• C V Raman

Articles written in Proceedings – Section A

• The origin of the colours in the plumage of birds

Observations are described with the feathers ofCoracias Indica which throw doubt on the correctness of the theory that the blue of these feathers is a simple Tyndall effect due to the scattering of light by minute air cavities within the substance of the barb. Observations with the “Ultra-opak” microscope show that the coloured layers may exhibit tints ranging over the whole spectrum. A simple Tyndall effect is thus definitely insufficient to explain the observed phenomena. Further studies indicate that the cavities responsible for the colours are extended structures. The two alternative possibilities, namely, diffraction by cavities not small compared with the wave-length and interferences from the surfaces of minute films are considered and discussed, without a final decision being reached.

• The Indian musical drums

The paper gives a detailed description of the results obtained by the author in the year 1919 which showed that in the Indian musical drums we have a circular drum-head which is loaded and damped in such a manner that all the overtones above the ninth are suppressed and these nine are grouped in such a manner as to give a succession of five tones in harmonic sequence. The vibrations of the drum-head present a striking analogy to the case of a stretched string giving one or the other of its first five harmonics; the drum-head divides up into 1, 2, 3, 4 or 5 sections giving the respective harmonics. The third, fourth and fifth harmonics are obtained by superposition of 2, 2 and 3 respectively of the normal modes of vibration. The corresponding superposed forms of vibration are readily obtained and demonstrated by means of sand figures. Numerous figures illustrate the paper.

• On iridescent sheels - Part I. Introductory

• On iridescent shells - Part II. Colours of laminar diffraction

• On iridescent shells - Part III. Body-colours and diffusion-haloes

• The diffraction of light by high frequency sound waves: Part I.

(a) A theory of the phenomenon of the diffraction of light by sound-waves of high frequency in a medium, discovered by Debye and Sears and Lucas and Biquard, is developed.

(b) The formula$$\sin \theta = \pm {{n\lambda } \over {\lambda * }} n (an integer) \ge 0$$ which gives the directions of the diffracted beams from the direction of the incident beam and whereλ andλ* are the wave-lengths of the incident light and the sound wave in the medium, is established. It has been found that the relative intensity of themth component to thenth component is given by$$J_m ^2 (2\pi \mu L/\lambda ) / J_n ^2 (2\pi \mu L/\lambda )$$ were the functions are the Bessel functions of themth order and thenth order,μ is the maximum variation of the refractive index and L is the path traversed by light. These theoretical results interpret the experimental results of Bär in a very gratifying manner.

• The diffraction of light by sound waves of high frequency: Part II

The theory of the diffraction of light by sound waves of high frequency developed in our earlier paper is extended to the case when the light beam is incident at an angle to the sound wave-fronts, both from a geometrical point of view and an analytical one. It is found that the maxima of intensity of the diffracted light occur in directions which make definite angles, denoted byϑ, with the direction of the incident light given by$$\sin (\theta + \phi ) - sin \phi = \pm {{n\lambda } \over {\lambda * }}, n (an integer) \ge 0$$ whereλ andλ* are the wave-lengths of the incident light and the sound waves in the medium. The relative intensity of themth order to thenth order is given by$$J_m ^2 \left( {v_0 \sec \phi {{\sin t} \over t}} \right) / J_n ^2 \left( {v_0 \sec \phi {{\sin t} \over t}} \right)$$ wherev0=2πµL /λ,t=πL tanφ /λ*,φ is the inclination of the incident beam of light to the sound waves,μ is the maximum variation of the refractive index in the medium when the sound waves are present and L secφ is the distance of the light path in the medium. These results explain the variations of the intensity among the various orders noticed by Debye and Sears for variations ofφ in a very gratifying manner.

• First annual meeting of The Indian Academy of Sciences. (Held at Bombay on 18th December 1935.) Presidential address

• The diffraction of light by high frequency sound waves: Part III - Doppler effect and coherence phenomena

The theory developed in Part I of this series of papers has been developed in this paper to find the Doppler effects in the diffraction components of light produced by the passage of light through a medium containing (1) a progressive supersonic wave and (2) a standing supersonic wave.

In the case of the former the theory shows that the nth order which is inclined at an angle$$\sin ^{ - 1} \left( { - \begin{array}{*{20}c} {n\lambda } \\ {\lambda *} \\ \end{array} } \right)$$ to the direction of the propagation of the incident light has the frequencyv – nv* wherev is the frequency of light,v* is the frequency of sound andn is a positive or negative integer and that thenth order has the relative intensity$$Jn^2 \left( {\frac{{2\pi \mu L}}{\lambda }} \right)$$ where μ is the maximum variation of the refractive index, L is the distance between the faces of the cell of incidence and emergence and λ is the wave-length of light.

In the case of a standing supersonic wave, the diffraction orders could be classed into two groups, one containing the even orders and the other odd orders; any even order, say 2n, contains radiations with frequenciesv ± 2rv* wherer is an integer including zero, the relative intensity of thev ± 2rv* sub-component being$$J^2 n - r\left( {\frac{{\pi \mu L}}{\lambda }} \right)J^2 n + r\left( {\frac{{\pi \mu L}}{\lambda }} \right)$$; any odd order, say 2n + 1, contains radiations with frequencies$$v \pm \overline {2r + 1} v*$$, the relative intensity of the$$v \pm \overline {2r + 1} v*$$ sub-component being$$J^2 n - r\left( {\frac{{\pi \mu L}}{\lambda }} \right)J^2 n + r + 1\left( {\frac{{\pi \mu L}}{\lambda }} \right)$$. These results satisfactorily interpret the recent results of Bar that any two odd orders or even ones partly cohere while an odd one and an even one are incoherent.

• The diffraction of light by high frequency sound waves: Part IV - Generalised theory

The essential idea that the phenomenen of the diffraction of light by high frequency sound waves depends on the corrugated nature of the transmitted wave-front of light, pointed out by the authors in their first paper, has been developed on general considerations in this paper. The results in this paper can be summarised as follows:-

If progressive sound-waves travel in a rectangular medium normal to two faces and the direction of propagation of a plane beam of incident light, the incident light will be diffracted at the angles given by sin-1(-nλ/λ*) and the light belonging to the nth order will have the frequencyv–nv*.

If the sound waves are stationary, the incident light will be diffracted at the angles given by sin-1(-nλ/λ*), an even order would contain radiations with frequencies,v,v±2v*,v±4v*,....,v±2rv*,...., and an odd order would contain radiations with frequenciesv±v*,v±3v*,v±5v*,....,$$v \pm \overline {2r + 1} v*$$,.....

A differential-difference equation has been obtained for the amplitude function of the diffracted orders whose approximate solution is satisfied by the Bessel Functions already obtained by the authors in their previous papers.

• Physical principles and applications of magneto-chemistry by Prof. S. S. Bhatnagar and Dr. K. N. Mathur

• The diffraction of light by high frequency sound waves: Part IV - Generalised theory

The essential idea that the phenomenon of the diffraction of light by high frequency sound waves depends on the corrugated nature of the transmitted wave-front of light, pointed out by the authors in their first paper, has been developed on general considerations in this paper. The results in this paper can be summarized as follows:—

If progressive sound-waves travel in a rectangular medium normal to two faces and the direction of propagation of a plane beam of incident light, the incident light will be diffracted at the angles given by sin−1 (−nλ/λ*) and the light belonging to thenth order will have the frequencyv–nv*.

If the sound waves are stationary, the incident light will be diffracted at the angles given by sin−1 (−nλ/λ*), an even order would contain radiations with frequencies,ν, ν ± 2ν*,ν ± 4ν*,.,ν ± 2*,., and an odd order would contain radiations with frequenciesν ±ν*,ν ± 3ν*,ν ± 5ν*,.,ν ± √2r+1ν*,..

A differential-difference equation has been obtained for the amplitude function of the diffracted orders whose approximate solution is satisfied by the Bessel Functions already obtained by the authors in their previous papers.

• Physical principles and applications of magneto-chemistry - by Prof. S. S. Bhatnagar and Dr. K. N. Mathur

• The diffraction of light by high frequency sound waves: Part V - General considerations—oblique incidence and amplitude changes

The essential idea that the phenomenon of the diffraction of light by high frequency sound waves depends on the corrugated nature of the transmitted wave-front of light has been developed on general considerations in this paper to apply for the case of the oblique incidence of the incident light to the sound waves. It is found that the intensity distribution will hot be symmetrical in general thus explaining the results of Debye and Sears, Lucas and Biquard, Bär and Parthasarathy. The consideration of the amplitude changes of the traversing beam of light explains the results of Hiedemann, Bär and Lucas.

We are highly thankful to Prof. Dr. R. Bär of Zürich for having kindly sent us a copy of the proof of a paper by him describing experimental tests of our theory which is now in course of publication in theHelvetica Physica Acta.

• The structure and optical characters of iridescent glass

• On the wave-like character of periodic precipitates

It is pointed out that the suggestion of an analogy between periodic waves and rhythmic precipitation would be without physical significance unless it can be shown that the characteristic superposition effects observable with waves are also demonstrable with Liesegang patterns. Fourteen photomicrographs and enlargements of Liesegang precipitates of silver chloride and of silver chromate are reproduced with the paper which show that such superposition effects are actually to be observed, both in regard to the intensity of the deposits and in respect of their geometrical configuration. These examples illustrate the varying effects of the superposition of two wave-trains when their wave-length, direction and amplitude are individually or collectively different. It is shown theoretically that when groups of waves interfere, we have a group-interference pattern on a large scale in addition to a wave-interference pattern on a fine scale, the two being separate and distinguishable effects. It is observed that the so-called primary and secondary rings obtained with silver chromate precipitates in gelatin are related to each other as a group is to the individual waves of which it is composed. Independent wave-interferences and group-interferences are exhibited by such precipitates.

• Haidinger’s rings in soap bubbles

By suitable arrangements which are described, it is possible to obtain soap-bubbles which are perfectly uniform in thickness and to maintain them in that state. Such bubbles exhibit by transmission or reflexion, interference figures consisting of concentric rings which are essentially of the same physical nature as the Haidinger rings due to a plane-parallel plate, besides being geometrically similar to them in configuration. Sixteen photographs are reproduced showing the interference figures of soap-bubbles of uniform thickness as also of the changes which occur in them when the films are allowed to drain. The question of the localisation of the interference figures of a curved plate is discussed.

• Reflection of X-rays with change of frequency - Part I. Theoretical discussion

• Reflection of X-rays with change of frequency - Part II. The case of diamond

• Reflection of X-rays with change of frequency - Part III. The case of sodium nitrate

• Colours of stratified media—I - Ancient decomposed glass

The paper describes a detailed microscopic study of the structure of the films of decomposed glass derived from an ancient Syrian vase excavated by M. Pupil, and a spectroscopic examination of their iridescence. The investigation makes it clear that Brewster’s explanation of the iridescence as due to films of air separating thin layers of glass is definitely erroneous. The material is optically and mechanically continuous, but has an open framework structure which is quasi-periodic or stratified. The stratifications are moderately regular with the result that in certain specimens, a limited region of the spectrum is totally reflected and the rest is freely transmitted, while in other specimens we have the opposite effect, namely that the whole of the incident light is reflected except for a limited region of the spectrum which is transmitted. At oblique incidences and especially near the polarising angle, the colours seen vary with the azimuth of the vibration and in different ways in these two cases. Mechanical pressure destroys the structure and with it also the iridescence. Liquids can penetrate into the structure of the film, but the latter becomes optically homogeneous and ceases to reflect light only when the refractive index of the liquid is equal to that of the glass (1·465). When the wetted film commences to dry, the liquid withdraws first from the larger cavities while it is retained in the smaller pores. This results in the optical stratifications being actually more pronounced than in the dry film, with the consequence that the flake appears black by transmission and silvery white by reflection.

• Quantum theory of X-ray reflection and scattering - Part I. Geometric relations

When X-rays fall upon a crystal, the characteristic vibrations of the crystal lattice may be excited thereby, in much the same way as in the phenomenon of the scattering of light in crystals with diminished frequencey, the excitation being a quantum mechanical effect. From the equations for the conservation of energy and momentum, the geometrical relations entering in this effect are deduced theoretically for the two cases in which the lattice vibrations fall within (1) the acoustic range of frequency and (2) the optical range. In the first case, the incident X-rays are scattered in directions falling within, a cone having the incident ray as axis and with a semi-vertical angle 2 sin−1 λ 2γ* whereγ* is the minimum acoustical wave-length. In the second case, we have a quantum-mechanical reflection of the X-rays with diminished frequency in a direction which generally follows the geometric formula 2d sin 1/2(θ+ϕ)=nλ where θ and ϕ are the glancing angles of incidence and reflection on the crystal spacings. For crystals with specially rigid bindings, the alternative fomulad sin (θ+ϕ)=nλ cosϕ is indicated as being more appropriate. In either case, the intensity of the reflection should fall off rapidly as ϕ and ϕ diverge.

• Reflection of X-rays with change of frequency - Part IV. Rock-salt

• The two types of X-ray reflection in crystals

• Crystals and photons

The excitation of the optical modes of vibration of a crystal lattice by radiations incident on the crystal is discussed. The optical vibrations can be described as oscillations of the interpenetrating lattices in the crystal with respect to one another. They give rise to a periodic variation of the physical constants,e.g., electric dipole-moment, optical polarisabilities, structure amplitudes, which influence the behaviour of radiation in various ranges of frequency in its passage through the crystal. The phenomena observed in the different ranges of frequency have a common feature, namely that the incident radiation excites the crystal vibrations of which the phases are everywhere in coherent relationship with the phase of the radiation field. The scattering of light or the reflection of X-rays with change of frequency appears as the result of the phase of the lattice vibrations varying from point to point in such manner that the crystal is, in effect, an optically stratified medium giving a monochromatic reflection of the incident rays at the appropriate angle of incidence determined by the spacing of the stratifications and the wave-length of the incident radiation. The description of the observed effects in the language of the wave-theory and in terms of the quantum hypothesis are complementary and do not in any way contradict each other.

The paper includes a review of 14 communications dealing with this field of research published during the year 1940 in theProceedings of the Indian Academy of Sciences.

• Conical refraction in naphthalene crystals

• The quantum theory of X-ray reflection: Basic ideas

• Quantum theory of X-ray reflection: Mathematical formulation

• Quantum theory of X-ray reflection: Experimental confirmation

• The thermal energy of crystalline solids: Basic theory

• New concepts of the solid state

The postulates on which the Debye theory of the specific heat of solids and the Born crystal dynamics are respectively based have been critically examined and shown to be theoretically untenable. Since a crystal is a three-dimensionally periodic grouping of similar oscillators coupled together, it follows that the modes of vibrations possible would be also spece-periodic, the geometric modes being determined by the characters of the atomic space-grouping in the crystal. They would further form a finite and enumerable set of monochromatic frequencies. The spectroscopic, X-ray and thermal behaviours of a crystal would on these views be radically different from those consequent on the Debye and Born theories. The experimental facts are found to contradict the conclusions of these theories and on the other hand, to be in full accord with the new concepts.

• The vibration spectrum of a crystal lattice

• The crystal symmetry and structure of diamond

• The nature and origin of the luminescence of diamond

• Birefringence patterns in diamond

• The crystal forms of diamond and their significance

• The vibration spectra of crystals - Part I. Basic theory

The paper presents the author’s theory of the vibration spectra of crystals from a fresh point of view. It is shown that the nature of the spectra is necessarily different in the two regions of frequency in whioh they represent respectively the characteristic eigenvibrations of the crystal structure and the stationary wave-patterns of elastic vibration. The eigenvibrations repeat themselves in volume elements within the crystal having twice the linear dimensions and eight times the volume of the lattice cells. The number of modes of eigenvibration is (24p-3),p being the number of atoms in each lattice cell. The spectral frequencies which are (24p-3) in number (or less by reason of crystal symmetry) ate accordingly monochromatic. In relation to the entire crystal, they are highly degenerate. The three missing degrees of freedom are exactly accounted for when the possible elastic vibrations which give a quasi-continuous spectrum of frequencies are enumerated. The limiting elastie wave-lengths come out as four times the lattice spacings of the crystal. The effects of anharmonicity are also considered. It is shown that they result in lowering and spreading out the spectral frequencies of the crystal when its temperature is elevated.

• The vibration spectra of crystals - Part II. The case of diamond

Considerations based on the crystal structure of diamond enable its nine eigenvibrations to be arranged on a descending scale of frequency. The magnitude of the force-oonstants involved can also be defined within narrow limits. The numerical values of the frequencies evaluated on the basis of the theoretical formulæ show a close agreement with the observed values. The geometry of the modes determines the changes in bond-polarisabilities and electron distributions produced by them, from which their activities in light-scattering and in infra-red absorption can be ascertained both in the first and in the second approximation. A comparison of the results with the experimental facts shows a striking agreement. The observed intensity of the second-order effects in relation to those of the first order indicates that the eigenvibrations are localised in volume elements comparable in size with the lattice cells of the crystal.

• The vibration spectra of crystals - Part III. Rocksalt

It is pointed out that the vibration frequencies of the rocksalt structure are determined entirely by short-range atomie interactions, since the effects of the Coulomb forces cancel out. The numerical evaluation of the nine eigenfrequencies on this basis leads to results in excellent accord with the observational data. Their activities in light-scattering and infra-red absorption are also discussed. The vibration most strongly active in light-seattering is that of the Cl ions normal to the octahedral planes, the Na+ ions remaining at rest. It is also pointed out that the peak of the infra-red absorption at 61 μ for thin films observed by Barnes and Czerny doesnot represent the frequency of oscillation of the Na and C1 lattices with respect to each other, but is shifted with respect to it owing to the activity of other modes in the vicinity.

• The vibration spectra of crystals - Part IV. Magnesium Oxide

The nine fundamental frequencies of the magnesium oxide structure ate theoretically evaluated. Expressed as infra-red wave-lengths, they are respectively 14·2, 14·7, 15·35, 17·1, 19·0, 21·1, 23·4, 38·8 and 54·4 μ. All except the last two are active in the infra-red and their positions cheek very closely with the absorptions observed by Barnes and Brattain, by Strong and by Fock. The octaves of the first seven fundamentals and numerous summational frequencies including also the two inactive fundamentals have been identified with the lines recorded by Barnes aud Brattain in the absorption spectrum of cleavage plates of various thicknesses.

• The vibration spectra of crystals - Part V. Lithium and sodium fluorides

The eigenfrequeneies of lithium and sodium fluorides have been theoretically evaluated and their observed spectroscopic behaviour is found to be in accord with the results. The greater disparity in the atomie weights of metal and halogen in the case of lithium fluoride than in sodium fluoride leads to some interesting differences in behaviour between the two substances. In both cases, however, the frequeney of maximum absorption doesnot correspond with the oscillation of the metal and halogen atoms against each other, but agrees with that of the oscillations in which only the fluorine atoms move, the metal atoms remaining at rest.

• The vibration spectra of crystals - Part VI. Sylvine

The nine eigenfrequencies of sylvine are evaluated, and it is shown that the wave-length at which the maximum absorption is exhibited by very thin films is much nearer the tirst than the third of them which is the so-called active oscillation of the potassium against the chlorine atoms. The absorption and reflection data over the whole range of wave-lengths are in general accord with the indications of the theory. The force-constants for sylvine are a little smaller than for rock-salt.

• The theory of the Christiansen experiment

The effects exhibited by a Christiansen filter can only be explained or understood in terms of wave-optics. A theoretical formula is derived in the paper for the distribution of intensity in the spectrum of the transmitted light, the variables involved being the wave-length of the light, the average size of the particles of the powder, the thickness of the cell and the difference in the refractive indices of the powder and the liquid for the wave-length under consideration. The characters of the halo observed around the light source are also discussed in terms of diffraction theory. The theory explains the facts of observation in a very simple manner and gives results in satisfactory accord with the available experimental data.

• The Christiansen experiment with spherical particles

• Diffraction of light by transparent spheres and spheroids: The fresnel patterns

The paper describes and discusses the diffraction effects observed when a beam of light traverses a transparent sphere immersed in a liquid of slightly lower index and emerges therefrom. The two most interesting features are firstly, a concentration of intensity along the periphery of the emerging light beam which is evidently in the nature of a caustic and secondly, a concentration of intensity along the axial ray which is in the nature of a continuous focus. These two features are each accompanied by a set of interference-rings and these appear superposed on each other. Significant alterations appear in these features when the particle has a spheroidal shape. With a birefringent sphere, two sets of caustics are, in general, observed. 12 Photographs illustrate the paper. *** DIRECT SUPPORT *** A00OCO56 00002

• The optical anisotropy and heterogeneity of vitreous silica

The paper describes the birefringence exhibited by vitreous silica, both in the naturally occurring material found in the Libyan desert and in the commercially available material in the forms of rods and disks. The facts revealed by the investigation are discussed. It is shown that Rayleigh’s belief that vitreous silica in the mass has a crystalline granular structure cannot be sustained. It is shown further that, besides the familiar stress-optical birefringence, a second kind of effect,viz., “structural birefringence” is also possible in amorphous solids and that this is particularly prominent in vitreous silica for reasons which are discussed.

12 photographs illustrate the paper.

• Structural birefringence in amorphous solids

The result reported in an earlier investigation with vitreous silica is now shown to be true also for other amorphous solids, including especially inorganic glasses; besides the well-known photo-elastic effect, another kind of birefringence may be observed differing from the former both in its origins and in its observable characters. This “structural birefringence” arises from anisotropy of structure present in the solid by reason of the circumstances of its formation. It is conspieuously seen with plate glass whose optical behaviour shows it to have a highly laminated structure, while in moulded glass, it exhibits itself as luminous streaks or sheets of variously curved forms.

Numerous photographs illustrate the paper.

• Crystals of quartz with iridescent faces

The paper is a study of the iridescence exhibited by some of the pyramidal faces of two crystals of transparent quartz in the possession of the author. Spectroscopic examination shows the reflections and the corresponding extinctions to be monochromatic. The thickness of the iridescent layer may be directly observed, and the number of laminations inferred to be present is sufficient to explain the observed characters of the iridescence. The nature of the stratifications in the crystal giving rise to the iridescence is discussed. Photographs of one of the crystals and of the spectral character of the reflections and extinctions illustrate the paper. *** DIRECT SUPPORT *** A00OC061 00002

• The lamellar structure and birefringence of plate glass

Using carefully prepared material with adequate magnification under conditions securing the optimum visibility, photographs exhibiting the lamellar structure of plate glass and the associated birefringence have been secured which exhibit far more detail than previously. The visibility of the structure is closely related to the diffraction phenomena to which it gives rise. The latter are described and discussed in detail.

• The structure of labradorite and the origin of its iridescence

• The luminescence of diamond and its relation to crystal structure

The relationships which exist between the luminescence of diamond and its behaviour in respect of birefringence are described and illustrated in the paper by a new series of photographs obtained with improved technique and with diamonds of the first quality. It is shown that the results fully support the conclusions reached earlier,viz., that the luminescence of diamond has a structural origin. It is also pointed out that the classification of diamond into two species as Type I and Type II does not correspond with reality and must therefore be discarded.

• The structure and optical behaviour of the ceylon moonstones

• The scattering of light in crystals and the nature of their vibration spectra

The facts of light-scattering in crystals are reviewed and the nature of the atomic movements and the character of their vibration spectra in the different frequency regions are deduced therefrom. Whereas the movements based on the translations of the lattice cells result in elastic wave motions in the solid with a continuous frequency spectrum, the modes based on their internal vibrations are localised and have monochromatic frequencies analogous to those of polyatomic molecules. The total degrees of atomic freedom are shared between the latter and the former in the ratio (24p − 3):3. The frequency shifts ordinarily observed in light-scattering arise from the group of (3p−3) modes in which the phase of the vibration is the same in adjacent cells of the lattice. But these as well as the 21p additional modes in which the phase alternates along the axes can give rise to shifts which are overtones and summations of their fundamental frequencies. The localisation of the internal vibrations permits of these overtones and summations appearing as frequency shifts with observable intensity. On the other hand, the continuous spectrum of elastic vibrations is completely inactive in light-scattering, apart from the particular case of a coherent reflection of the light waves by the elastic wave pattern.

• The vibration spectra of crystals and the theory of their specific heats

The enumeration of wave-patterns within an enclosure on a scale of wave-lengths or frequencies presupposes that the waves are perfectly undamped and that the enclosure is perfectly reflecting. In any material medium, however, wave-propagation is necessarily damped and such damping may be so enormous as altogether to preclude wave-propagation. It follows that it is not permissible to identify the modes of atomic vibration in crystals with wave-patterns. Since the specific heat theories of Debye and of Born-Karman are based on such identification, they cannot be sustained.

For any mechanical model to represent the dynamic behaviour of a crystal, it is necessary that it should satisfy the requirements for dynamic similarity. When these requirements are satisfied, the behaviour of the model does not support the ideas underlying the Debye and Born-Karman theories, but on the other hand agrees with the results of the theory of the dynamics of crystal lattices put forward by the writer in 1943.

The phenomena of light-scattering observed in crystals are also discussed and it is shown that the experimental facts are incompatible with the ideas underlying the Born-Karman theory.

• On the iridescence of potassium chlorate crystals - Part I. Its spectral characters

Spectrograms obtained with five iridescent crystals of potassium chlorate at varying azimuths and obliquities of incidence have been obtained and are reproduced with the paper. Some of the results observed are explicable in terms of the general theory of the optical behaviour of a regularly stratified medium,viz., (a) the appearance of a whole series of subsidiary bands accompanying the principal maxima and distributed asymmetrically about them and (b) the variation of the spectral width of the principal maximum with change of azimuthal angle and obliquity of incidence. Other striking effects are however also observed which are not so explicable,viz., when the azimuthal angle is nearly zero, the principal band splits into a doublet the components of which drift apart progressively and also shift towards shorter wavelengths with increasing obliquity of incidence. When the azimuthal angle is 90° the crystals exhibit the principal maximum as a triplet, the central component of which has a width of the same order of magnitude as the separation of the doublet in the preceding case, while its outer components are much further apart.

• On the iridescence of potassium chlorate crystals - Part II. Polarisation effects

A simple explanation is given why the reflections vanish when the light is incident in the symmetry plane of the twinned crystals. Physical considerations enable the law of polarisation for twin-plane reflections to be derived for directions of incidence adjoining the plane of symmetry. It is further shown that the spectral character of the reflections stands in the closest relationship with the polarisation law thus derived. An explanation is given for the appearance of doublets and triplets respectively in the spectra observed when the incidence is oblique and the azimuth of such incidence is nearly zero and 90° respectively. It is a necessary consequence of the theory that the outer components in these two cases should be plane-polarised, in one case in the reciprocal fashion and in the other case normally. The theoretical results are strikingly confirmed by observations on the polarisation of the spectral components. Photographs are reproduced illustrating these effects.

• On the iridescence of potassium chlorate crystals - Part III. Some general observations

The paper describes the results of a study of an extensive collection of material. The spacing of the stratifications giving rise to monochromatic reflections has been found to range from 2·7µ to 0·14µ. The monochromatism becomes sensibly more perfect in the reflections of higher orders. Variations in intensity from order to order are also noticeable and these are ascribed to the alternate lamellæ in the twinning being of different thickness. Instead of a single series of monochromatic reflections, regularly spaced groups of reflection maxima are also observed in some cases. The components in each group of such reflections may be wide apart or else may be closely spaced. The nature of the stratifications in these cases is discussed.

• On the polarisation and spectral character of the iridescence of potassium chlorate crystals

It is shown from theoretical considerations and confirmed by the spectrograms reproduced in the paper that the sharply defined monochromatic reflection observed at nearly normal incidences splits up into a quartet in the general case of any arbitrary azimuth and obliquity of incidence. The outer components disappear thereby reducing the quartet into a doublet when the azimuthal angle is small. But if the azimuthal angle be 90° the two central components merge and the quartet reduces to a triplet. When the crystal is rotated in its own plane the two central components of the quartet come together, overlap and move out again in the same direction, thereby giving rise to a reversal of their polarisation characters. They owe their origin to the alternate layers of the polysynthetically twinned crystal being of unequal thickness.

• The diffusion haloes of the iridescent feldspars

Labradorite, the moonstones from Ceylon and Korea and other varieties of feldspar exhibiting iridescence have been investigated, and in all cases it has been found that such iridescence is the consequence of a diffusion of light within the material and not a true optical reflection. By a suitable technique, the diffusion haloes can be photographed and from their geometric positions, colour and angular dimensions, important conclusions can be drawn regarding the structures responsible for the iridescence. The plagioclase feldspars usually show two haloes geometrically related to each other according to the twinning law. The Ceylon and Korean moonstones differ in this respect; while the former invariably shows only one halo, the latter exhibits one, two or four according to the number of components present in the individual crystal.

• Dr. K. R. Ramanathan on his sixtieth birthday

• The molecular scattering of light - Nobel lecture delivered at Stockholm, 11th december 1930

• The structure of opal and the origin of its iridescence

A study of the optical behaviour of iridescent opal indicates very clearly that the silica present in the material has a regularly stratified structure in which the alternate layers differ in refractive index, such difference being small but the same throughout the stratifications. A critical examination of the X-ray diffraction patterns of cryptocrystalline hyalites exhibiting optical phenomena identical with of analogous to those of precious opal confirms this finding and enables the two species of silica present in association with each other and giving rise to these phenomena to be identified respectively with high and low cristobalite. The different optical effects exhibited by a stratified medium when the spacing of the stratifications and the extent of the domains in which they are present are varied have been observed with different specimens of hyalite and are illustrated in the paper by a series of photographs.

• The structure and optical behaviour of iridescent agate

A detailed study has been made by optical and X-ray methods of two plates of banded agate which display iridescence over part of their area. The light transmitted by the banded areas is found to be completely polarised with the vector normal to the planes of banding. On the other hand, the wavy superposition patterns exhibited by the iridescent areas disappear for the same vibration direction. From these facts and the observed optical characters of the diffusion and diffraction phenomena it is deduced that the crystallites of quartz form fibres elongated in the direction of a crystallographica-axis, while their principal orc-axes lie in the planes of banding but are orientated in a periodic manner in these planes so as to build up a structure which functions as a diffraction grating. The X-ray results support these findings. More generally also, they indicate that the banding of agate is a consequence of the presence in it of groups of crystallites of quartz having common specific orientations.

• The structure and optical behaviour of iridescent crystals of potassium chlorate

Iridescent crystals of potassium chlorate exhibit geometric patterns of reflection and extinction respectively when a field of diffuse monochromatic light is viewed by reflection at or transmission through the crystal. The patterns consist in general of four closed curves, two of which are polarised with their vibration directions parallel to the plane of symmetry of the crystal and the two others perpendicular thereto. The configuration of the patterns exhibits a perfect concordance with the spectral character of the reflections or extinctions observed with incident white light at corresponding azimuths of incidence and thus furnishes a complete picture of such spectral behaviour. Photographs of the geometric patterns are reproduced with the paper as also of the conoscopic patterns exhibited by the iridescent crystals on the stage of a polarising microscope. The paper also reports the observation that the twinned crystals of potassium chlorate function as diffraction gratings and give polarised spectra when light traverses them along their composition planes of twinning.

• The structure and optical behaviour of iridescent opal

The X-ray investigation of the structure of the cryptocrystalline hyalites reported in an earlier paper has now been revised using cameras of higher resolving power. Precise measurements of the resulting photographs reveal that low-tridymite and high-cristobalite are present associated with each other in this material. Investigation of the structure of common opal exhibiting a waxy lustre leads to similar results. From a detailed examination of the diffuse X-ray patterns given by gem-opals as well as a comparative study of the iridescent hyalites and opals, it is concluded that in both of these materials, the presence of alternating layers of high-cristobalite and low-tridymite is responsible for the iridescence.

• The structure and optical behaviour of iridescent shells

Some remarkable optical effects exhibited by nacreous shells have been observed and reported, the following amongst others: The monochromatic reflections and extinctions split into two polarised components at oblique incidences as a result of the birefringence of the material. Light traversing the stratifications obliquely suffers extinction by reason of diffusion by the crystallites of aragonite, this being most rapid for the component of vibration in the plane of incidence. Striking changes are also observed in the character of the diffusion haloes with increasing obliquity of observation, a particularly noteworthy feature being that the different parts of the diffusion field are differently polarised.

• The structure and optical behaviour of some natural and synthetic fibres

When a narrow pencil of light which comes to a focus in the plane of a photographic film traverses a single fibre set transversely to it in its path, the light diffracted by the fibre in various directions records itself on the film when adequate exposures are given. Photographs thus obtained with single fibres of cotton, wool, silk, rayon and chrysotile are reproduced in the paper. The birefringence of the fibres exhibits itself by the non-disappearance of the pattern when two polaroids crossed with respect to each other are placed one on either side of the fibre, the axis of the latter bisecting the angle between their vibration directions. The diffraction patterns indicate the inner structure of the fibres and are strikingly different for the different materials.

• On the polycrystalline forms of gypsum and their optical behaviour

The paper brings to notice the remarkable optical effects exhibited by a polycrystalline form of gypsum which is different from both alabaster and satin-spar in its structure. It is not a fibrous material but consists of fine rods orientated nearly parallel to theb-axis of gypsum and exhibits a ready cleavage along planes perpendicular to that axis. A source of light viewed through a plate of the material exhibits, in general, three concentric circles which are polarised in a characteristic fashion. The source itself appears as a luminous point on the second or middle circle. It is shown that these circles arise by reason of the reflection of light at the boundaries between the rod-like crystals composing the material, for which the name “fascicular gypsum” is accordingly proposed. A theoretical explanation of the phenomena is given and photographs of the same are reproduced. Observations on the optical behaviour of alabaster and of satin-spar are also reported.

• The structure and optical behaviour of pearls

The paper embodies a study of the structure of the material composing pearls and of the optical effects which they display. The following topics are dealt with: (1) Birefringence, (2) X-ray-diffraction patterns, (3) The reflection-diffraction spectra, (4) The diffusion haloes of reflection and transmission, (5) The whispering-gallery effect, (6) The spectral character of iridescence and the influence of birefringence thereon, (7) The transmission spectra. The most noteworthy result of the investigation is to show that the diffusive properties of nacre play a major role no less important than that of the reflection by its stratifications in the optics of pearls.

• On the chromatic diffusion halo and other optical effects exhibited by pearls

The paper discusses the origin and character of the coloured diffusion halo exhibited by pearls surrounding the reflected image of a light source seen at their surface. Twelve photographs illustrative of various types of halo are reproduced. Other aspects of the optical behaviour of pearls are also described and discussed with illustrative photographs.

• The structure and optical behaviour of iridescent calcite

Arrays of multi-coloured images of a distant light-source arranged in geometric patterns are exhibited by calcite rhombs traversed by twinning layers in several directions simultaneously. The paper reproduces four photographs of such patterns and also discusses the theory of the reflection and refraction of light by twinning layers in calcite. The large difference between the ordinary and extra-ordinary dispersive powers results in a linear source observed through such a layer appearing drawn out into spectra chanelled by interferences. Interference bands also fringe the sharply defined boundaries seen separating the different parts of the optical field of reflection and refraction.

• X-ray studies on polycrystalline gypsum

X-ray diffraction patterns have been recorded and are reproduced in the paper showing clearly the existence ofthree polycrystalline forms of gypsum with specific structural characters which are readily distinguishable from each other: (a) alabaster; (b) satin-spar, which is a truly fibrous material with the fibres orientated along the mineralogicalc-axis; and (c) fascicular gypsum which is an aggregate of rods having theirb-axes or crystallographic symmetry axes parallel to each other and the two other axes showing only a limited range of variation, and hence not fibrous in the proper sense of the word.

• X-ray study of fibrous quartz

The results of optical and X-ray examination of specimens of fibrous quartz from the Bababudan Hills in Mysore are described. They indicate that the material may be described as polycrystalline quartz with a strongly preferred orientation for the crystallographicc-axis along the length of the fibres.

• The structure of amethyst quartz and the origin of its pleochroism

Comparative measurements with clear quartz and amethyst show conclusively that these two materials do not differ measurably in their density. Amethyst and clear quartz also resemble each other in not giving any Tyndall effect of the kind so conspicuously observable with smoky quartz. These facts indicate that amethyst is a crystalline material very similar to colourless quartz in its make-up, but with a different electronic configuration belonging to a lower symmetry class. The optical biaxiality and the pleochroism of amethyst then follow as natural consequences. This view of the nature of amethyst is confirmed by X-ray diffraction studies made with a section plate of amethyst free from internal twinning but exhibiting colour bands and colour sectors over its area.

• On the structure of amethyst and its genesis in nature

Amethyst is diamagnetic, its susceptibility being not measurably different from that of colourless quartz. The optical characters indicate only monoclinic symmetry, of which the diad axis coincides with one of the three electric axes of the associated quartz. An immediate explanation of why three colour sectors usually appear in amethystine quartz is thus forthcoming. The nature of the modifications in structure which alter trigonal to monoclinic symmetry is indicated. A study of an extensive collection of material indicates that the change of structure occurs during the growth of the crystal from material containing ferric impurities and is consequential on the progressive elimination of these impurities which are finally deposited as a dome of discrete particles on the boundary between the amethyst and the colourless quartz.

• On the optical behaviour of crypto-crystalline quartz

The polarisation of the light regularly transmitted by fibrous chalcedony and the character of the diffraction spectra exhibited by iridescent agate are described and discussed. It is shown that the phenomena point conclusively to the laminations in iridescent agate responsible for the diffraction effects being a consequence of the periodic orientation of the c-axis of quartz along the length of the fibres. Photographs illustrative of the optical effects and of the X-ray diffraction patterns of the materials are reproduced.

• The theory of the propagation of light in polycrystalline media

A formula based on wave-theoretical considerations is deduced which gives the coefficient of extinction of plane-polarised light traversing a polycrystalline aggregate in terms of the wave-length of the light, the size of the particles and their birefringence. The general formula covers the case where the particles have preferred orientation expressible by three different probability numbers for three mutually perpendicular directions, and the special case of isotropic orientation is readily derivable therefrom. The significance of the results is discussed in relation to the facts of observation.

• A generalised theory of the christiansen experiment

A formula is derived for the transmission coefficient of a Christiansen cell containing particles of a birefringent material whose interstices are filled up by a liquid of suitably adjusted refractive index. The consequences of the formula and especially the influence of the birefringence on the spectral character of the transmitted light are discussed.

• The christiansen experiment with birefringent powders

Optical effects analogous to those exhibited by isotropic materials in a Christiansen cell are also observable with birefringent materials in a fine state of subdivision. While the transmitted light is fully polarised, the diffusion halo is depolarised in part and exhibits colours between parallel and crossed polaroids which are complementary to each other.

• The structure and optical behaviour of jadeite

The phenomenon of semi-transparency exhibited by the finer varieties of jadeite is discussed. X-ray diffraction studies and theoretical considerations based on wave-optics alike indicate that this is a consequence of the very small particle size of the crystallites forming the aggregate.

• The elastic behaviour of isotropic solids

• On the theory of the elasticity of crystals

The fundamental aspects of the phenomenological theory of elasticity are critically examined and it is shown that the tensor representation of the elastic strains and stresses in the general case should be in the unsymmetrical form. On this basis, the stress-strain relationships are deduced and tabulated for the different crystal classes. The equations determining the velocities of wave-propagation in different directions are also obtained and tabulated. Static deformation problems are then discussed and it is shown that in the particular case of homogeneous strains, the elastic constants group themselves in linear combinations which are equivalent to the elastic modulii of the theory in its familiar form. In wave-propagation, however, the strains and stresses are heterogeneous and hence all the elastic constants are involved and appear in linear combinations which are different and also larger in number than those which figure in the formulæ for homogeneous deformations. These results are completely in accord with the consequences of the atomistic theory based on interatomic forces of the most general type.

• Corrigenda

• Evaluation of the four elastic constants of some cubic crystals

• The birefringence patterns of crystal spheres

Light from an extended source traversing a sphere reaches foci lying on a concentric spherical surface of a larger radius determined by the refractive index. Hence, if the incident light be polarised and the sphere is viewed through an analyser, the interferences arising from the birefringence of the material are focussed by the sphere itself on such concentric surface and rotate with the sphere when the latter is rotated. Photographs of such patterns in typical cases are reproduced.

• The physics of crystals

Einstein's view of a crystal as an assembly of immense numbers of quantized oscillators having a common set of vibration frequencies is not only the logical and correct view of the matter but also proves itself when fully developed to be an eminently successful view. It gives us a deep and quantitative insight into the thermal behaviour of solids. The nature of the vibration spectra of crystals indicated by it is confirmed in detail by the results of spectroscopic studies with diverse materials and by various techniques and with especial completeness by studies on the diffusion of light in crystals.

The ideas underlying the specific-heat theories of Debye and Born are irreconcilable with the observed spectroscopic behaviour of crystals and especially with the effects exhibited in their second-order spectra of light-scattering.

• The diamond

• The specific heats of crystals - Part I. General theory

In Einstein’s atomistic approach to the specific heat problem, a crystal is regarded as an assembly of sets of individual harmonic oscillators, each set consisting of a great number of oscillators having a common frequency of vibration. In the present paper, this view is developed and an expression is obtained for the thermal energy of the crystal which appears as a summation of (24p — 3) terms arising from the individual monochromatic frequencies of internal vibration of the dynamic units of the crystal structure each containing 8p atoms, with a supplementary term which takes account of the translational movements of the same units manifesting themselves as a continuous spectrum of frequencies of vibration within the crystal.

• The specific heats of crystals - Part II. The case of diamond

The specific heat of diamond in the temperature range between 15° and 1100° absolute has been computed theoretically, making use of the nine spectroscopically determined vibration frequencies of the diamond structure as well as their known degeneracies, and further taking the lowest of these nine frequencies to be the upper limit of frequency in the residual continuous spectrum as explained in Part I of the paper. The results are compared with the experimental observations of DeSorbo from 15° to 300° absolute and of Magnus and Hodler from 300° to 1100° absolute. A highly satisfactory agreement between theory and experiment emerges.

• Quantum theory and crystal physics

The fundamental notions of quantum theory and thermodynamics indicate that a crystal should be regarded as an assembly of an immense number of oscillators whose energy states are quantised and which form a system in thermodynamic equilibrium. They also indicate that the spectroscopic properties and the thermal behaviour of crystals stand in the closest relation to each other. We are thus left with the problem of discovering and enumerating the oscillators of the different sorts comprised in the crystal and of determining their scheme of energy levels. This may be done by methods analogous to those which have proved successful in the field of molecular spectroscopy. The results obtained are in perfect agreement with the observed spectroscopic properties and thermal behaviour of crystals.

• The specific heats of crystals - Part III. Analysis of the experimental data

The functional dependence of the specific heat of a crystal on the temperature may with advantage be expressed as a variation with temperature of the effective average frequency of the atomic oscillators, the same being determined from the argument of the Einstein function which gives the observed specific heat at that temperature. The usefulness of this representation is shown in the paper by a detailed discussion of the experimental data for diamond. It emerges that the distribution of frequencies adopted in the Debye theory is irreconcilable with the observed course of the frequency-temperature curve. It is also pointed out that the large excess which the specific heat calculated from that theory exhibits over the observed values in the region of low temperatures shows that the ideas on which that theory is based are misconceived and that the theory itself is untenable.

• The specific heats of some metallic elements - Part I. Analysis of the experimental data

• The specific heats of some metallic elements - Part II. Approximate theoretical evaluation

• The specific heats of some metallic elements - Part III. The characteristic frequencies

The specific heat data themselves enable us to evaluate more precisely the four characteristic frequencies of each metal determined approximately in Part II from their elastic constants. Making use of the new values, the complete specific heat curve is theoretically deduced and shows good agreement with the observations in the lower part of the temperature range, but deviates observably in its upper part, as is to be expected in view of the progressive fall in the frequency of the atomic oscillators with rise of temperature indicated by the analysis of the data in Part I. This diminution of the frequencies is a consequence of the anharmonicity of the oscillators which also results in the thermal expansion of the metal. Copper, aluminium, silver and lead form a sequence in the order of increasing coefficients of thermal expansion as also in the magnitude of the temperature coefficients of atomic vibration frequency indicated by their specific heat data.

• The specific heats of crystals and the fallacy of the theories of Debye and Born

• The heat capacity of diamond between 0 and 1000° K.

The evaluation of the heat capacity of diamond on the basis of the theory of specific heats advanced by the author is discussed and the results are compared graphically with the latest available experimental data. A striking over-all agreement emerges over the whole of the temperature range between 0 to 1000° K. The experimental values are however slightly in excess of the theoretical ones in the limited range between 50 and 150° K., the difference in the value of Cp being a maximum of 0·007 at about 100° K. and ceasing to be noticeable both below 50° K. and above 150° K. This small excess is explained as a consequence of the use in the experimental determinations of industrial diamonds whose spectroscopic behaviour is observably different from that of the ideal material.

• The diffraction of x-rays by diamond: Part 1

• The diffraction of X-rays by diamond: Part II

• The diffraction of X-rays by diamond: Part III

• Percussion figures in crystals

The impact of a hard steel sphere on the optically polished surface of a solid results in a permanent deformation of the surface and also produces fractures or rearrangements in the interior of the solid. These have been studied with crystals of quartz, calcite, barytes and felspar and also with a few polycrystalline solids. The results of the study show clearly that the nature of the percussion figure exhibited by a solid is a characteristic property of the material and is related to its inner structure and symmetry. The paper is illustrated by a series of photographs.

• Christiaan Huyghens and the wave theory of light

• The optics of mirages

• Caustics formed by diffraction and the geometric theory of diffraction patterns

• Huyghens’ principle and the diffraction of light - Part I. Theoretical considerations

The conventional treatment of diffraction problems based on the socalled Principle of Huyghens as analytically formulated by Kirchhoff is based on a misunderstanding of the original ideas of Huyghens regarding the propagation of light. It seeks to express the luminous effect due to the primary source as a summation of the effects of secondary sources situated on the elementary areas of a surface in free space enclosing the point of observation. Since the diffraction of light is a consequence of the presence of obstacles in the path of the light waves, the optical character of the obstacles and their configuration in space are of the very essence of the problem. It follows that the approach adopted in the Kirchhoff theory is misconceived and erroneous. It is however possible to base a theory of diffraction on Huyghens’ concept of partial waves and his explanation of the reflection and refraction of light at the boundary between media with different optical properties. But this leads to results which differ fundamentally from those indicated by Kirchhoff’s formula. It is shown that the issue which thus presents itself is readily capable of experimental test.

• The perception of light and colour and the physiology of vision - Part I. The mechanism of perception

• The perception of light and colour and the physiology of vision - Part II. The visual pigments

• The perception of light and colour and the physiology of vision - Part III. The carotenoid pigment

• The perception of light and colour and the physiology of vision - Part IV. Ferroheme and ferriheme

• The perception of light and colour and the physiology of vision - Part V. The colour triangle

• The perception of light and colour and the physiology of vision - Part VI. Defective colour vision

• The perception of light and colour and the physiology of vision - Part VII. General summary

• The vibrations of the MgO crystal structure and its infra-red absorption spectrum - Part I. The results of experimental study

Records have been made of the infra-red absorption spectra between 5µ and 24µ of magnesium oxide in the form of polished cleavage plates of various thicknesses ranging from 7·5 millimetres down to 20 microns. Films with an effective absorption path ranging from 1 micron to 16 microns have also been prepared by two different techniques and studied. They give results in close agreement with each other.

A critical comparative study of the data reveals that the infra-red absorption by MgO has its origin in a set of distinct modes of vibration of the crystal structure possessing discrete frequencies. The highest of these frequencies corresponds to an infra-red wavelength 20·40µ. It is strongly active as a fundamental and also as overtones. The infra-red absorption spectra enable us to recognize the presence of three other modes with lower frequencies which are inactive as fundamentals but are strongly active as overtones. The characteristic frequencies of MgO (including the highest) revealed by the investigation are respectively in wave-numbers 490 cm.−1, 423 cm.−1, 365 cm.−1 and 313 cm.−1 The corresponding wavelengths are 20·40µ, 23·64µ, 27·4µ and 32µ.

The present investigation shows that the results reported earlier by other authors which were obtained with fumed MgO films are spurious and hence that all theoretical discussions based thereon are valueless.

• The vibrations of the MgO crystal structure and its infra-red absorption spectrum - Part II. Dynamical theory

The fundamental property of a normal vibration indicated by the classical dynamics,viz., that the particles in the system oscillate with the same frequency and in the same or opposite phases, considered in relation to the three-dimensionally periodic structure of a crystal enables the possible modes of atomic vibration in a crystal to be uniquely characterised and enumerated. The simplicity and high symmetry of the structure of MgO enables this procedure to be carried further and the modes of normal vibration to be completely described and explicit formulæ obtained from their frequencies. It emerges that the structure of MgO has nine distinct frequencies of vibration. Expressions have been derived for these frequencies of these modes, both in the first and in the second approximation.

• The vibrations of the MgO crystal structure and its infra-red absorption spectrum - Part III. Comparison of theory and experiment

The description of the nine normal modes of vibration and their frequency formulæ given in Part II enable them to be grouped together in respect of infra-red activity and arranged in each group in diminishing order of frequency. A detailed comparison then becomes possible between the consequences of the theory and the experimental results set out in Part I. A comprehensive and satisfactory agreement emerges from the comparison. The modes can be identified and their frequencies determined directly from the spectroscopic records. The manner in which the reflectivity of an MgO surface varies with the wavelength of the infra-red radiation also receives a satisfactory elucidation.

• The vibrations of the MgO crystal structure and its infra-red absorption spectrum - Part IV. Evaluation of its specific heat

The specific heat of MgO at various temperatures from 50 to 850° absolute is computed by adding up the Einstein functions corresponding to the nine modes with discrete frequencies indicated by the dynamical theory and confirmed by infra-red spectroscopy. To this is added the contribution from a residual spectrum of vibrations of lower frequencies, the existence of which is also indicated by the dynamical theory. A very satisfactory agreement emerges over the whole range of temperatures between the calculated and observed specific heats.

• The spectroscopic behaviour of rock-salt and the evaluation of its specific heat - Part I. The structure and its free vibrations

The nine normal modes of free vibration of the rock-salt structure have been deduced theoretically and fully described. They have been arranged in descending order of frequency and an approximate estimate of their frequencies is also given. The mode of highest frequency is that in which the Na and Cl lattices oscillate in opposite phases.

• The spectroscopic behaviour of rock-salt and the evaluation of its specific heat - Part II. Its infra-red activity

Infra-red activity is shown to be a consequence of the periodic movements of the electron clouds in the crystal excited by the field of the incident radiation. The accompanying oscillations of the positively charged nuclei determine the frequencies but are not themselves the cause of the activity.

It is shown that of the nine modes of free vibration of the rock-salt structure, the mode of highest frequency is intensely active both in the first and the higher orders. Four other modes are inactive in the first order but active in higher orders. The remaining four are totally inactive. Spectrographic records of the absorption of rock-salt over a wide range of thicknesses are presented and explained in terms of the activity of these modes. The results reported by Mentzel and by Barnes and Czerny on the transmission spectra of rock-salt are explained on the same basis.

• The spectroscopic behaviour of rock-salt and the evaluation of its specific heat - Part III. The spectrum of light scattering

All the nine normal vibrational modes of the rock-salt structure can give frequency shifts in light-scattering which are twice their respective frequencies but are of very different intensities, determined by their degeneracies and the nature of the movements of the Na and Cl nuclei in those modes. The doubled frequencies in cm.−1 with their respective degeneracies are 360 (3), 340 (4), 314 (8), 300 (6), 280 (4), 258 (3), 235 (8), 220 (3), 184 (6). The spectroscopic facts are in full agreement with the theoretical deductions.

• The spectroscopic behaviour of rock-salt and the evaluation of its specific heat - Part IV. Specific heat and spectral frequencies

The spectroscopically determined vibration frequencies of the rock-salt structure are made use of for a theoretical evaluation of its specific heat as a function of temperature. The results thus obtained are compared with the measured specific heats. The agreement between theory and experiment which emerges demonstrates the correctness of the approaches made alike to spectroscopic theory and to the theory of specific heats.

• The infra-red absorption by diamond and its significance - Part I. Materials and methods

The author’s collection of diamonds includes one hundred polished plates of diverse thicknesses and sizes and exhibiting a varied behaviour. This form of diamond is exceptionally well suited for critical studies of the optical properties of diamond. The importance in the study and interpretation of the infra-red absorption by diamond of a parallel investigation of other properties is indicated. Of particular importance are three of them,viz., ultra-violet transparency, birefringence and luminescence. Simple and convenient methods for studying them are described.

• The infra-red absorption by diamond and its significance - Part II. A general survey of the results

Approximately ten per cent. of the total number of diamonds form group A and another ten per cent. group B. These two groups exhibit highly contrasting characters. Group A diamonds are isotropic and optically perfect, are opaque to ultra-violet of wavelengths less than 0·3µ and exhibit a visible blue luminescence. Group B diamonds are visibly birefringent, their transparency extends well beyond 0·3µ and they are non-luminescent. The two groups differ strikingly in their infra-red behaviour. These facts taken in conjunction indicate that the two groups of diamond differ fundamentally in their crystal structure.

• The infra-red absorption by diamond and its significance - Part III. The perfect diamonds and their spectral behaviour

The perfect diamonds exhibit an absorption which is readily recognised as including the first, second and third order spectra. From the features observed in these spectra it is inferred that the diamond structure has eight discrete frequencies of free vibration,viz., 1332, 1273, 1219, 1176, 1087, 1010, 746 and 624 cm.−1 The fifth and the sixth frequencies appear very prominently with doubled frequency as sharp peaks in the second-order absorption spectrum, while a summation of the seventh and eighth frequencies is recorded with extraordinary strength and sharpness by reason of its contiguity to the active fundamental of highest frequency.

• The infra-red absorption by diamond and its significance - Part IV. The non-luminescent diamonds

The non-luminescent diamonds exhibit the infra-red absorption spectra of the second and third orders, while the first order is totally absent. A critical examination of the spectrographic records shows clearly that the second-order spectrum is based on the same vibrational modes with discrete frequencies as the first, the activities of the modes, however, being different in the two cases.

The non-luminescent diamonds exhibit a type of birefringence which arises from the presence in them of laminations orientated parallel to the octahedral planes or to the dodecahedral planes of the crystals or to both.

• The infra-red absorption by diamond and its significance - Part V. The composite diamonds

Photographs are reproduced of seven plates of composite diamond exhibiting in each case the variations over its area of the ultra-violet transparency, the blue luminescence, the yellow luminescence and the birefringence. The composite nature of the diamond is also demonstrable by the spectrographic record of its infra-red absorption. The significance of the geometric character of the patterns and of their mutual relationships is discussed.

• The infra-red absorption by diamond and its significance - Part VI. The free vibrations of the structure

It is shown that the structure of diamond has eight discrete frequencies of free vibration. The mode of highest frequency is an oscillation of the two interpenetrating lattices of carbon nuclei with respect to each other. The other frequencies represent the oscillations of the octahedral or cubic layers in the crystal either normally or tangentially to themselves.

• The infra-red absorption by diamond and its significance - Part VII. The characteristic frequencies

The absorption spectra of four exceptionally large plates of diamond which were recorded in the NaCl range of the infra-red spectrograph have been critically studied and analysed. From the study it emerges that the structure of diamond has eight characteristic frequencies of free vibration which are respectively 1332, 1273, 1219, 1176, 1087, 1010, 745 and 624 cm.−1

• The infra-red absorption by diamond and its significance - Part VIII. Dynamical theory

The eight characteristic frequencies of vibration of the structure of diamond are theoretically evaluated in the first, second and third approximations, taking successively into account the interactions of each nucleus with its 4, 16 and 28 neighbours. A satisfactory agreement emerges between the calculated frequencies and those observed spectroscopically.

• The infra-red absorption by diamond and its significance - Part IX. The activity of the normal modes

The features appearing in the second-order absorption of diamond are discussed and explained in terms of the periodic variations with doubled frequency of the electronic charge-density resulting from the nuclear vibrations. The origin of the first-order absorption spectrum exhibited by the perfect diamonds is also discussed. The observed facts indicate that the electronic states in these diamonds possess only tetrahedral symmetry, while in the diamonds which do not show the first-order absorption exhibit the full octahedral symmetry.

• The infra-red absorption by diamond and its significance - Part X. Evaluation of the specific heat

• The vibration spectrum of lithium fluoride and the evaluation of its specific heat

The records of the transmission percentages of infra-red radiation by thin plates of lithium fluoride enable the frequency of the vibration of the lithium and fluorine nuclei against each other in opposite phases to be precisely determined. The frequencies of the four inactive modes can be computed therefrom. Four other modes are active as overtones and their frequencies can be directly determined from the records. A theoretical computation of the specific heat of lithium fluoride on the basis of the spectroscopic data alone thus becomes possible. A very satisfactory agreement emerges between the theoretically computed and experimentally determined values of the atomic heats of the crystal over the entire range of temperatures from absolute zero to 500° K.

• The specific heats of the alkali halides and their spectroscopic behaviour - Part I. Introduction

The sixteen alkali halides which form the subject of the memoir,viz., the fluorides, chlorides, bromides and iodides of lithium, sodium, potassium and rubidium all possess the rock-salt structure but exhibit a remarkable diversity in their physical properties. Especially notable are the values of their elastic constants, the published determinations of which indicate striking differences in the nature and strength of the binding between the metal and the halogen atoms in the various cases.

• The specific heats of the alkali halides and their spectroscopic behaviour - Part II. The free modes of atomic vibration

It is shown that crystals having the rock-salt structure have nine different frequencies of atomic vibration exhibiting the features of normal modes. One of them is an oscillation of the metal and halogen atoms in opposite phases. Four others are coupled oscillations of the atoms appearing in the cubic layers, while the remaining four are oscillations of the atoms in the octahedral layers. The oscillations in these eight modes alternate in phase from layer to layer and are respectively normal or tangential to those layers.

• The specific heats of the alkali halides and their spectroscopic behaviour - Part III. The interatomic forces

It is shown that the restoring forces which arise by reason of the relative displacements of the atoms in the alkali halides during a normal vibration may be expressed by five force-constants which are designated byα, β γ, φ andgy. The first two are the principal ones and correspond respectively to a stretching of the bonds between adjacent metal and halogen atoms and to a change of the bond-angles.γ is the operative force-constant for relative displacements of metal and halogen atoms separated from each other by a distanced√3.φ andψ are the force-constants for the relative displacements of like atoms situated at a distanced√2 from each other,φ being the constant for the metal atoms andψ the constant for the halogens.

• The specific heats of the alkali halides and their spectroscopic behaviour - Part IV. The equations of motion

Explicit formulæ are obtained for the frequencies of the nine normal modes of vibration in terms of the five force-constantsα, β, γ, φ andψ. The formulæ show that the principal mode in which the metal and halogen atoms oscillate with opposite phases has also the highest frequency of vibration. The formulæ also enable the four octahedral modes and the four cubic modes to be arranged amongst themselves in a descending order of frequency.

• The specific heats of the alkali halides and their spectroscopic behaviour - Part V. The evaluation of the frequencies

Simplified formulæ involving only two force-constantsα andβ are given for the frequencies of the nine normal modes. Reasons are given for identifying the two force-constants as being respectively the products of the bulkmodulus and of the shearing modulus of the crystal by the distance between adjacent metal and halogen atoms. Calculations made on this basis of the nine frequencies of the rock-salt structure exhibit a highly satisfactory agreement with the spectroscopic data.

• The specific heats of the alkali halides and their spectroscopic behaviour - Part VI. The atomic vibration spectra

The frequencies of the nine normal modes of atomic vibration have been tabulated for all the sixteen alkali halides. The results of the calculation are in striking accord with the results of the spectroscopic studies in the two leading cases of lithium fluoride and sodium chloride respectively. The manner in which the structure of the vibration spectra varies with the relative weights of the atoms of metal and halogen is described and discussed.

• The specific heats of the alkali halides and their spectroscopic behaviour - Part VII. Evaluation of the specific heats

The determination of the normal modes of atomic vibration in the earlier parts of the memoir also enables us to identify and enumerate the oscillators of which the quantised energies of vibration constitute the thermal energy of the crystal. Besides the oscillators with the nine discrete frequencies, there are others which give rise to a residual spectrum of vibrations with lower frequencies. The distribution of frequencies in that spectrum is determined and its contribution to the thermal energy is evaluated.

• The specific heats of the alkali halides and their spectroscopic behaviour - Part VIII. Their infra-red activity

The dispersion, absorption and reflection of infra-red radiation by the alkali halides receive a satisfactory explanation as consequences of the electric field of the incident radiation inducing a periodic displacement of the negative electric charges located between each pair of metal and halogen atoms in the crystal. The dielectric behaviour also receives an acceptable interpretation on the same basis. The appearance of infra-red absorption at wavelengths corresponding to the overtones of the frequencies of atomic vibration indicates that the oscillating units in the crystal have dimensions comparable with those of the unit cells.

• The specific heats of the alkali halides and their spectroscopic behaviour - Part IX. Spectral shifts in light scattering

The spectral shifts of doubled frequencies observed in the scattering of light by the alkali halides—rock-salt for example—are discussed and explained and it is shown that they demonstrate the validity of the approach to the theory of their specific heats developed in the present memoir.

• The specific heats of the alkali halides and their spectroscopic behaviour - Part X. The lithium salts

The great disparity between the atomic weights of the constituent metal and halogen atoms has a notable influence on the character of the vibration spectra as also on the thermal behaviour of the lithium halides. The atomic heat rises rather steeply in the lower ranges of temperature and this is followed by a relatively slow increase towards the limiting value at higher temperatures.

• The specific heats of the alkali halides and their spectroscopic behaviour - Part XI. The sodium salts

Computations of the atomic heats of the four sodium halides are presented and compared with the measured values. The spectroscopic data are the basis of the calculations in the case of NaCl and the atomic vibration frequencies determined from the elastic constants in the others. The vibration frequencies for NaF have been corrected to take account of the interactions between atoms of the same species which are strong in that crystal.

• The specific heats of the alkali halides and their spectroscopic behaviour - Part XII. The potassium and rubidium salts

The atomic heats of the potassium and rubidium halides are computed on the basis of the table of vibration frequencies given in Part VI and compared with the observed values in the cases for which these are available. The differences noticed are explained as arising from the octahedral modes having been assigned frequencies lower than the actual ones in the calculation.

• The infra-red behaviour of sodium fluoride

Twelve spectrophotometer records of the absorption by NaF plates are reproduced covering the wavelength range between 7µ and 23µ for absorption paths ranging from 21 mm. down to 0·18 mm. The octave of the fundamental mode of highest frequency records itself as a sharply-defined absorption at 18·2µ. This gives 275 cm.−1 as the fundamental frequency, in fair agreement with the theoretically computed value of 281 cm.−1 It also fits in with the observed infra-red reflexion maximum at 36µ.

• The dynamics of the fluorite structure and its infra-red behaviour - Part I. Introduction

The properties of fluorite, both as observed in the naturally occurring mineral and as exhibited by the synthetically prepared crystals, are briefly described and discussed.

• The dynamics of the fluorite structure and its infra-red behaviour - Part II. The free modes of vibration

It is shown that the fluoride structure has 14 different frequencies of vibration corresponding to the same number of normal modes with degeneracies of 3, 3, 3, 6, 3, 6, 3, 6, 4, 8, 4, 8, 4 and 8, besides three translations, making up a total of 72 degrees of freedom. The normal modes have been described and represented diagrammatically.

• The dynamics of the fluorite structure and its infra-red behaviour - Part III. Activity of the normal modes

It is shown that the first of the two principal modes of vibration is strongly active in the absorption of infra-red absorption both as a fundamental and as a series of overtones and that the other mode would be wholly inactive. The position is reversed in the scattering of light with shifts of frequency; the first mode is not allowed, but the second is permitted.

• The dynamics of the fluorite structure and its infra-red behaviour - Part IV. The spectrophotometer records

The spectrophotometer records enable us to determine 28·0µ as the characteristic wavelength and 357 cm.−1 as the characteristic wave-number of the infra-red active mode of oscillation of the calcium and fluorine atoms against each other in opposite phases. This mode is active also as its overtones, the octave in particular appearing as a conspicuous and well-defined dip at 14·0µ in the transmission curve. By reason of its contiguity in frequency with the strongly active mode, the vibration of the two fluorine lattices against each other which gives rise to an observable frequency shift in the scattering of monochromatic light also displays an induced infra-red activity and is recorded in the transmission curve as a sharp inflexion located at 15·6µ. The corresponding wave-number 641 cm.−1 is just double the frequency shift of 321 cm.−1 observed in light-scattering.

• Spectroscopic evaluation of the specific heats of potassium bromide

The spectrum of free vibrations of the structure of potassium bromide is determined spectroscopically from the scattering within the crystal of the resonance radiation of the mercury arc. The modes are recorded with doubled frequency shifts. The identification of these shifts as arising from the various modes of vibration is made on the basis of the frequencies as computeda priori from the dynamic theory and from a consideration of their observed spectral intensities. From these spectral frequencies, the specific heat of the crystal can be evaluated as a function of the temperature. When the variations with temperature of the vibration frequencies are taken into account, a satisfactory agreement emerges between the theoretically computed and experimentally observed specific heat data.

• Floral colours and the physiology of vision - Part I. Introductory

Monochromatic light is composed of energy-quanta which are all equal. Our perception of colour is thereby brought into the closest relationship with the notions of the quantum theory. Polychromatic light, however, stands on a different footing and the problem of the colour which it exhibits demands separate consideration. The relationship between the spectral composition of such light and its observed hues can only be ascertained only by the observational study of a great number of cases. It is pointed out that a vast mass of material exhibiting colour and highly suitable for investigations of this nature presents itself to us in the products of the biological activity of trees and plants,viz., their leaves, flowers and fruits.

• Floral colours and the physiology of vision - Part II. The green colour of leaves

The light emerging with sensible intensity after passage through the material of a green leaf is observable in the spectral regions of green and red extending from 520 mµ to 645 mµ. These limits are set by the carotenoid and the chlorophyll pigments in the leaf which exercises powerful absorptions at smaller and at greater wavelengths respectively. The characteristic absorption bands of the chlorophylls can be seen under strong illumination at the extreme red end of the spectrum. But they do not sensibly influence the observed colour of the leaf, since the extreme red is of very low luminous efficiency. Actually, the operative cause which determines the observed colour of the leaf is the absorption by the leaf pigments manifested in the yellow region of the spectrum between 570 mµ and 590 mµ. The colour of the leaf appears a deeper green with increasing strength of that absorption.

• Floral colours and the physiology of vision - Part III. The spectrum of the morning glory

The flowers of the Morning Glory (Ipomea learii) exhibit a bright blue colour of almost spectral purity in daylight. Visual observations, confirmed by spectrum photographs, show that this visual sensation results from the removal of the yellow and orange radiations from the complete spectrum, the relative intensities of the red, green and blue-violet regions remaining unaltered. The effect observed may be interpreted as the result of the masking of the visual effect of the red and green sectors by the blue sector in the spectrum in these circumstances.

• Floral colours and the physiology of vision - Part IV. The queen of flowers

The flowering treeLagerstroemia Flos Reginae (also known asL. Speciosa) has two varieties bearing purple and pink flowers respectively. Spectroscopic examination shows that the purple colouration represents the entire spectrum of white light in which the limited region from 570 mµ to 590 mµ is absent. The pink colour results from a weakening of the spectrum in the range of wavelengths from 520mµ to 570 mµ.

• Floral colours and the physiology of vision - Part V. The blue of the Jacaranda

Spectroscopic observations show that the blue colour of the flowers of the Jacaranda tree is ascribable entirely to two weak absorption bands, one appearing in the yellow and the other midway between the orange and red sectors, the rest of the spectrum of white light showing no other observable variation from its normal distribution of intensity.

• Floral colours and the physiology of vision - Part VI. Comparative study of three cases

The spectral composition of the colours exhibited by the flowers ofSolanum grandiflorum, Nymphaea caerulea andThunbergia grandiflora has been studied. The results are surprising and an explanation is offered for them in terms of the masking or blocking out of the visual effect of the longer wavelengths in the spectrum by the shorter wavelengths, the necessary condition for which is the removal of the yellow sector, accompanied by a weakening in intensity of the red end of the spectrum.

• Floral colours and the physiology of vision - Part VII. The aster and its varied colours

Asters exhibiting vivid colours may be placed in two strikingly contrasted groups, each containing three sub-groups. Spectroscopic examination shows that the perceived colours of one group ranging from purple to violet arise from an extinction of the yellow, while the colours ranging from pink to rose-red of the other group are the result of an absorption in the green.

• Floral colours and the physiology of vision - Part VIII. The spectra of the roses

The characteristic hue designated as rose-red arises from a suppression of the green sector in the spectrum, the radiations of both longer and shorter wavelengths coming through freely. The more complete the absorption of the green is, the more saturated does the resulting hue appear. The reason for the dominance of the red sensation and the saturated hues observed in these circumstances with many varieties of roses is discussed.

• Floral colours and the physiology of vision - Part IX.Hibiscus andBougainvillea

The spectroscopic behaviours of the flowers ofHibiscus syriacus andHibiscus rosa sinensis are quite different. The purple colour in the former case is due to an absorption in the yellow and the red in the latter to an absorption in the green. The purple and red varieties ofBougainvillea show differences of the same general nature and having a similar origin.

• Floral colours and the physiology of vision - Part X. Flowers exhibiting band spectra

The absorption spectra of the blue flowers ofClitoria ternatea and of the purplish-red flowers of the orchidAerides multiflorum, have been recorded. They show a striking similarity with the absorption spectra of the petals ofCineraria exhibiting those colours. Various yellow flowers exhibit a banded structure in the blue-violet regions of the spectrum which they only feebly transmit.

• Floral colours and the physiology of vision - Part XI. A review of the results

The results emerging from the study of the individual cases have been brought together in this part of the memoir and illustrated by further examples. In particular, the special role in the physiology of vision played by the yellow region of the spectrum and the remarkable manner in which its presence or absence determines the character of the sensory impressions produced by polychromatic radiation are described. It also emerges that in certain circumstances, the sensory effect of the two parts of the spectrum on either side of the yellow may be masked or suppressed, one by the other, orvice versa.

• Floral colours and the physiology of vision - Part XII. Some concluding remarks

The results of the present studies on the visual perceptions of polychromatic radiation support the fundamental thesis that the primary physiological sensations are those excited by monochromatic light. The so-called trichromatic hypothesis and the theories of colour vision based on it are not logically sustainable. They are further contradicted by the facts of observation described in the present memoir.

• The new physiology of vision - Chapter I. Introductory

• The new physiology of vision - Chapter II. Visual sensations and the nature of light

• The new physiology of vision - Chapter III. Corpuscles of light and the perception of luminesity

• The new physiology of vision - Chapter IV. Corpuscles of light and the perception of form

• The new physiology of vision - Chapter V. Corpuscles of light and the perception of colour

• The new physiology of vision - Chapter VI. Vision in dim light

• The new physiology of vision - Chapter VII. The perception of colour in dim light

• The new physiology of vision - Chapter VIII. The perception of polarised light

• The new physiology of vision - Chapter IX. The structure of the fovea

• The new physiology of vision - Chapter X. The major visual pigments

• The new physiology of vision - Chapter XI. The carotenoid pigments

• The new physiology of vision - Chapter XII. Chromatic sensations at high luminosities

• The new physiology of vision - Chapter XIII. Blue, indigo and violet in the spectrum

• The new physiology of vision - Chapter XIV. The red end of the spectrum

• The new physiology of vision - Chapter XV. The chromatic responses of the retina

• The new physiology of vision - Chapter XVI. Further studies of the retinal responses

• The new physiology of vision - Chapter XVII. Location of visual pigments in the retina

• The new physiology of vision - Chapter XVIII. The visual synthesis of colour

• The new physiology of vision - Chapter XIX. Perception of colour and the trichromatic hypothesis

• The new physiology of vision - Chapter XX. Superposition and masking of colours

• The new physiology of vision - Chapter XXI. The green colour of vegetation

• The new physiology of vision - Chapter XXII. The colours of flowers

• The new physiology of vision - Chapter XXIII. The colours of the roses

• The new physiology of vision - Chapter XXIV. Floral pigments and the perception of colour

• The new physiology of vision - Chapter XXV. The colours of natural and synthetic gemstones

• The new physiology of vision - Chapter XXVI. Structural colours

• The new physiology of vision - Chapter XXVII. The colours of interference

• The new physiology of vision - Chapter XXVIII. Observations with a neodymium filter

• The new physiology of vision - Chapter XXIX. The reproduction of colour

• The new physiology of vision - Chapter XXX. The photo-mechanical reproduction of colour

• The new physiology of vision - Chapter XXXI. The integration of colour by the retina

• The new physiology of vision - Chapter XXXII. Defects in colour vision

• The new physiology of vision - Chapter XXXIII. The testing of colour-vision

• The new physiology of vision - Chapter XXXIV. The nature and origin of defects in colour-vision

• The new physiology of vision - Chapter XXXV. The faintest observable spectrum

• The new physiology of vision - Chapter XXXVI. The postulated duality of the retina

• The new physiology of vision - Chapter XXXVII. The spectrum of the night-sky

• The new physiology of vision - Chapter XXXVIII. The adaptation of vision to dim light

• The new physiology of vision - Chapter XXXIX. Daltonian colour vision

• The new physiology of vision - Chapter XL. The colours of lolite

• The new physiology of vision - Chapter XLI. Photography in colour

• The new physiology of vision - Chapter XLII. Further observations with the neodymium filter

• The new physiology of vision - Chapter XLIII. The colours of fluorspar

• Zonal winds and jet-streams in the atmosphere

• The atmosphere of the earth

The processes by which the movements of the surface of the earth due to its rotation around the polar axis can influence the atmosphere above are considered in detail. It emerges that the fast-moving areas in the equatorial belt on the surface of the earth play a highly important role in determining the behaviour of the atmosphere. The jet-stream in the sub-tropical regions, the westerly zonal winds in the region of middle latitudes and the easterly surface-winds in the equatorial belt are explained on this basis and shown to stand in close relationship with each other. The winds observed in the polar belt are also discussed and explained.

• The diamond: Its structure and properties

A critical study of the crystal forms of diamond from various sources demonstrates that the symmetry of the structure may be either that of Class 32 or Class 31, in other words that the structure may be either centrosymmetric or non-centrosymmetric. Diamonds belonging to Class 31 may however exhibit a pseudo-octahedral symmetry of external form by reason of the interpenetration of oppositely directed structures having the lower symmetry. The existence of diamond with two differing structures provides an insight into the many remarkable properties of this material,viz., the striking differences observed in the infra-red absorption spectra, differences in transparency to ultra-violet rays, the differences in the intensity of their X-ray reflections and the variations in the intensity and colour of the luminescence exhibited by them.

The modes of atomic vibration in diamond can be completely described and their frequencies evaluated by very simple procedures. The vibration frequencies can be determined experimentally by observations of the frequency shifts in the scattering of light or by infra-red spectroscopy, the results by the two methods being fully in agreement. The heat capacity of diamond may then be computed, giving results in highly satisfactory concordance with the observational data.

The principal mode of atomic vibration having a frequency of 1332 cm.−1 is triply degenerate. These vibrations can be excited in the lattice planes of diamond by the incidence of monochromatic X-rays if it belongs to crystal Class 31. The three-fold degeneracy of the vibration reveals itself as the three distinct spots in the resulting dynamic X-ray reflection by the octahedral lattice planes.

The complete electronic frequency spectrum of diamond has been evaluated by a very simple procedure. The results are highly successful in explaining the known optical and spectroscopic properties of diamond.

• Floral colours and their origins

A new orientation is given to the subject of floral colours by the author’s discovery that these colours may be placed into two distinct spectral categories, which have been designated by him respectively as the spectrum of florachrome A and of florachrome B. Typical of these two categories are the colours ofDelphinium ajacis (larkspur) in the blue and pink varieties respectively, the former showing the spectrum of florachrome A and the latter that of florachrome B. As a general rule, all blue flowers exhibit the spectrum of florachrome A which consists of three distinct and clearly separated bands of absorption appearing respectively in the red at 630 mμ, in the yellow at 580 mμ and in the green at 540 mμ. The spectrum of florachrome B also consists of three distinct bands of absorption, but these now appear in the orange-yellow at 590 mμ, in the green at 545 mμ and in the blue-green at 505 mμ. Spectra exhibiting these features are reproduced with the paper. Their explanation is discussed and it is shown that they owe their origin to an electronic absorption frequency located at the first of the three bands combining with vibrational transitions, the oscillator being the CO group present in the structure of the florachrome.

• The florachromes: Their chemical nature and spectroscopic behaviour

This memoir presents detailed studies of the two florachromes discovered by the author and shown by him to be responsible for the colours exhibited by a great many flowers, the two florachromes being present in the petals either separately or together as the case may be. Their characteristic absorption spectra have been photographed and reproduced and also represented as spectrophotometric records of their aqueous solutions and of the acetone extracts of the floral pigments. In appropriate circumstances, the florachromes in solution are found to be quite stable and continue to exhibit their characteristic spectroscopic behaviours permanently. The interesting discovery is recorded that Florachrome B is present as the colouring matter of the fleshy leaves of the shrubSetcreasia purpurea and can be readily obtained therefrom. The relation between the structure of the florachromes and of the well-known organic compound flavone which is itself a colourless solid is discussed and an explanation is given why there are two florachromes with distinct spectroscopic behaviours.

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