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OUR BOOK SHELF. Beiträge zur Physik der freien Atmosphäre. Edited. with the cooperation of a number of distinguished meteorologists, by R. Assmann (Berlin) and H. Hergesell (Strassburg). Vol. i. Part i. burg: Trübner, 1904.)

the advantage either to the patentee or to the community of allowing what may in reality be a specification of a valuable invention to be marred by an official statement as to certain prior specifications. (Strass-There is a fear that an official with insufficient experience of practice either in works or in the Chancery Court may attach too great importance to what are known as paper anticipations, and by insisting on referring to them prevent a patent which otherwise might have been the basis of a successful manufacturing process, and be good enough to stand attack in the courts, from being even looked at by any manufacturer. However this may be, it is impossible to cast any doubt upon the Patent Office without paying a tribute to the great courtesy with which the humblest stranger who goes there is met, and the help that he is sure to receive short of professional advice. The library, too, and its arrangement is an admirable feature.

Os receiving the first number of a new periodical, the question of the need and room for such a publication first rises to one's thoughts. It must be admitted that it is not easy to see the necessity for a magazine so highly specialised as the one before us. That the investigation of the upper atmosphere is a separate branch of study in itself is very questionable; and there are already the Meteorologische Zeitschrift, the Veröffentlichungen der internationalen Kommission fur wissenschaftliche Luftschiffahrt, and the Illusinerte Aeronautische Mitteilungen, all suitable for the discussion of such investigations.

The subject-matter of this first number of the Beitrage is exceedingly interesting, and of no little importance. It contains three articles, each by a high authority on the subject dealt with.

The first, by Prof. Hergesell, is devoted to proving that kites can be raised to great heights quite independently of the weather conditions where a large expanse of water and a high-speed motor-boat are at the disposal of the observer, this being the same result as that arrived at by Rotch and by Dines. The more immediate object of the present article is to urge the possibility and necessity of founding an observatory on Lake Constance specially devoted to the investigation of the upper atmosphere.

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In the second article Prof. Assmann describes year's simultaneous kite ascents in Berlin and Hamburg," with special reference to the existence of a warm current of air flowing almost constantly between 500 metres and 1000 metres above the surface. That such a current should exist is very interesting, and further observations as to its extent, strength, and permanency are very much to be desired.

The remaining article treats of the methods employed by Dr. A. de Quervain in determining the paths traversed by balloons sent up with registering instruments only. The methods described can only be employed so long as the balloon remains within the range of vision of a telescope; they are really trigonometrical. The first is the simple method of two theodolites at the ends of a base line, and the second similar, with the exception that only one theodolite is used, the heights of the balloon at the moments of observing with the theodolite being obtained later from the curve drawn by the barograph carried with the balloon.

Articles for future numbers, which are to be
lished as may be found convenient, are promised by
Prof. Sprung, Prof. Wiechert, Dr. J. Maurer, and
Dr. A. de Quervain.

G. C. S.

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A Manual of Mining. By M. C. Ihlseng and E. B.
Wilson. Fourth edition. Pp. xvi+723. (New
York: John Wiley and Sons; London: Chapman
and Hall, Ltd., 1905.) Price 218. net.
BASED on the course of lectures delivered at the
School of Mines of Colorado, Prof. Ihlseng's book,
which is regarded in America as the best text-book
on the subject, has been enlarged under the joint
authorship of Mr. Wilson to include coal mining,
which received scant attention in previous editions.
Excepting that ore dressing and coal washing are
not touched upon, it now covers much the same
ground as Sir C. Le Neve Foster's "Elements of
Mining and Quarrying." The arrangement is, how-
ever, altogether different. The book is divided into
two parts, mining engineering and practical mining.
The former deals with prospecting, preparatory work,
methods

of mining, power generation, hoisting machinery, electric generation and water power, hoisting machinery and underground conveyances, underground haulage systems, wire rope transmission, the compression of air, pumping, mine gases, ventilation, distribution of air, the illumination of

mines, and accidents in mines.

The second part deals with shafts, sinking in running ground, timbering, driving drifts, tunnels and gangways, drilling and boring machines for explorations, miners' tools, channelers, drills and coalcutters, and blasting. It is difficult to see the object of this division into mining engineering and practical pub-mining. In this country it is not usual to draw a sharp distinction between theory and practice in engineering work. Moreover, the order of the chapters in each section does not appear to be so logical as that followed in English and Continental textbooks. Thus on p. 30 the steam shovel is described, but it is not until p. 621 that we come to a description of the ordinary pick and shovel. On p. 47 the blasting of coal is dealt with, but it is not until p. 685 that the operation is described and the theory of blasting explained. The book contains much useful information, but the lack of method in the arrangement cannot fail to militate against its use as a text-book. The illustrations, many of which are excellent, are largely borrowed from makers' catalogues, and are not nearly so useful for educational purposes as rough sketches specially drawn would be.

The Inventor's Guide to Patent Law and the New Practice. By James Roberts, M.A., LL.B. Pp. viii+ 109. (London: John Murray, 1905.) Price

23. 6d. net.

This is a well written handbook on British patent law and practice in which the inventor will find information of use to him. The new practice referred to in the title is the search by officials of the Patent Office for anticipations within the fifty years prior to in application, and the possible enforced statement as to these which the patentee may have imposed upon his own specification.

While the information derived from a search by officials of the Patent Office may be of the greatest u to a patentee, there is considerable doubt as to

The frequent misprints in figures in the index and in the references should have been carefully guarded against in a book intended for students. Several

names also are incorrectly printed, and the references given at the end of the chapter on mine illumination mostly refer to ventilation. On p. 681 the student is taught to load a hole "with nitroglycerine by pouring from a tin cup upon the fuse with its cap and covering the mass with water." Evidently the Coal Mines Regulation Act has no analogue in a country where, as the authors point out, "each new camp, untrammelled by tradition to keep it in the rut of prejudice, displays its genius for organisation and absorbs the latest devices, tried and true." The Practical

Photographer. (Library Series.) Edited by Rev. F. C. Lambert. No. 16, Pictorial Composition. Pp. xx+64. No. 17, Animal Photography. Pp. xxiv+64. (London: Hodder and Stoughton, 1905.) Price Is. net.

IN the first of these books the editor gives an interesting account of the pictorial work of Bernard Alfieri, illustrating it with six excellent reproductions of this well-known worker's studies. Among the other sections of the book, which are written by various authors, those on the principles of composition, by Arthur Burchett, and some notes on composition in landscape, by Horace Mummery, will be found of great practical value. In these the pen and ink sketches showing the several methods of producing balance in pictures call for special attention. Other articles, such as that on the arrangement of the foreground, are well worth perusing. Numerous well reproduced illustrations, serving as examples of good and bad composition, accompany the text. The second of the above books appeals to another class of photographers, for, with the exception of the editor's article on the pictorial work of Viscount Maitland, it is devoted to the photography of animals. Like the former bock, numerous authors have contributed to the text, and a very wide range of points of view is included. It is written on the same practical lines, and is accompanied by fifty-five well selected illustrations. Both volumes will add to the value of this useful library series. Determination des Espèces minérales. By L. M. Granderye. Pp. 184. (Paris: Gauthier-Villars,

46

n.d.) Price 2.50 francs.

IN this little book, which is a publication of the Encyclopédie scientifique des Aide-Mémoire," the author has apparently attempted to devise a royal road for the determination of a mineral species. For this purpose he has compiled a number of lists of the more common minerals arranged according to physical characters, viz. crystal-system, colour, structure, density, &c., and has supplemented these with some instructions on blowpipe analysis and chemical examination in the dry way. Such lists are certainly of great value for determination purposes, but, as regards the more common minerals, at any rate, it would be a mistake to encourage the student to rely upon any methodical scheme of determination to the neglect of an acquisition of a thorough knowledge of the characters of the individual species. For many minerals, especially with imperfectly crystallised specimens, we fear these tables would prove an uncertain guide in the absence of any observations of the optical characters or of chemical examination in the wet way. In Brush and Penfield's standard work on determinative mineralogy it is true that no account is taken of the optical characters, but sufficient importance is given to chemical tests in the wet way. The tables are not altogether free from errors and misprints; thus a saline taste is attributed to sodalite, rhodonite is described as a carbonate, and the density of wolframite is given as 5.5 on one page and 7.5 on another. The book concludes with a list of 600 minerals with their principal characters, viz. density, hardness, &c.

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.] The Dynamical Theory of Gases and of Radiation. I AM glad to have elicited the very clear statement of his view which Mr. Jeans gives in NATURE of April 27. In general outline it corresponds pretty closely with that expressed by O. Reynolds in a British Association discussion at Aberdeen (NATURE, vol. xxxii. p. 534, 1885). The various modes of molecular motion are divided into two sharply separated groups. Within one group including the translatory modes, equipartition of energy is supposed to establish itself within a small fraction of a second; but between the modes of this group and those of vibration included in the other group, equipartition may require, Mr. Jeans thinks, millions of years. Even if minutes were substituted for years, we must admit, I think, that the law of equipartition is reconciled with all that is absolutely proved by our experiments upon specific heat, which are, indeed, somewhat rough in all cases, and especially imperfect in so far as they relate to what may happen over long intervals of time.

As I have already suggested, it is when we extend the application of the law of equipartition to the modes of æthereal vibration that the difficulties thicken, and this extension we are bound to make. The first question is as to the consequences of the law, considered to be applicable, after which, if necessary, we may inquire whether any of these consequences can be evaded by supposing the equipartition to require a long time for its complete establishment. As regards the first question, two things are at once evident. The energy in any particular mode must be proportional to 0, the absolute temperature. And the number of modes corresponding to any finite space occupied by the radiation, is infinite. Although this is enough to show that the law of equipartition cannot apply in its integrity, it will be of interest to follow out its consequences a little further. Some of them were discussed in a former paper,' the argument of which will now be repeated with an extension designed to determine the coefficient as well as the law of radiation. As we consider the motion of an introduction, stretched string of length 1, vibrating transversely in one plane. If a be the velocity of propagation, the number of subdivisions in any mode of vibration, the frequency fis given by (1)

f=ag/2l

a

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128..e.Adλ

(9) as the total energy of radiation per unit of volume corresponding to the interval from A to λ+dλ, and in (9) e is proportional to the absolute temperature 0.

Apart from the numerical coefficient, this is the formula which I gave in the paper referred to as probably representing the truth when a is large, in place of the quite different form then generally accepted. The suggestion was soon confirmed by Rubens and Kurlbaum, and a little later Planck (Drude Ann., vol. iv. p. 553, 1901) put forward his theoretical formula, which seems to agree very well with the experimental facts. This contains two constants, h and k, besides c, the velocity of light. In terms of A it is 8nch dx E dλ= Ashika - Į

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(10)

(11)

in agreement with (9). E dλ here denotes the volumedensity of the energy of radiation corresponding to dλ.

A very remarkable feature in Planck's work is the connection which he finds between radiation and molecular cunstants. If N be the number of gaseous molecules in 4 rubic centimetre at o° C. and under a pressure of one atmosphere, k = 1·013× 10" 273N

(12) Though I failed to notice it in the earlier paper, it is evident that (9) leads to a similar connection. For e, representing the kinetic energy of a single mode at temperature 9. may be identified with one-third of the average kinetic energy of a gaseous molecule at that temperature. In the virial equation, if N be the total number of molecules,

so that

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e = pv 2N

(13)

If we apply this to one cubic centimetre of a gas under
standard conditions, N has the meaning above specified,
71, and p=1013× 10o C.G.S. Accordingly, at o° C.
e=1-013× 10 2N,

and at @

@=

1-013 × 10" × A
2×273N

(14)

Introducing this into (9), we get as the number of ergs per cubic centimetre of radiation

64.7.1013.10.9.dx
273.N.A'

(15)

@being measured in centigrade degrees. This result is eight times as large as that found by Planck. If we retain the estimate of radiation used in his calculations, we should deduce a value of N eight times as great as his, and probably greater than can be accepted.

the law of equipartition as laid down by Boltzmann and Maxwell. My difficulty is to understand how another process, also based upon Boltzmann's ideas, can lead to a different result.

According to (15), if it were applicable to all wavelengths, the total energy of radiation at a given temperature would be infinite, and this is an inevitable consequence of applying the law of equipartition to a uniform structureless medium. If we were dealing with elastic solid balls colliding with one another and with the walls of a containing vessel of similar constitution, energy, initially wholly translational, would be slowly converted into vibrational forms of continually higher and higher degrees of subdivision. If the solid were structureless, this process would have no limit; but on an atomic theory a limit might be reached when the subdivisions no longer included more than a single molecule. The energy, originally mechanical, would then have become entirely thermal.

Can we escape from the difficulties, into which we have been led, by appealing to the slowness with which equipartition may establish itself? According to this view, the energy of radiation within an enclosure at given temperature would, indeed, increase without limit, but the rate of increase after a short time would be very slow. If a small aperture is suddenly made, the escaping radiation depends at first upon how long the enclosure has been complete. In this case we lose the advantage formerly available of dividing the modes into two sharply separated groups. Here, on the contrary, we have always to consider vibrations of such wave-lengths as to bear an intermediate character. The kind of radiation escaping from a small perforation must depend upon the size of the perforation.

Again, does the postulated slowness of transformation really obtain? Red light falling upon the blackened face of a thermopile is absorbed, and the instrument rapidly indicates a rise of temperature. Vibrational energy is readily converted into translational energy. Why, then, does the thermopile not itself shine in the dark?

It seems to me that we must admit the failure of the law of equipartition in these extreme cases. If this is so,

it is obviously of great importance to ascertain the reason. I have on a former occasion (Phil. Mag., vol. xlix. p. 118, 1900) expressed my dissatisfaction with the way in which great potential energy is dealt with in the general theory leading to the law of equipartition. RAYLEIGH. May 6.

The Cleavage of Slates.

In his critique of Dr. Becker's theory of slaty cleavage in NATURE of May 4, "A. H." says that it is substantially the same as mine, and rightly objects that, "if the cleavage plane were a plane of shearing it would correspond with a circular section of the ellipsoid" of distortion. It is true that I made that suggestion in the body of my first paper on cleavage in the Geological Magazine, 1884, but in a postscript to that paper I stated that a conversation with Mr. Harker had led me to the conclusion that the cleavage surfaces are determined by the position of the principal axes of the ellipsoids of distortion produced by a shearing movement, and to this view I have ever since adhered.

“A. H."' says that "there are many slates in which the strain ellipsoid is actually presented in deformed spherical concretions or colour-spots." Is this certain? Is it not probable that these discolorations took place after the rock became a slate? In that case the chemical influence emanating from the foreign particle, usually obvious in the centre of the spot, found the greatest conductivity in the direction of the longest axis of the ellipsoid, the next greatest along the mean axis, and very little along the least. It is from this property of little conductivity across the cleavage that slates are eminently suited for roofing. I have a piece of a school slate with two sharply defined oval A critical comparison of the two processes would be of patches, of each of which the two diameters are 25 mm. interest, but not having succeeded in following Planck's and 16 mm. The thickness of the slate is less than 4 mm., reasoning I am unable to undertake it. As applying to and yet the discoloration does not pass through to the all wave-lengths, his formula would have the greater value other side. If these spots are sections of ellipsoids formed tf satisfactorily established. On the other hand, the out of spheres by compression, the resulting condensation reasoning which leads to (15) is very simple, and this must have been incredibly enormous. The spots in Borrowformula appears to me to be a necessary consequence of dale slates are of a different character from spots of dis

coloration. They existed in the rock before cleavage was induced. Many of them are broken up like broken eggshells. Those which are complete lie with their longest axes in the plane of cleavage, and would well agree with the theory that they were deformed along with the enveloping rock by a shearing process, and that the plane of the greatest distortion was the plane of cleavage.

In my paper on cleavage and distortion in the Geological Magazine I pointed out that it is to Sir John Herschel that we are indebted for the theory of the molecular movement, which, I remarked, was in fact a "shear "-a term which has now been universally accepted for this kind of action in rocks; and in my Physics of the Earth's Crust " I have explained how the crumpling in the harder and cleavage in softer layers of a rock would simultaneously arise from such a shearing O. FISHER.

"

movement.

Harlton, Cambridge, May 8.

A Relation between Spring and Summer. A FAIR idea of the larger fluctuations of a given meteorological element may be had by means of a two-fold smoothing process, e.g. adding the series of values in groups of five (1 to 5, 2 to 6, 3 to 7, &c.), and then doing the same with those sums. In each case the sum is put opposite the middle member of the group.

When this is done with (a) the amounts of rainfall in spring (March to May) at Greenwich since 1841, and (b) the numbers of warm months in summer (same place and period), we have the two curves in the diagram. The 1845 9 33 '6 '5'9'73 '7 '81 '5 '9 '93 '7 '01'5

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FIG. 1.-Smoothed curves of spring rainfall and summer warmth. lower one (that for summer) is inverted, so that its crests represent few warm months, or coolness.

One must be struck, I think, with the similarity of the curves; four long waves (roughly) in each, those of the lower curve lagging in phase somewhat (one to three years) on those of the upper curve. The four centres of wetness, as we may call them, of the spring series are followed at a brief interval by four centres of cold in the summer series, and the four centres of dryness in the former, at much the same interval, by four centres of warmth in the

latter.

Let us look briefly at the nature of those centres, and we may do so by indicating, first, the character of the group of five springs about each of the dates 1849, 1862, 1878, and 1888 (wave-crests of upper curve), and the corresponding summer groups (wave-crests of lower curve). We find in each group of five springs an excess in the total rainfall, and at least three of the five wet; further, in each summer group a small number of warm months.

5 Springs

about Rainfall

1849 28.5

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1862 28.5

+3.8

3

1863

5

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1881

1888 27.9

+32

3

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Here the relations are all of an opposite character. To what are those long waves of variation to be attributed? And can any physical explanation be given of the sequence which has been indicated? Perhaps some of your readers may be able to throw light on these points. I will only remark that there is no obvious connection with the sun-spot cycle. Thus the first two crests in the upper curve come close after maxima (1848 and 1860), while the two latter are near minima (1878 and 1889).

With regard to the point now reached by this curve (a), the rainfall of the present spring (already in excess, May 10) should extend it upwards, but it must apparently be near another crest. Some help in forecasting our summers might perhaps be derived from a consideration of the facts above given. ALEX. B. MACDOWALL.

Fictitious Problems in Mathematics.

IN NATURE of April 27 (vol. lxxi. p. 603) your reviewer finds fault with Cambridge examiners for endowing bodies with the most inconsistent properties in the matter of perfect roughness and perfect smoothness-" A perfectly rough body placed on a perfectly smooth surface." Your reviewer adds, the average college don forgets that roughness or smoothness are matters which concern two surfaces. not one body.

Will your reviewer give a reference to some page of Whittaker's book (that under review), or to some page of any other text-book used in the last half-century at Cambridge, in support of his charge against Cambridge examiners? Fifty years ago, William Hopkins was still directing the mathematical teaching of Cambridge, and enforcing the conservation of energy where friction is taken into consideration. A perfectly rough sphere moving on a rough surface is intended to mean that, during the motion considered, the sphere rolls without any slip. A perfectly rough sphere moving on a smooth surface" would no doubt be equivalent to 'A sphere moving on a smooth surface"; but where does the phrase occur?

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THE alleged inaccuracies of language in stating the assumed conditions of smoothness or roughness prevailing between two bodies in contact are unfortunately so common that it is the exception rather than the rule to find any problem in which these conditions are correctly worded. In working through a chapter of Besant's "Dynamics with a class the other day, I came across no less than two problems in which a perfectly rough body was supposed to be in contact with a second body which in turn rested against a third perfectly smooth " body. In these cases the framer of the question carefully avoided giving any information as to the roughness or smoothness of the middle body, so that the inaccuracy of language might easily be overlooked. But this does not apply to the following example :

66

"A person is placed at one end of a perfectly rough board which rests on a smooth table. Supposing he walks to the other end of the board, determine how much the board has moved. If he stepped off the board, show how to determine its subsequent motion" (Routh, "Elementary Rigid Dynamics,' 1882 edition, p. 69, example 4). At the time of writing the review I was quite unaware that such an example had found its way into a text-book written by so careful a teacher of applied mathematics as Dr. Routh, and it says much for the prevalence at Cambridge of these erroneous forms of statement that this wording failed to attract the author's attention. Since writing my review, it has been brought to my notice that similar inaccuracies widely prevail in the statement of problems involving so-called " perfectly elastic" or "inTHE REVIEWER.

elastic bodies."

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with the general geography, Mr. Ferrar with physical geography, Lieut. Royds with meteorology, Dr. Wilson with seals and birds, and Mr. Hodgson with the marine biological collections. Captain Colbeck also contributes a paper on the Antarctic sea-ice, discussing the observations made on the Southern Cross in 1898-1900 and on the Morning in 1902-4. Without attempting to summarise the contents of each paper, we may try to indicate what are the chief problems which have attracted the attention of the members of the expedition, and what materials they have provided for their discussion. All things considered, perhaps the most important questions concern the remarkable ice conditions observed by Captain Scott and Mr. Ferrar. "There are innumerable glaciers on the coast of Victoria Land," says Captain Scott, "but the great majority merely discharge local névé fields lying in the valleys of the coastal ranges. Very few run back to the inland ice, and these may be divided into two classesthe living and the dead. In the long stretch of coast between Cape Adare and Mount Longstaff, over 11° of latitude, there appears to be only four living ice-discharges from the inland. "The Ferrar glacier is typical of the dead glaciers; the ice lies in the valley practically stationary, and gradually wasting away from the summer thawing." "The Ferrar glacier probably contains as much

ice as any hitherto known in the world; the Barne and Shackleton glaciers contain a great deal more, and since they are now in such a diminished state it is interesting to think what vast streams of ice they must have been at their maximum." "To what extent the inland ice sheet stood above its present level is also interesting to surmise; one would submit a possibility of 400 or 500 feet."

Again, referring to the Great Barrier, Captain Scott says:-"... the barrier edge sixty years ago was in advance of its present position, in places as much as 20 or 30 miles."

These facts, along with many others, such as Ferrar of observations by Dr. Wilson and Mr. moraines and erratics high above the level of the icesheet, all go to show that "the majority of curious and often vast ice-formations met with in the Ross

sea must be regarded, not as the result of present day conditions, but as the rapidly wasting remnants of a former age.

One of the most remarkable observations is that while, as just explained, the ice from Victoria Land does not make any important contribution to the ice-barrier in the Ross Sea, that ice is moving northward at the rate of about 600

yards in a year. Captain Scott believes that the greater portion of the ice-sheet in the Ross Sea is afloat, and that the high coast line of Victoria Land continues southward in a direction towards Graham's Land. Here there is obviously a fruitful source of discussion, but whatever the result, with regard to the distribution of land and sea, it may be taken as proved beyond doubt that the ice in at least this part of the Antarctic regions is in a state of fairly rapid retreat, and it is known that the same thing is happening in the Arctic regions.

Mr. Ferrar's geological observations in Victoria Land have an important bearing on the problem of the outline of the land mass, as well as great intrinsic

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FIG. 2.-Mount Erebus with smok".

value. In the Royal Society range a gneissic platform was found, probably of Archæan age, and above it in order are granites, sandstone, and basalt. The granites are, according to Mr. Ferrar, of two ages; the sandstone is 2000 feet thick, while the basalt caps the sandstone, forming plateaux which have been dissected by denudation, and probably also broken up by faulting. At the base of the basalt a thin carbon

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