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The infrared spectrometer applied to the structure of carbon disulphide Rogers, Edward de Lancey 1948

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^ 5 /3 7 THE INFRARED SPECTROMETER APPLIED TO  THE STRUCTURE OF CARBON DISULPHIDE by •EDWARD d e LANCEY ROGERS A Thesis submitted i n p a r t i a l f u l f i l m e n t of the requirements f o r the Degree of MASTER OF ARTS IN THE DEPARTMENT ABSTRACT The infrared absorption spectrum of carbon disul-phide in the vapour state has been remeasured in the region from 2 to 15 microns. A total of six bands were measured in the region less than 15 microns. They were located at 3.38, 3.51, 4.29, 4.58, 6.52, and 11.4 microns. The mea- -surements were made with a Perkin-Elmer spectrometer with a D.C. breaker type amplifier and Brown recorder. C e l l lengths up to 100cm were employed. The wave lengths of the observed absorption hands are given in a table, and graphs are shown of the percentage transmission over the wave drum setting of the spectrometer. Phase shifting thyratron circuits, suitable for the accurate control of conditions of the absorbing media, are discussed. Of interest are the measurements of the structure of the V 3 band at 1535 cm"1. The side band located at the long-wave length side of the 1)3 band i s due to the isotopic effect produced by C 1 3. The bands obtained are such as to support the conclusion that carbon disulphide i s a linear triatomic molecule. ACKNOWLEDGMENT The Author i s pleased to express his gratitude to Dr. A. M. Crooker, of the Department of Physics at the University of Bri t i s h Columbia, under whose able su-pervision this work has been undertaken. This research was made possible through the generosity of the National Research Council of Canada. TABLE CF CONTENTS. Page. I. Introduction . . 1 II. Theory . . . . . . . . . . . . 4 A. Vibrational Properties of Polyatomic Molecules. • • 5 B. Rotational Properties of Polyatomic Molecules ~ 15 C. Symmetry Properties of Polyatomic Molecules 18 D. The Molecule YX 2 19 III. Experimental 25-A. Spectrometer and Accessories . . . . . 25 B. Installation 29 C. Temperature Control. 35 D. Alignment of Spectrometer 42 IV. Results . 45 A. Calibration 45 B. Results* * 49 V. Conclusion 54 VT. Bibliography 74 I L L U S T R A T I O N S Diagrams To face Page I. Block Diagram of Chamber • . . 32 II. Circuit Diagram of Temperature Control I.. 36 III. Panel of Temperature Control . 39 IV. Circuit Diagram of Temperature Control II. 40 V. A. Energy Distribution v.s. Wavelength . . 43 B . Energy v.s. S l i t Width at 2.5/t . . . . 43 Plates I. View of Interior of Chamber. . . . . . . . 56 II. Temperature Control (Side View) 57 III. Control Panel, Temperature Control and Spec-trometer • . . . . . . . . . . . 58 IV. Temperature Control (Showing wiring) . . . 59 V. Temperature Control (Rear View). . . . . . 60 VI. D.C. Amplifier and Brown Recorder 61 VII. Calibration Chart, BeOenT^-to 720cm"1 . . . 62 VIII. Calibration Chart, 800cm-1 to 1200cm"1 . . 63 IX. Calibration Chart, 1200cm-1 to 2000cm"1. . 64 X. Calibration Chart, 3200cm-1 to 3900cm"1. . 65 XI. Calibration Curve, 700cm-1 to 1300cm-1. . 66 XII. Calibration Curve, 1260cm"1 to 2000cm-1. . 67 XIII. Calibration Curve, 1800cm"1 to 3900cm"1. . 68 XIV. The Difference Band V g - v*1 69 XV. Structure of the v 3 Band • . 70 XVI. The Combination Band ^ , 4 \Jg 71 ILLUSTRATIONS (Continued) Plates Page XVII. The Combination Band V 3 • 2 72 XVIII. The Combination Bands Vg • 2 and V l * 2 \ * % • • • • • • 7 3 Tables To face Page I. -Table of Components of Temperature Control I . 36 II. Table of Components of Temperature Control I I . 41 III. Values used in Making Calibration Curves . . . 46 IV. Absorption Bands of Carbon Disulphide Vapour . 52 INTRODUCTION. The object of the work undertaken was to study the infrared absorption spectrum of carbon disulphide i n the range 2 ^ to 15^, to extend observations, at present recor-ded by others and to investigate the effects on the spec-trum of pressure and temperature changes i n the absorbing medium. The spectrum of l i c p i d carbon disulphide has been clas s i f i e d in' terms and combinations analogous to those that have been found to exist for carbon dioxide. The selection rules for the energy level transitions i n a l i -near symmetric molecule are well known. I t has been indi-cated that the molecular configuration of carbon disulphide i s linear and symmetrical. Thin ce l l s of carbon disulphide - 2 -are f a i r l y transparent from visible region to 24>< except for tne regions of 4 . 6 ^ and 6 . J J A . Sanderson (1) has shown that the rotational lines are equally spaced, again indica-ting a linear configuration of the molecules. The Raman spectrum of carbon disulphide has been widely studied and energy-level calculations based on this work have proved of great value. Many substances have strong absorption bands i n the region between 1/s and 15^ . However, in this region, thin layers 0.1-mm in thickness of carbon disulphide are quite transparent. As a result, carbon disulphide may be used as a solvent i n the study of the absorption spectrum of compounds. Carbon tetrachloride, on the other hand, i s strongly absorptive between 12^ and 1S/c and so i s not so desirable. In succeeding sections, the theory of the infrared spectrum of polyatomic molecules i s f i r s t outlined, with specific reference to the case of the molecule of type YXg of which carbon disulphide i s a representative. F i r s t the vibrational properties of polyatomic molecules are consi-dered, then the rotational properties followed by the sym-metry properties. A general resume of the experimental installation i s next outlined. This i s followed by a des-cription of two temperature controls designed to control the temperature of the absorption c e l l of the spectrometer. (1) Sanderson, J.A., Physical Review, vol.50, p.209, 1935. The calibration of the spectrometer i s next described and photographs of the calibration traces and curves are i n -cluded. Absorption curves obtained for the six bands of carbon disulphide located at 3.38, 3.51, 4.29, 4.58, 6.52, and 11.4 microns are displayed and the results discussed. - 4 -II. T H E O R Y . Correlations between molecular configurations and i n f r a r e d spectra are a very potent means of q u a l i t a t i v e analysis. Moreover, when several atoms are brought toge-ther one immediately needs to know whether such an aggre-gation w i l l form a molecule. I t was not u n t i l the advent of a quantum mechanical treatment, that the p h y s i c i s t was able to i n t e r p r e t the r u l e s of valence that had been deve-loped to supply the answer. H e i t l e r and London (1) showed that valence i s connec-ted with the symmetry c h a r a c t e r i s t i c s of the wave functions of the outer electrons i n each atom. These ideas a r i s i n g from the theory of the formation of homo^olar diatomic molecules can be extended to molecules with more than two atoms. By-assuming that a stable configuration of the ato-mic nuclei does exist, then the space configuration o f the nucl e i and the force function acting upon the n u c l e i i n the (1) H e i t l e r W., and London, F., Z e i t s c h r i f t f u r Physik, vol.44, p.456, 1927. - 5 -neighbourhood of their equilibrium position may be consi-dered. A. VIBRATIONAL PROPERTIES OF POLYATOMIC MOLECULES A resume of the vibrational spectra of diatomic mole-cules w i l l be made as the theory can be directly applied to the polyatomic case. Let the two molecules A and B be in a position of stable equilibrium at r 8 8 r 0 . When the two molecules are very close then the-force i s very large and tends to separate them. The force vani-shes at r s r Q and the lin e a r i t y of the curve in this re-gion i s a measure of how nearly the oscillator may be considered as simple harmonic. For larger r the force reaches a maximum at the point of inflection of the-poten-t i a l curve and as r increases towards i n f i n i t y the poten-t i a l approaches asymptotically a straight line whose height represents the work of dissociation of the molecule. Since infrared absorption bands are concerned with transi-tions from lowest energy shells to those not far distant, the most useful region for the present purpose that that where the force function i s nearly linear. The wave function i s only different from zero in the immediate neighborhood of r = r Q . The frequency of radia-tion emitted and absorbed i s close to the mechanical fre-quency. The intensity of radiation is near the classical - 6 -value obtained from electrodynamics and varying on the square of the amplitude of the change of the electric mo-ment. This applies also to polyatomic molecules. I f s i s the number of atomic nucleii having an equilibrium position, then the internal degrees of freedom w i l l be n = 3s - 6. I f q i q 2 q s are the displacements from the eq u i l i -brium position and remembering that amplitude i s small compared to distances involved: T - £<a i : Lq 2 • -• a^qg 4 2a 1 2q 1 4 2 * ) V = i ( b n q f • — • b n nq2 • 2b 1 2q 1q 2 • ) n By linear transformation q^ * ^^pi^s.* t&iB becomes, T * £(x| • x| • • x 2 V = i ( \ x f • Agx| • • \y2 Thus H = • H 2 • • where * £ p | • £ A J X | Converting to wave mechanical notation: V-,Vo V V V V ^ V l V 2 V n = [fil U/2 T ny2) "<yn) Here ^ < y i ) V i i s the V^ Hermitinn orthogonal function where y± a (2ir)% IT&^j Then function' v/* "(V±*^)h^/2T - 7 -and V i i s an integer. The c l a s s i c a l theory shows that the system w i l l vibrate with a number of characteristic frequen-cies given by: v>± = h\/2rf~so y± - 21i$h~^Xi and WVi = (Vi • ^ h i ^ . [It = TT e Car) i - i * -y 2/2 - T 2 ye (y) (// = 7T 2 ( 2 y 2 - l ) e (y) 3 4 4 3 -y 2/2 " 3 (2y d-3y)e Let the components of R, the electric moment of the system, along three perpendicular axes i n the molecule be R^  R^  R^ . Anyone of these can be expressed: Where (R^-)0 i s the permanent electric moment in they direc-tion while the coefficients A k may be determined for any system whose Hamiltonian i s known. These matrix elements are: , YE— vn r** r+° M v n v i : v n ? V i — * v n -* -*> ^ 1 > ^ n ) / ( y i ) ^n.) But the Hermitian orthogonal function vanishes unless the v" and V1 d i f f e r by one. Then ••«< y V ^ l -06 ' - 8 -V l v n Thus the diagonal elements R - ( R . ) 5 V l — v n 5 0 and R / 1 V ^ . A f c h ^ S 3 / 2 ^ >v x v k - 1 v n r k w i l l be the only matrix elements remaining from R^- ; the others w i l l be zero. Thus based on two approximations, namely, that the mo-tion i s small compared to the inter atomic distances and that the force f i e l d s are linear near the equilibrium position, the above expression for the electric moment gives the de-sired-selection rules and these are seen to indicate that the frequencies of radiation emitted and absorbed are the same as obtained by classical calculations. The above selec-tion rule w i l l not be obeyed rigorously due to multiple changes in the quantum numbers giving r i s e to harmonic and overtone bands. The intensity I i s d i f f i c u l t to determine as the band consists of rotation lines whose width i s much narrower than the degree;of resolution of the spectrometer. The fine struc-ture lines may be broadened by examining the gas under high pressure or by using so l i t t l e gas that the transmission i s always high. The true intensity might be ten times the ap-parent intensity. The intensity of absorption between two states with quantum numbers a and b has been calculated by Tolman (1). (1) Tolman, R.C., S t a t i s t i c a l Mechanics with Applications . . to Physics and Chemistry, New York, 1927. •Ig = (87r%^ a/3ehg a)(R|) 2(l-e~ M ) Here g a and g^ are the weights of the two states, H a the number of molecules per c.c. in state a and R^ i s the elec-t r i e moment due to b a. The components give <>2 - op* • %y • which, when comparing several fundamental absorption bands, reduces to the form: ( l j ) k = drr g l/3cg 0)(A| • B§ • eg) and this i s similar to the class i c a l form. The wave mechanical treatment of the vibration spectrum of molecules accounts for the system absorbing and/or emit-ting radiation with a range of 'normal• frequencies which correspond to those obtained by the cl a s s i c a l theory of small oscillations. The amplitude of the electric moment for the normal vibrations governs the intensity of the absorption of the corresponding fundamental bands. Certain molecules have been solved by making use of models of the molecules and by making certain assumptions in order to obtain an expression for the potential energy. Geometric symmetry of the molecule was assumed i n i t s equi-librium configuration. The potential function was also as-sumed to have the same symmetry as the geometric configura-tion. (1) This theory can be applied to the triatomic molecules (1) Brester, e.^.yVKristallsyrametrie und Reststrahlen, 1923. - 10 -of the type YX 2. The substance under investigation, carbon disulphide, i s a s p e c i a l case of t h i s type of triatoraic molecule. In the general ease at the tri a t o m i c molecule of the type YX 2, i t can be assumed that the atoms l i e at the cor-ners of an isosc e l e s t r i a n g l e , with Y at the vertex and with the poten t i a l function of the same form. "S) ^ * s ^ n e frequency wMch occurs when the fo r c e f i e l d between the X atoms i s very much stronger than that between the X atom and the Y atom. As the Y-X forces increase, the Y atom be-comes perturbed but the symmetry i n the force f i e l d causes i t s motion to be along the bisec t o r of the apex angle. In the l i m i t i n g case the problem becomes s i m i l a r to the v i b r a -tion of a mass point e l a s t i c a l l y bound to a r i g i d bar. V 2 w i l l be a normal vi b r a t i o n when the two X atoms move i n p a r a l l e l directions and opposite to the Y atom. The motion of the Y atom r e l a t i v e to the centre of g r a v i t y of the X atoms has an amplitude which i s that of a harmonic o s c i l -l a t o r having a frequency\) 2 and a mass/*-- 2mM/(2ra*M) where m i s mass of each X atom, and M i s mass of the Y atom. "^3 r e s u l t s from the t i p p i n g of the X atoms r e l a t i v e to the Y atom. Using the approximation that the amplitudes of the motion are small compared to the distances at equi-librium, the Y atom moves along a l i n e perpendicular to the bisect o r l i n e . The e l e c t r i c moment changes perpendicularly to the l i n e b i s e c t i n g the apex angle. The amplitude of the - 11 -displacement of the Y atom relative to the centre of gravity of the X atom is that of ah oscillator of frequency V^, and mass yU3 = 2mM/(2m#M)2* 2mM2/(2m*M)2tan2«^ where i s half the apex angle. This displacement i s independent of the force f i e l d s but dependent on the masses of particles and the geometry. When the 2nd and higher order theory i s developed i t i s found that, while v^ 2 deviate from the simple harmonic oscillator, they s t i l l remain symmetrical about the line bisecting the apex angle. Thus overtone bands, i f any, w i l l appear at n^V^ « where n^ and n 2 are integers and the fine structure w i l l be similar toV-^ and V 2. However* for the harmonic 113-1)2, the change of electric moment w i l l be along the bisector line for even n 3 and perpendicular for odd n3« Owing to the presence of B 3 , the general overtone, n l ^ l * n2"^2 * n3 v3> w i l l follow the same rule. This can be shown by wave mechanics. There are two special casesj f i r s t when a l l the atoms are equal, and second when the three atoms l i e along a straight l i n e . The second case i s of interestihere as CS 2 i s an example.of this type-. Here for t h e v i b r a t i o n , the charge of electric moment i s zero and the Y atom remains stationary. The* frequencies"^2 snd"^ are both active. The distance between the X atoms remains unchanged. For the linear model with only two degrees of rotational freedom, there should be four normal frequencies, because the Y atom - 12 -may move with linear motion and with isotropic motion in a plane perpendicular to the axis of the figure. The analysis of the motion may be summarized as follows. With respect to a Cartesian set of axes with the £ axis along the figure axis, l e t the X atoms, mass m, have coor-dinates x^ y^ z-^  and x 2 y 2 z 2 8 1 1 ( 1 ^ e Y atom, mass M, have coordinates x 3 y 3 z3« The kinetic energy T i s thus: - s w*2 «2 «2 «2 «2 »2\ / « » w*2 «2 .2* T = (|)(x£ • y-L • z£ • x 2 • y 2 • z|) • (|)(x 3 • y 3 • z 3) If q i s the change i n distance between x± y^ z i m ^ *2 y 2 z2> and i f x y z gives the relative displacements of Y relative to the centre of gravity of the X atoms, then T - <m/4)q2 « W 2 ) ( i 2 • y 2 4 ft2) w i t h ^ = (2mM)/(2m * M) The coefficients of the cross terms vanish and leave V* = IT2* v ^ q 2 4 2T? v | ^ ( x 2 • y 2) • 2 T T 2 V | A Z 2 . Converted to polar coordinates these equations are: T = (ffl)q2 • ( u ) ( * 2 4 r 2 4 r 2 0 2 ) 4 2 V° = T7 2 ^ fraq 2 • 2 U 2 y j ^ r 2 • 27J2 >)|^z 2 The general solution (1) i s the wave equation AV1 ^ V 3 K V 2 ^ ^ / (1) Dennison, D.M., Reviews of Modern Physics, vol.3, p.280. - 13 -with err 27r[Vnj/2h]^q ** The energy constant has the form W° = h • £) • h 1>2(V2 • 1) • h ^ 3 ( V 3 • J) There are V 2 • 1 independent wave functions for each value of V 2 and this i s the weight of each state. V 2 V 3 and 1 are a l l positive integers. For each value of Vg there are a number of values of 1 of which Vg i s the highest. This describes a system similar to the vibrating molecule system. Here one and one only of V^ V g or V 3 changes by one and where the spectrum consists of A ^2 ^3 where V n i s zero due to symmetry considerations. By introducing small perturbations to this motion, the kinetic energy i s unchan-ged by the potential energy becomes V" • V when V i s a function of q, z, and r. V must be independent of 0 and must be an even function of e and of r . For each 1 except l = o , there are two wave functions whose dependence upon iesf ~ie^ e> i s the same but which depend upon 0 as e aW e . The degeneracy caused by the f a l l i n g together of two energy levels whenever 1 o cannot be removed by taking into account any number of higher approximations with per-turbing functions of the form V* but i t w i l l be removed by the magnetic f i e l d caused by the rotation of the molecule as a whole. Two conclusions depending on the symmetry properties or the kinetic and potential functions and not on the order of approximation are: (1),for elements giving the components of the electric moment perpendicular to the axis may have values ?r o i f ZJ1 s • 1,'^Vg i s an even integer ^Vg i s an odd integer. (2),. The elements giving the component of the electric moment along the axis may have values differing from zero i f £>1 = o, <s>V3 i s odd ^ V 2 i s even. Thus i f Bg i s even, the change of the electric moment i s along the figure axis while i f n 2 i s odd, i t l i e s perpendicular to this axia. For collinear and symmetrical atoms, say CS 2, the sum of the figure of any two observed bands (overtones funda-mentals or combination bands) w i l l not be the frequency of an active overtone. This may be indicated by considering the two active frequencies to be 0 1 and 0 2 . n: • n « n: • v 2 = (nj • n 2 ) t / 1 • <n| • Here, since i / 1 and x) 2 are active, »2 • n 3 i s odd n| « n| i s odd hence (n|- • np • (ni * n|) i s even Which make Jx • V inactive. 15 -B.. ROTATIONAL PROPERTIES OF' POLYATOMIC MOLECULES. .. . . Rotational energy possessed by a molecule i s exhibited by a fine structure of the near infrared bands and by the existence of a far infrared absorption spectrum. As the far infrared i s more d i f f i c u l t to explore experimentally, i t i s usual to examine the fine structure in the near i n -frared. The vibration can be treated, separately from the rotation of the molecule and the results combined. There are two assumptions which must be made. The f i r s t i s that the rotational forces between atomB i s small compared with the vibration forces. The second i s that, as before, the amplitude of vibration i s small compared with interatomic distances. vibrational quantum numbers respectively and when each forms an orthogonal set. By considering two systems of orthogonal axes with both origins at the centre of gravity of the system, one fixed i n the molecule and the other fixed i n space the matrix elements for the electron momentum of one set of axes can be found and this again leads to the selection rules. The far infrared bands are caused by changes i n the rotational quantum numbers. Only when the molecule has a Thus H = Hy • and ^ T V Y R correspond to the rotational and - 16 -permanent dipole moment w i l l such bands have a definite i n -tensity. The product of the vibrational and rotational matrix elements w i l l give the matrix element representing the near infrared bands. The quantum mechanical solution of the problem of the symmetrical top rotator has been solved (1). The total an-gular momentum P, the component of P along the C axis P c and the component of P along the Z axis P z are P 2 = J ( J • l ) h 2 / 4 7 T 2 P„ = Kh/2-jr P z = Mh/2TT The weights of the states are: gjK r 2J t 1 K = 0 gjK = 2(2J • 1) K f 0 By an exaaination of the matrix elements representing the electric moment, a determination may be made of the selection rules and intensities. Two types of bands may be produced i n the near infrared vibration-relation bands of a symmetrical top molecule. Parallel bands where the elec-t r i c moment oscillates along the C axis and perpendicular bands in which the electric moment oscillates perpendicular to the C axis. In the parallel type band the selection rules are: ='±:1» 0 aid AK =0. The intensities of the lines of parall e l band may be (1) Reiche, F., and Rademaker, H., Zeitschrift fur Physik, vol.41, p.453,/?*7. - 17 -indicated by: 0 _ o - branch = A l ([2j(J 2-K 2)/4j)e . . .. ' . K=0 0 branch = A j f | o ( K 2 ( 2 J * l ) / 2 J ( J * l ) j e ^ ( j 2 t J ^ • branch i j " 1 = ( l j „ 1 ) e 2 ^ where O' = h2/877%kT. When the moment of inertia C=0 then these expressions be-come those for. the- diatomic molecule: i l l = ( « 4 ) , - ^< j 2 * J > and i j " 1 * (AJ/4)e- ' M 8 " The perpendicular type band has considerable fine struc-ture and depends on the ratio of the moments of inertia. The intensity of the absorption lines of the K t h negative single band w i l l be: - branch I ^ - i 1-1 = (A(J»K-I)(J TK)/8J) e" ^  J ) ~ °^ ^ 0 branch l£ f ._!= A ^  ((2J*l)(J-K*l)(J*K)/8J(J*l))e J r J—K • branch tjf1 ^ = ( i j j - i |. 1)((J-K*l)(J-K)/( J^K-WfK)^ 2^ For cases where o° i s small the summation may be replaced by integrals. The more complex polyatomic molecules cannot be repre-sented by the symmetrical top rotator but can be solved by the use of the asymmetrical top rotator. This theory has - 18 -been developed f u l l y by H.A. Kramers and G.P. Ittmann (1) and by 0. Klein (2). In a l l eases the allowed transitions are those for which = * l , 0. Transition probabilities can be calculated and then dependence on the change of electric moment and moment of ine r t i a obtained. The intensity rela-tions are also developed i n these investigations. C. SYMMETRY PROPERTIES CF POLYATOMIC MOLECULES. The frequencies present i n the infrared spectra of poly-atomic molecules are dependent on the vibration and rota-tion of the molecules. The spectra are dependent on the quality of two or more of the atomic nuclei forming the molecule. The energy states of systems consisting of seve-r a l equal particles may be separated into a number of classes. Each of these classes w i l l have a symmetry character which i s determined by the effect on the wave functions when par-t i c l e s of the system are interchanged. I t has been shown by Heisenberg (3) that no transitions may take place between states possessing different symmetry characters. Symmetrical wave functions w i l l thus be associated with energy states of the seme class and so transitions may occur from a state of one class to a state of any other class. The d i f f i c u l t i e s arising from consideration of a system with r different -—-classes behaving as r different systems with no intercombina-(l)Kramers,H.A. and Ittmann,G.P., Zeitschrift fur Physik, vol.60, p.663. ^*>-C2)Elein,0., Zeitschrift fur Physik, vol.58, p.730./?*?. (3)Heisenberg,W., Zeitschrffit fur Physik, vol.39, p.499. /9*6. - 19 -tions i s removed by application of the Pauli Exclusion Principle. The single symmetry class which exists i s either totally symmetrical or t o t a l l y anti-symmetrical depending upon whether the nucleus contains an even or an odd number of particles. The energy of a polyatomic molecule can be expressed as the sum of the four energies - electronic, vibrational, rotational, spin - which are in descending order of magni-tude. The t o t a l wave function of the molecule may conse-quently be written: The limits placed on the symmetry of a molecule by the exclusion principle does not place similar limits on the symmetry of a component of this wave function. Transition probabilities w i l l depend on the size of the factor which permits the transition. Should this be the nuclear spin, then the transition probability would be small. D. THE MOLECULE YX2. In applying the the above considerations to the mole-cule YX 2 the electronic transitions need not be of concern as the electronic state remains unaltered by the transitions giving r i s e to infrared spectra. The vibrational, rota-tional and spin wave functions, however, must be considered. Where V3 i s an even integer the wave function upon reversing the directions right and l e f t , remains unchanged - 20 -but, i f V 3 i s an odd i n t e g e r , the wave f u n c t i o n r e t a i n s i t s form but undergoes a change i n s i g n c o r r e s p o n d i n g t o symmetrical and a n t i s y m m e t r i c a l modes of the v i b r a t i o n a l p a r t o f the wave f u n c t i o n . The symmetry c h a r a c t e r of the p a r t o f the wave f u n c -t i o n depending on r o t a t i o n , when the l e a s t moment o f i n e r -t i a f a l l s a l o n g the b i s e c t o r of the apex angle, i s t h a t the lowest l e v e l i s always symmetrical, the next two are a n t i symmetrical, the next two symmetrical e t c . When the middle moment of i n e r t i a f a l l s a l o n g the b i s e c t o r of the apex angle, t h e l e v e l s are a l t e r n a t e l y symmetrical and a n t i s y m m e t r i c a l . For even J the lowest and h i g h e s t l e v e l s are symmetrical and f o r odd J , they a r e a n t i symmetrical. The f i n e s t r u c t u r e l i n e s o f the near i n f r a r e d bands correspond t o simultaneous changes i n bot h v i b r a t i o n a l and r o t a t i o n a l quantum numbers. A p p l y i n g the r u l e t h a t t r a n -s i t i o n s may occur only between l e v e l s h a v i n g l i k e symmetry c h a r a c t e r s , i t f o l l o w s t h a t i n a near i n f r a r e d band c o r -r e s p o n d i n g t o an even change i n the v i b r a t i o n a l quantum number V 3, the f i n e s t r u c t u r e l i n e s w i l l be caused by t r a n s i t i o n s between r o t a t i o n a l l e v e l s h a v i n g the same sym-metry. When V 3 i s odd, t r a n s i t i o n s w i l l be between r o t a -t i o n a l l e v e l s of o p p o s i t e symmetry c h a r a c t e r s * ' F o r the l i n e a r molecule, the symmetry c h a r a c t e r w i l l be the same as above when the v i b r a t i o n a l p a r t i s c o n s i -dered. The wave f u n c t i o n i s symmetrical f o r even v a l u e s - 21 -of V 3 and antisymmetrical for odd values while i t i s inde-pendent of V 1 # An interchange of the two X atoms can be effected and the resulting behaviour of the wave function may be calcu-lated. When^^s 0 a l l states with even J are symmetrical, and, anti symmetrical for J odd for that part of the wave function depending on V g, 1, J and M. When L / 0 there are two coincident levels, one of which is symmetrical for an interchange of nuclei and the other -antisymmetrical. The symmetry characteristics of the wave functions of the molecule of type YX 2 w i l l depend on the nuclear spin wave functions which can be obtained in the same way as for homopolar diatomic molecules, (1) The fine structure of the near infrared bands of molecules of the type YX 2 should consist of two sets of lines. One set arises from transitions between two levels for which the vibrational and rotational wave functions are symmetrical. The wave function of the levels giving rise to the other set are antisymmetrical. Intercombination lines between the two sets w i l l be faint due to the small-ness of the spin interaction. The ratio of intensity of these two sets of lines w i l l be S • 1 where S i s the spin S quantum number. A l l the levels giving both sets of lines, are either symmetrical or anti symmetrical in the vibration-rotation spin parts of their wave functions. (1) Herzberg, G., Molecular Spectra and Molecular Structure, Vol.1, Diatomic Molecules, Nww York, 1939. - 22 -Experimental results have given much confirmatory evidence1 in favour of the above theory. In particular, the infrared absorption spectrum of CS 2, in the vapour state has been measured by Bailey and Cassie (1). By using the values obtained by Krishnamurti (2) for the chief, lines i n the Raman Spectrum in conjunction with their own readings in the infrared, they were able to conclude that the CS 2 molecule was linear and symmetrical.- The doublet structure was shown to be associated with the excitation of the syms metrical mode of vibration of the rectilinear molecule which i s optically inactive but capable of combining with the other modes of vibration to give bands in the infrared, where the doublet structure was f i r s t observed. Doublet structure i s therefore attributable to the excitation of two types of vibration associated with s l i g h t l y different amounts of energy and corresponding to two types of binding. Bailey and Cassie (3) calculated the value of the moment of inertia and found i t to be 264 x 10~ 4 0gr.cm 2 and from i t , using ^  ^  = h/4 -n 2I 0c, the rotational line separa-tion within a vibrational-rotational band was found to be of the order of 0.2cm"1. The molecule i s , however, symme-t r i c a l and rectilinear and the fine structure .should (exhi-b i t alternating intensities corresponding to the symmetri-cal and the an t i symmetrical functions with the result that (l)Bailey, C.R., and Cassie, A.B.D., Proceedings of the Royal Society, London, vol.132, p.236,1931. (2}Krishnamurti, K., Indian Journal of Physics, vol.5,p.109. (3)Bailey, C.R., and Cassie, A.B.D., l o c . c i t . one set should have an almost vanishing probability and the apparent effective separation should be twice this amount. Bailey and Cassie checked their results by ther-mochemical data on determination of the heat of formation. Dennison and Wright (l)also concluded that the CSg molecule was linear and symmetrical. The differences between the observed infrared bands were shown to corres-pond to the Raman frequencies. A very intense absorption band was found whose envelope possessed P, Q and R bran-ches lying at 389.4, 396.8 and 405.8cm""1. The doublet se-paration obtained from these reflection grating measure-ments was 16.4cm"1 which leads to I = 172 x 10*^9g.cm2 and a distance between S atoms of 2.54 x 10_8cm. These values were in accord with theory and while lower than those obtained by Bailey and Cassie (2) are due to better dispersion in the method of measurement. Fermi (3) showed that the energy levels of the mole-cule may possess perturbation terms which are of the f i r s t order in contrast to normal theory where perturba-tions are always sedond order. The f i r s t order perturba-tions may be shown to go over into the usual second order perturbation expression when the difference between and 2 ^ i s large compared with certain of the anharmonic constants. ( l j Dennison, D.M., and Wright, M., Physical Review, . vol.38, p.2077, 1931. (2) Bailey, C.R., and Cassie, A.B.D., Proceedings of the . Royal Society, London, vol.132, p.236, 1931. (3) Fermi,E., Zeitschrift fur Physik,vol.71, p.250,1931. Work by Sanderson (1) on the infrared absorption of CS 2 in the 4.6/* band revealed that the rotational lines are equally spaced, Average values of B and B' were found to be 0.112 and 0.111 while the separation of the P and R branches of the band i s 13.3 cm"1. The best representation of the rotation al lines i s by means of the relation V = 2184.50 • 0.224M - 0.00025M2 Sanderson's measurement of the location of the centre of the band at 2184.5 cm"1 did not agree with previous deter-mination of 2179 cm"1 and 2167 cm"1 by Bailey and Cassie. Sanderson was able to resolve 27 lines in the R branch and 30 in the P branch. Due to the antisymmetrical nature of the wave function in the sulphur nuclei, alternate rota-tional lines are missing. Since both nucleii obey the sane s t a t i s t i c s , the missing lines in the CS 2 spectrum are those for which the J of the lower state i s odd. Adel and Dennison (2) while working with C0 2, exten-ded this work by introducing a second order energy pertur-bation and computing the correction term for a general l i -near symmetrical triatomic molecule/ Modification of this formula is possible sb that i t isapplicable to the CSg molecule. (1) Sanderson, J.A., Physical Review, vol.50, p.209, 1935. (2) Adel, A., and Dennison, D.M., Physical Review, vol.43, p.716,1933. - 25 -I I I . EXPERIMENTAL. Before actual Investigation of the-infrared spec-trum of carbon disulphide could be commenced, i t was nece-ssary-to undertaker several modifications of the spectrometer, to build certain additional components, to devise a method of maintaining a continuous low humidity atmosphere in which to operate tiie spectrometer, and, to build temperature controls so that the temperature of the absorbing medium might be held under controlled conditions for extended periods. The salient portions of this experimental arrange-ment w i l l now be outlined. A. SPECTROMETER" AND' ACCESSORIES. A Perkin-Elmer-spectrometer Model 12-B was used as the dispersing instrument in these investigations. The prism face is 55mm. by 75ram. and an offi'axis mirror of 27cm. fo-cal length i s used as the collimator. The instrument w i l l - 26 -not be described in detail here as a complete description i s available in the instruction book accompanying the instrument. Auxiliary equipment includes a Perkin-Elmer Breaker" Type D.C. Amplifier, Brown Recorder and Sola power-stat. A NaCl prism (most useful range 2.5 - 1 5 microns; 4000 - 666 cm"1) was used. The radiation from a source passes through a collima-tor, absorption,cell, monochrometer and i s absorbed by a thermocouple. The signals from this thermocouple are ampli-fi e d by tjie D.C. amplifier and recorded on the Brown recor-der. The source used in the spectrometer i s a globar ele-ment which i s an attempt to approximate black body radia-tion. This source i s provided with a water cooled housing and has a normal operating power of 200 volt amps. For a fixed s l i t width the maximum radiation was found to occur in the region of *2yU . The thermocouple i s a high vacmmi compensated type of bismuth-bismuth t i n elements. The thermal elements are opposed and so arranged that one measures the radiation passing through the spectrometer and the other corrects for ambient temperature. Its sensitivity i s approximately 0.3 microvolts per erg per secondl Although rated a being com-pensated to over 95%, there i s evidence of slight d r i f t . Variations of room temperature despite the very heavy ther-mal lagging of the spectrometer and the thermostat control of room temperature, as later described^ accounted i n part - 27 -for i n s t a b i l i t i e s i n tne thermocouple output. The pressure inside the thermocouple is kept low by means of a getter of activated charcoal. The thermocouple approaches i t s f i n a l output i n about l£ seconds after i t i s exposed to radiation. A reasonably smooth trace is obtained when the amplifier i s not operated on too high gains. The signal from the thermocouple i s fed into a pair of breaker points operated at 80 cycles per second by a synchro-nous motor mounted i n the amplifier. Thus the direct cur-rent signal is converted into a low voltage alternating cur-rent which i s subsequently amplified by step-up transformers and three stages of R.-C coupled amplification. The result-ing signal i s r e c t i f i e d again by a second set pf breaker points operated directly from the same control shaft as the f i r s t pair. Data on the amplifier are as follows: Breaker frequency - 80 cycles per second Voltage amplification (approx.) - 1000 to 300,000 Input resistance (d.c.) - 30 ohms Input noise level (optimum) - 2 x 10~ 9volts Non li n e a r i t y - less than ^% Power - 50 watts, llOv, 60 cycles. The recorder is provided with a f i l t e r which is adjus-ted to cut off at about 2 cycles per second so that 60 cycle pick up and high frequency noise are kept out of the recor-der. The response time of the recorder i s four seconds for — 28 — f u l l scale deflection, and, two seconds for 10 percent de-flection. Tne sensitivity i s ten mi l l i v o l t s for f u l l scale deflection. Reproducibility is 0.2% or better. The Brown recorder contains a self-calibration device which automati-cally places a small calibration mark of approximately one quarter inch in length on the chart every 10 minutes. The Brown recorder and D.C Amplifier are shown i n Plate VT. The wave length micrometer, which rotates a Littrow mirror inside the spectrometer, i s a r b i t r a r i l y calibrated from 1 to 2000. Each small division corresponds to 16.1 secohds of arc. A range of 9 degrees covers a l l the spectra of the L i i 1 , KBr and NaCl prisms. When the instrument was obtained there was no wave drive or control panel. A wave drive capable of driving the spectrometer wave micrometer at four speeds - 62, 124, 312, and 624 seconds per revolution of 100 scale divisions and a control panel to enable the operator to activate separately or simultaneously the pen, chart drive motor and wave drive motor, was designed ancl bui l t by Mr. M. Mitchenen a co-worker on this project. Moreover, an auto stop switch was provided whereby the pen, chart and wave drive would stop automatically at the completion of one revolution of the wave length micrometer on the spectrometer. The wave drive motor operates the spectrometer from longer wave lengths to shorter ones as this direction reduces the errors due to d r i f t to about half those observed when i t i s run in - 29 -the opposite direction. An automatic safety switch was added to the spectrome-ter so that, i f the wave drive were to drive the wave leng-th micrometer beyond the calibration, the power would be turned off. This was accomplished by mounting a micro-switch in such a position that the arm activated by the wave-length micrometer would t r i p the switch when the micro-meter was tuned beyond i t s calibration. The micro switch operated a relay which in turn opened the power c i r c u i t . The spectrometer i s enclosed and a drying agent i s kept i n both the prism and the source compartments. As a result, the amountoof water vapour absorption i s reduced. I t i s not necessary, ordinarily, to completely remove the water vapour as the absorption bands produced ay water vapour and carbon dioxide serve as internal calibration and a constant check on the resolution of the instrument. B. INSTALLATION The spectrometer has a tendency to d r i f t when sub-ject to changes in temperature. A maximum variation of three degrees i s permissable. Thus the spectrometer should be located in a temperature controlled space. Moreovery the location should be as free from vibration as possible. The recorder method of measurement of the output of the thermo-couple i s not as c r i t i c a l i n this respect as i s a galvano-meter but vibration s t i l l remains an important consideration. - 30 -The windows of the spectrometer and sample c e l l s are of rock s a l t which i s slightly hygroscopic. Exposure to an atmosphere of more that 60% relative humidity causes thick fog to appear on them and for higher humidities the windows and prism would dissolve. With NaCl windows, a relative humidity of 50% can be tolerated for extended periods; however, 30% i s much to be prefered. Fortunately fogged windows transmit better i n the infrared than in the visible and may thus be used long after they appear fogged. As a compromise, i t was decided that before the NaCl prism could be taken from i t s sealed container, i t would be necessary to provide an atmosphere of 40% humidity or less. Attempts to reduce the humidity of the entire Research room to 40% or less having failed, i t was decided to con-struct a an aller chamber thus reducing the magnitude of the dehumidifieation task. A double walled box of dimentions 6'x 9'x 8* was constructed with sheets of well seasoned three play with 2-inch spacing between inner and outer walls. This space was packed with rock wool and both walls lined with mois-ture resistant paper on the inner surfaces next to the rock wool. A l l joins were vapour sealed and an airlock system of double doors provided for entrance and exit. The airlock is of dimensions 1.51 x 2.5" x8'. A General Electric commercial refrigeration unit i s - 31 -used to reduce the humidity inside the chamber. The con-densing unit i s powered by a % HiP., 110 volt, 60 cycle, single phase, continuous duty motor. In addition to the condensing unit, this unit consists of cooling coi l s with fan, back pressure valve, throttle valve and solenoid valve. A type H63A Humidity Controller made by the Minne-apolis Honeywell Regulator Company was employed. This i n -strument has a range of 20 to 96 percent R.H. and a d i f f e r -ential of 2 percent R.H. at 50% (slightly wider above; slig h t l y lower below 50% setting). A Friez thermostat with a d i f f e r e n t i a l of 3°F. at 65°F. was used. The refrigera-tion unit employs Freon gas as the active thermal agent. The main functions of these controls are as follows. The throttle valve is variable and controls the rate of f l u i d input to the cooler c o i l s by means of a gas pressure bellows actuated by a thermal probe attached to the exit flow tube. If the temperature of the exit gas i s low, then the bellows in the throttle valve contracts, thus diminish-ing the rate of flow of input f l u i d and vice versa. The back pressure control i s situated on the condenser unit and controls the on-6ff operation of the pump. The control i s actuated by the pressure of the returning gas. I f the pressure i s low, corresponding to a cold return temperature, the pump w i l l stop and vice versa. This control can be reset for any temperature. In the case under discussion, i t was set for a pressure corresponding to a temperature of 35° F. To Face Page 32. DIAGRAM I. - 32 -The solenoid valve i s an on-off control on the input f l u i d flow to the cooling coil s . I t i s actuated by the humi-distat. The solenoid valve cuts out the flow of input f l u i d thus causing the return pressure to drop actuating the back pressure control and stopping the motor of the conden-sing unit. Thus, the motor of the condensing unit may be stopped (or started) in either of two ways.:' 1 . By the action of the back pressure control alone. 2. By the solenoid valve action followed by the back pressure control. The condensing unit was mounted outside the chamber as in Diagram I . The cooling c o i l s and fan unit was bolted to the ceiling inside the chamber in the corner above the position marked for.the temperature control i n this same diagram. As the electric motor used to drive the fan of the cooling c o i l unit was of the induction type and so of non-variable speed, a system of adjustable louvers had to be designed so that the rate of flow of air past the cooling coils could be controlled. These louvers were designed to limit the 'air intake 1 of the fan. The slower the flow of air past the cooling coils the lower the temperature to which the a i r might be cooled and consequently the more moisture that could condense out of the air onto the coils, collect and run down the drain. Beyond the cooling c o i l , mounted to i t but screened - 33 -from i t by metal screening to prevent heat radiation, three 660 watt cone heaters were mounted. The primary of the relay controlling the heaters i s in series with the thermostat and the contacts of a second re-lay whose primary i s across the terminals of the condensing unit motor. Thus the heaters can be turned on or off by the action of the thermostat i f the motor of the condensing unit is in operation. However, i f the motor is not running,(con-t r o l described above) then the heaters w i l l not operate. QSiis cont.ro 1 was introduced to reduce f i r e hazard due to over-heating. If the fan were allowed to remain in operation after the condensing unit had been stopped by one of the above con-trols, then the moisture, that had already been condensed out of the system but had remained on the co i l s , would eva-porate and would be reintroduced into the system. To prevent this, a relay with primary across the terminals of the motor of the condensing unit and secondary contacts in the fan ci r c u i t was installed. Hence, when the motor stops, the fan must also stop. This arrangement permits control of humidity and tempe-rature independently. The cir c u i t , as installed, maintains a steady 40% relative humidity even when four persons are in the chamber. A minimum of 32% relative humidity can be attained. The location of the apparatus inside the chamber i s - 34 -indicated i n Diagram I. A photograph of the experimental arrangement i s shown i n Plate I. On the extreme l e f t can be seen a portion of the powerstat by which the voltage i s re-gulated to any-given value. Next to i t can be seen a watt^ meter arranged in the c i r c u i t to give a continuous reading of the power input to the globar. Next the control panel followed by the temperature control which w i l l be described in detail in Part III C, of this report. On the riglit i s seen the perkin-Elmer Spectrometer model 12-B. Comparison with Plate III w i l l give an indication of the thermal lagging which was applied to the spectrometer, absorption c e l l and leads to the D.C. amplifier. I t w i l l be seen that the spec-trometer and amplifier have been part i a l l y enclosed with a shield. This acts as a thermal shield from any sudden varia-tions in temperature due to the on-off action of the heaters. In addition, electrostatic shielding for the thermocouple and amplifier i s provided as the majority of this cover i s made of sheet iron separated by asbestos. The mercury manometer to measure the pressure insidd the absorption c e l l i s seen extending to the floor in front of the spectrometer, in Plate I. The 100 cm. absorption c e l l i s not in position in the picture but can be seen rest-ing on top of the box which surrounds the spectrometer. Directly above the temperature control in this same i l l u -stration w i l l be seen the expansion coils and fan unit, and, the box containing the three 660 watt heaters. The louvre - 35 -system for controlling the air flow over the coils may be seen towards the l e f t of this unit and the. drainage pan and tube may be seen extending from the bottom of the unit.. C. TEMPERATURE CONTROL. Before useful readings of an absorption spectrum can be taken, accurate control must be obtained of the conditions under which the absorption occurs. A one meter gas c e l l was obtained from the Perkin-Elmer Company. Using this c e l l , i t was proposed to- investigate changes in the absorption spectrum due to variations of the temperature and pressure of the absorbing medium. It was therefore necessary to design and construct a temperature control which woulft be accurate to at least • 0.1°C. and capable of controlling the temperature of this c e l l for extended periods without lag or d r i f t . The minimum range of this control should be from room temperature to 100°C. I t would be preferable that the device should be compact, and, so that i t might be adapted to other uses at a later date, should be capable of controlling at least 500 watts. To meet these requirements,two phase shifting thyratron circu i t s were adopted. The overall dimensions of the f i n i -shed control are 9^ x 11 x 16^ - ins. The weight i s 25 lbs. approximately. The sheet aluminium cover i s so designed that i t could be removed for inspection purposes without To Face Page 36. DIAGRAM II - 36 -affecting the c i r c u i t or the operation of the control. Air-vents are provided i n the lower sides and upper rear of the cover to provide suitable circulation of a i r . In Diagram I I i s shown the c i r c u i t diagram (1) of tem-perature control I . The values of the components of the c i r -cuit are shown in Table It T A B L E I. Table of Components ~ of Temperature Control I. Rl = 50 ohms R 1 0 » 2000 Watt,110 v.heater coil. R 2 = 50 ohms R-i-i = 20 ohms,6 amp.variable re-sistor. R3 = 0-100 ohms (variable) c l = 0.26>cf R4 ,R 5 - 50,000 ohms c 2 = 0 . 2 5^f R6 = 30-100 ohms (fixed) c 3 - 8 ^ f R 7 - 10,000 ohms C 4 * 0.007^ f (300 v.) Rs = 250,000 ohms > CS * O . l ^ f . Rg = 1 0 6 ohms L = Hammond #372, 700 H. Choke. Vi = 6J7G tube. V 2 = FG57 thyratron tube. B = 270 volts with tap at 90 volt. El> E2 = 1 1 5 volt* 6 0 cycle. Filament Transformer, Hammond 167B for 6J7G. Filament Transformer, Hammond #1123, 5V., 50 V.A. for FG57. Ti = 115v, 60"cycle to 5 volt centre tapped. T 2 = Audio transformer, Hammond #312, 50-200 ohm input to , 1000 ohms. U J Benedict, M . , Review of Scientific Instruments,vol.8^g.252. - 37 -A general view of the control i s shown in Plates II and V, while Plate IV shows the internal wiring. Both Ej_ and E 2 are from the same 115 volt, 60 cycle supply to ensure that no phase shift i s introduced from ex-traneous sources. A polarized plug was used on the mains cable and this c i r c u i t fused for 10 amperes. Every effort was made to reduce stray f i e l d s which would effect the phase shifting properties of the device. As w i l l be seen from Plates IV and V, the alternating current" bridge and amplifier stage i s completely separated and shielded from the thyratron c i r c u i t . Shielded cable was used wherever there was a p o s s i b i l i t y of stray f i e l d s and great care was taken to ensure that the shielding was connected securely to the chassis, which was in turn grounded. The resistors used were either non-inductively wound as were R^ , R2, R3, Rg, or so placed in the c i r c u i t as to be free from pick up fron stray f i e l d s . The optimum rate of change of terminal voltage with temperature for an A.C. bridge c i r c u i t such as the one here described can b e easily shown to exist when a l l four arms of the bridge are of equal value. The circuits described in this paper were both designed so that this maximum sen-• s i t i v i t y could be attained. R^ , and R 2 and R3 were non-inductively wound by hand from B. and S. #28 guage "Advance" wire (o(= 0.00002 per degree Centigrade, resistance = 1.81 ohms per foot). Due to this low temperature coefficient of - 38 -resistance of "Advance" wire, these resistors may be consi-dered to be invarient under the small temperature changes of the control chassis. R 3 i s provided with both coarse and fine control and a "check" switch which inserts or removes a resistance of ap-proximately 1.5 ohms (the value is not c r i t i c a l ) into the R 3 branch of the bridge, to f a c i l i t a t e the adjustment of the sensitivity of the bridge. The R 3 branch i s also provided with a f i v e position switch by which the value of R 3 may be varied in steps of 20 ohms up to 100 ohms. This arrangement was devised in order that the instrument might be readily adapted to a number of resistance thermometers, R6, of di f -ferent resistances between 20 and 100 ohms. In any case, Rg should be non-inductively wound from B. and S. #28 guage or thicker resistance wire. A wire with a temperature coef-ficient of resistance per degree centigrade of at least 0.003 should be used. R7, Rg, and Rg are standard low wattage resistors. i s a standard slide wire laboratory resistor outside the unit i t s e l f . R 1 Q is the heater which i s wound around the absorp-tion c e l l . Heater and c e l l are then encased in asbestos and f e l t lagging. The transformer T 2, was chosen so that i t matched the impedance of the bridge (approximately 50 ohms) to the im-pedance of the 6J7G tube. An inexpensive audio transformer such as the one l i s t e d in Table I is very satisfactory for P A N E L OF TEMPERATURE C O N T R O L . - 39 -the purpose. The value of the condenser, C 4, was so chosen that it i s in resonance with the inductance L at 60 cycle. For this reason, any tube that i s capable of high amplification may be used in place of the 6J7G with few changes in the c i r -cuit. A larger value of L would be most acceptable but i f used, a corresponding value for C 4 would be necessary. The adjustment of this c i r c u i t i s direct and rapid. The greatest sensitivity of the thyratron occurs when i t passes current for one quarter cycle. Hence R n i s ad-justed so that the tube can pass a maximum current equal to approximately twice that required to maintain constant tem-perature. The control of R4, Rg is then moved so that the greatest continuous variation of anode current with change in R3 i s obtained. This change in R3 i s effected by using the 'check1 switch. I f R4 i s too small, on-off operation results; i f R4 i s too large, the sensitivity of the control is greatly reduced. After these adjustments, the d i a l set-tings of R 3 may be calibrated directly in terms of tempera-ture. A diagram of the control panel of the temperature con-t r o l is shown in Diagram III, Switch A controls the 110 volt 60 cycle alternating current to the entire unit. When placed i n the "on" position, the transformers supplying f i -lament current to the FG57 and to the 6J7G as well as trans-former T-j_ are energized. Switch B is in the plate c i r c u i t To Face Page 40. DIAGRAM IV. - 40 -of the FG57. The thyratron requires a heating period of five minutes. After the lapse of this period of time with switch A i n the "on" position, the unit may be put in oper-ation,by placing switch B i n the "on" position. Failure to wait this period may result, i f not incomplete destruc-tion, at least i n serious damage to the emissivity of the filament of the thyratron. D i s the control for R 4 , R 5 . When turned counter-clockwise, R 4 i s decreased. F i s the 'check' switch and introduces 1.5 ohms into the R 3 branch of the bridge when in the "on" position. G i s the coarse control and E the fine control of the value of the resis-tance in the R 3 branch, C i s the 5-positicn switch intro-ducing 20, 40, 60, 80, or 100 ohms into Rg. Obviously the resistors controlled by C, E, G and that shorted by F, must a l l be in series. The meter while graduated from 0 to 50, reads 5 amperes f u l l scale. I t i s in the plate c i r -cuit of the thyratron. The operational r i s e i n temperature of the control in the most c r i t i c a l region, that of the^bridge, was found not to exceed 10° C. As the three arms of the bridge are of "Advance*! wire, this change in temperature produ-ces negligible d r i f t in the control. In Diagram IV is shewn the c i r c u i t diagram of the second temperature control. The values of the components of the ci r c u i t are l i s t e d i n Table I I : R-L = 50 ohms R 2 = 50 ohms R3 - 50 ohms R4 = 50 ohms R5 - 10 meg ohms Ci = 8 / f C 2 = O.lyUf Co = COOS/*/" Table of Components of Temperature Control II. R 6 = 1500 ohms R7 = 1 meg ohm R 8 = 250,000 ohms Rg s 2000 watt, llOv.heater c o i l R. = 40 ohms, 6 amp.variable resis-10 V x = 6J7G tube tor. V 2 = FG105 thyratron tube B = 270 volts with tap at 90 volts E - L , E 2 = 115 volt, 60 cycle. Filament Transformer, Hammond 167B for 6J7G. Filament Transformer, Hammond #1123, 5v., 50 V.A. for FG105. T^ = 115v, 60 cycle to 5 volt, c B n t r e tapped transformer. T2 s Audio transformer, Hammond #312, 50-200 ohms input to 1006 ohms. The construction i s essentially the same as in the tempera-ture control f i r s t described. R^ , R 2 and R3 are wound non-inductively from "Advance" wire while R 4 i s non-inductively w o u n d from "Hytimco", a resistance w i r e of high temperature coefficient of resistance as well as high r e s i s t i v i t y . In this control, a permanent phase shift of 90 degrees i s ob-tained between the plate voltage and gri d voltage of the - 42 -t h y r a t r o n by means o f condenser Cg. Temperature c o n t r o l r e s u l t s from the increment "or decrement t o t h i s phase s h i f t o b t a i n e d when the b r i d g e becomes unbalanced. I f the tempera-t u r e of the body to be c o n t r o l l e d Is too h i g h , then the r e s i s t a n c e of R4 i s too l a r g e and the phase angle between p l a t e v o l t a g e and g r i d v o l t a g e o f the t h y r a t r o n i s i n c r e a s e d so t h a t the t h y r a t r o n i s f i r i n g f o r l e s s time per c y c l e than i t was b e f o r e . I f the temperature should f a l l , the R 4 i s too s m a l l and the t h y r a t r o n f i r e s f o r a l o n g e r time per c y c l e than b e f o r e . The s e n s i t i v i t y of the c o n t r o l can b e - r e a d i l y a d j u s t e d by v a r y i n g the s e t t i n g o f the potentiometer R 5. m t h i s c i r c u i t an FG105.thyratron was used, thus p e r m i t t i n g up to 5 amperes i n the h e a t e r c i r c u i t . Temperature c o n t r o l i n a range from room temperature to 140°C. with an ac c u r a c y of at l e a s t ± 0.05°C. has been a t t a i n e d . With f u r t h e r adjustment, i t I s pr o b a b l e t h a t t h e accuracy w i l l be i n c r e a s e d t o £. 0.01°G. The u n i t i s completely p o r t a b l e end i t s o p e r a t i o n d i r e c t . The maximum c u r r e n t i s l i m i t e d b y the c u r r e n t c a r r y i n g c a p a c i t y o f the t h y r a t r o n i n the p r e s e n t c i r c u i t s but by means of a s u i t a b l e system of shunts, c o n t r o l of up t o 5 k i l o w a t t s should be p o s s i b l e w i t h o u t a p p r e c i a b l e d ecrease i n s e n s i t i v i t y . D. ALIGNMENT OF SPECTROMETER. Great c a u t i o n must be e x e r c i s e d throughout the adjustment procedure not t o f o g or damage the r o c k s a l t To Face Page 43. .DIAGRAM V A. Energy, Distribution vs Wavelength. DIAGRAM V B... Energy vs S l i t Width at 2.5^ . DIAGRAM V A and B. - 43 -prism or windows. They should not-be touched with the f i n -gers or breathed upon, and rubber gloves should be worn in handling them. The order in which the different parts are set up is such that most of the parts need to be adjusted once only and their adjustment i s not affected by subsequent changes. A low power microscope mounted v e r t i c a l l y with a 45 degree prism attached to the bottom, a mercury arc of high inten-sit y and a cardboard box to replace the monochromator cover are of aid i n the alignment. The general alignment of the system should be f i r s t checked to ensure that the light i s f a l l i n g approximately on the centres of the various optical parts. The centers of the source, s l i t s and mirrors are a l l at the same height, 2\ inches, above the base of the spectrometer. The detailed alignmBUt procedure of the spectrometer w i l l not be given here as i t i s set forth completely and i n great detail in the "Instruction Manual for Infrared Spectrometer, Model 12-B" which accompanies the instrument. The energy distribution with wave length, using a sodium chloride prism, has the general appearance as indi-cated i n Diagram V-A. The peak of the curve occurs i n the region of 2.5^*. The band at approximately 3^ **, i s due to carbon dioxide and water vapour. That at 4 ^ i s due to carbon dioxide while the band at 6 ^ i s due towater vapour. The band at 1 5 ^ i s due to carbon dioxide. The variation - 44 -of the energy as a function of s l i t width at the peak of the energy curve is shown i n Diagram V-B. I t should be a straight line passing through the origin. The fact that i t does not pass through zero could be r e c t i f i e d by a chan-ge in the index on the s l i t micrometer of the indicated amount. Otherwise a correction factor may be added to each setting of the micrometer. The curve at the bottom end however indicates the s l i t s do not close simultaneously. The curve shown i s the optimum obtained after many reset-tings of the s l i t s . The resolution obtained with ths spectrometer depends on the wave length and s l i t width used. The width of the band of nearly monochromatic light which is isolated by the instrument can be calculated. The traces showing the vari-ation i n resolution with wave length i s shown in the "In^x struction Manual". The band width used i s the half inten-sit y width, which i s equal to the separation of two barely resolvable lines. This matter i s considered in some detail by R.B. Barnes, R.S. McDonald, and Van Z. Williams in their a r t i c l e . (1) (1) Barnes, R.B., McDonald, R.S., and Williams, Van Z., Journal of Applied Physics, vol.16, p.77, 1945. - 45 -IV. R E S U L T S The calibration procedure and the resultant ca-libration curves are f i r s t discussed. This i s followed by those results pertaining to carbon disulphide which have been obtained to date. A. CALIBRATION. The arbitrary numbers of the wave length drum were calibrated into wave numbers by observing the settings cor-responding to known lines and absorption bands. The absorp-tion bands of water vapour and carbon dioxide gas occuring as atmosphere constituents were used for calibration of the longer wave lengths. In addition the absorption spec-trum of ammonia gas was used. In this manner a f a i r l y large number of calibration points distributed throughout - 46 -TABLE III. VALUES USED IN MAKING CALIBRATION CURVES. Drum Setting Wave Number in cm~l Drum Setting Wave Humb' in cm"1 517 667.0 1184 1054.4 589 720.7 1198 1066.3 748 807.7 1207 1075.8 765 .812.4 1218 1085.1 798 823.2 1228 1096.1 807 830.9 1236 1104.1 812 833.0 1248 1117.4 814 834.9 1253 1123.0 843 848.0 1268 1141.3 855 854.0 1284 1159.7 885 868.2 1298 1177.9 893 872.7 1313 1195.9 947 888.3 1325 1213.4 955 892.4 1337 1231.1 984 908.4 1355.7 1261 1049 948.8 1361.5 1272 1055 952.0 1389 1314 1082 972.4 1391.6 1320 1111 992.8 1403 1340 1131 1007.2 1415 1363 1136 1012.6 1420.3 1376 1155 1027.3 1427.5 1388 1161 1033.8 1430.7 1396 1177 1046.9 1435 1406 - Al -TAB3JS III. (Continued from Page 46.) Drum Setting Wave Number in cm"*1 Drum Setting Wave -Mm in cm 1441.7 1420 1537 1700 1447 1431 1541.5 1718 1449 1437 1545.7 1736 1454.2 1449 1549 1751 ' 1458 1459 1554.5 1774 1461 1466 1559.5 1794 1464.4 1474 1562.5 1812 1470.5 1491 1567 1830 1473.5 1498 1570 1846 1477 1508 1575 1870 1480.3 1518 1579 1891 1481.8 1523 1582.5 1911 1486.4 1535 1585 1922 1489 1542 1588.5 1944 1495 1560 1592.3 1968 1498.5 1571 1597 1993 1501.4 1578 1640 2336 1506.8 1596 1644 2367 1514 1618 1703 3217 1516 1624 1708 3337 1519.4 1637 1711 3434 1524 1649 1718 3617 1527.3 1664 1722 3741 1529.5 1671 1726 3882 1533 1685 - 48 -the spectrum was obtained. Plates VTI, VIII, DC, and X are photographs of actual traces obtained from the recorder in the regions and under the conditions indicated. Identification of the bands was made from the work of Oetgen, Chao-Lan Kao and Randall. (1) The frequency in cm'1 of each band identified i s indicated below the trace, while the figures above the trace indicate the wave drive,readings. Together the sp&ctra of these three substances - car-bon dioxide, water vapour and ammonia - provide over 100 points in the region between 2.5^* and 15^ *- from which the calibration curve may be obtained. In Table III i s dis-played the wave length drive drum setting and the corres-ponding values of the wave numbers i n cm""1 which were ob-tained from the recorder traces, and which were used as calibration points for the spectrometer. Plates XI, XII, and XIII are photographs of the c a l i -bration curves which were plotted from the above readings for the regions 700 - 1300 cm-1, 1260 - 2000 cm - 1 and 1800 -3900 cm"1 respectively. Each of the original calibration curves i s plotted on a sheet of graph paper of approximate-l y 20 x 30 inches. These originals are used for i d e n t i f i -cation of wave numbers from wave drive drum settings. (1) Oetgen, R.A., Chao-Lan Kao, and Randall, H.M., Review of Scientific Instruments, vol.13, p.515, 1942. - 49 -B . RESULTS. The number of' fundamental vibrations for a molecule, of n atoms is 3n - 6. For carbon disulphide there would be 3 such fundamental bands, V^, -\Jg, and Vg. In addi-tion to these there are many combination and harmonic bands. The observed spectrum does not show such a large number of absorption bands. This reduction in the number is due to the fact that a number of the bands are located beyond the range of the instrument and that the symmetry properties reduce the number of vibrations which would be active in the infrared absorption. A total of six bands were found in the region less than 15 microns. Tney w ere located at 3.38, 3.51, 4.29, 4.58, 6.52, 11.4/r. Cell lengths of 160 cm to 10 cm were employed depending oh the degree of absorption necessary to display the band to best advantage. A l l measurements were made using a sodium chloride prism and were made at 20°C. The graphsl of percentage transmission vs wave length drum setting were obtained from the recorder traces for these six bands. To obtain these graphs, the distance was measured between two f i d u c i a l lines placed on the recorder trace by means of the switch "Microvolt Test" in the ampli-f i e r . This distance was then .divided into a number of sub-divisions. The base line was drawn between the two ends of the trace corresponding to periods when the aluminized - 60 -s h u t t e r was c l o s e d and consequent ly when t h e r e was no s i g -n a l on the thermocouple . The v e r t i c a l d i s t a n c e s between the base l i n e and t h e t r a c e were then measured c o r r e s p o n -d i n g to each o f t h e s u b d i v i s i o n s . T h i s procedure was c a r -r i e d out f o r each of t h e t r a c e s o b t a i n e d , f i r s t w i t h a known p a t h l e n g t h o f carbon d i s u l p h i d e and then w i t h the same c e l l evacuated. The r e a d i n g s o b t a i n e d f o r t h e cartoon d i s u l p h i d e were d i v i d e d b y t h o s e o b t a i n e d from the t r a c e of the vacuum end the q u o t i e n t m u l t i p l i e d , by one hundred to g i v e t h e p e r c e n t t r a n s m i s s i o n . The wave l e n g t h drum s e t t i n g c o r r e s -ponding t o each o f the f i d u c i a l l i n e s and hence to each o f th§ s u b d i v i s i o n s was known, hence, the graphs of percentage t r a n s m i s s i o n vs wave l e n g t h drum s e t t i n g c o u l d be p l o t t e d . Photographs of these are shown i n P l a t e s XIV t o X V I I I . The d i f f e r e n c e band v*3 - ^ i s shown i n F l a t e X I V . The a b s o r p t i o n minimum c o r r e s p o n d i n g t o t h e m i s s i n g Q branch occurs at 928 wave l e n g t h drum s e t t i n g w h i c h , b y r e f e r e n c e to P l a t e X I , corresponds, t o 877cm""1. The P branch , on the r i g h t , i s w e l l d e f i n e d w h i l e the R branch i s a l i t t l e b r o a -d e r . The band i s of medium i n t e n s i t y as can be seen from the c e l l l e n g t h and pressure v a l u e s g i v e n . The s t r u c t u r e of the -0 ^  band i s shown i n P l a t e X V . I t i s a s t r o n g band o c c u r r i n g a t 6 . 5 2 ^ ( 1 5 3 6 c m " 1 ) f o r the vapour of carbon d i s u l p h i d e . The g r a p h was o b t a i n e d as an average of s i x independent s e t s of r e a d i n g s , each w i t h a c e l l l e n g t h of 10cm. and an extremely s m a l l p r e s s u r e . The - 51 -P and R branches are well defined on the right and l e f t of wave length drum setting 1486.7. A definite "side band can be seen on the long wave length side of the band. The existence of this side band i s strongly dependent on the conditions in the absorbing medium. I f the pressure i s too high, there i s a general broadening of the band. I f the pressure i s too low the side band disappears and the P and R branches remain. The combination toand V i • V 3 is shown in Plate XVI. This graph was the result of averaging four independent sets of readings, each taken under the same conditions. The band . occurs at 4.58 microns (2185cm-1), and i s f a i r l y weak. Plate XVII shows the combination band V 3 • 2 Vg. T h e band i s very weak. It occurs at 4.29" microns (2332cm"1). The combination bands ^ 3 * 2 ^  and • v*3 • 2 l / g are shown in Plate XVIII. These bands occur at 3.51 and 3.38 microns (2838 and 2959 cm"1) respectively. The reso-lution of the instrument when using a rock salt prism i s too low to allow the structure of the bands in this region of the spectrum totbe observed. A lithium fluoride prism would provide the necessary resolution. In Table IV are shown the observed and calculated va-lues based on the indicated values of the fundamental v i -brations v i , \)2> and ^ 3 , The calculated values of the wave number when using the value of 1535cm"1 for v* are o seen to agfee much more closely with the observed values - 52 -than those when V 3 = 1523cm"1 i s used. The results of other observers are likewise brought more closely into agree-ment, by use of this value for v?3. TABLE IV. Absorption Bands of Carbon Disulphide Vapour. Wave Number Wave Length Observed Calculated Observed. cm"1 cm"* Microns % • 655(1) 655 397 397 *3 1535 i 2 1523 1535 6.52 V3 877 t 1 868 880 11.4 V l • V3 2185 *- 5 2178 2190 4.58 *3 • 2V2 2332 * 5 2317 2329 4.29 *3 • 2\ 2838 ± 6 2833 2845 3.51 • >3 • 2 ^ 2959 4 6 2972 2984 3.38 The probable errors stated i n Table IV were obtained in the following manner. An accuracy of plus or minus half of one division was assumed* in the wave drive drum setting on the instrument. Then, by using the three calibration .charts, photographs of which are shown in Plates XI, XII, and XIII, the corresponding probable errors were obtained for the various regions of the spectrum. For bands of wave length less than 5yU the error in the experimental values cannot be less than Sera"1. As a consequence, from Table IV i t w i l l be seen that the case for the use of ^ = 1535 cm-1 i s further strengthened as by i t s use the agreement between observed and calculated values becomes closer. When the absorbing medium employed is in the l i q u i d state, i t i s to be expected that some changes in the spec-trum w i l l occur due to the closeness and association of the molecules i n the l i q u i d state. Moreover a l l these bands occur at longer wave length in the liquid than in the va-pour. The band V^, which arises from the transition, (1 O°0£—0 0°0) from the ground state was not observed in vapour, but i t has been observed by other workers i n the liq u i d . This i s i n accord with the theory, since,the pro-ximitycof the neighbouring molecules in the li q u i d or solid might exert sufficient force on the molecule to produce a certain degree of asymmetry thus permitting the transi-tion. The side band observed i n the structure of "0 ^ (Plate XV) on the long wave length side i s due to the iso-tope effect of C 1 3 s2 2. - 54 -V CONCLUSION. The i n f r a r e d a b s o r p t i o n spectrum of carbon d i s u l -phide i n the vapour s t a t e has been remeasured i n the r e g i o n from 2 to 15 microns. A t o t a l o f s i x bands were measured, and were found t o be l o c a t e d a t 3.38, 3.51, 4.29, 4.58, 6.52, and 11.4 microns. While the u l t i m a t e o b j e c t , t h a t o f the i n v e s t i g a t i o n of the anomalous bands o f the carbon d i -s u l p h i d e molecule under d i f f e r e n t c o n d i t i o n s o f a s s o c i a t i o n , has not been f u l l y r e a l i z e d t o date, work on t h i s w i l l c o n t i n u e w i t h a thorough i n v e s t i g a t i o n of the changes i n the a b s o r p t i o n spectrum due t o changes i n the temperature and p r e s s u r e of "the absorbing medium. The V> 3 terra has been confirmed and i t s s t r u c t u r e i n -v e s t i g a t e d . A measure o f the a b s o r p t i o n of carbon d i s u l -p h ide vapour a t a s t a t e d temperature and pressure has been a t t a i n e d . The bands o b t a i n e d are such as t o s u p p o r t the c o n c l u s i o n t h a t carbon d i s u l p h i d e i s a l i n e a r t r i a t o m i c - 55 -molecule. The side branch shown on the long-wave length side of the fundamental band at 6.52/fis due to the iso-topic effect produced by C 1 3. Although the exact spectrum of any compound cannot be found without measurements, a great deal of i t s quanti-tative form can be predicted from a knowledge of" the re-lation between infrared spectra and molecular stuucture. When the differences between the absorption frequencies of the different components are great enough, identifica-tion can often be made directly, especially when the sample i s known to contain relatively few possible struc-tures. As the infrared absorption spectrum of a compound i s the sum of a l l the possible vibrations of i t s parts, this spectrum i s a unique property of the compound which gives r i s e to i t . There i s one to one correspondence between spectrum and compound. Correlation between the molecular configurations and the infrared spectra may be used for accurate analysis both i n the research labo-ratory and i n industry. - 57 -TEMPERATURE CONTROL (SIDE VIEW) - 59 -T E M P E R A T U R E CONTROL ( S h o w i n g I n t e r n a l W i r i n g ) P L A T E I V -60-TEMPKRATURE CONTROL (Rear View) PLATE V PLATE VI - 6 2 -CF)L/BRRTI0H C H R R T FOR PEIrtFRfi-REDSpecrffoAiETEfAloDEL /JB SE*IRL 2'S WrrHA/oC( Qt/SM trvTHE WEJ&19A » ' = i.69.Qf!f tav7Zocrn' It. \= /A to/S/A CflLIBRP T/O/V FRoAl THE SIM COj. flSSOHFT'W BFWD PERFORMED MARCH lDE.MTiF/Cnr/O.Yr#0'\'\ P.S.I t3,f/S/?+2 SWT WIDTHo-/emm. TEZ^P 7<^'F G-LOBRR POWER 20OW#Trs MflWMVM &a//vio htv/*up/Ty 3S- °/A . WAVE-DRIVE 5f£~ED * ''3" f<E* XEV C£U <£AT6_ 40<v*-PfE5SO/?EC /so inn? S/3 •. feoxes ffE/ow rv/nie t*£ f*^f*e.*'cs£t VT c/n~' f ' S u / T E S neovE ro/rve w^ver- .>>r/v£ / ? £ ~ & r . / v G s PLATE VII - 63 -PLATE VIII - 64 -PLATE IX PLATE X PLATE X I I - 6 8 -3751 * I : —— c RL/BR#r/oA/ rut I Sex/A* SrecTXQfitert*/looct /JO i BSOO •V- Jl oor»C TO - V - / 34-JO _] 4 . F**v ffSZ sg, j f y * / 5 * ^ . • / / 3300 i t 1 V I % if ."FA' Z700 ry 2250 sap isio IS 90 If 10 Wflf£ J"0 /(, 7 » c /-v Gtvisla ) PLATE XIII - 69 -IO0 * 80 O to I to S o GO 40 10 T H E DIFFERENCE- BAND T e m p e r a to re : 20°C P r e s s u r e : 30c»*» Cell L e t ^ t h : 100cm fi f i • 070 960 950 940 9 3 0 920 910 Wavelength D r i / v n PLATE XIV 70 -PLATE XV - 71 -THE COMBINATION BAND T e w > p e r a t u r e *. ZO°C py ess u v e ; 2 0 c*n. Cei l Lectin ; 1 0 0 c * . . • 1618 \6lO \GZl IG24- 1626 1628 1630 PLATE XVI - 72 -JOO 80 I 60 I £ 40 zo THE COMBINATION BAND Temperature '. 20°C Pressure . 5 0cm Cell Length ; lOcw IG43 164a |G4f 1640 1639 1638 \637 PLATE XVII - 73 -PLATE XVI I I - 74 -B I B L I O G R A P H Y 1. Adel, A., and Dennison, D.M., Physical Review, vol.43, p.716, 1933. 2. Bailey, C.R.., and Cassie, A.B.D., Proceedings of the Royal Society, London, vol.132, p.236, 1931. 3. Barnes, R.B., McDonald, R.S., and Williams, Van Z., Journal of Applied Physics, vol.16, p.77, 1945. 4. Bartunek, P.P., and Barker, E.F., Physical Review, vol.48, p.516, 1935. 5. Benedict, M., Review of Scientific Instruments, vol.8, p. 252, 1937. 6. Bhagavantum, D., Nature, vol.126, p.995, 1930. 7. Bjerrum, N., Verb, der deutsch Physik Ges., vol.16, . p.737, 1914. 8. Brester, C.J., Kristallsymmetrie und Reststrahlen, Utrecht, 1923. 9. Dennison, D.M., Philosophical Magazine, vol.1, p.195, . 1926". 10. Dennison, D.M., Reviews of Modern Physics, vol.3, pp.280 and 297, 1931. 11. Dennison, D.M., and Hardy, J.D., Physical Review, vol.39, p.938, 1932. 12. Dennison, D.M., and Wright, N., Physical Review, vol.38, p.2077, 1931. 13. Fermi, E., Zeitschrift fur Physik, vol.71, p.250, 1931. 14. Goodeve, C.F., and Stein, CP., Transactions, Faraday Society, vol.25, p.736, 1929. n 15. Heisenberg, W., Zeitschrift fur Physik, vol.39, p.499, 1926. 16. Heitler, W., and London, F., Zeitschrift fur Physik, vol.44, p.455, 1927. - 75 -17. Herzberg, G., Molecular Spectra and Molecular Structure, vol.l» Diatomic Molecules, New York, 1939. 18. Herzberg, G., Infrared and Raman Spectra of Polyatomic Molecules, New York, 1946. 19. Klein, 0., Zeitschrift fur Physik, vol.58, p.730, 1929. 20. Kramers, H. A., and Ittmann, P., Zeitschrift fur Physik, vol.60, p.663, 1930. 21. Krishnaraurti, K., Indian Journal of Physics, vol.5, p.109, 1930. 22. Leiberman, L.N., Physical Review, vol.60, p.496, 1941. 23. Martin, P.E., and Barker, E.F., Physical Review, vol.41, p. 291, 1932. 24. Oetgen, R.A., Chao-Lan Kao, and Randall, H.M., Review of Scientific Instruments, vol.13, p.515, 1942. 25. Plyler, E.K., and Sleator, W.W., Physical Review, vol.37, p.1493, 1931. 26. Plyler, E.K., Stair j R., and Humphreys, C.J., Journal of Research, National Bureau of Standards, vol.38, p.211, 1947, R.P.1769. 27. Plyler, E.K., and Humphreys, C.J., Journal of Research, National Bureau of Standards, vol.39, p.59, 1947, R.P.1814. 28. Rawlins, F.I.G., and Taylor, A.M., Infrared Analysis of Molecular Structure, Cambridge, 1929. 29. Reiche, F., and Rademaker, H., Zeitschrift fur Physik, vol.41, p.453, 1927. 30. Salant, E. 0., and Rosenthal, J.E., Physical Review, vol. 42, p.812, 1932. 31. Sanderson, J.A., Physical Review, vol.50, p.209, 1935. 32. Schaefer, Matossi and Aderhold, Physikalische Zeits-chrift, vol.30, p.581, 1929. 33. Sirkar, S.C., Indian Journal of Physics, vol.10, p.189, 1936. 34. Sleator, W.W., Astrophysical Journal, vol.48, p.125, 1918. 35. Tolman, H.C, S t a t i s t i c a l Mechanics with Applications to Physics and Chemistry, Hew York, 1927. 36. Urey, H.C, and Johnston, H., Physical Review, vol.38, p.2131, 1931. 37. Venkateswaran, S., Philosophical Magazine, vol.14, p.258, 1932. 38. Wood, R.W. and Collins, 6., Physical Review, vol.42, p.386, 1932. 39. Yates, B., Physical Review, vol.36, p.555, 1930. 

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