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exerting a pressure on the ions against the translation resulting from radiation; besides this force an electromagnetic force--of second order of the ratio of velocity of translation to velocity of light-may arise from the moved charges of the ions and act on the vibrating electrons. The experimental research of the light of Kanal-strahlen emitted normally to their direction has given the following results. The observations have been made on hydrogen; the velocity of the Kanal-strahlen was o'9.10° and 1'2.10° cm. sec.-1. The spectrograms were taken with a prismspectrograph and with a concave grating of 1 radius.

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The total radiation of the line spectrum (Ha, Hß, is partially polarised, and the electrical vibrations parallel to the direction of translation have a greater intensity than the vibrations at right-angles to the direction of translation. The difference of intensities is very small.

The lines of hydrogen (when observed normal to the Kanal-strahlen) are displaced towards the red, when compared with the lines emitted by the slow ions in the negative glow. The displacement seems to be proportional to the wave-length, and also proportional to the of velocity. The displacement of the centre of HB is square approximately 0-8 Ångström unit for a velocity of 12.108

cm. sec.-1.

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Inversion-point of the Joule-Kelvin Effect.

IN discussing the Joule-Kelvin effect for a fluid like hydrogen, which shows an inversion point above which heating takes place on free expansion, it is usually assumed that this point is unique. Thus, for example, Olszewski has fixed it experimentally at -80°.5 C. An examination of the consequences of any of the usually assumed equations of state (such as Van der Waals's or Dieterici's) easily reveals the fact that it must in reality be a function of the pressures to which the gas is subjected. But this is not all. If these consequences are examined for the inversion point corresponding to an infinitesimal change in pressure, it is seen that all the equations of state (which at the same time indicate a critical point) demand that there shall be two inversion points (if any) for any given pressure, and that, moreover, for sufficiently high pressures no inversion point will exist. Different equations of state, while unanimous in the above respects, indicate very different temperatures at which inversion should occur. desire to point out, therefore, that a complete determination of the inversion points corresponding to various pressures affords an exceedingly sensitive means of discriminating between characteristic equations and of indicating the direction in which these require modification. This matter is discussed in detail in a paper shortly to be published. ALFRED W. PORTER. University College, W.C., February 19.

A Definition of Temperature.

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A BODY containing heat is in a condition from which it tends to release itself (by radiating or conducting away heat), and this tendency only ceases when the body has passed into a heatless condition. The temperature of a body is the measure of its tendency at any instant to recover this heatless state (cf. Maxwell, 'Theory of Heat, 10th ed., p. 32). This suggests a mechanical analogy; a body containing heat is analogous to an elastic medium in a state of strain, from which it tends to release itself in virtue of its restitutional forces; the magnitude of the restitutional force when a body is in a given strained condition measures its tendency to release itself from that strain, and so is analogous to the temperature of a body when in a given thermal condition. The quantity of work

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stored up in producing this strained condition, and which can be given out again when the body returns to its unstrained condition, is analogous to the quantity of heat the body contains when at a given temperature; it is quite easy to show that we can completely represent the thermal condition of a body by means of a model consisting merely of an elastic rod subjected to a tension. therefore, is analogous to a tension or pressure. We are A temperature, now in a position to give a real physical meaning to the temperature "of a body, and so enable it to be measured in absolute units like a mass or a length. Let us take a molecular body devoid of all heat motion and plunge it into a medium the temperature of which is T. Then the medium will exert an intermittent pressure or force on the molecules, thus setting them into motion and generating heat motion in the body. It can easily be shown that this force cannot be infinite, or a cold body placed in a hot medium would instantly acquire the temperature of the medium, whereas it always takes a definite time to do so. The maximum force which the medium exerts on a molecule at rest when placed therein is the numerical value of its temperature. Hence we arrive at the following definition of temperature :—

A molecule at rest when placed in a medium possessing temperature is subjected to an intermittent pressure; the greatest value of this pressure is the correct measure of the temperature of the medium in the neighbourhood of the molecule. Another method of stating the same thing is to say that the greatest force required to hold a molecule at rest when placed in a medium is the measure of the temperature of the medium. Still another statement is to say that the temperature of a medium is the magnitude of the force tending to drive heat motion into an absolutely cold body placed therein. A temperature, therefore, should be measured as a pressure in dynes per sq. cm. All the ordinary laws of thermodynamics, the flowing of heat from bodies of higher to bodies of lower temperature, Waterston's hypothesis, &c., follow quite simply as a consequence of this definition, as the reader can doubtless work out for himself. GEOFFREY MARTIN. Kiel, February 10.

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MR. ALFRED TINGLE (January 4, p. 222) and Mr. CarusWilson (January 11, p. 246) may be interested to know that at the caves of Ellora, near Aurangabad, one of the pillars in the rock-cut temples has the same property of sounding under a blow.

doorway leading to an inner shrine, and if struck with the The pillar is a massive one close to, or part of, the clenched fist emits a deep note.

So far as I recollect, this property was confined to a portion of the pillar. W. G. BARNETT.

Poona, January 29.

THE NILE QUEST.1 THE story of the search for the sources of the

Nile is the longest and most interesting in the annals of geographical exploration. It dates from the earliest days of geography; it has ever presented new problems; and the quarrel over the boundary between the Congo Free State and British East Africa, in the Upper Nile basin, is the latest example of political muddles due to geographical ignorance. The sources of the Nile roused speculation in the earliest days of Egyptian geography, owing to the mysterious rising of the Nile at the driest and hottest time of the year. The view that the river rises owing to the melting of equatorial snows was for long accepted; but it is now known to be the effect of the rainy season on the Abyssinian Mountains, as the contribution from the equatorial snowfields is insignificant, and even the great reservoir, the Victoria Nyanza, gives only a minor addition to the Egyptian floods. The story of the Nile is of especial interest to British students of geography, as the larger share to the solution of its problems has been contributed by British explorers, and practically the whole of the Nile basin, with the exception of Abyssinia, is now under British administration.

The story of the exploration of the Nile is here well and interestingly told. Sir Harry Johnston is known for his literary skill, and for the artistic sense which leads him to denounce (p. 161) "the unspeakable barbarism of the British Administration " in cutting down the fine trees that once grew beside the Ripon Falls; and his distinguished success in the administration of Uganda has given him an especial personal interest in the sources of the Nile, and full access to the latest information. His volume is worthy of a place among the excellent geographical handbooks in Dr. Scott Keltie's "Stories of Exploration." Sir Harry Johnston begins his narrative in the times when, as he tells us (p. 18), 2500 years ago, Phoenicians or Sabæans worked the goldfields of Rhodesia, and with the story of Diogenes, told to Marinus of Tyre in the first century, and preserved to us by the record of Ptolemy in the second century. He continues the history to recent surveys made under the British and Anglo-Egyptian administrations. The story is so long and so full that in 318 pages the author is able to give only brief sketches of the various expeditions.

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Georg Schweinfurth, one of the greatest of African explorers." He defends d'Abbadie against the unjust attacks of Beke, and reminds us that Paez and Lobo were predecessors of Bruce. He describes the journey of Marchand (p. 245) as one of the most splendid feats in African exploration." The author perhaps somewhat underrates the early contributions of the Portuguese; but he reprints a copy of Dapper's map of 1686; so he enables the reader to judge for himself as to the extent of the facts then known about tropical Africa, and as to the nature of the mistakes made by European cartographers in their interpretation of the verbal reports of the untrained Portuguese travellers. D'Anville's map, which is much praised by the author, is less accurate in regard to the

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FIG. 1.-A Hima of Mpororo, near Karagwe. From "The Nile Quest.

But he gives an exceptionally complete list of them, and his short, critical sketches are a most useful introduction to the original literature. The most valuable part of the book is its account of the minor expeditions, and especially of those carried on from Khartoum from 1840 to 1860. The author writes with wide sympathy for the explorers of all races and all nations, and he gives foreign workers their full share of praise, including Mademoiselle Tinné, gracious demi-goddess" of the Egyptian Soudan, and

"the

The Nile Quest, a Record of the Exploration of the Nile and its Basin." By Sir Harry Johnston, G.C.M.G., K.C.B., in "The Story of Exploration," edited by Dr. J. Scott Keltie. Pp. 365 (London: Alsten Rivers, Ltd.)

Upper Nile and the Victoria Nyanza than Dapper's, though issued nearly a century later, and nearly a century and a half later than some of the authorities whom Dapper copied. The Portuguese mistake of giving several outlets from Tanganyika, which Sir Harry Johnston says shows that the Portuguese were "ignorant of the simplest principles of hydrography," was a similar mistake to that made by his own hero, Speke, in giving too many outlets from the Victoria Nyanza. The author quotes with praise Scott-Elliot's " very neat and truthful little map of the eastern and southern flanks of Ruwenzori, a map which until quite recently has been somewhat overlooked by those who have compiled charts of this

region " (p. 269). The ethnographical and zoological references in the book show high expert knowledge, but it may be noticed, perhaps with surprise, that on pp. 297 and 298 he accepts the theory of the marine origin of the fauna of Lake Tanganyika.

has more fully developed an idea that he was first led to enunciate in 1888, after the publication of Lord Kelvin's Baltimore lectures on molecular dynamics. Prof. von Lindemann's method consists, not in deriving an empirical relationship between the waveThe illustrations in the book are numerous and lengths or frequencies of the spectral lines, but in excellent, and it is illustrated by two fine maps by investigating mathematically the possible waves which

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Bartholomew, showing the orographic features, and the characteristics of the surface and vegetation in north-eastern Africa. J. W. G.

THE FORM OF THE ATOMS IN RELATION TO THEIR SPECTRA.

SINCE Balmer's important discovery in 1885 that

it is possible to calculate the wave-lengths of the first nine lines of the hydrogen spectrum by means of a simple formula, the existence of series of lines, obeying simple mathematical laws, has been established in the case of the spectra of several other elements, notably by the researches of Rydberg and of Kayser and Runge. Among the various attempts that have been made to account for these series of lines, and, in general, for the different spectra, the most promising seems to be that of Prof. F. von Lindemann, of Munich, who in some recent papers

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1 "Zur Theorie der Spectrallinien," Sitzungsber. Math. phys. Classen der Kgl. Bayer. Akad., 1901, xxxi., 441: 1903, xxxiii., 27; a lecture, printed in the Suddeutsche Monatshefte for September, 1905, of which a translation is published in the Monist for January of this year, contains a popular summary of the earlier work and an outline of results not yet published in detail.

a hypothetical atom can send out into the luminiferous ether.

His assumptions are the simplest possible. His atom consists of a certain amount of elastic isotropic matter of definite shape. The mathematical theory of the different kinds of vibrations of which such a body is capable is well understood, but the actual working out for any special case is difficult because it depends on functions which have to be discovered for each shape, and are, generally speaking, new to mathematicians. The wave-lengths of each kind of vibration sent out into the ether appear always as roots of a transcendental equation involving those functions. Such an equation has an infinite number of roots, each when real corresponding to a definite line. One equation thus corresponds with a " series " of lines. The theory gives for one body a number of such equations, and therefore a number of such "series" of lines, which together form the whole spectrum. This agrees with observed facts.

Prof. von Lindemann investigates, in the first paper quoted, the case of a spherical atom, filled throughout with matter of a definite density and elasticity. In this case, which is comparatively a simple one, the

calculation can be carried fairly far, but it is found that the spectral lines so deduced obey a law of distribution simpler than any that has yet been found by experiment to characterise any substance. Although atoms are usually assumed for physical calculations to be spherical, such a shape apparently is not really possessed by the atom of any substance; but by using the result established in this case, a simple relationship is shown to be necessary between the wave-lengths of the spectral lines of two similar elements and their atomic weights. If these two elements are conceived as being built up of the same material, having the same form, density, and elasticity, and only their size different, the wave-lengths of corresponding | spectral lines of the two elements are shown to be proportional to the cube roots of their atomic weights; given the lines of one of the elements, those of the second element can be calculated from the equation

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where and are the corresponding wave-lengths, W and W the atomic weights of the two elements. The elements of the following groups are found to obey this rule with a greater or less degree of approximation:

(1) Zinc, cadmium, and mercury.

(2) Magnesium, calcium, barium, and strontium. (3) Silver, copper, and gold.

As an illustration, the following series of lines of magnesium and calcium may be given. The arrangement and wave-lengths are those adopted by Kayser and Runge.

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From the similarity of their spectra, the elements in each of the foregoing groups appear to be similarly constructed, and the probability of this is strengthened by the analogy of their chemical properties. On the other hand, chemical analogy does not necessarily imply similarity of form in the elements, as is shown in the case of the alkali metals (lithium, sodium, potassium, rubidium, cæsium); these elements, in spite of their close chemical similarity, do not exhibit the simple relationship connecting wave-length and atomic weight found in the groups already named. Either these elements may be considered as built up of different kinds of matter, or if of the same material as possessing different shapes.

Assuming that matter is uniform, the shape of the atom may be varied, and instead of the simple sphere the case of an elongated ellipsoid of rotation, formed by revolving an ellipse round its major axis, may be considered. The mathematical theory shows that the spectral lines of such a luminous ellipsoid depend on

three numbers, and that therefore these lines will be capable of arrangement in groups according to three principles. These numbers are obtained as the roots of certain transcendental equations, and are to be calculated from the lengths of the axes of the ellipsoid, its density and elasticity, a calculation, however, which on account of its difficulty is hardly practicable. The first of the three numbers determines a group of corresponding lines, a so-called series; the different possible values of the number determine a certain sequence of such series. The second number determines in each series a subordinate group of lines, and the third number a single definite line in each subgroup. The manner in which this third number enters into the calculation shows, moreover, that the frequencies of the single lines in the subgroups will exhibit among themselves constant differences, differences, that is, depending solely on the nature of the given ellipsoid. A type of distribution of the spectral lines is thus afforded by the theory which corresponds with the well known law of distribution established by Rydberg and by Kayser and Runge in the case of the alkali metals. The atoms of these metals (Li, Na, K, Cs, Rb) may therefore be considered as elongated ellipsoids of rotation, the axial lengths being fully defined in the case of each element, and different in the different elements.

A flattened ellipsoid of rotation, the so-called spheroid, is by calculation found also to give rise to groups, series, and subgroups, but the law of constant differences is not so generally applicable. The roots of the transcendental equations are, in this case, partly imaginary, so that several groups consist of a single strong line, others of a limited number of lines. Such a grouping is actually found in the case of the metals gold, silver, and copper. Hydrogen is also of this type, its atom probably consisting of a thin, round plate, which is to be considered as the limiting case of a flattened ellipsoid.

In the more general type of ellipsoid, that with three unequal axes, the wave-lengths of the spectral lines also depend on three numbers, defined by certain equations, but in this case the lines cannot be arranged in series and groups, but range over the whole spectrum. Only when the form of the ellipsoid approximates to that of an ellipsoid of rotation will a few series arise. Such a distribution appears to obtain in the spectra of the alkaline earths (barium, strontium, calcium, and magnesium), that is, with elements lying intermediate in chemical behaviour between the alkalies and ordinary metals; the form here approaches that of the elongated ellipsoid of With zinc, cadmium, and mercury, the rotation. form approximates to the flattened type of the rotation ellipsoid.

Perhaps the most striking consequence of the theory is that which follows from an alteration in the shape of one of the simple ellipsoids of rotation. Such a solid can be imagined as being gradually strained in such a way that it passes into the more general ellipsoid with unequal axes. During such deformation the spectral lines will gradually and continuously change, and the mathematical theory predicates that out of each single line eight others can arise. It appears, indeed, that the Zeemann effect, or the resolution of a single line into two or more other lines under the influence of a magnetic field, is explicable on this hypothesis. It may be observed that the normal triplet which should result according to Zeemann's simple theory does not, as a matter of fact, occur by any means frequently, the arrangement of the resolved lines having been shown by recent work to be of a more complex character than was originally supposed. Such a complexity finds a simple explanation in Prof. von Lindemann's theory of strain.

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the calling of a conference by the Government of the United States to be held at Washington in October, 1884. At this meeting, which was attended by representatives of twenty-five nations, but who, it must be remembered, had no power to bind their Governments to any plan of action, it was resolved that "the Conference proposes to the Governments here represented, the adoption of the meridian passing through the centre of the transit instrument at the Observatory of Greenwich as the initial meridian for longitude." This resolu tion was voted for by representatives of twenty-two countries, one representative took the opposite view, and two countries, of whom France was one, abstained from voting.

Two other types of solids in addition to those establishing a time-system which should be common to already mentioned are susceptible of mathematical | the whole world, an early stage in the movement was treatment, namely, the solids derived by the rotation of a circle round an axis not passing through its centre. When the axis does not cut the circle a ring with a circular section is produced, such as an ordinary finger ring, which is open at the middle. When the axis cuts the circle, a solid, which Lindemann calls a "Wulst" or roll, and resembles in form orange or an apple-is generated. A particle having the first of these shapes, when rendered luminous, would, according to the mathematical theory, give rise to lines having wave-lengths dependent on four numbers, to each of which a series of values can be given. The kind of spectrum which results can best be explained by imagining the spectrum due to a luminous particle of the elongated ellipsoidal type to be displaced several times in succession, the relative position of the lines being slightly modified in each shift. Such a spectrum has already been found to characterise oxygen and helium; the oxygen spectrum, indeed, according to Runge and Paschen, appears as if derived from that of an alkali metal by a series of successive displacements. An atom of the second type, with a shape similar to that of an apple, when rendered luminous, would, according to the calculations, give rise to a spectrum such as would be produced by successive displacements of the lines due to a flattened ellipsoid. The spectra of sulphur and selenium seem, indeed, to be of this type, being derived from a spectrum like that of oxygen by substituting single strong lines for certain groups of lines. The atom of oxygen thus appears to have the form of an open ring, the atom of sulphur or selenium that of a "Wulst.

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Certain interesting consequences concerning the chemical properties of the elements follow from a consideration of their shape, and have been developed by Prof. Lindemann. That the ring-shaped oxygen atom, for example, is a dyad with regard to hydrogen

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once follows from the plate-like shape of the hydrogen atoms, two of these being necessary to close the two apertures of the ring. A distinction, moreover, such as is actually found to exist, is introduced at the outset between valency with regard to hydrogen and valency with regard to oxygen. Apart from speculations of this kind, Prof. von Lindemann's work has great significance at the present moment, in that it demonstrates the possibility to derive those physical constants which most clearly define and characterise the individual elements from the conception of a single kind of matter merely by introducing the idea of shape. It is, of course, possible that the atoms do not possess strictly, but only approximately, the simple shapes which can be treated mathematically. If this were so, slight changes would be introduced into the transcendental equations, and the deduced values, for example those in the table given, can be considered only as a first approximation; but the approximation is sufficiently close to justify the belief that the general type of the transcendental equations is correct. W. A. D.

THE TIME OF FRANCE.

A NOTE from the Paris correspondent of a daily journal stating that the proposal to adopt Greenwich time in France is again being brought forward, a desirable reform which would bring our nearest neighbour into harmony in this respect with almost the whole of Europe, may be considered a sufficient reason for giving some facts on the subject under discussion.

Without going back to the earliest proposals for

Following on this, a resolution was passed at the meeting adopting the principle of a universal day which should begin at mean midnight of the initial meridian, a scheme containing the germ of the present hourly zone system. But a more practical step had already been taken by the managers of the American railways, who, in November, 1883, had adopted the now well-known system in which the American continent is divided into five zones, the time used in each of which is respectively 4, 5, 6, 7, and 8 hours slow on Greenwich. It says much for the breadth of view of the American railway managers, who thus rose above all consideration of national feeling and selected a zero which was likely to suit the convenience of the greatest number, and set an example which must have done much to forward the scheme.

Since 1884 there has been no open international intercourse on the subject, but gradually the zone time system has made its way. In 1892 Belgium and Holland began to use Greenwich time; in 1893 mid-European time, one hour fast on Greenwich, was made the legal standard time in Germany and Italy; in the next year the same time was adopted in Switzerland and Denmark, and in 1895 in Norway. Mid-European time had already been in use in Sweden many years, and on the Austrian, Hungarian, Servian, and Macedonian railways since 1891, but, strangely enough, Vienna, the home of Dr. Schram, who was one of the leaders of the movement for the unification of time. has not adopted any legal standard time. The meridian of Pulkowa happens to be 2 hours 1 minute east of Greenwich, and since the time of this meridian is used for telegraph work and on the railways of Russia, it may be considered that this country uses east European time, two hours fast on Greenwich, which is also used for some purposes in Turkey. Since Greenwich time was made the legal time of Spain in 1900, it will be seen that almost the whole of Europe has fallen in line. France has not held aloof for want of consideration of its merits. In 1896 the proposition that the Greenwich meridian should be adopted in France was brought by M. Deville before the Chamber of Deputies, and being voted on was accepted by that body, but the matter went no further, the reason for which may be inferred from the proceedings at the meeting of the Astronomical Society of France held on December 2, 1896. At that meeting several of the leading scientific men of France were present, and among them M. Bouquet de la Grye, who, after expressing his astonishment that scientific men had not been consulted before such a proposition was made, proceeded to raise objections. It was true, said he, that the meridian of Greenwich had been chosen as initial because of the greatness of England's seapower; but, he asked, how long would this continue? England's supremacy in this respect might pass away just as had that of other nations, and what then?

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