April 8, 1922] 



NA TURE 



445 



falls off much more rapidly than according to the 

 [formula. These observations are significant in view of 

 le observation by the present Lord Rayleigh that the 

 mattering power of saturated carbon di-oxide vapour 

 21° C. is only io2 times that of the gas at atmo- 

 )heric pressure, whereas according to the Einstein- 

 loluchowski formula, it should have been 855 

 les as great. 



The failure of the formula indicated above is 

 specially surprising in view of its successes in other 

 "rections, namely, in the case of gases obeying Boyle's 

 iw, in the case of liquids under ordinary conditions, 

 and, with certain restrictions, even in the case of 

 solids. In attempting to find an explanation of the 

 failure, at first sight one naturally seeks to find 

 some flaw in Einstein's theory, or in the application 

 of it, but the very successes of the formula in other 

 cases would tend to discourage such an attempt. 

 The formula was deduced by Einstein by applying 

 Boltzmann's principle of entropy-probability in order 

 to find the magnitude of the fluctuations of density 

 of the fluid arising from thermal agitation and de- 

 ducing the light-scattering due to these fluctuations 

 by application of Maxwell's electromagnetic equa- 

 tions. It is clear that density fluctuations due to 

 thermal agitation must occur ; that their magnitude 

 is proportional to the square root of the compressibility 

 of the medium as contemplated in the theory may 

 be confirmed independently by identifying the thermal 

 energy of the molecules with the energy of sound- 

 waves of all possible wave-lengths in an enclosed 

 volume of the fluid and equating the energies. Further, 

 the idea that the non-uniformity of the density of the 

 medium is the factor determining light - scattering, 

 at. least according to the wave-theory, is confirmed 

 by the very complete analysis of the problem given 

 by the late Lord Rayleigh in one of his final papers 

 {Phil. Mag., Dec. 1918, p. 449). How, then, are we to 

 escape the difficulty ? 



A very luminous suggestion made by Jeans in 

 his " Dynamical Theory of Gases " (page 203) is 

 here of great help. Jeans distinguishes between two 

 kinds of clustering in fluid media, mass-clustering and 

 molecular-clustering, and points out that they tend 

 to become identical at the critical temperature. 

 Einstein's theory is based on the idea that the 

 tluctuations of density and the resulting scattering 

 of light are both due to mass-clustering. If, however, 

 we assume that it is molecular-clustering that is of 

 importance and results in an increased scattering 

 of light, it is easy to see that in the case of molecules 

 such as carbon di-oxide, which are ordinarily non- 

 associated, the clustering of molecules would only 

 be appreciable near the critical temperature, and that 

 at lower temperatures the clusters would rapidly 

 break up and resolve themselves into single molecules. 

 A double molecule would scatter four times as 

 strongly as a single molecule, a triple molecule nine 

 times as strongly, and so on, and if we assume that the 

 energy-effects of separate molecules or groups are 

 additive, and calculate the number of associated 

 molecules from thermodynamic principles, it is 

 easy to give the theory quantitative expression and 

 explain the increased scattering near the critical 

 point, and the rapid fall at lower temperatures. 



But the fundamental difficulty remains, why the 

 mass-clustering considered by Einstein does not, as it 

 should, according to the classical wave-theory of 

 light, give rise to an increased scattering of light ? 



To the present writer, at any rate, it appears that 

 this contradiction of the electromagnetic theory 

 by experience may have to be classed with its 

 other known failures in the theory of photo-electricity 

 and other modern fields of inquiry. We may, in 

 fact, have to adopt the quantum theory of the 



NO. 2736, VOL. 109] 



structure of light as propagated in space (and not 

 only when it is absorbed or emitted) in order to 

 explain the facts of molecular diffraction. Fuller 

 experimental data which are now being obtained in 

 the writer's laboratory may pave the way towards 

 the clearing up of this fundamental question. 



C. V. Raman. 

 210 Bowbazar Street, Calcutta, March 2, 1922. 



The Radiant Spectrum. 



Prof. Raman in his reply of February 9 to my 

 criticism of his first letter of September i, does not 

 refer to the fundamental difference of opinion between 

 us. For it Was the statement " the phenomenon is 

 due to diffraction by the corneal corpuscles," to 

 which I took exception, because I could not find in 

 his letter, or in Brewster's paper, any evidence on 

 which such a conclusion could be based. 



With regard to the corneal corpuscles, Schafer 

 writes in his "Essentials of Histology" (p. 363, 

 edition 6), "Between the laminae (of the cornea) lie 

 flattened connective tissue corpuscles, which are 

 branched and united by their processes into a con- 

 tinuous network ; there is, of course, a corresponding 

 network of cell spaces." Since, then, the corneal 

 corpuscles lie within the substance of the cornea, 

 their optical effect will depend on their opacity to 

 light, or on the difference between their refractive 

 index and that of their surroundings. Now if there 

 was opacity, or a difference in refractive index, they 

 should be visible under the microscope. But such 

 is apparently not the case. Staining with haemat- 

 oxylem or some other suitable reagent, is necessary 

 in order that they may be visible, and therefore their 

 opacity, or difference in R.I., must be slight. We 

 conclude, therefore, that they will cause but slight 

 diffraction in a ray of light passing through the 

 cornea. In shape the cells themselves are highly 

 irregular, and they average in man 20-30 m in dia- 

 meter. Their nuclei in man are roughly oval in 

 shape, about i6ai in diameter. In order that these 

 structures should produce the type of diffraction 

 pattern described by Prof. Raman, there should be 

 two sets of them, nearly circular in outline, with 

 diameters of 13 m and 7 ix respectively. But a 

 further point arises: Prof. Raman describes slight 

 relative movements on the part of the diffraction 

 pattern, which he compares with those which occur 

 when a film of milk on glass is held in front of the 

 eye. This movement, he states, ceases if the eyelids 

 and eyeball be kept motionless for a short time. 

 Q)uld the corneal corpuscles undergo this movement 

 lying as they do in lacunae in the substance of the 

 cornea ? And even if they could, why should their 

 motion cease when the lids and eyes are kept still ? 



Not only has no evidence been advanced by Prof. 

 Raman in support of his statement that the corneal 

 corpuscles are responsible for the diffraction pheno- 

 mena, but also the shape, size, situation, and optical 

 properties of these structures would appear to be 

 antagonistic to the view. 



With regard to the scattering of light by a prism, 

 the following experiment will be found to demonstrate 

 the effect. On the bed of a spectrometer are placed, 

 base to apex, two glass prisms of equal dispersion, 

 with optically good and clean surfaces (see Fig. i). 



LS. C 5. 



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p.p.' r/ M. £ 



V\r,. I. — L.S., Arc or Pointolite. C, Cmidenser. .S., Slit. T.*, Lens of 

 Collimator. P. & P.>, Prisms. T.', I.ens of Telescope. M , Met.-»1 Strip. 

 K., Eye of Observer. 



The telescope eye-piece having been removed, a 



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