complex NO3 group. In order to complete a stable arrangement around the four nuclei, the NO, group has borrowed an electron from the sodium atom, leaving it a positively charged ion. These ions are arranged in the same way in NaNO, and NaCl, each ion being surrounded by six of the opposite sign. The form of the NO, group has, however, distorted the structure so that the crystal is rhombohedral instead of cubic.

In MgCO, the arrangement of the atoms is the same as in NaNO3. The magnesium ion has a double positive charge, the CO, ion a double negative charge. As a result of the greater electrostatic forces, the dimensions of the structure are reduced, the distance between magnesium and oxygen centres being 2:00 A., as compared with 2:38 Å. in the case of sodium nitrate. This will make it clear why the divalent element appears to occupy a smaller space in a crystalline structure than the monovalent element preceding it in the periodic series.

The large diameters assigned to the electropositive elements as compared with the electronegative elements do not imply a corresponding difference in the dimensions of the atomic structure. They are an expression of the fact that the electropositive element does not share electrons with neighbouring atoms, it is always surrounded by a complete stable shell. The repulsion between this outer shell and the shells of neighbouring atoms keeps the atom at a distance from its neighbours, so that it appears to occupy a large space in the crystal structure.

It is interesting to compare the structure of graphite with that of diamond from this point of view. The graphite crystal has been analysed by Debye and Scherrer*. It corresponds to a diamond structure in which, firstly, the dimensions of the whole structures parallel to a trigonal axis have been lengthened in the ratio 0.598: 1, and, secondly. the carbon atoms in the pairs of (111) planes of the diamond have been so displaced that they lie very nearly in the same plane. The atoms in a (111) plane are therefore very much. closer to each other than they are to the atoms in the next planes. This may be explained by supposing that they are sharing electrons with their neighbours in the (111) planes but not with the other atoms, the very ready cleavage parallel to (111) lending support to this view (cp. Debye's paper). In such a case as this, the analogy of the crystal structure to a set of spheres packed together obviously

* Debye and Scherrer, Phys. Zeit. xviii. (June 1917). Phil. Mag. Ser. 6. Vol. 40. No. 236. Aug. 1920.

breaks down. The distance between neighbouring carbon atoms in graphite is 1-45 Å.

14. It has been seen that in each period the diameters of the electronegative atoms appear to approach a lower limit. If it is true that these atoms share electrons when combined together in the crystal, the diameters which have been assigned to them should give an estimate of the diameters of the outer shells in which the electrons are situated.

In the first short period the diameters assigned to the atoms of carbon, nitrogen, oxygen, and fluorine are 1.54 A., 1·30 Å., 1·30 Å., 135 A. The first three of these have been calculated from compounds in which the atoms share electrons, the nitrates, carbonates, and diamond. No compound in which fluorine shares electrons has been analysed, but evidence has been given that it occupies the same volume as oxygen. The outer electron shell which these atoms tend to complete is that of Neon. We may therefore estimate the diameter of the outer neon shell as being 1.30 A. Since two electrons at least are held in common by the elements this estimate may be somewhat too large.

In the second short period the diameters of silicon, sulphur, and chlorine are 2·35 Å., 2·05 Å., 2-10 Å. The structure of phosphorus has not yet been analysed. The diameter of the outer Argon shell appears to be 2·05 Å.

In the first long period, the lower limit to which the diameters tend is 2.35 Å. The structure of arsenic has not been analysed, but it crystallizes in a form isomorphous with antimony, the structure of which has been recently determined by James and Tunstall. If its structure is that of antimony, the distance between the nearest atoms is 2.52 Å. Selenium has been assigned a diameter of 2.35 Å., bromine a diameter of 2.38 Å. Other elements in the same period tend to approach this limit. When manganese and chromium act as acid-forming elements and so share electrons with other atoms, they enter into compounds isomorphous with the sulphates and selenates, and the molecular volumes of the compounds are very nearly those of the selenates, so that the atoms appear to have dimensions identical with those of selenium. The distances between atomic centres in iron, nickel, and copper are 2:47 A., 2:39 A., 2.55 Å. These figures confirm the estimate of 2:35 A. as the lower limit to which the diameter tends.

In the second long period, the distance between atomic centres in gray tin is 2.80 A., in antimony 2:80 A. Tellurium

and iodine have been assigned diameters of 2.66 Å. and 2-80 Å. The evidence for the lower limit is imperfect, but it may be estimated as 2·70 Å.

The diameters of the outer electron shells of the inert gases therefore appear to be

On Langmuir's theory, the crystal of an electropositive element consists of an assemblage of positively charged ions held together by electrons which are free to move in the structure. The empirical relation between inter-atomic distances in compounds is less accurate when applied to the metals, perhaps as a result of the different nature of the forces in this latter case. For instance, in a number of isomorphous series the substitution of magnesium for iron decreases the molecular volume, yet the distances between atomic centres in metallic magnesium and iron are 3.22 Å.* and 2:47 Å, respectively. Silver and sodium form many isomorphous salts of nearly identical molecular volume. The distances between atomic centres in crystalline silver and sodium are 2.87 Å. and 3·72 Å. Isomorphous salts of the same molecular volume are formed by rubidium and thallium, by strontium and lead, substances whose atomic volumes differ widely. The relations shown in fig. 3 hold most accurately for compounds and for the electronegative elements.

The electropositive elements crystallize in the cubic or hexagonal systems. This was pointed out by Barlow and Pope, and used as a basis for the theory of close-packing in crystalline structures, since an assemblage of equal spheres packed together in the closest manner has either cubic or hexagonal symmetry. It is now known that the atoms of some metals are not arranged in a close-packed manner. Nevertheless, the idea of a metal as an assemblage of positive ions held together by electrons indicates a reason for the simple crystalline structure. Each atom has the same relation to its neighbours, it is not bound in any way to one rather than another of them, and the assemblages will take a form like the arrangement of a set of equal spheres. The crystal of an electronegative element, on the other hand, where atoms are linked by holding electrons in common, will have a more complicated structure, as is the * A. W. Hull, Phys. Rev., July 1917.

case for sulphur, selenium, tellurium, iodine, arsenic, antimony, bismuth.

15. In order to obtain a more complete knowledge of the distances between atoms which hold electrons in common, the examination of salts such as the nitrates, chlorates, bromates, sulphates, and selenates would be desirable. The investigation of these salts presents some difficulty, since their crystalline forms are complex. The symmetry of the crystal is of less assistance in determining the arrangement of the atoms than it is for the simple crystals, as it is of a much lower type. It is hoped that the empirical relations formulated in this paper will help in this investigation. The conception of the atoms as a set of spheres of appropriate diameters packed tightly together limits the number of possible arrangements and aids in deciding the correct disposition of the atoms. The scheme may be of assistance in analysing the structure of crystals such as quartz*, sulphur, and the alkaline sulphatest, crystals for which the dimensions of the lattice are known, but which have so far proved too complicated for complete analysis.

Summary.

1. An examination of the distances between neighbouring atoms in a crystal leads to an empirical relation determining these distances. The distance between the centres of two atoms may be expressed as the sum of two constants characteristic of the atoms. The arrangement of the atoms in a crystalline structure may therefore be pictured as that of an assemblage of spheres of appropriate diameters, each sphere being held in place by contact with its neighbours.

2. This empirical law is summarized by the curve of fig. 3, where the constants for a number of elements, arranged in the order of their atomic numbers, are plotted. The curve is periodic and resembles Lothar Meyer's curve of Atomic Volumes. Each atom occupies a constant space in any crystalline structure of which it forms part. The space occupied by the alkaline metals and alkaline earths is greatest, that occupied by the electronegative elements least.

3. The accuracy of the relation is discussed. Variations of the order of 10 per cent. between the calculated and observed distances occur, so that the law is only approximately true. Nevertheless, it is of considerable assistance * W. H. Bragg, Proc. Roy. Soc. A. vol. lxxxix. (Jan. 1914). Ogg and Hopwood, Phil. Mag. [6] xxxii. p. 518 (1916).)

in the analysis of the more complex crystal structures, since the conception of the atoms as an assemblage of spheres of known diameters packed tightly together limits the number of possible arrangements which have to be tried in interpreting the diffraction of X rays by the crystal.

4. The physical significance of the relation is examined with reference to Langmuir's theory of atomic structure. From this point of view, it follows that two electronegative atoms are situated close together in a crystalline structure because they share electrons, and the spheres representing them are therefore assigned small diameters. On the other hand, an electropositive element does not share the electrons. in its outer shell with the neighbouring atoms, and is therefore situated at a distance from other atoms so that it appears to occupy a greater space in the structure.

5. It is shown that the relation is less accurate when applied to the crystals of metals, which, on Langmuir's theory, consist of an assemblage of positive ions held together by electrons which have no fixed positions in the structure.

6. From the distance between electronegative atoms holding electrons in common, an estimate is made of the diameter of the outer electron shell in the inert gases. Manchester University, April 1920.

XIX. The Dissociation of Iodine Vapour and its Fluorescence. By ST. LANDAU, B.Sc., Lecturer in Physics at the Governmental Technical School, Warsaw, and ED. STENZ*.

T

I. The aim of this work.

THE researches of R. W. Wood on the fluorescence of the vapours of sodium, mercury, and iodine are generally known; he discovered the remarkable phenomenon of optical resonance in these vapours. The most complicated relations were found by Wood in the case of iodine vapour; the number of lines in the absorption spectrum of iodine is estimated by Wood to be 40,000-50,000. Different "resonance spectra" may be obtained, when the exciting line covers different absorption lines.

We put the following question: Is the complicated vibrating system, which corresponds to these various resonance

* Communicated by the Authors. Presented by Prof. L. Natanson to the Polish Academy of Sciences (Cracow) 18th Nov. 1919.

† Phil. Mag. March 1918, p. 236.