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The Raman effect Fowler, Horace Wesley 1928

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T H E  R A M A N  .EFFECT  - BY HORACE  WESLEY  FOWLER iY-  A Thesis submitted for the Degree MASTER  OF  ARTS  in the Department - of PHYSICS  The University  of APRIL  British 1929  Columbia  r^r.v-'^/r-  - b Chapter II. The Raman Effect. A. General Observations and. Theories. 1. Raman's Discovery.  21.  2. Anti-Stokes Lines.  24.  3. Criticism and Extension of the Theory.  29.  4. Continuous Raman Spectra.  32.  5. Broad Raman Lines.  33.  6. The Effect of the Physical State.  34.  7. The Effect of the Exciting Wave-length.  35.  8. The Effect of Molecular Structure.  35.  9. Polarization of Raman Spectra.  36.  10.Coherence.  39.  B. Experimental Arrangements. 1. Sources of Light.  42.  2. Containers for Scattering Media. (a). Liquids.  47.  (t>). Gases.  50.  (c). Solids.  50.  3. Light Filters.  53.  4. Taking the Spectrograms.  54.  5. Other Considerations.  57,  C. The Raman Effect in Relation to Other Secondary Radiations.  58.  Bibliography.  66.  Key to Abbreviations.  71.  LIST  0F  PLATES.  - o I.  Raman Spectrogram for Carbon Tetrachloride. (To face Page 24).  II.  Arrangement for using an {Atmospheric Pressure Mercury Arc for Light Scattering Experiments with Liquids.  (To face Page 49.)  III. A Quartz Crystal Prepared for Light Scattering. (To face Page 52.) LIST  OF  FIGURES.  1.  Martin's Arrangement for the Purification of Liquids. Page 14.  2.  Cross-tube for Gases.  16.  3.  Straight Tube for Gases.  17.  4.  Martin's Photometric Arrangement.  18.  5.  Langer's Energy-level Diagram for Carbon Tetrachloride. 31.  6.  An Atmospheric Pressure Mercury Arc Lamp.  43.  I.  Langer's Hollow Mercury Arc Lamp.  46.  8.  Wood's Liquid Light Scattering Tube.  48.  9.  Ditto.  49.  10. Arrangement for for Carbon Crystals. II. Wood's Raman Spectrogram Tetrachloride. - o - o - o - o - o - o -  52. 55.  INTRODUCTION.  i.  One may cause atoms and molecules to emit light by heating them or by bombarding them with electrons. This kind of radiation has been designated "primary radiation". Radiat(don emitted by atoms or molecules as a result of their being 'irradiated' from another source is called "secondary". Fluorescence is of this kind. So also is the ordinary scattering of light in solids, liquids, or gases, - by which the sky, deep water, or large bodies of clear ice appear blue. Investigation of this latter phenomenon , both theoretical and experimental, has been pursued a long time. Prominent in this field recently have been a group of physicists working in the laboratories of India, where, during the past seven years, chiefly under the direction of Professor C. V. Raman, the theory of ordinary molecular scattering has been developed on very solid foundations. While studying the -state of polarization of certain fluorescent light from liquids, Raman and K. S. Krishnan 1 made the surprising discovery that, apart from any fluorescent effect,  some light being scattered had wave-lengths longer  than the incident light. They later discovered also the presence in the scattered radiation of light of shorter wave-length than that of the incident light. Spectrograms of the scattered light showed much of the light of modified frequency to be 1. - (93)* * Bracketed numbers in footnotes refer to numbers of articles in the Bibliography (Appendix A., page ).  ii.  concentrated in lines, differing by certain definite frequencies from those of the incident light. From this fact Raman developed a tentative explanation of the whole phenomenon, an explanation which seems to have been amply  justified by  the subsequent experiments of many investigators. The fact that this has been done so quickly is, in itself, an indication of the extreme importance of the discovery in the eyes of many scientists. In the short time that has elapsed since Raman, in his address delivered on March 16, 1928 before the South Indian Scientific Association at Bangalore, announced hi s discovery , papers and communications having it as their subject have been published in nearly every journal dealing with light, - many papers in some of them. Even the bibliography ( which must of necessity be an incomplete one) which was used in the preparation of this thesis, contains references to over fifty articles and communications written explicitly about the "Raman effect". Its importance is stressed by 2 Darrow in his usual dramatic style as follows:  " - - scatter-  ing of light has just sprung into prominence as the most inviting and most ardently invaded field of physics, because of a discovery such as, it had been supposed, could never happen again.  It seemed that experimantal physics had been so thor-  oughly developed - or, to change over to an ancient metaphor, that the field had been so thoroughly harvested and then so exhaustively gleaned - that nothing important could possibly 1. (93). 2.(22).  iii.  remain to be discovered unless by measurements of great precision, or by radically new apparatus, or by applying voltages or other agencies on a scale as yet untried. Yet in the spring of 1928 a mode of scattering visible light was discovered, by a physicist working with a quite ordinary spectroscope, a quite ordinary source of light and some very familiar chemicals, all of which had been available to everyone for && least fifty years. The physicist who thus saw what for a half a century the whole world had overlooked was C. V. Raman of Calcutta." This thesis is an attempt, by a survey of a large part of the published literature related to the Raman effect, to summarize our present general knowledge of this phenomenon, and of its important theoretical implications. Incidentally, there will be described experiments on modified scattering performed in this laboratory by Mr. Harold D. Smith,B.A., and the author. Before proceeding to a discussion of the data and theories involved, it will be foundprofitable to review, in a brief fashi on, the historical developement of the theories and knowledge of ordinary light-scattering,(  the now so-called  "classical scattering", in which no change of wave-length occurs),  and some of the experimental procedures that have  been developed in studying it, -  as these latter form the  basi s for subsequent experiments on the subject of this paper.  CHAPTER If. CLASSICAL A.  SCATTERING  GENERAL OBSERVATIONS AND THEORIES. 1  1, Early Investigations.  The early history of light-scat-  tering is associated with attempts to explain the cause of the blue color of the sky, and, as such, goes back at least as far as Leonardo di Vinci,  who is said to have attributed it 2  to scattering by suspended particles. Lallemand and Soret in 1869 discussed light-scattering in water, disagreeing as to whether it was due to suspended particles or to the water itself. At that time,Sir John Herschel's intense interest in the analogous problem for air caused John Tynda^t to take up the investigation, the result of which was also published in 3 1869  #  Using an incandescant bulb as a source, he studied the  scattering in gases, both dust-free and containing small particles precipitated chemically, and described his methods in detail. It is from his work that light-scattering by pure gases and liquids has come to be called the "Tyndall effect", and light so scattered as "Tyndall light". Using a method suggested to him by Prtff. Stokes, he investigated the effect of the angle of scattering on the polarization of the scattered light The fact that Brewster's law ( i.e., that the index of refract ion is equal to the tangent of the polarizing angle)  requir-  ed the'reflection' in air to be by air to give the results observed, 1. (145).  lefd to the idea of scattering as a sort of 2. (51).  3. (140).  2.  molecular reflection. Much has been dine on scattering by the atmosphere since that time, the most important being by the late Lord Rayleigh and by the present Lord Rayleigh, 1 whose work confirms the theories of his father. The most active present worker in this field is probably J. J. Tichanowski, 2 who has recently  published most interesting results of his  investigations of the effect of the observer's altitude on the polarization of scattered light received from the sky. 2. Rayleigh's Theory for Gases Obeying Boyle's Law: In showing that the molecules which are in the atmosphere are sufficient to give ris? to the blue of the sky, #3 by reason of the light which they scatter, Lord Rayleigh developed a theory for scattering by gases obeying Boyle's law, on the assumption that, under these conditions, the molecules are relatively far apart, ( fteyond eacl^ther's field of influence), and are distributed at random. By this theory, I, the intensity of light transmitted through one cm. of gas otf index of refraction jj, and having n^ molecules per cc. was given by: 1  - Ioe"kX'.  (1).  where k, the coefficient of attenuation is given by  3 h, X*  K  )  '  being the wave-length of the light. This is found by 1. (115).  2. (139).  3. (113) and (114).  - 3 -  Cabannes and others to give results agreeing with observations, especially if one considers the intensity in the path of the incident light to consist of the incident energy, minus the scattered energy, plus that part of the total scattered energy which is sent in the direction of the incident beam. This theory, as far as it goes, has withstood a recent attack by Larmor 1 . 3.  Raman and Ramanathan's Theory  for Gases in General.  In their paper on "The Molecular Scattering of Light p in Dense Vapourst  and Gases",  Raman and Ramanathan general-  ized Rayleigh's theory to make it applicable to gases not obeying Boyle's law, Basing theirs on the well known Boltzmann distribution law that "the chance that two molecules are a finite distance r apart is less than the chance that they are a very great distance apart in the ratio e -  3  (3).  where the integral expresses the potential energy of the configuration. This leads to the result Isc=< instead of  & R T p  (4).  ^  ^  (5).  as required by Rayleigh's law. ( f> is the isothermal compressibility, and the other symbols have their usual significance). It will be seen that (4) reduces to (5) when Boyle's law is 1.(58).  2.(77).  3.(42). p.132.  ] obeyed,  for then,  - 4 -  (2>=  f  and pv=nRT.  4. The Theory of Einstein and Smoluchowski for all Fluids. It is remarkable that this revised formula by Raman and Ramanathan should agree well with one developed in a totally different manner by Einstein 1 in developing an explanation by Smoluohowski for the opalescence of fluids near their critical state. This latter theory was developed entirely from thermodynamical considerations of local fluctuations in density and makes no use whatever of the molecular hypothesis. ,-l-Z.t Einstein arrived at the expression r ^ JTVYAO1-  (6)f  for the transverse scattering, where A(: is the variation in dielectric constant per uni-t volume (f) .With the help of Maxwell's electromagnetic theory, this reduces to irlRTp  T  ( M ' - o V ^ r V  ,„. pe"r"o:=: " "  1  For gases and vapours this becomes -  I  sc  =  ^TL^-ifRTp A*  (8)#  p  A similar expression has been obtained by H. A. Lorentz , using the theory of probability. The Einstein-Smoluchowski theory is more general and of wider application than that of Lord Rayleigh (as Rayleigh himself has pointed out), and has be en confirmed by Raman and Ramanathan in the case of ether in both liquid and"*avpour phases from -30 C to 217 C. ® 1.(25). 2. (6<)). 3. (For up-to-date summaries of the theories for liquids see (86) and (98A<)..  - 5 -  4. Modifications for Depolarization and for Critical Conditions.  According to the Einstein-Smoluchowski  theory, the light scattered transversly should be completely polarized (also according to Rayleigh's theory 1 ) in a direct on perptMclieukv 2 the incident beam. The present Lord Rayleigh discovered that it was not perfectly polarized. The imperfection of polarization has been measured by photographic methods by him 3  4  -stfHi by Cabannes , and by Gans . Cabannes has shown that there is )!& slight increase in the intensity of scattered light due to this imperfection of polarization, and that the Rayleigh expression for scattered intensity may be corrected by mul>'tiplying it by the factor  &J  6(6-7p 1 + p)  where P  ratio of the weaker ( parallel to the incident beam)  is the compon-  ent to the stronger component of the scattered light.This whole factor is commonly referred to as the 'C abannes correction",  and p is the measure of "depolarization". Except in this  correction factor, it is usually expressed as a percentage. It has been found applicable also to the Einstein-Smoluchowski expression for scattered intensity. The correction becomes very important when p is large. All formulae show that the scattering varies as which explains the predominence of blue and violet in scattered light. Einste in has pointed out on mathematical grounds, that his formula does not apply in the immediate vicinity of 1.(145)p.624.  2.(116).  3.(14).  4.(37).  - 6 -  the critical temperature, where opalescence "becomes marked. Ornstein and Zernike 1 have developed an amended formula, applicable in this region, according to which the scattered intensity varies as  A  . This theory is supported by the 2 i  work of D. K. Bhattacharya , Andant , and Raman and Ramanathan^. 6. Rocard's Theory, and the Determination of Avogadro's Number:  Rocacd5 has recently given a method of calculating  the diffusion of light, taking account of oscillations due to intermolecular forces, and has obtained results agreeing with observed values for water, ether, benzene, and gaseous ethyl chloride. The final expression for the intensity of the scattered light,by this theory as well as by those previously described, involves N, Avogadro's number.( The number of molecules per gram-molecule.) Thus, by observing the value of the intensity, one can use the scattering formulae to ob6 7 tain N. Cabannes has so used them, and Raman and K. S. Rao ^ ^ Q 2, found N=7.3x lCr° for water. Scott Ewing*5, of the University of California, has made some very accurate determinations of N in this way, - claiming accuracy to five significant figures. Rocard has also used his theory for this purpose. 7. Depolarization and Anistropv. The imperfection of polarization of scattered light has, from its discovery, been associated with some kind of 1.(72). 2.(7).  3.(3). 4.(81).  5.(129)." 8.(27). 7.(79)p.639. 6.(14).  - 7 -  lack of symmetry of the molecule, theory based on symmetrical molecules or spherical patticles predicting the scattering of perfectly polarized light. "Optical anistropy" is the name given to the quality of the molecule which gives rise to the scattering of unpolarized light. Many investigators have attempted to discover just what constitutes this property,and even yet have not completely done so. 1 It is generally conceded that it does not consist only in departure from symmetrical shape  t  if shape is represented by the chemical graphical  formula, although substances represented by formulae of the benzene ring type all have low depolarizations. Anistropy seems to be a function o^both chemical association and geometrical shape. More complicated theory, leading to expressions for intensity and depolarization^ of scattered light for the case 3 of crystals has been developed by L. V. King , The relation between depolarization and temperature, and the effect of the physical state ( liquid, vapour, etc.)  have been investigated  by many, including Raman and Ramanathan 4 , S. R. Rao 5 , and 6 I. R. Rao . Raman  axso  f 0 U n d that, for many liquids, the de-  polarization varied approximately inversely as the wave-length, and that its value for a liquid was much greater than for the corresponding vapour. Martin has found the depolarization to vary as a direct function of the intensity,  the light of very  weak lines being nearly perfectly polarized. l.(l03)(Special reference on anistropy). 2. (80)4(36). 2.(46). 4.(82). 5.(110).  6.(108).  - 8  -  8. Scattering bv Particles. Colloidal and Otherwise. Scattering by particles ( as contrasted from molecules)  has been made the subject of many investigations. As Lord Rayleigh 1 developed theory for scattering  early as 1871,  by particles (droplets)  small in comparison with the wave-  length of light, which has been found by Was. Shoulejkin to hold for particles whose diameters do not exceed--. Rayleigh u assumed only that the dielectric constant of the particle (and hence its refractivity) differed from that of its suro roundings. J. J. Thomson'0 has dealt with the case of metal spheres of these sizes.  Recently Nugent and Walmsley^have  studied scattering due to particles of metallic oxides dispersed in dry air. They concluded that observed variations in the Tyndall light depended on the sedimentation and changes in aggregation'^ of the solid particles. In general, the scattered intensity varied as the  2/3 power of the density of the scat-  tering material. G. Mie  has studied the case of colloidal particles of  the size treated by Rayleigh and Thomson, and Shoulejkin 5 of Moscow, has extended the theory to include very large particles. His paper is an extremely interesting one. He reports on the effect on intensity and polarization of the size of the scattering particle over a widS range, and describes remarkable distributions of depolarization in various directions about the scattering particle, showing depolarization under these J114!2. (138).p.437.  3.(144). 4.(65).  5.(134).  conditions to "be a function of the scattering angle. He concludes that the value of the scattered intensity is a smooth continuous funetion of the size of the scattering particle, even up to the point where the latter is large in comparison with the wave-length, and where ordinary laws of reflection and refraction obtain. (This is in accord with Darrow's idea that " Light may be scattered by particles of any size from atoms up to drops of water. Even reflections from larger bodies may be considered as the resultant of the light scattered by the particles of which these are made.") 1 Shoulejkin, in a p paper "On the Colour of the Sea"  in 1923 stated that this  color cannot be explained by either  -—  (l) the intrinsic color of water due to selective absorption or (2) Bftyleigh's scattering by microscopic particles or bubbles of gas,  alone, but by these factors, together with-  03) selective reflection by larger particles of clay, plankton, etc.,  and,  (4). fefleeted light from the sky. 3 In 1927, after pointing out that usual theories,assuming uniform density and each particle to act as an independent source, were not always valid, Raman 4 developed a theory for colloidal scattering, based on  variations of osmotic pressure  and of refractive index with the concentration of the colloid5 al particles. hao ohown that at any given angle of Lange eLango has shown that, since 1.(22)p.65. 3.(58A). 5.(56). 2.(133). 4.(84A).  - 10 -  scattering, the depolarization factor depends on the size of the scattering particle, determinations of depolarization maybe used as a method of obtaining the size of these patticles. He found depolarizations to be zero for such spherical particles as colloidal rubber and mastic. In another paper 1 ,  he  deals with depolarization and absorption of colloidal gold of dimensions ranging from  to 1 6 0 ^ , - finding the scattering  to be a maximum for medium-sized particles. 9, Scattering by Mixtures and Solids. As is well known, there are many substances (e.g. phenol and water)  which in a liquid state dissolve eacl^other complex-  ly, and form a single phase above a certain temperature,called the critical solution point; below it they are only partially soluble, and divide into two co-existent phases. Such mixtures exhibit a marked opalescence or turbidity in the neighborhood of this point when they are brightly irradiated. Einstein  2  and Smoluchowski  3  gave attention to this case of  scattering, and their approximate formulae were rigorously revised by Raman and Ramanathan 4 , in whose paper is given an excellent outline of the theories for mixtures to that date. They do not mention, however, important work done in this field in 1913 by W. J. Fawcett 5 , ft to that of W. H. Martin  on  although reference is made  carbon disulphide and ether, and  on benzene and normal hexane. The theory of Raman and Ramanathan was supported as regards both intensity and depolarization 1.(55). 2.(25).  3.(136). 4.(78).  ~5~( 30). 6.(63).  - 11  -  by the work of A. N. Banerji 1 and acetone, and by that of  on mixtures of carbon bisulphide p Durgadas Banerji  on gaseous  mixtures, in the case of air and C0 2 > More recently, Ramdas has studied light-scattering by gaseous mixtures of oxygen and carbon-dioxide at 32°C,  for pressures ranging from 20 to  120 atmospheres. He found that for either pure gases or mixtures, the intensity of scattered light sure, for moderate pressures.  varied as the pres-  Very high-pressure changes  seemed to have no effect on the intensity. In mixtures of 0 and COg,  for increasing concentrations of COg, intensity  curves approached those of pure COg. In dust-free liquids there is a transverse scattering of light (mainly unpolarized)  on account of local fluctuat-  ions in density and random orientations of molecules, which cause the fluid to be optically inhomogeneous. In mixtures there is, in addition, a polarized transverse scattering due to local variations in composition, and consequent variations in refractive index. This persists when the mixture congeals into an amorphous solid. Raman has shown this scattering to occur with optical glasses 4 , in a way which shows it to depend on the index of refraction and on chemical constitution, and not on accidental inclusions. 10. Surface Scattering. Closely related to opalescent phenomena near the critical temperatures of liquids and vapours, and to those near 1.(4).  2.(5).  3.(t05).  4.(84B).  - 12 -  the critical solution points of liquid mixtures, is the scattering of light by free liquid surfaces, which has been investigated very extensively, particularly by L. A. Ramdas. A most excellent detailed description of this work, as well as of ordinary 'internal1 scattering, is given by Raman in his 2925 secretarial report to the Indian Association for the Cultivation of Science. 1 In it, the molecular nature of surfaces (and of evaporation) is vividly described, and it is pointed out that their toughness and turbulence is inversely proportional to the surface tension of the substance. Since scattering is due to inhomogen&ty, one would expect it to be greater for the rougher surfaces. The intensity of scattered light is found to vary inversely as the surface tension, both for different liquids and for the same liquid under changing temperature. The brilliancy of scattered light at the critical temperature then follows from the fact that the surface tensions approach zero at that point. This is probably the critical opalescence previously described. The illuminated surface, when viewed under a microscope, shows no structure; hence, the roughness of the surface is of molecular dimensions. This may be considered to constitute the "transition layer" obliquely  of Drude's 2 theory for the  elliptic polarization of A reflected light on the basis of the electromagnetic theory. It would thus seem that surface scattering is merely molecular scattering under the special con1. (82A)pp.93-106.  2.(24)p.287.  - 13 -  ditions which obtain in this transition layer, and that the marked opalescence observed near the critical temperature, common to both kinds of scattering, - is merely the result of the approach of surface layer conditions to those holding for ordinary 'volume' scattering. Analogous to this are the phenomena of surface scattering at the interface between two  li-  quids, and the opalescence observed in mixtures near their critical solution points. Surface-scattered light must be viewed from directions near those of the regularly reflected or refracted rays, (extWfli: cept in the case of^mercury surface, which may be seen from any direction). "When this is oblique to the surface, (as it usually is) the observed light is elliptically polarized, as it would be in the case of reflection. 1 B.  EXPERIMENTAL ARRANGEMENTS.  1. Sources of Illumination. In most experiments on classical light-scattering, the scattering media have been irradiated with a  concentrated  beam of sunlight, or with the light f0Dm a mercury arc. The former has been used in the majority of cases, and in some instances where great intensity was required, the sunlight was passed through the objective of a large astronomical telescope  1.(24) p. 287.  2. (80).  - 14  -  2. Purification of the Scattering Media. In most cases it was ^oundf1 necessary to have the scattering substance in a very pure state. The method used to secure pure, dust-free liquids has usually been that due to Martin, and very fully described by Kenrick and Martin. 1 sists in  It con-  repeated slow dis-  tillation of the liquid in Vacuo , in a sealed vessel consisting of two bulbs joined by a rather long glass tube.  Fig.l. (See Fig.l.)  The bulb into which the liquid is last distilled  is sometimes sealed off and used in the experiment as the container for the scattering liquid. For most liquids, four or five distillations were found sufficient, but special difficulty was usually experienced in the case of water. In fact, Raman  2 and Ramanathan  found it necessary to distil water many times,  and then to allow it to stand undisturbed for about three months. It was then distilled several times more before being used. They made a practice of purifying large quantities and varieties of liquids at once, storing them in specially constructed shelves for later use. Preparation and purification of gases is described by Raman and K. S. Rao 3 , and by A. S. Ganesan. 4 These exper1.(62) & (64). 2.(82). 3.(80). 4.(36).  - 15  -  imenters rendered gases and vapours dust-free by passing them through tubes packed with cotton wool. Asbestos wool was used for gases which would act upon cotton. 3. Containers for Scattering Media. As has been mentioned above, scattering liquids were usually used in the bulbs or flasks into which they were finally distilled. Precautions had to be taken, however to minimize the reflection of light by the sides of the vessel. For this purpose, the flasks were usually painted dead black and immersed in a tank (the inner sides of which were also black) con&tining liquid of as nearly as possible the same index of refraction  as the liquid being observed. The necessary open-  ings were provided for the entrance and exit of the direct beam of light, and for the observation of the transvejjsUy scattered light. As the light scattered by gases and vapours is much less intense than that by liquids,  page  ), special  arrengements had to be made in these cases to prevent reflection in the direction of the observer or spectrograph. To accomplish this, Raman and his fellow-workers developed a form of cross-tube as indicated in Fig.2. was passed from A to B,  1  The irradiating beam  through suitable apertures G and H  in the tube, E and F were inlet and outlet respectively for the vapour or gas. The scattered radiation was viewed from D, which was enclosed in a small light-proof room or 'booth 1 , provided to accustom_the observer's eye to seeing light of  1. ( 8 0 ) .  - 16  -  very low intensity. Several plans were tried for preventing the reflection of light from C. One satisfactory method was to cement to the tube at J a long-necked bottle (from which the bottom had been first removed), and to cement to the neck c  Fig. 2. of the bottle, which had been cut at an oblique angle, a deadblack glass diffusing screen, ^ater^a horn-shaped end, drawn from a large glass tube,* (shown atU{£)  was found more suit-  able than the bottle and screen. When properly shaped, this These. cannot possibly reflect light back into the tube. TSi&s-E tub GOtubes were usually made of iron, and, when temperature control was required, were, along with the cotton wool straining-tubes surrounded by electric heating coils.  Ganesan^"  has developed  a satisfactory method (by chemical precipitation) of coating * Luring the past year, these 'horn' reflectors have been much used in Raman effect experiments. 1.(36).  - 17  -  the inner walls of these tubes with a dead black paint which is unaffected by gases, even at high temperatures. For nitrous oxide, carbon-dioxidd, and some organic vapours, Narayan 1 has  4. Measurement of Depolarization. The value of the depolarization ratio, p  , is usually  determined by the method due to Cornu. It consists in passing the beam of scattered light through a nicol and a double image (Wollaston) prism.The two images formed by the Wollaston are each due to plane polarized light, the plane of the one being at right angles to that of the other.  If the nicol be rotated  about its axis in the beam, two positionswill be found for it which make the images formed by the Wollaston to appear equally bright. If 0 the nicol, then  be the angle between these two positions of P = tav\\6 I 2  (9).  2  Raman and Rao the angle  9  have repeatedly used this method, determining visually, and they state in the latter cited  paper that they consider it a very reliable method.  •©»«-.  Kenrick and Martin 3 have described a photographic 1.(69).  2.(80) & (79).  3.(45).  - 18 -  method for determining value of P  f> . Ramanathan 1 has found that the  .found in the visual way above described is slightVf  in error if the rays of the irradiating beam are not parallel to one another, the error being of the order of 0.14^ for a convergence of the beam of 3°, and 0.38^ for one of 5°. Rao  has applied corrections for this 2 ,  I.R.  but he later 3 claims  to have found that a correction is unnecessary,  as the values  determined depend in no way on the convergence of the beam. 5. Measurement ,of the Ratio of Intensities of the Scattered to the Incident Light. Both visual and photographic methods have been used in determining this quantity. The essentials of the former are merely those of an ordinary photometer,  I.e., arrangements  whereby two adjacent parts of an object or visible 'field* may be illuminated at the same time,  the one by scattered light,  and the other by non-scattered light from the irradiating source. Jig. 4 illustrates a simple arrangement used by 4 Martin  . A contains the  scattering medium, receiving light from the source S. The transversely scattered light illuminates the field B. The exciting beam, after passing throught the flask, is  Fig. 4.  directed, by means of the 1. (103). 3.(39).  2, (108).  4.(62).  - 19  -  «  plane mirrors C and D the same time as B.  to the field  which can be viewed at  Sometimes it is necessary to place screens  of known absorbing power  in the path of the more intense  beam, in order to facilitate comagrisons in photometer or illuminometer determinations. ' .. When such are needed here, they are placed at 3P. In investigations as to the relation between wave-length and scattering power, filters transmitting the various required wave-lengths may be inserted at G. An original and more complicated photometric system, involving several partial reflections,  and the use of diffus-  ing screens made of thin white blotting paper is described and illustrated by Durgadas Banerji 1 in a  paper"0nthe  Scattering  of Light in Mixtures of Air and Carbon-dioxide". Intensity ratios may also be determined photographically, either by finding the respective lengths of exposures required to produce equal blackening on the photographic plate, with the light intensities being compared, and all other conditions unchanged, - or,  by finding the respective apjferture  diameters (of the camera diaphram) required for equal blackening, with all the other conditions (including the exposure time) constant.  Account is taken, of course, of the absorptf-  tion coeffieients of any screens or filters used. ~ The sun has generally been found to be the most satisfactory source of light for photometric determinations. 2 Raman and Ramanathan found that the ratio of intensity of the scattered light to that of the incident light ranged from 1. (5).  2.(82).  - 20  10  t0  1U  -  for liquids, and that, in some liquids, blue  and violet irradiation  excited a fluorescence in the green  region, the intensity of which was about scattered radiation, -  of that of the  that is, - about 4 x 10~ 7 of that of  the ineident light. The scattering power of a block of Jena glass was used as a standard in making comparisons of the scattering powers of different substances.  - 21  CHAPTER  -  II.  THE RAMAN EFFECT. A.  GENERAL  OBSERVATIONS  1.  Raman's Discovery.  AND  THEORIES •  In 1925, Raman and Ramanathan 1 discovered and studied a secondary radiation accompanying the light ordinarily scattered from some liquids. Investigation with prisms and filters showed that this light was largely unpolarized, and that it consisted of a continuous range of frequencies in a region of the spectrum rather remote from the position of the light / 2 which excited it. (As predicted by Stokes' law,  it was of  longer wave-length than the exciting light.) These considerations lefcd them to conclude that the phenomenon was one of fluorescence. Further studies of this kind leij.d, in the spring of 1928, to the remarkable discovery of Raman and Krishnan mentioned on page i. They were using the usual scattering flask arrangement with a strong beam of sunlight. As on previous occasions, they had two complementary color-filters, - one transmitting violet and blue light, and absorbing light of longer wave-length, - and the other absorbing just the wavelengths that were transmitted by the first.  When both were  placed in the incident beam no scattered light was seen, as there was no light incident upon the flask. When, however, the 1. (82).  2. (145). Chap.XX. p.559.  - 22  -  second filter, absorbing blue and violet, was placed in the path of the scattered light, the track in the liquid was seen, - faintly green,  although, due to the first screen, no green  light was entering the liquid! Furthermore, no light which passed through the first screen could pass through the second. In contrast to the instance previously mentioned, this green light was very strongly polarized. More careful examination with a spectrograph, - expended to many liquids, to vapours and gases, and even to amorphous solids,ement  le^d to the announc-  referred to in the introduction. In the Bangalore lec-  ture, investigations were described showing: 1.  That the effect was observed in the widest variety of  physical conditions, (gas, Vapour, liquid, crystal, and amorphous solid,), having been found in more than eighty substances. 2. That the modified radiation is strongly polarized. (This is a true scattering effect.) 3. That modified scattered radiations consist, in many cases, of lines of varying degrees of sharpness, in displaced positions. They are often accompanied by some nebulosity of continuous spectrum, which is also strongly polarized. 4.  That, for any one scattering substance,  the change  in frequency,,- represented by the distance on the spectrum between the line due to the scattered light of modified wavelength and that of the unmodified wave-length ("classical scattering") - is the same, and is independent of the exciting frequency. Furthermore, there may be several modified lines  - 23  near each unmodified line,  -  but their relative distances from  the exciting line (and hence, from one another) are always the same fofc the same substance. *  From this it follows that if  the incident light is represented by a bright-line spectrum, each of the more intense exciting lines will be accompanied by its 'pattern' of Raman lines (satellites). Since the shift in frequency was found to be characteristic of the scattering substance, Raman of course looked to the scattering substance for the explanation, and soon found one well in accord with the ideas of the quantum theory. He discovered that the frequencies  many known absorption bands  in the infra-red spectra of these substances (**) represented an absorption of energy by the molecule (***) just equal to that (*) Henceforth, these scattered lines of modified wave-length shall be referred to as "Raman lines", and all unmodified scattered lines as "incident lisss" or "exciting lines", although they also are scattered. "Scattered lines" shall not be used, unless in the proper sense, i.e., to include both modified and unmodified lines. The literature of the subject has been rendered ambiguous , and in some cases misleading, by the careless use of these words. (**) Infra-red radiations may be studied by spectrographs methods, although^considerable difficulty in procuring refractive agents suitable for these wave-lengths. A. H. fffund (73A), has used satisfactorily a reflection method (the method of "residual rays") utilizing the fact that energy of a wavelength corresponding to an absorption band or line of a substance is not reflected by that substance to as great an extent as energy of other wavelengths. He used this method with glycerin. (***) It is shown from mechanical considerations in standard texts on spectroscopy, that spectral lines or bands which would represent the possible changes in rotational or in rotational and vibrational energy of molecules would fall in the infra-red region of the spectrum, agreeing reasonably well with the positions of bands that have been observed. Changes in rotational energy would result in lines in the far infrared (wave-length of 50-100^); changes of both rotational and (Continued at the foot of page 24.)  - 24  -  which would be lost by the light quantum in suffering a change in frequency noted in the Raman spectrum for that substance. The picture he suggests, then, is that an incident quantum of radiation may  give up some of its energy to a molecule( this  being expended in increasing the rotational or vibrational energy of the molecule, or both), and be scattered with the energy it has left, being then a quantum of degraded frequency. He considers the ratio of the intensities of the modified line to that of the unmodified line to be a moasngipo measure of the probability that a quantum will lose that energy. As this is low, it appears that most quanta keep all their energy on be- ing scattered, - the relative intensities in many cases (determined by methods described in Chapter I ) being of the c order of 1:500, or b.2%. 2."Anti-Stokes Lines. It was mentioned in the introduction that Raman later discovered modified lines on the short wavelength (higher eneggy) side of those which excited them. His failure to discover them along with the others was probably due to their faintness as compared with the other lines.*  Furthermore,  they seemed less to be expected, on account of Stokes 1 we&l* Such lines may be seen in the example given for CC1 4 , Plate I, facing this page, The modified lines are marked with arrowheads, those of enhanced frequency being indicated in red. The source of light, whose spectrum is shown on either side of that of the scattered light, was the atmospheric pressure mercury arc described on page 43. Note particularly the Raman lines on either side of the 4358^ group of exciting lines. ***( Cont'd, from page 23), vibrational energy would result in lines in the near infra-red (wave-length of a few v ). (l37)pp416-425. and (125)pp.407-411.  PLATE I  (To face  page •o w <0 i. <J O -H C o u i.  if 4038-3  Hoo'Z 44 I&-0 4447-or + &OJ. 4 5- 13 .9  CA C. ai —r <V 3 <> 3 -o a> O  - 25  -  known law of fluorescence} (also known as "Kirchoff*s law  2  ),  namely, that the wavellength of fluorescent light can never be shorter than that of the light which excites it. Since these lines of enhanced frequency obviously constitute a violation of this law, they have been called "anti-Stokes lines" or "anti-Stokes terms".* (Darrow 3 considers it cruel to perpetuate a mistake in this way. Perhaps he is thinking of the last sentence of page 154 of his "Introduction to Contemporary Physics",) It will be noted that the same frequency differences are found for the anti-Stokes lines as for the Stokes lines The anti-Stokes lines have also the same intensities relative to on^iknother as do the corresponding lines of degraded frequency. The result is that each group constitutes a "mirror image" of the other, the exciting line being regarded as the mirror. The comgprative faintness of these ^ti-Stokes lines is quite in accord with the explanation proposed by Raman as to their origin. It was merely that these lines resulted from quanta which received energy from £he molecules  i they  had struck. That is, - the impinging quantum gathered up some energy from a molecule already in an excited state,('inducing 1 that molecule to return to its normal energy state) and then rebounded as_a_quantum,of greater energy A recording itself in Many exceptions to this principle have also been found in fluorescence. See (148) 1. (125) & (145).  2.(144A).  3.(22A).  - 26  -  the spectrum on the ultra-violet side of the exciting line. Ramdas expresses this very clearly in these words^"The incident quantum of radiation may be scattered with its energy unaltered, in which case it re-appear3 with its original frequency. On the other hand, an exchange of energy may occur between the quantum and the molecule, in which case the scattered radiation has lower or higher frequency, as the case may be. A transference of energy from the quantum to the molecule will naturally occur much oftener than the reverse process, as, at ordinary temperatures,  but few molecules are in a position  to part with any energy." It is further found that the ratio of the intensity of an aiti-Stokes line to that of its corresponding Stokes line is the same order as the proportion of molecules in the higher level of energy, as given by the relation f -  (10)  where: h is Planck's constant, k is the Boltzmann constant per molecule, This would support the assumption that transitions of the molecule to and from the higher energy level are equally probable. On this basis, f of the above equation would represent the ratio of intensities. Using this, Raman and Krishnan 2 calculated for CC1 4 corresponding to shifts in wave number (cm."*'1") of 219, 312, and 457, obtaining l/2|8, l/4.4;and 1/8.8, for 30°G. By a photographic method, they roughly estimated the 1.(106)p.l32.  2.(97).  - 27  -  observed values to be 1/3, 1/5, and l/lO. They point out that this theory is sufficient to explain why negative (anti-Stokes) line* of relatively large frequency shift are not found. The decrease in intensity of anti-Stokes lines with increase in frequency shift is reported by Pringsheim and Bosen 2 for the cases of mfcfthylene chloride, chloroform, carbon tetrachloride, acetylene dichlorid*£e, tetrachlorethylene, acetylene, benzol, monochlorbenzol, and toluol. On the basis of the above equation one would also predict the anti-Stokes lines to become more intense with a rise in temperature. Apparently thi3 idea was implied RawJas iv^  >  Rand as Jagr the words "at ordinary temperatures" in the passage above quoted. This prediction has been shown to be fulfilled in some cases. Brickwedde and Paters 1 have observed the effect with quartz over a range of temperature from -180°C to 550°C, noting that anti-Sfokes  lines become brighter, and Stokes  lines remain constant or become slightly fainter, with a rise t in temperature. They state the usual theory concisely in the words: "Intensities of Raman lines vary as the populations of the initial states which give rise to them." They also observe that all modified lines become more diffuse with a rise in temperature. (Wood 3 has shown that the intensity of Stokes and anti-Stokes fluorescence behaves in the same way.) Raman and Krishnan 4 cite the surfender of energy to the quantum by the molecule as the first direst 1.(11).  2.(74),  3.(148)  4.(97).  experimental  - 2 8 -  evidence of"induced emission" of radiation by molecules. They point out that this idea, sometimes described absorption",  as"negative  first put forward by Einstein 1 in his celebrat-  ed paper on the derivation of Planck's radiation formula?: -o,nd and forms  an  essential feature of his theory; also, that the  idea figures prominently in the theory p ed by Kramers  and Heisenfeerg.  of dispersion  develop-  They also point out that  the -possibility of a process of this kind,  in respect to the 3  electronic state of an atom, was first contemplated by Smekal. It occurs to the writer that it would be of interest to know if the "excited states" involved in the above theories are in any way analogous to the "metastable states" described by 4 Darrow , An atom in this state cannot return to its normal state by the spontaneous radiation of its energy, but must await an ancounter with another atom which is capable of receiving this energy. Would a light quantum serve just as well? The above considerations must make evident why so much interest was immediately shown in the discovery of Raman and Krishnan. Scientists realized its importance, not only as a powerful tool for use in the exploration of the otherwise nearly inaccessible regions of the infra-red spectrum, and the investigation of molecular structure and behavior,  but also  as a most valuable piece of evidence in support of the quantum theory, andthe the cause of rather «C marked change in our conception of behavior of a quanta, 1. ( 2 5 A). 3.(135). 4.(22)p.224. 5.(See footnote 1, p.29.) 2.(For a fuller treatment of this, see (91).)  - 29 -  3. Criticism and Extension of the Theory. It should be stated here that the explanatory theory proposed by the discoverers has not been left entirely untouched by other investigators.Almost  immediately after the  announcement, Cabannes, in a published statement  , attributed  the Raman effect to what he termed "optical beats", which he claimed to have predicted in 1924, but which had not previously been demonstrated. Furthermore, Saham Kothari, and ToshniS  (University of Allahabad) disagree with the statement 4  of Raman and Krishnan that the discovery constitut es a confirm <i ation of Einstein's "negative emission theory!'. They consider it, however, to be the negatively modified scattering predict5 ed by Smekal. What will probably turn out to be the most constructive criticism, and a real extension to the theory, has come from R. M. Langer, of the U. S. Bureau of Standards. He has found that many observed Raman lines cannot be accounted for on the basis of the theory put forward by Raman, - there be1. (See footnote 5,p.28.) Cabannes has pointed out that, while the quantum theory could account for the effect observed for benzene, i.e.,scattered light of frequencies V.i N.-^i , ^o+^j., « — etc., the frequencies predicted by the wave theory would be merely V« , V c , (See (17)). Several unpredicted applications of our knowledge of the Raman effect have been suggested; i.e., that it will explain the presence in some spectra oif lines not previously accounted for,- notably, in the many-lined secondary spectrum of hydrogen (See (2)*,which has so far not been properly interpreted, and in the rather complex spectrum of the Zodiacal light. (See (107)). 2.(18). 3.(131). 4.(90). 5.(135).  - 30  -  ing no infra-red absorption bands of the required frequencies. He has also found that many known infra-red bands do not seem to be represented in the Raman spectra. 1 Furthermore, even when there are found infra-red absorption bands, and Raman lines to correspond to them, there seems to be no correlation between their intensities. In seeking an explanation, he has found that most of these otherwise unaccounted for Raman lines p can be shown to differ in frequency from the exciting line, ' not by an absortion frequency, (although these also may appear) but by differences between these.  This is merely a way of  saying that Raman lines may result from energy transitions in the molecule which do not necessarily (and do not all) involve its normal state. Banger illustrates his contention by an examination of the data for CCl^, and constructs a tentative energy level diagram (See fig. 5.) showing a scheme of transitions which are nearly all actually represented by Raman lines. (Transitions not so represented are indicated in the figure by dotted liiies).  He points out that, on the basis of  the original explanation, only two of a system of five Raman lines have corresponding absorption bands. These two are the weakest ones,- but their absorption bands are very strong. His 1. Raman and Krishnan themselves have calculated frequencies of more modified lines than they have observed, for benzene, toluene, and carbon tetrachloride. (97). 2. When there is any doubt as to what incident wave-length is exciting any given Raman line, the question can easily be settled by noting which Raman lines dissappear as various incident lines are absorbed by selective color-filters placed in turn in the path of the incident light.  - 31  -  numbefj -frequency-  11 0 CD « M w Of !n) 0 ^  3 ¥  £  >  p-« l (  r  O) <t to  >*  »  *  \  II(  (  +1 ' 51 1  w1 = n 0 • <3  C CO D N  ;  />» 0>  SI i >f l '1 1 M ! 5: 1 =,  1 /  s \•  H O  \  f  c +» r/  •3 « * \  >•  •>  Figure 5. theory seems to be well supported by the examples that he has worked out. "The significance and power of scattering experiments in unravelling (sic) infra-red data is much greater than if they merely check the infra-red measurements. With their help, and with more precise data, it is hoped that the vibrations of more complex molecules wil be interpreted.1,1 The principle of this theory was apparently  first suggested  by F. Rasetti,(California Institute of Technology) who found 9  it useful in explaining the observed data for COg.~  It seems  probable that this scheme, if completely established, may lead to a series notation for Raman spectra. 1. (57).(R.M.Langer)  2. (111A).  - 32 -  4.  Continuous Raman Spectra. So far, little mention has been made of the nebulos-  ity or continuous spectrum frequently observed about sharp exciting lines in Raman spectra. In a discussion of this in the case of benzene, Raman and Krishnan 1  suggest that, while  •te transfers of energy represented by displaced lines probably result in changes of the vibrational energy of the molecule, transfers represented by the continuous spectrum of modified frequency may result in changes of rotational energy of the molecule.  In support of this, they cite the fact that nebul-  osity is strongest around unmodified lines, and is unsymmetri^ cal about them, being most intense, and extending farthest on the long wave-length side. They also point out that the range of this continuous spectrum is of the right2 order to be explained in this way.  McLennan and McL^ed  have concurred in  this, apparently on the basis of the assumption that, for such cases, the usual selection rules are violated. They also claim that two-quantum transitions of rotational energy can be d«monstrated with scattered light. Raman and Krishnan have later suggested  3 that, in  accordance with this theory, the comparative prominence of this nebulosity observed for edense madia is probably the ree* suit of the continuous impedlnce to rotation which must exist under those conditions. That this would be less noticeable for media with geometrically symmetrical molecules seems to be 1. (95). 2.(68). 3.(97)p.30.  - 33  -  borne out in the case of carbon tetrachloride. 1 Raman  2  found  that the continuous scattered spectrum for benzene decreased when the benzene was heated, although that of the unmodified lines increased. Also, the intensity of the continuous spectrum decreased when the benzene was diluted with water. Venkateswaran 3 observed similar results with glycerin. "Ressuits indicate that the transformation of monochromatic incident radiation into a general otf- white radiation is closely connected with the special state of molecular aggregation which gives rise to high viscosity."  4  This seems to be sup-  ported by observations on acetic, butric, and proprionic acids Intermolecular forces of a gravitational or elec4» trical nature have also been suggested as giving rise to the scattered nebulosity. It seems that a comparison of the continuous intensities for the liquid and gaseous phases of the same substance should furnish evidence to determine the value of this suggestion. 5. Broad Raman Lines. Some substances (e.g.,water) give extremely diffuse Raman lines. Martin  5  has observed this in other liquids whose  graphical formulae contain the(OH)group ,  and has suggested  that the diffuseness may be due to some property of this group Many diffuse lines appear sharp and intense on the long wave/*  length side, and nebulous on the other. Wood reports that - - - 6.(151). 1. Even for CC1 4 the continuous spectrum is quite noticeable. Notice the region around the 4358A group of exciting lines in Plate I.(Opp.P.24). 2.(88);3.(l4l)p.ll8;4.(142)&(143).  - 34 -  higher resolving power has shown some of these to be doublets, the line on the red side being the more intense. He considers, however, that higher dispersion is not generally required for this work, as the lines are rather broad, -although often not nearly as broad as one would expect from the width of their corresponding infra-red absorption bands.  1  6. The Effect of the Physical State. A comparison of the Raman effect for different states o of the same substance is of interest, that, in the case of ice and water,  I. R.Rao  has found  the corresponding bands  are equally (and very) intense, and shifted so much that they may be observed with a direct vision spectroscope. In agreement with infra-red absorption data, the bands for ice are sharper, and of slightly shorter wave-length than those for water. Raman lines for gases and vapours are very faint in comparison with those for the corresponding liquids. (See page ). 1. Of interest in connection with this paragraph is the report of Raman and Krishnan in "Nature" of Aug.1925 (p.278), of nebulosity or "wings" in classical scattering spectra. In "Nature", Dec.8, 1928, they recall this, and report it for such aromatic compositions as benzene, toluene, etc., which kw4great optical anistropies.R.V.Krishnamurthy has found it, in addition to Raman lines,for CS2. Aliphatic compounds, such as carbon tetrachloride, ether, and alcohol show it but feebly. It is thought to be a result of changes in totational energy of the scattering molecules, - but, unlike the continuous spectrum of the. Raman effect, consists of unpolarized light. The author believes that he has observed it in the spectrum of light scattered from benzene. 2. (109). Indian Journal of Physics:Vol.Ill;Part Sept. 30, 1928.  I.p.129,  - 35  -  7. The Effect of the Exciting Wavelength. As was pointed out in Chapter I, the intensity of the classicaHy scattered light varies inversely as the fourth power of the wave-length, this fact explaining the color of the over-head sky, and of transver^Ly viewed beams of intense light in pure dust-free liquids. Raman and Krishnan """noticed that the spectrograms for scattering due to CCl^, while showing the intensity of the green line  5460.7A  to be much great-  er than that of the ultra-violet line 3906.5A, showed a modified line excited by the latter  be much more intense than  the corresponding modified line ( i.e.,of equal freguency shift) excited by the former. This behavior was so marked as to be visible through a spectroscope. (Eor lines in the visible region, of course). It would thus appear that the intensities of the modified lines change even more rapidly with wave-length than required by Rayleigh's inverse fourth power law. This is confirmed by the work of W. E. Meggers and R. M. Langer, of the U. S. Bureau of Standards, who found that the intensity of modified lines of a given frequency shift increases slowly as the exciting frequency ifi increased, although the relative intensity and character of the different modified lines due to a given exciting line are about the same no matter which exciting line is taken. 8. The Effect of Moecular Structure. As is evident from the previous discussion, and to be 1. (97).p.33.  - 36  -  expected from the accepted theory,the Raman line pattern about any exciting line is associated with the nature of the scattering substance. Raman and Krishnan  1  early found sim-  ilarities in the modified line patterns due to liquids containing chemically similar groups, and Cabannes 2 ,in November, 1928,  reported the modified scattered radiation of each of  the halogen derivatives of phosphorous, arsenic, antimony, bismuth, carbon, silicon, and tin  to be concentrated in four  chief lines, the characteristic frequencies of which decreas•z regularly with atomic weight. Venkateswaran  has very recently  published interesting data on this point for the cases of the fatty acids, He believes some of the frequency shifts to be associated with the (CH) groups of the graphical formulae, and some with the (OH). 9. Polarization of Raman Spectra. Raman and Krishnan communicated the results of their preliminary investigation of the polarizatiops of modified scattering to "Nature" in June, 1928, 4  and, more recently, 5  have given a more complete report. They found: (a). All unmodified lines (classical scattering) in any one spectrogram are polarized to practically the «ame extent. (b). For a given shift of frequency, the modified^ lines excited by the different incident lines are polarized to the same degree, but differ in polarization from the unmodified lines. 1.(92).  5  5.(See footnote 3 of page 37). 2.(19A). 3.(143). 4.(94)p.31.  - 37  (c).  -  Modified lines corresponding to differSftt frequency  shifts are polarized to different extents, the intensity of the weaker component varying from nothing to about 50% of that of the stronger line. (P=0 to 50%), (d). Negative lines (i.e., of enhanced frequency, - "antiStokes" lines) are polarized to the same extents as the corresponding positive lines. (e). Strong Modified lines are usually more polarized tnan feeble ones. (f). The general continuous spectrum scattered by amyl alcohol is strongly polarized. They offer e, tentative explanation of these facts, similar to that proposed for classical scattering. As has been shown, when the incident light is unpolarized, the light scattered by optically isotropic particles would be completely polarized. The plane of polarization would be perpendicular to the direction of propagation of the incident beam ( i . e p a r a l l e l to the plane of some of its vibrations). 1 The manner in which molecular assymmetry (anistropjr) leads to imperfection of polarization in unmodified scattered light is pictured in detail p by Raman and Krishnan , who suggest a similar sort of reasoning to explain the polarization facts of modified scattering. 1. (145)p.625. 2.(97)p.32. 3. (Venkateswaran found this true for glycerin; he also noted that dilution by water to one half strength had no noticeable effect on the degree of polarization. See (141).  - 38  -  They propose the assumption of three different probabilities for energy transitions along three principal axes of the molecule, these axes, and their respective Einstein probability coefficients being different for different energy transitions. This seems sufficient to explain both the differences in polarization of modified lines of different frequency shift, and the independence of polarization on the incident wave-length. This, together with the previously suggested probability theory,(See page 26, equation 10.) of the initial energy state of the molecules, also explains the equality of polarization of corresponding negative and positive lines. Raman and Krishnan suggest that the relatively perfect polarization of unmodified scattering,(which is a result of the symmetry of the p molecule as a whole), may be explained -fey- on the assumtion that the effective anistropy is the resultant of the anistropies of all the individual transitions (suitably weighted) of the molecule, of which those corresponding to the infra-red frequencies are typical examples. Interesting results have been reported for the case when the incident beam is plane polarized.^It was found that of the modified lines 4400A,4419^,and4447A, excited by 4358A plane polarized,  4447A is missing when the spectrum is ex-  amined in the plane of polarization of the incident light,but Vhen observed in a direction perpendicular to thia, appears with an intensity about twice that of the other two lines. 1. (59).  - 39  -  o The oscillations of 4447A thus appear to he linear while those of the other frequencies are not. This is apparently in accordance with the following quotation from Wood: 1 for classical scattering: "  the direction of vibration of the  light scattered in a direction perpendicular to the incident beam is the direction in which no light is scattered when the incident beam is plane polarized,if we imagine the obstacle actually set in vibration. Transverse waves, then, would not be given off in the direction in which the incident vibration takes place,  "  10. Coherence. Considerations of the state of polarization of scattered light are closely related to the problem of its celaerence, (i.e..whether it is a 'mass' or aggregate effect of associated molecules (which in some way "cohere"),or whether it is the resultant of the independent and unrestricted behaviors of individual molecules (or particles).) Thus, one would expect that scattering by vapours would be found to be less coherent than scattering by liquids, as in the former state the molecul es are less under one another's influence. A uharacteristic of coherent emission would be a definite phase relationship between the radiations from neighboring molecules, which would.tend to obscure theit characteristic polarization. This would lead to the prediction that the polarization of light scattered by any substance would be much smaller for the lil.(l45)p.626.(Direction of vibration = that of electric vector  - 40  -  quid than for the vapour. This is generally true. Furthermore, if the modified scattering is an incoherent form of radiation, its polarization should be comparable to that of the classical scattering for the vapour.only. Similar reasoning would apply with respect to intensities. Those of incoherent radiations would vary as the density (the number of scattering particles per unit volume). This seems to site- have been observed by Venkateswaran-^for glycerin and for glycerin and water mixtures, and by Ramdas for ether. The latter found the ratio^ of intensities of Raman lines for liquid and vapour to be 300;1, and that of the densities under these conditions to be roughly 250:1. It would follow, then, that only coherent scattering would undergoe the marked increase in intensity observed near the critical temperature or the critical solution points of many substances and produce opalescence. The careful study by 3 4 Bogros and Rocard , and also that by Martin , of the case of water and phenol in these respects would indicate modified radiation to be incoherent. This is, of course, in accordance with the feebleness of the effect for gases in comparison with that for liquids. Had not this been so, it is probable that either Rayleigh or Cabannes would have discovered modified scattering long ago in their careful work with gases, previously described. 1.(141).  2.(106).  3.(127).  4.(66).  - 41  -  Cabannes has studiet the secondary radiations in the light diffused by quartz 1 , and for the reason quoted below, apparently concludes that crystal scattering, modified of otherwise, would be coherent. He states: "D'apres le principe de correspondance, l'effet de polarization de la lumi&re emise d&pend de la nature et de 1'orientation du vibrateur qui l'emet. Or ce vibration, suppose lineair ne peut pas €tre k la fois parallele et perpendiculaire a 1'axfi oblique. II faut done, semble-t-il, qu'un certain nombre de vibrateurs se groupent en on systlme poss^dant la sym^trie du cristal pour emettre des vibrations concordantes dont la composante i ou I (suivant le cas) est detruite par interferences. Le spectre de diffusion des cristaux ne serait done pas emis par des sources incoh&rentes," Although the weight of evidence seems to be in favour of the incoherence of Raman radiation, further investigation is desirable, especially as regards liquids, in p view of the fact that, contrary to expectations, Ramdas foundt the Raman lines for liquid carbon dioxide to become intense, along with the classical lines, as the rising temperaature approached the critical state at which opalescence occurs. If Raman radiations be satisfactorily shown to be incoherent, further study of their character in relation to fluorescence will be required, as that also is an incoherent  1.(20).  2.(106).  - 42  -  type of secondary radiation. Since the latter has been shown -TVE,  to consist of A emission of energy a finite time after it has been absorbed, Ruark  1  has suggested that this property may  utilized in settling this interesting question.  He would  simply determine if there is any time lag in the Raman effect2 He has suggested for this the method of Abraham and Lemoine, which has measured time intervals as small as 2 x 10~® sees. B  EXPERIMENTAL ARRANGEMENTS•  1. Sources of Light. Practically all investigators of the Raman effect have used some form of mercury arc lamp as a source of light. In most cases, including those of Raman and his associates, the lamp has been of the ordinary low pressure type, probably supplied with cooling vanes, and operated from 110-volt D.C. mains. The arcs have usually, but not always, been contained in quartz. Those used by Raman 1 were of about 3000 candleo power, but I. R. Rao , working successfully with ice, used one of only 500 candle-power. With this type of lamp, condens ing lenses of various diameters wlfere used to secure an intense beam of light. In studying the Raman effect with hydrochloric acid gas at atmpspheric pressure,  contained in one of his scatter  ing tubes (to be described later), R. W, Wood 5  used a Cooper  Hewitt mercury arc 4 about five feet long, the tube and arc be ing completely surrounded by cylindrical aluminium reflectors 1.(130). 2.(147A). 1.(106). 2.(109). 3.(152). 4.(41A)p.251.  - 43  -  It was by an arrangement such, as this that the first photograph of the Raman effect secured in this laboratory was obtained. In this case, the tubes were cooled by a blast of air blown along them, away from the spectrograph, and from the anode of the arc. The scattering tube contained commercial carbon tetrachloride.The current used varied from 2 to 4 amps. A mercury arc of a type specially suitable for experiments on scattering is shown in Figure 6. It has been used with great success by R. M . Langer, Research Associate at the U. S. Bureau of Standards. He kindly furnished this department with the information which le£d to its adoption here for this work. The structural details are indicated in the illustration.  - 44  -  For the purpose of damping the oscillations of the mercury columns, Langer used pointed electrodes which extended into the side constrictions. It was found here, however, that the constriction themselves were sufficient to do this, and that it was easier to keep the arc running with shorter electrodes as illustrated. They consisted of parts of steel knittingneedles, "bent as shown in the figure. This lamp worked well only when filled with very clean *  boibled mercury;and was started as follows: It was connected, in series with a heavy resistance^consisting -• •• ' ' V.of long coils of nichrome wire, to a 250-volt D.C.circuit  i "vtith a current  of about 2 amperes flowing* heat was applied by means of a gas flame to the to the centre of the horizontal portion, until mercury vapour formed and separated the liquid mercury. Then and there an electric arc of great intensity formed, extending for about three centimetres along the tube. It was necessary to lower the lamp into cold water or to direct a blast of air against it as quiekly as possible after the lighting of the arc, as heat was evolved at a very rapid rate, - so rapid, in fact, that the former method of cooling could not be used with arcs made of glass tubing. In one second the temperature would rise so high that lamps even of hard pyrex would crack on being plunged into water. Since quartz could be used with this method of cooling, which was much the more satisfactory, an arc lamp of this material was used. The water in the cooling tank was kept circulating.  - 45  -  When the lamp arced, the current would drop to about % its initial value. The outside variable resistance was then decreased (by "shorting" portions of the coil). As this was done, the intensity of the light would increase very markedly, and the arc would gradually lengthen in the tube. The current would stay about constant, showing that the decrease in ren— sistance in the outside circuit was offset by an increase in resistance in the lamp,(and hence an increase in potential drop between its electrodes). The highest power used here was about 383 watts. Under this condition the current was 1.8 amperes, and the resistance of the lamp was 118.3 ohms. The P.D. across the arc was about 212.9 volts, and across the whole circuit, (which included about 25 ohms in series), about 258 volts. About twenty minutes was required to bring the power of the lamp up jfo this value, as the arc would go out if the series resistance was decreased too rapidly. When the lamp was operated in this way, tha water supply nozzle in the bath had to be placed so as to direct a strong stream of cold water along the heated part of the tube. The water was removed from the tank by a pump. This type of arc possesses a special advantage for this kind of work, in that it can be placed very close to the scattering substance, which can thus be made to receive a lar^g part of the light emitted, on account b£th of the large angle subtended at the source, and of the source's proximity. Its shape is well adapted to the arrangement of reflectors about  - 46  -  it, so that nearly its entire luminous output may be used. Since the mercury vapour is at atmospheric pressure, the lines of its spectrum are rather diffuse, - but sharp enough for most scattering experiments. Most of the emission is concentrated in the visible region. For sharper photographs, Langer has used a quartz cylinder vacuum arc as shown in figure 7. This arc has a hole Quartz  c  \NlVieW \l  /  S cotter r mj  ^IT  Tubt  At-c  Qlictrlz Arc  L o n y vUelivial -Section  i H  Mercury.  Figure 7. along the axis, in which the scattering tube is placed. Langer, and Uchida and Kimura, 1 who have also used this arrangement, found difficulty in cooling the scattering substance. It was found best to use a tube which did not completely fill the axile hole, and to circulate water through this space between the arc and the inner tube. If  the ultraviolet light causes  chemical action in the scattering liquid, the latter may be circulated through the tube, and filtered and cooled elsewhere 1.  (140A).  - 47  -  in the circuit. 2. Containers for the Scattering Media. (a) liquids• In experiments on modified scattering by liquids, Raman and his fellow workers  have continued to use the "immersed  flask" arrangement which has been described in connection with their experiments on classical scattering.(page 15). These were used, of course,  with the sources of light first  mentioned in the previous section. The author has experimented unsuccessfully with a small cubical glass vessell (about 7 cm. to the side). A concentrated beam was directed into one side of the vessel through a diaphram, and reflected back toward the source by a mirror placed on the other side. The intensity in the liquid was thus doubled. The beam was carefully kept away from the side or top tor bottom liqmid surfaces, and was visible in the liquid, when e viewed transversly, as a pale blue track. "'II A more satisfactory arrangement (Figure 8.),described by Wood, 1 ' consists of a tube, flattened or fitted with a window of plafae glass or quartz at one end (through which the scattering is observed), and drawn off in the shape of a 2 curved cone at the other end." (See fig. 3, page 17). The 1.(150)p.731. 2. Uchida and Kamura report satisfaction in using this type of tube. See (140A). C. E. Bleecher, in his work with Xylol, found that much shorter exposures were required with a tube of this kind than with the flask arrangement as used by Raman. See (9).  - 48 -  liquid is introduced through this conical end. A small bulb, blown in this end as shown in the figure, is useful as an expansion overflow reservoir in experiments at high temperatures and the liquid surface level in it may serve as a rough thermometer.  A glass bead is placed on the outside at the inter-  Figure 8. section of the axis of the tube (straight part) with the side of the 'horn 1 . With an incandescent bulb placed near this, it appears as a bright "star" when viewed through the window of the tube. This is of very great assistance to one in the aiming of the spectrograph, which must be done very carefully if reflected light from the sides of the tube is to be kept out of the camera. The liquid is ilMminated from a mercury arc lamp whose axis is placed parallel to the tube, and as close as possible to it. A water cooling system has to be provided. When the Cooper-Hewitt or other type of low pressure arc is used, "This may consist of a larger tube surrounding the liquid tube,  - 49  -  sealed at the ends by bored rubber stoppers, and provided with the fiecessary inlet and outlet. Reflectors are provided  Ifef lector  as indicated in figure 9. The one under the scattering tube may consist of a piece of bent aluminium, or the under side of the tube itself may be silvered and painted. A simpler arrangement  TlVf leeW  is that consisting of a row of small water outlets, placed  Figure 9. over the tube near the arc,  the lower metal reflector serving  as a trough to collect and drain off the water which has flown down around the tube. When an arc lamp of the cap^illary U-tube type, which itself must be immersed in a water bath, is employed,  the  problem of cooling the scattering tube is comparatively simple C-fatiYij -tVis The arrangement shown in Plate I I . w a s used in this laboratory and i 3 very similar to that recommended to this department by Langer. (in his arrangement, a rubber stopper was used at each end of the straight part of the tube, and the^reflector was not in the water bath.)  The lower reflector is of sheet al-  uminium, and was sec^ured closely  to the scattering tube by  means of friction tape. The upper reflector, which is put in place after the arc has been struck and lowered into position, was very carefully designed, so as to direct the maximum  P L A T E H.  (To face page 1-9)  - 50  -  possible amount of light toward the centre (axis) of the scattering tube. There is about 1 mm. clearance between the arc and the upper reflector, and about 2 mm. between the arc and the scattering tube. The water inlet nozzle is placed so as to direct a strong stream through this space under the reflector, which itself is well covered by the bath, (b), Gases. The horn-shaped reflector used in the "Wood" type of liquid scattering tube, was first used in connection with the cross-tube apparatus developed in Calcutta for the study of classical scattering in gases and vapours.(See Fig.2,page 16.) No account has been seen, however, of the use of such a crosstube in Raman effect experiments. Wood has used his liquid tube successfully for HC1 gas, illuminating it, as has been 1 mentioned above (page 42), with a Cooper-Hewitt lamp. Ramdas, in studying the effect with ether vapour, used the usual flask method, the vapour saturating the space over a free liqiiid surface at the bottom of the flask. In studying CO liquid and vapour over a wide range of temperatures, he used a strong steel tube provided with thick windows. (c). Solids. Ice and quartz are the only solids which have been much examined so far. In using these, Ramakrishna Rao 2  merely  illuminated them by a concentrated beam from a 500 candle-power mercury arc, (in quartz). Neither the quartz nor the ice 1.(106).  2.  (109).  - 51  -  were placed in any container. (The moisture from melting ice would collect on the sides of a container and obstruct the passage of light.) The slit (if the spectrograph was placed close to the scattering solid, the axis of the collimator being normal to the incident beam. By means of suitable apertures, light was kept away from places from which it would be reflected toward the spectrograph When ice was used, large clear blocks were supplied every two hours during the exposure?, which were a\rout one hundred hours long! Crystals of quartz were used in the above way in this laboratory. Spectra of considerable intensity were secured with exposures of a few hours, but they showed no Raman lines. It was considered that this was due to excessive reflection from surfaces and from imperfections within the crystal, which was not a very clear one. Wood has studied quafctz, calcite, and glass with the arrangement shown in Figure 10."^ The solid was groung to the shape of a rectangular prism. The front face of the block was painted black, with the exception of a circular aperture, and a bent cone of glass was cemented to the back face. This cone was filled with glycerin and painted black. As with the tube, p a glass bead was provided for collimation.  At the edges of th  the upper face, four small glass rods were attached, to form a wall for retaining a pool of water, this being constantly 1. (I50)p.734. 2. For detailed information concerning the lining-up of a spectrograph with the aid of such a device, see (150)p,735.  - 52  -  Figure 10. renewed by a small stream which kept the block cold. The prism was mounted at a slight angle on a sheet of reflecting aluminium, so that the water overflowed on the cone side, and the front window remained clear. In further attempts to photograph the Raman effect with quartz, the author used a small but very clear quartz prism 4.5 x 1.6 x 1.4 mms.(See Plate III., facing this page.) The ends were painted black, a large rectangular aperture being left in AC for the emission of the scattered light, and a very small circular opening being left at the centre of BD as an aid in the lining-up of the spectrograph. The sides BC, CD, and DA were silvered, the silver being covered with a £a coat of black paint for its protection. This prism was to be used in water, and illuminated by the U-tube type quartz arc, which was placed close to the top face AB,  and which extehded about 10 cms. beyond it,  away from the spectrograph. An aluminium shield and reflector  PLATE  (To face page 5 2 )  - 53 -  was used to prevent any light from entering the prism except from the top, and, along with the upper reflector, to reflect light into the crystal from that part of the arc which projected beyond the prism. At first a metal diaphram was used at the front face, instead of the painted opening as illustratv ed. It had to be discarded on account of the tendency the formation of bubbles at its edges. 1  These reflected a  great deal of tight into the spectrograph. With the final arrangement, the light emitted through the aperture was considered to be wholly due to scattering, but no Raman lines were photographed with exposures of the length taken, - i.e.,about » five hours. It was believed that larger prisms were required for this work. 3. Li^it Filters. It is often desired, as in studies of the effect of wave-length on some characteristic of scattered radiation, to irradiate the scattering medium with monochromatic light, or with the light of a very narrow range of the spectrum. For this purpose, filters are used to absorb the radiation of wave-lengths not required. Various glass filters (such as the Corning ultra-violet glass G-586, which transmits a narrow region around 3650.1A) and various aqueous solutions will do P this. The solution most used is one of quinine sulphate ,which 2. (141)p.107. 1. It was first thought that the babbles seemed to form more rapidly when the arc was running than when it was not, but a separate series of very careful tests, extending over a week, failed to show that any part of the emission of tha lamp, infra-red, visible, or ultra-violet,-influenced in any way the rate of formation of bubbles of dissolved air or oxygen.(^f .a  - 54  along with a blue glass filter,  -  absorbs practically all the «  mercury arc spectrum except the 4358A group of lines. With the flask containers first described, such liquid filters may be contained in cells with plane parallel glass sides, and placed in the incident beam of light. With the types of tubes illustrated in Figures 7, 8, and 9, however,  the filtering  solution must constitute the cooling liquid, and be circulated by means of a pump in a closed circuit, in some part of which it is cooled. 4. Taking the Spectrograms. Most spectrograms of Raman scattering have been taken on ordinary small spectrographs, the use of the Hilger Model E£ quartz spectrograph being most frequently reported. Aside from aiming^he spectrographs at the ends on long tubes, (See footnote 2,page 51.i there is no special technique involved in this part of the work. Exposure time varies greatly with the optical arrangement and scattering substance used. With bulb containers, exposure times range from a few hours to about fifty hours. With a scattering tube of the "Wood" type, and a U-tube arc, Langer reports obtaining Spectrograms of Rajaan lines for benzene in about a second, although an exposure of fifteen or thirty minutes was required for the plate to be exposed sufficiently to be measured. With similar apparatus, the author found an exposure of about two hours to be necess(Continued from the footnote of page 53.) The bubbles were considered to consist of dissolved gases, as there was no bubble formation in water that had been boiled.  - 55  -  ary in order to secure a plate such as that whose print appears on Plate I. The direct comparison spectra (a) and (c)  exposed for ten and thirty seconds respectively, the  latter being much over-exposed in order that all the faint lines -be shown, of the incident light be shown. The spectrograph used was of very short focus and large light-gathering power, (being from  ten to tventy times as fast as most  spectrographs), and was constructed in this laboratory. Its refracting system consisted of two resolution was very small,  60° glass prisms, and its O o  the range from 3650A to 6700A being shown in 3 cms. on the plate from which the enlargement mounted on Plate I was made. A contact print from this plate is shown  Figure 11.  here.  Past spectrographs like this have usually been found necessary for work with gases and with crystals. Rao used one like thio for the hundred-hour exposure for ice, mentioned above. For gases, Ramdas"*"  used a quartz prism spectrograph,  fitted with collim^or and camera lenses of f  2  apertures respectively. 184 hours.  1.5 and  ~f 5.  He exposed for various times up to  His prism was placed so that the line 4046A was  at its position of minimum deviation.( His dispersion was 0 / ° much less than 1/5 of ours, being "only 3650Ato 5802Ain 4 mm." 1,(106)p,134. 2. This merely means that focal length;diameter of the aperture::1.5:1. or ::5.1, as the case may be.  - 56  -  In view of this, his published plates are remarkably good)) He found it impossible to get the whole spectrum in focus, "owing to the curvature of the focal plane" -(I). In this laboratory, similar difficulty was experienced, but it was due to chromatic aberration of the collimating lens. Hence the collimator scale was calibrated to enable its being set to bring any desired region of the spectrum into sharp focus. Rasetti 1 required 48-hour exposures for GO and CO^ Raman scattering, using a fast spectrograph with -f- 2.7 lenses. Wood  P  R\  has obtained Raman lines for HC1 at 100 C in a long  tube illuminated by a Cooper-Hewitt arc, in 24 hours. The kind of spectrograph used was not specified. The exposure times necessary are of bourse influenced by the use of light screens and filters; they may be greatly reduced by the super-s4nsitization of the photographic plates, for instance , with a  ammonium hydroxide solution, or with  erythrosine.^ Langer and Meggers have discussed the merits of prism spectrographs for this work, and point out that their disp perston is small in the long wave-length region of the visible spectrum, where the c o n s t a t frequency-shifts of the Raman lines would result in comparatively large and accurately measurable distance-shifts. They have therefore tried for the effect with a 21 foot concave grating, and have obtained excellent, highly dispersed spectrograms in 1 or 2 hours. 1.(111A).  2.(153).  3.(107).  - 57  -  5. Other 9on3ideration3. A comparatively new, and very sensitive scientific instrument, the microphotometer, (which draws a graph showing intensity plotted against frequency or wave-length) has been found of great service in the study and measurement of spectograms, especially in the cases where faint Raman lines are well nigh obliterated by the nebulosity or continuous spectrum which surrounds them. Venkateswaran 1  has used it in measur-  ing the Raman spectrogram for glycerin. The measurement of plates is usually made  by means of an ordinary travelling  micrometer, and wave-lengths determined by the use of Hartmann£  2 $ simplified interpolation formula,~ the incident or unmodified mercury lines being used as standards. The methods described for classical scattering have been used for the determination of depolarizations and relative intensities of Raman lines. Photographic methods for the latter involve the taking of a graded set of exposures, with either the aperture or the exposure time being varied. Such tests have shown the average Raman lines to have 1/500 the intensity of the scattered lines which respectively excited them, is, - (see p. 20), 3 5 x 10" 8 the exciting wave-length.  that  of the incident intensity of  This should make obvious the necess-  ity for the elimination of all reflected light from Raman spectra. - - - - - - - - - - - - - - 1.(141). 2.(41A) p.245. , 2. Thus, the intensity of the Raman effect is groatre than that of the fluorescence noted by Raman and Ramanathan,(82), which was of the order of 4 x 10~ 7 if the incident intensity.  - 58 -  C.  THE RAMAN EFFECT IN RELATION TO OTHER SECONDARY RADIATIONS * It should now "be found profitable to consider the Raman  effect in relation to other radiation phenomena of this kind. This is done so well in the general reference here cited, that only an outline (for the sake of completeness) of the kinds of secondary radiations so far known, and of the accepted theories as to their origin, will he presented here. 1. The Compton effect, - discovered in 1904, but measured and properly interpreted for the first time in 1922 by Arthur Compton: This is an example of a quantum's giving energy to e^free or nearly free electron, the latter using it in changes of translational kinetic energy - (changes in speed) Since this is a non-quantized form of energy, the quantum may lose any amount of it in this way. The limitations of the transfer of energy placed upon it by the law of the conservation of momentum explain why it is the electron which must necessarily be deemed the scattering *©bstacle 1 , and why only quanta of X-ray frequencies have sufficient Energy to lose enough to cause a measurable change in frequency. Compton effect spectra are line spectra only because the change in frequency is a function of the scattering angle (i.e., the frequency shift observed depends on the angle of observation. * General reference on this section - (22A). For a briefer summary of this, by the same author, see (22J3).  - 59  -  If all the modified, scattered X-rays could be observed at once or if they could all be photographed on the same spectrogram, they would, in accordance with the theory of unquantized transfer of energy, include efcery frequency from the exciting frequency down to the limit permitted by the conservation of energy restriction, i.e.}  1-2M jj c 2—  ... „ of the exciting frequency.  2. Scattered band spectra in the X£ray region, first observed 2 in 1923 by G. L. Clark and W. Duane  : This case is somewhat  similar to the Compton effect. Here, however, the energy lost by the quantum is parti}' used in breaking up (ionizing) a molecule, and the remainder goes to increasing the kinetic energy of translation of the inn or ions. This latter part is non-quantized, and gives rise to the width of the bands. As might be expected here also, only X-ray quanta have sufficient energy. It is usually considered that the process is one of extracting one of the inner electrons from the molecule, and "speeding it on its way". 3. Scattered modified line spectra in the X-ray region, totally distinct from the Compton effect, and more like that observed by Clark and Duane: These were first observed by B. Davis and D. P. Mitchell 3 in the spring of 1928, in the spectrum of X-rays scattered by graphite. In this, it is con1. The momentum of a quantum of frequency Y and energy hy is cT where c is the velocity of light in vacuo (Cm/sec.) The energy may be considered as kinetic. (8)p.l87. 2.(20A).  3.(66).  - 60  -  sidered that the quantum does merely the first operation of the "Clark and Duane" effect, i.e., extracts an inner electron It confers no kinetic energy upon it. The energy is transferred therefore, in fixed amounts, resulting (in the spectra) in lines displaced in frequency by amounts equal to the ionizing potentials divided by h.(Planck's constant). 4. the case in which quanta suffer a change in frequency due to a transfer of energy to or from a molecule. with a resultant change in the vibrational or rotational energy of the molecule or of both.' 'Ib ijii® 0 £t&o of crystal*- This is the Raman effect. In the case of crystals, it was discovered independently in the early spring of 1928 by C. V. Raman and K. S. Krishnan in India, and by G. Landsberg and L. Mandelstam in Russia (according to Darrow). The original discovery in liquids is undoubtedly due to Raman and Krishnan. This case has been fully described in the previous pages. 5. The case in which energy of incident quanta is absorbed by substances,( usually only when the frequency of the quantum is equal to (is in resonance with}} one of those of the substance) and after a finite time,is re-emitted by the substance as a radiation of another (usually lower) frequency; This is fluorescence. The change in frequency is explained by considering the molecule to return to its initial state via an inter mediate energy level,  the enrgy being emitted in two lots. ft  Mention should also be made here of an observation re-  - 61 -  ported in June, 1928 by J. Cabannes and P. Daure 1 , and already referred to in the literature as the "Cabannes-Daure effect". a They observed for gaseous butane a scattered line shifted .81A toward the red. This is the right order of shift for the Compton effect if the scattering angle is 90°. The difficulty in explaining, however, arises from the fact that, unlike either Compti>n of Raman effects, there was observed no unmodified line. No satisfactory explanation has been given. There is another kind of radiation which may best be termed a tertiary radiation.  Sometimes fast-moving electrons,  wh&ich have been given their kinetic energy by primary radiation^ when struck by quanta as free electrons ^  in the  Compton effect, or as bound electrons in the"Clark and Duane" effect), have excited atoms to radiate by striking them. The last stage in this process, in itself, is merely asequence case of primary radiation; but since it is the third of a ana^a of events (primary radiation, secondary radiation, and second primary radiation), it has sometimes been called a tertiary radiation. Lines thought to be due to this are sometimes seen in Compton effect spectrograms. In the first four cases outlined above, (cases of scattering) the radiation at an angle of 90° from the incident beam is polarized to varying extents. It must now be obvious that all these cases are illus% trations of one very general principle, namely,1. (19).  that a  - 62 -  quant tun may lose all (in which case it disappears) or any part of its energy, or may receive energy, in an encounter with a molecule or atom, retaining its identity even though its frequency is changed. As has been mentioned previously, this was first stated in a general form by Smekal 1 in 1923,  2 and developed by Kramers and Heisenberg in 1924.  The stat-  ment of this principle may be varied to place emphasis on other aspects of the fact. As stated here, however, it shows the accepted conception of a quantum to have evolved considerably from that of a "fixed, unchangeable packet of energy". Darrow has forcefully presented the argument for this new quantum 3 (for it is no less than that) in the following eloquent plea:  "  We have accepted for years the principle  that an electron may give up part of its energy and keep the rest - that the life-history of an electron is an endless sequence of gains and losses of kinetic energy, of speedingsup and slowings-down, during which the identity of the electron is never lost. Why should we not have thought likewise about the quantum? Yet it has been almost an article of faith that a quantum must give all of its energy,or none - either vanish altogether, or retain its frequency unchanged. 2. The following footnote appears on page 91 of (22A): "I am told that Kramers tried vainly to persuade a number of experimental physicists to look for the effect. At present thay must be feeling like the astronomers whom Adams vainly pressed to make haste in looking for the planet Neptune, until finally someone else discovered it." 1. (135).  (22A) pp.91 & 92.  - 63 -  Of course, till 1922 there was no compelling evidence that a corpuscle of light may suffer a change in frequency in rebounding from a particle of electricity or matter. However, it does not seem to have occurred to anyone that the want of evidence was in any way surprising, or that it should be possible to find quanta scattered with a change of Energy. The reason for this satisfaction, I suspect, was perfectly simple. It did not seem possible that a quantum should give up part of its energy, for its energy was inseparably lin^ked with its frequency, and its frequency seemed to be itsc one:', indissoluble and characteristic feature. As well say that an electron might lose part of its charge and still be the same electron, or that an atom might lose part of its mass and still yet remain the same atom, as that a quantum migfrt give part of its frequency without ceasing to be itself! Now this contention - if one may call it a contention lost its force through the discovery that electrons also are endowed with frequency and wave-length, or in other words that negative electricity like light possesses both qualities of corpuscles and qualities of waves. Whenever a corpuscle of electricity parts with kinetic energy, whenever a corpuscle of light parts with energy, the associated wave-length is augmented. If we suppose that an electron retains its identity when its wave-length changes, how can we deny like continuity of existence to a quantum? If we admit that an electron may suffer a change of wave-length in rebounding from  - 64 -  from an atom, how may we "be surprised when a quantum does the like? It is true that the corpuscle of electricity has other features than wave-length: a charge which apparently never changes, a mass which apparently never falls below a certain minimum. The quantum does not have an immutable quality corresponding to charge, and we do not know of any lower limit to its mass short of complete dissappearance. But for either is j m sort of coi-pasclee, the wave-lengthy principle, variable. We say that all electrons are of one kind, but may have any speed. Should we not also say that all quanta are of a single kind, though they may have any frequency?" Two more quotation will serve to conclude this paper. They require no comment. "Apart from its special application to the explanation of the blue light of the sky, the subject of the molecular scattering of light possesses very great interest, standing as it does in intimate relationship with the fundamental problems of optics, such as the propagation of light, and the reflection, fefraction, dispersion and extinction of light in transparent media. Its study has already yielded information which is of first rate importance in testing theories of atomic and molecular structure, and promises to be even more fruitful in the future in the same direction. It is also not improbable that the study of the problems of the molecular scattering of light may serve to elucidate the nature of radiation itself, namely, to determine whether it consists oiff  - 65  -  some form of continuous disturbance, moving through space as contemplated by Maxwell's Electromagnetia Theory,  or whether  it consists of discrete entities or "quanta" as conceived of by Einstein." (From the introduction to a paper on "The Molecular Scattering of Light in Dense Vapours and Gases", by G. V. Raman and K. R. Ramanathan, Phil.Mag.Series 6,Vol. 45; page 113, January. 1923.) (7?). "It appears to me that this very beautiful discovery, which has resulted from Raman's long and patient study of the phenomena of light scattering, is one of the most convincing proofs of the quantum theory of light that we have at the present time." (From a cablegram by Prof. R. W. Wood, of the Loomis Laboratory, New York, to "Nature"; published in Vol.122, No. 3071, page 349, September 8. 1929.  The author takes pleasure in acknowledging his indebtedness to Dr. G. M. Shrum, Associate  Professor of Physics,  for valuable suggestions and assistance, particularly with the making of scattering tubes; to Mr. Harold D. Smith for co-operation in the experiments described; and to Mr. Chas. Duplouich for assistance in the preparation of quartz crystals for use. The University of British Columbia, West Point Grey, B. C., April 11, 1929.  - 66 -  BIBLIOGRAPHY The numbers on the left are those cited in the footnotes of the text. 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C., (See No. 59.) 45. Kenrick, Frank B., & Martin;P.R;21;373; 1923, P.R; Series 2;21;377; 46. King, L. V., 1923, 4 >7 ^ ii ii ii N; May 19, 1923, Kothari, D..S., (See No. 131.) 48. Krishnan, K. S., N;122;#3074;477; Sept. 29, 1928. 49. " " " N;122;#3078;650; Oct.27,1928, 50. " " " N;122;#3086;961; Dec.22,1928. (See also Nos.85,86,87, & 89-97. 50A. " " » P.I.A.C.S;9;251; 1926 51. Lallemand & Soret; C.R;69;1294; 1869 52. Landsberg, G., Zeits.f Phys;43;773; 1927 53. " " " ;45;442; 1927 54. » » C.R; (with Mandelstam)July 9^1928 55. Lange, B., Zeits.f Phys.Chem;132; Feb. 1928 56. " " " " " 132;l-2;Jun.'27  22. Darrow, Karl K.,  - 68 -  :;;lL3;,/3097; 345 ; -ar.9, 19::9 o ( . ijanger, R..... P.II;37;161; 1919 58. Larmo r, Zeits.f Fhyc .Che:r.; £7 ;^57 ; 1910 5 8 A,Le E1 an c o. Ka,yro, Lepape, (See No. 16.) iiall;!.'; 122 ;#3G85 ; 921; Dec. 15 28 59. Lindemann, F. A . , 1'eeley F.R.3.A;13;92; 1911 60. Lorentz , I'. /••• . , Ze i ts.f. Fnys;50;11-12;op7C9-80;28 61. 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