ probability " that the N tion, with illustrations from meteorology and ventil- resonators shall be as they are. Without discussing the ation. The treatment of the important subject of legitimacy of assigning entropy to a single resonator, we radiation, especially in relation to temperature and may at present suppose S defined by S=k/N log W+cons. thermodynamics, is unusually complete and clear, and

The function W, as at present defined, seems to me to presents in a simple, connected form a number of

have no meaning: Planck (in common, I know, with most important results which the student would have

many other physicists) speaks of the “ probability difficulty in finding elsewhere.

event, without specifying the basis according to which the The experimental

probability is measured. This conception of probability pirit is maintained throughout the work in such a

seems to me an inexact conception, and as such to have no manner that the student will feel that he is learning place in mathematical analysis. For instance, a mathe, *rom a practical master of the subject, and will un- matician has no right, quâ mathematician, to speak of consciously imbibe something of the attitude of mind the probability that a tree shall be between six and seven sof the original investigator.

H. L. C. feet in height unless he at the same time specifies from

what trees the tree in question is to be selected, and how. The Oxford Atlas of the British Colonies. Part i.

If this is not so, may I ask, “What is the probability British Africa. Seventeen maps:

(Oxford Geo

that a tree shall be between six and seven feet high? graphical Institute : William Stanford and Co., When Prof. Planck calculates the probability function Ltd., n.d.) Price 25. 6d. net.

W, he in effect assumes that a priori equal small ranges l'he first thirteen plates consist of coloured maps, and of energy are equally probable. Thus he tacitly introduces the remaining four are outlines intended for use as as the basis of his probability calculations an ensemble "test" maps or for other class purposes. The first

of systems of resonators such that the number of systems map shows a hemisphere in which Cape Colony in which the energy of any given resonator lies between rccupies the centre, and it is possible from it to see

E and E+dE is proportional simply to de. This, of at once the relation of South Africa to the other

course, he has a right to do, only he must continue to continents. Map ii. is a political map of the world

measure probability according to this same basis. drawn in accordance with Mollweides's equal area

The systems of resonators are in motion, their motion

being governed by the laws of dynamics. Will they, as projection, and the student will notice at a glance the the motion progresses, retain the statistical property which ipparent distortion in shape, though the relative has been the cause of their introduction, namely, that the sizes of land areas in different parts of the map are number of systems in which the energy of any given furrectly shown. In addition to meteorological charts, resonator lies between and E+dE is proportional simply the atlas includes physical and political maps of

to dE? It is easily found, by the method explained in my Vfrica, and maps of Cape Colony, Natal and Zulu

Dynamical Theory of Gases ” (S211), that in general land, the Transvaal and Orange River Colony, they will not; the probability function W is not simply a Rhodesia, and of West, East, and Central Africa.

function of the coordinates of the system. Prof. Planck's

position is as though he had attempted to calculate the High Temperature Measurements. By H. Le Chate- probability that a tree should be between six and seven

lier and 0. Boudouard. Authorised translation and feet high, taking as his basis of calculation an enclosure additions by Dr. G, K. Burgess. Second edition.

of growing trees, and assuming the probability to be a Pp. xv +371. (New York : John Wiley and Sons;

function only of the quantities six and seven feet. His London : Chapman and Hall, Ltd., 1904.)

ensemble of systems has not yet reached a statistical

Price 128. cd. net.

“ steady state.

Prof. Planck supposes his function S to possess the
Is preparing the present edition it was found neces-
UTY to make a large number of additions, and the where `T

property of the entropy function, so that I'T=ds/dU,

is the temperature. Combining this with bwk now gives a useful summary of what is known Planck's calculation of S, we find skrut pyrometry. The advances in optical pyrometry

1/T=kle log (1 +€/U)

(1) during the last few years are recognised by the Here e is a small quantity, a sort of indivisible atom ruthors, and a useful chapter on the laws of radiation of energy, introduced to simplify the calculations. We has been inserted. I number of pyrometers are de- may legitimately remove this artificial quantity by passing cribed, but the discussion of the principles involved to the limit in which e=0. In this way we obtain is in general more adequate than the description of

1/P=k/U.

(2) instruments. Vo mention is made of some of the hest of these in use in this country.

Thus the mean energy of each resonator, according to

this equation, is the same multiple of the temperature, no NO. 1865, VOL. 72]

1

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matter how many degrees of freedom the resonator

Of course,

aware that Planck's law is in good possesses, or what the form of its potential energy. agreement with experiment if h is given a value different Indeed, according to this argument, equation (2) is proved from zero, while my own law, obtained by putting h=o, for any dynamical system, e.g. the molecules of a gas. cannot possibly agree with experiment. This does not

It is, however, known that equation (2), with Planck's alter my belief that the value h=o is the only value which meaning of k, is true if, and only if, the energy of each it is possible to take, my view being that the supposition dynamical system is expressible as the sum of two squares. that the energy of the ether is in equilibrium with that It can, indeed, be shown directly that this latter condition of matter is utterly erroneous in the case of ether vibrais exactly the condition that Prof. Planck's assumed basis tions of short wave-length under experimental conditions. of probability calculations shall be a legitimate basis, i.e.

J. H. JEANS. shall be independent of the time. Happily, this condition of the energy being a sum of two squares may be sup- On the Spontaneous Action of Radium on Gelatin posed to be satisfied by Planck's resonators, so that we

Media, may regard equation (1) as true for such resonators.

The equation has, however, no physical meaning, owing to the

Since my communication to NATURE on the subject of presence of the arbitrary small quantity e, and can acquire engaged, my attention has been directed to the fact that

the experiments in which I have been for some time past a physical meaning only by putting e=0. merely to equation (2), which can be obtained much more

M. B. Dubois, in a speech at Lyons last November, stated readily from the theorem of equipartition.

that he had obtained some microscopic bodies by the Taking udy to be the law of radiation, where v is the

action of radium salts on gelatin bouillon which had been

rendered “ aseptic," but in what manner it is not stated. reciprocal of the period of vibration, Planck introduces

I write to direct attention to the fact, as also to add from his first paper the equation =(8*v*%*)U.

that M. Dubois's experiments were quite unknown to me. (3)

Moreover, the theory that some elementary form of which in combination with equation (2) would lead to the life, far simpler than any hitherto observed, might exist law of radiation,

and perhaps be brought about artificially by " molecular (8nk/c%)Tvädv .

(4) and atomic groupings and the groupings of electrons"and this, on replacing v by c/^, becomes

in virtue of some inherent property of the atoms of such SmkT1-4da

(5)

substances as radium-was pointed out in my article on the

“Radio-activity of Matter" in the Monthly Revier, which agrees with my own result. Planck arrives at equation (3) by the help of his assumption of näturliche

November, 1903, whilst the experiments which I have been Strahlung," but I believe it will be found that this carrying out to verify this view have been for a long time

known in Cambridge. assumption " is capable of immediate proof by the

Although I did not make a speech on the subject, ! methods of statistical mechanics. Except for this, and the

demonstrated the growths to many people at the Cavendish other differences already stated, the way in which ex

and Pathological laboratories early in the Michaelmas Term pression (5) has been reached in the present letter is

last year. identical, as regards underlying physical conceptions, with the way in which it has been obtained by Lord Rayleigh confirmation, and much delay was also caused in taking

So momentous a result as it seemed required careful and myself.

the opinions of various men of science before I ventured to Planck does not reach expression (5) at all, as he does not

write to you upon the subject. pass from equation (1) to equation (2). Instead of putting

That M. Dubois's experiments have been made quite €=0, he puts erhv, where h is a constant, and this leads independently I do not entertain the slightest doubt. at once to his well known law of radiation. It will now

Some critics have suggested that these forms I have be clear why Planck's formula reduces to my own when

observed may be identified with the curious bodies obtained 1 =s. For taking 1=3 is the same thing as taking by Quincke, Lehmann, Schenck, Leduc and others in

recent times, and by Rainey and Crosse more than half a The relation e=hv is assumed by Planck in order that

century ago; but I do not think, at least so far as I the law ultimately obtained may satisfy Wien's “ displace

can at present judge, that there is sufficient reason for ment law," i.e. may be of the form

so classifying them together. They seem to me to have 23/c3 |(T/vbdv . .

(6) little in common except, perhaps, the scale of being to This law is obtained by Wien from thermodynamical

which as microscopic forms they happen to belong. considerations on the supposition that the energy of the

JOHN BUTLER BURKE. ether is in statistical equilibrium with that of matter at a uniforın temperature. The method of statistical

The Problem of the Random Walk, mechanics, however, enables us to go further and determine the form of the function f(T/v); it is found to be

Can any of your readers refer me to a work wherein Smk{T/v), so that Wien's law (6) reduces to the law given ing the knowledge of any existing solution provide me

I should find a solution of the following problem, or failby expression (4). In other words, Wien's law directs us

with an original one? I should be extremely grateful for to take e=hy, but leaves h indeterminate, whereas

aid in the matter. statistical mechanics gives us the further information that the true value of his h=o. Indeed, this is sufficiently straight line ; he then turns through any angle whatever

A man starts from a point O and walks 1 yards in a obvious from general principles. The only way of elimin

and walks another 1 yards in a second straight line. He ating the arbitrary quantity e is by taking e=0, and this is the same as h=0.

repeats this process n times. I require the probability that Thus it comes about that in Planck's final law

after these n stretches he is at a distance between and

p+ or from his starting point, O.
8nch
da

(7)

The problem is one of considerable interest, but I have 45 echikiT-1

only succeeded in obtaining an integrated solution for tuy the value of n is left indeterminate ; on putting h=0, the stretches. I think, however, that a solution ought to be value assigned to it by statistical mechanics, we arrive at found, if only in the form of a series in powers of i'r, once at the law (5).

when n is large.

KARL PEARSON. The similarities and differences of Planck's method and The Gables, East Ilsley, Berks. 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,

British Archæology and Philistinism. but that I carry the method further than Planck, since At the end of the second week in July two contracted Planck stops short of the step of putting h=o. I venture skeletons were found in a nurseryman's grounds near the to express the opinion that it is not legitimate to stop famous British camp at Leagrave, Luton. Both were short at this point, as the hypotheses upon which Planck greatly contracted; one, on its right side, had both arms has worked lead to the relation h=0 as a necessary straight down, one under the body the other above, the consequence.

other skeleton lay upon its left side, with the left hand

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