Band 24, Heft 4

Aus dem Relativitätsprinzip folgt ohne Verwendung des empirischen Prinzips von der Konstanz der Lichtgeschwindigkeit, daß die Lorentz-Transformation die einzig denkbare Alternative zur (raumzeitlich asymmetrischen) Galilei-Transformation ist.

Keywords The Feynman diagrams and rules of a field theory with local four fermion coupling are transformed into a theory of interacting fermions in a finite dimensional Hilbert space constructed on Z 3 points of a cubic lattice. The propagator is derived for the lattice space theory and the formal similarity and the qualitative differences are discussed and compared with conventional field theories. The mass produced by the interaction is calculated by compensation of the first order self-energy diagrams (Hartree-Fock-approximation). The solution for coupling constant W > 0 violates the chiral symmetry, the solution for W < 0 the cubic symmetry of the theory. The second order corrections to the mass operator are calculated. They diverge in the limit Z→∞ like if W is proportional to which is necessary for a finite mass in the HFapproximation. Under the same assumption the maximum divergence is like in any order of the perturbation theory. The mass operator is finite including second order contributions if W is proportional to . In this case the higher order contributions decrease like .

The N-2θ-sector of the Lee-model is solved in the special case of the "dipol-ghost" , and a unitary S-matrix is constructed. A general instruction is presented to construct the physical subspace of the whole state space with indefinite metric. This method is always applicable, if there are couples of "good" and " bad" ghosts. Another model with positiv definite state space is described, which has the same S-matrix a s the Lee-model with "dipol-ghost' 2 in the N-θ-and N-2θ-sector.

The theory of non radiative electronic transitions is represented in two papers. In the first of these we calculate wavefunctions, energies, matrix-elements etc. In the second we discuss the general reaction mechanism and apply the theory to two examples. The wavefunction of a crystal volume containing one defect is calculated on the base of a microscopic theory. For our numerical discussion we used as an example an anion vacancy in MgO, LiF, NaCI, NaBr, KC1, KBr, KJ. The results are collected in Table 1 and 2. As far as experimental data have been available they agree completely with our results.

A general formalism to describe radiationless electronic decay (RED) is developed. Two con­ditions are derived that must be fulfilled to make RED possible. Using the data derived in part I of this paper the general formulae are applied to a F-center in KCl and MgO. In KC1 th e con­ditions for RED are not fulfilled while in MgO RED proves to be more probable th an radiative decay. This is in complete agreem ent w ith experim ental knowledge.

In these experiments continuing the work on interaction published in 1 , the magnetic field, i.e. the retarding force, has been increased. This produces reflected shocks that leave the inter­action region, but the steady state could not be achieved.

The linearized Boltzmann equation of kinetic theory for the electrons of a weakly ionized plasma under the action of an alternating electric field E = cos ω t {E x , E y , E z } and a circularly polarized magnetic field B R = B {cos ω B t, sin ω b t, 0} is solved. The direction-dependent part f 1 (r, v, t) of the distribution function contains especially higher harmonics with frequencies 2 ω B , ω± ω B , ω±2ω B . These overtone frequencies are generated - unlike the higher harmonics obtained by Margenau and Hartman - by a cross drift mechanism and are present even if the isotropic part f 0 of the electron distribution function is assumed to be time-independent. The physical meaning of the various contributions to the distribution function f 1 is discussed in detail.

The electron distribution function is calculated explicitly for a weakly ionized plasma under the action of an alternating electric field E = {0 , 0 , E oz cos ω t} and a circularly polarized magnetic field B R = B c {cos ω B t, sin ω B t, 0} rotating perpendicular to the a.c. field. Furthermore, a constant magnetic field B 0 = {0, 0, B 0 } is taken into account. The isotropic part f 0 of the electron distribution function which contains, in special cases, well-known standard distributions (distributions of Druyvensteyn, Davydov, Margenau, Allis, Fain, Gurevic) shows a resonance behaviour if the frequencies ω, ω c = (q/m) B c , ω 0 = (q/m) B 0 , and ω B satisfy the relation ω= This can be understood as a generalized cyclotron resonance phenomenon.

The general theory of Torrey for magnetic relaxation by isotropic translational diffusion has been applied to investigations of nuclear and electronic relaxation in liquids. The theory leads to a general correlation time (d distance of closest approach of interacting spins, <r2> mean square flight path. D diffusion constant). It could be shown that the theoretical model fits the experimental data obtained in organic solutions of free radicals. The correlation times of dimethoxyethane and toluene exhibit activation energies of 3.0 and 3.1 keal/mole respectively at high temperature. Dimethoxyethane corresponds to the limiting case of the random flight theory where <r 2 > « d 2 , whereas Tn toluene <r 2 > ≈ d 2 is obtained.

First and second-order quadrupole effects of the 11 B nuclear magnetic resonance have been measured in polycrystalline samples of dimere dimethylaminoboranes and tetramethylboracene. With the theory of powder patterns for first and second-order quadrupole interaction the nuclear quadrupole coupling constants e 2 q Q/h and asymmetry parameters η of 11 B have been determined. For these measurements boron-free inserts had to be constructed for the probes of the Varian Wide Line Spectrometer DA 60.

The mean esr linewidth of hfs components of aqueous mangenese salt solutions has been measured a t 9 GHz and room temperature from small to medium concentrations, also with added diamagnetic salts. In all cases the linewidth depends on the viscosity of the solutions. Further, already at very small concentrations a specific anion dependend line broadening has been observed, evidently resulting from ion pair formation. Roughly spoken, in the whole concentration range two anion families exist. Nitrate and halides show smaller line broadening, they form ion pairs with long lifetime. Sulfate, acetate and formiate show larger line broadening; they form ion pairs with short lifetime.

By means of a time-of-flight method the electron drift velocity ν_ in ethane was measured at densities between N = 1,5 · 10 19 and 1,1 · 10 21 cm -3 (450 Torr ≦p 20 ≦ 33390 Torr). Below E/N = 10 -18 and above E/N = 10 -16 Vcm 2 (E/p 20 < 0,03 and > 3,3) ν_ is independent of density N, in the intermediate region ν_ decreases at a given E/N with increasing density. This means a violation of the similarity rule. As function of E/N at a given X the relative drift velocity q = ν_ (p)/v (450 Torr) shows a resonance curve with a minimum at E/N = 6,5 · 10 -18 {E/p 20 - 0,2). This effect can be described, assuming that the electron is attached to the C 2 H 6 - molecule for a short time τ. The cross section for the electron attachment, Q a , has a resonance maximum at electron energies of ~ 80 meV. Q a is shown to be ≦ 10 -15 cm 2 and the life time to be ≦ 10 -14 sec. - In propane a similar density-effect is found.

The hexagonal lattice constants a, c of β-O 2 and Ar/β-O 2 mixtures were measured in the range 32 ... 4 °K by electron diffraction. A sharp maximum of c accompanied w ith a sudden decrease of the mean crystal size by more than an order of magnitude at 18 °K was found for im pure β-O 2 . The transform ation β-O 2 → "am orphous" O 2 which takes place on electronirradiation of β-O 2 below 17 °K may therefore be simply a breaking up of the impure O 2 -crystals into tiny pure crystals caused by mechanical stress due to built in foreign molecules.

Molecular hydrogen was excited by selective absorption of ultraviolet radiation of appropriate wavelength into the vibrational levels ν′ 3, 4, and 5 of the electronic D ( 1 II u )-state. For the radiation bandwidth chosen the molecule was only formed in the rotational levels J = 1 and 2 of the R-branch. The excited molecules decay by predissociation into two hydrogen atoms of translational energy which is equal to one half of the difference between the excitation and dissociation energies. One of the atoms is formed in its first excited state. The formation of the excited species can be proven by its fluorescence (Lyman α -radiation). As a result the measurements show, that the excited atoms are all in the metastable 2S-state and not in the short-lived 2P -state. Without electric fields these metastable atom s loose their excitation energy in collisions with the surrounding hydrogen molecules. One part (a) follows an induced transition to the electronic ground state by the emission of Ly α -radiation (1216 Å), the other part (b) is transformed to products or undergoes an energy transfer process without emitting Ly α -radiation. If a quenching field is applied spontaneous emission will compete with collisional deactivation, which allows the deactivation cross sections to be calculated. These cross sections are between 50 and 100 Å 2 (a) and about 50 Å 2 in case (b). In case (a) the collision cross section increases with the velocity of the particles whereas in case (b) a constant value was found.

Massive potassium -layers are deposited by evaporation in ultrahigh vacuum upon a glasssubstrate. The photoelectric sensitivity of these very pure layers, which are polycrystalline, liquid or monocrystalline (solidified from melt), is measured in the spectral range from 380 nm to the threshold wavelength. From this the work function is determined by the Fowler-theory. The adaptation of the experimental points to the theoretical Fowler-curve succeed also in the short wave region of the spectrum, if the photoelectric sensitivity is referred to the light energy absorbed within the exit dephts of photoelectrons. The Fowler equation is also available to the liquid phase. At the phase-change liquid-solid and solid (solidified)-liquid, respectively, no measurable alteration of the work function am ounting to 2.30 ± 0.02 eV occurs. A significantly higher work function of 2.39 ± 0.01 eV, however, is obtained on polycrystalline potassiumlayers. consisting of (110)-planes. The quantum yields and the quantity constant of about 2.3 · 10 -11 electrons/(photon degree 2 ) calculated from the Fowler-equation do not show any discontinuity at the melting point. Within the measuring accuracy they are also independent of the crystalline constitution of the potassium.

Die allgemein übliche Charakterisierung gewaschener Graphit-Eisen(III)-chlorid-Einlagerungsverbindungen nach ihrem Eisenchloridgehalt allein ist unzureichend, weil die aus gesättigten Verbindungen eluierte Eisenchloridmenge eine Funktion der Teilchengröße der Graphitkristalle ist. Diese Ergebnisse stützen die zuerst von Rüdorff und Landel beschriebenen Anschauungen, daß nach Eluieren des Eisenchlorids in den Randzonen die Graphitstruktur zurückgebildet wird. Dadurch wird das Kristallinnere vor einem weiteren Lösungsmittelangriff bewahrt, und die Struktur der ersten Verbindungsstufe bleibt dort erhalten.. Der bisweilen beschriebene Unterschied zwischen Natur- und Synthesegraphit im Eisenchlorid-Maximalgehalt gewaschener Einlagerungsverbindungen läßt sich ebenfalls durch die Teilchengrößenfunktion erklären und braucht nicht auf die unterschiedliche Herkunft der Graphite zurückgeführt zu werden. In dem vom Lösungsmittel nicht angegriffenen Verbindungskern sind ca. 40% der verfügbaren Schichtfläche nicht mit Eisenchlorid besetzt. Dichtemessungen und Röntgen-Untersuchungen ergeben, daß die Kohlenstoffschichten in diesen Bereichen nicht aufgeweitet sind, sondern den gleichen Schichtabstand wie der reine Graphit aufweisen. Aus der Linienschärfe der Röntgenreflexe folgt, daß die Ausdehnung der kohärenten Bereiche mit Graphitstruktur in c-Richtung im Mittel über 800 Å beträgt. Der für Graphit typische anomale Diamagnetismus tritt bei den Einlagerungsverbindungen trotz dieses Graphitanteils nicht auf.

Mit Hilfe der Elektronenbeugung an Gasen wurde die Molekülstruktur des Cyclobutadieneisentricarbonyls bestimmt. Übereinstimmend mit NMR Messungen in Lösungen ergibt sich für den Cyclobutadienring eine quadratische Struktur. Die wichtigsten geometrischen Parameter sind: C Ring -C Ring = 1,440 ± 0,007 Å , Fe-C Ring = 2,053 0,004 Å, Fe-C carbonyl = = 1,780 ± 0,004 Å, C carbonyl - O = 1,148 ± 0,004 Å, ∢ CcarbonylFeCcarbonyl = 98,1 0,8°. Die Wasserstoffatome des Cyclobutadienringes sind um einen Winkel von 8,6 ± 6,3° zum Eisen hin geknickt.

The half-life of 210 Pb has been calculated from measurements of the specific activity and the 210 Pb-concentration of a 210 Pb-solution. The specific 210 Pb-activity was determined by measuring the daughter product 210 Po using an α-spectrometric isotope dilution method with 208 Po as tracer. The 210 Pb-concentration was measured by mass-spectrometric isotope dilution analysis. A half-life of 22.26 ± 0.22 ( = 2 σ) years has been obtained.

Extensive paramagnetic susceptibility studies between liquid helium and room temperature have been carried out on polycrystalline samples of the two organometallic Np(IV)-complexes Np(C 5 H 5 ) 4 and (C 5 H 5 ) 3 NpCl. From a combined interpretation of the corresponding 1/ Xm -vs-T-and μ 2 eff -vs-T-curves, respectively, is suggested that, in accordance with the tetrahedral molecular symmetry to be assumed for Xp(C 5 H 5 ) 4 , a cubic Τ 8 crystal field level should lie lowest in this compound. The zero field splitting is apparentlv smaller th an 5 cm -1 .

ZnSb zeigt wie einige andere Halbleiter bei tiefen Temperaturen die eigenartige Erscheinung einer negativen magnetischen Widerstandsänderung, d.h. eine Abnahme des elektrischen Widerstandes im Magnetfeld. Die Größe dieses Effektes wurde in Abhängigkeit vom Magnetfeld H und von der Ladungsträgerkonzentration p untersucht. Für das Auftreten der Erscheinung können Grenzen in bezug auf p und H angegeben werden. Die Messungen an einkristallinem und polykristallinem Material zeigen unterschiedliche Resultate. Die Ergebnisse werden vor allem in bezug auf verschiedene Komponentenzerlegung in positive und negative Anteile der Widerstandsänderung diskutiert.

Es wurden Mischkristalle der Zusammensetzung Zn 0.5 Cd 0.5 Sb durch Zonenschmelzen hergestellt. Die so erhaltenen und durch In-Dotierung n-leitenden Proben erwiesen sich in den elektrischen Eigenschaften als wesentlich stabiler als polykristallines Material, was auf eine Beteili­gung von Korngrenzen bei den n-p-Umwandlungserscheinungen dieser Mischkristalle hindeutet. Nun möglich gewordene Messungen der elektrischen Transportgrößen (elektrische Leitfähigkeit, Hall-Effekt, Thermokraft, transversaler Nernst-Ettingshausen-Effekt) in Abhängigkeit von der Temperatur ergaben, daß bei Zimmertemperatur n-leitende Proben bei tiefen Temperaturen p-Leitung zeigen. Die Ergebnisse werden diskutiert.

The rotational transitions J = 1 → 2 and 2 → 3 were measured in 115 In 19 F. From these spectra the following molecular parameters have been determined: the Dunham-coefficients Y 01 , Y 11 and Y 02 , the quadrupole coupling constants, eqQ, in the ν = 0 and v = 1 vibrational states as well as the spin-rotation coupling constant c In .

A formula is derived for the calculation of the centrifugal distortion constants τ αβγδ in the case where the vibration problem is solved by using dependent internal symmetry coordinates. We have calculated the τ’s and the D's with this new formula for a model of cyclopentene with a planar carbon ring (Point group C 2v ). The τ-values calculated are (in units 10 85 sec 2 (gem 2 ) -3 ): τ xxxx = - 5.27, T xxyy = 1.48, τ xxzz = - 0.96, τ yyyy = - 5.52, T yyzz = - 1.22, T zzzz = - 0.63, τ xyxy = - 2.85, T yzyz - 0.07, T zxzx = - 0.07. The D's calculated are (in units 10 -8 cm -1 ): D J = 7.9, D K = 5.1, D JK = - 12.1. The values for D J and for D JK are within the accuracy of the published experimental values. Thus, cyclopentene is the first ring molecule, the centrifugal distortion constants of which could be calculated.

A theoretic treatment is given for the planar ethylene-like (D 2h ) model, the corresponding twisted (right-angled) model (D 2d ), and the general case of D 2 symmetry. The correlations between the various symmetry species which pertain to the molecular vibrations of the considered models are explained. Complete sets of symmetry coordinates are proposed. The G matrix is given for the general D 2 model. Also the various types of Coriolis couplings are discussed, including the relationships between C α elements involving the degenerate a and b species in the twisted (D 0 ) model. Some of the most im portant C α elements are listed. Sets of symmetry coordinates are also given for the allene (D 2d ) and butatriene (D 2h ) type models.

In this contribution selection rules for rotation torsion transitions are considered for completely asymmetric molecules. Quade gave two descriptions of this type of molecules resulting in two different invariance groups of both Hamiltonians lead to indentical selection rules.

Short-lived radionuclides have been measured in fallout of Chinese nuclear tests. The measured yield ratios of the nuclides 95 Zr, 111 Ag, 115 Cd, 156 Eu, 237 U and 239 Np have been corrected for fractionation effects and compared to calculated ratios. Free parameters of the calculation such as most frequent neutron energy, time integrated neutron flux, and fission material were ad­justed by means of a least square criterion. For the tests 2, 3, 5 and 7 the most frequent neutron energy was found to be 5 keV. The corresponding Maxwellian neutron fluxes were within 10 21 and 10 24 n/cm 2 . In addition, 14-MeV neutron fluxes within 10 19 and 10 22 n/cm 2 had to be assumed. The analysis yields as average of the converted fission material a mixture of 235 U and 238 U with 7-99% of 235 U. - The fractionation of 140 Ba in surface bursts corresponded to that in air bursts.

It is shown by calculations (classical treatment) that fine structure is to be expected in angular distributions of channeled particles. This fine structure will be superimposed on the normal smooth channeling line profile. It is due to coherent channeling. It requires high angular resolution and thin single crystals of uniform thickness for experimental detection. The fine structure pattern is sensitive to the details of the crystal potential.

The theoretical treatment of a number of stationary kinetic phenomena requires the solution of a system of linear equations. An algorithm is described which enables an algebraic solution to be found by means of a digital computer using probably a minimum length of calculation time. This algorithm is derived mainly from arguments based on the theory of graphs; its essential feature is the use of numerical operations on the indices of the coefficients of the equations. The algorithm is illustrated in terms of a special model of the membrane.

Das F 2 wurde unter Berücksichtigung aller Elektronen mit dem ALLGEMEINEN PROGRAMMSYSTEM/SCF-MO-LC (LCGO)-VERFAHREN für einige Kernlagen behandelt. Im Energieminimum ergab sich eine Gesamtenergie von - 198.1137 at. E., ein Gleichgewichtsabstand von 1.408 Å sowie eine Ionisierungsenergie von 17,40 eV. Die Schwingungsfrequenz wurde zu 1118 cm -1 berechnet. Nach einer Abschätzungsformel ergab sich weiter die Bindungsenergie des F 2 -Moleküls zu 1,62 eV (Dissoziationsenergie 1,54 eV). The F 2 -molecule has been calculated by means of the GENERAL SCF-MO-LC (LCGO) PROGRAM SYSTEM for some nuclear configurations. In the minimum energy there was found a total energy of -198.1137 atomic units, an equilibrium distance of 1.408 Å as well as an ionization energy of 17.40 eV. The frequency of vibration gave 1118 cm -1 . After an estimation formula the bond energy for the F 2 -molecule led to 1.62 eV (dissociation energy 1.54 eV).

Das bei Normaldruck und unter 375 °C stabile a-Barium besitzt ein kubisch-raumzentriertes Gitter. Zwischen 350° und 380 °C erfolgt eine allotrope Um­ wandlung zum /^-Barium von bislang unbekannter Struktur 1. Kleine Partikel mit Radius unter 5)jl lassen sich ent­ weder durch Strahlungskühlung oder Wärmeleitung rasch abschrecken, so daß die metastabile Modifikation einfriert, oder bei der Analyse durch einen Elektronen­ strahl bis in den Stabilitätsbereich dieser Modifikation erhitzen. Dies wird mit dem folgenden Ergebnis illu­ striert, das an metallischen Partikeln aus einer Zwei-phasen-Strömung ins Vakuum gewonnen wurde. Gepreßte Ba-CuO-Mischungen (in molarem Mischungs­ verhältnis 2,5:1) wurden in Verbrennungsgefäßen von 50 cm3 gezündet, die mit einer Wolframdüse versehen waren. Die Reaktionsprodukte (Tröpfchen von Ba, BaO, Cu und gasförmiges Ba mit N2 bei 2500 °K) strömten innerhalb von 300 msec in eine Vakuumkam­ mer von 20 m3 bei einem Anfangsdruck von 10-5 Torr. Die Teilchen dieser Zweiphasen-Strömung wurden mit einem besonderen Auffanggerät 2 in einem Abstand von 330 cm von der Düse gesammelt. Um Oxidation der Teilchen zu vermeiden, wurde das Auffanggerät nach dem Experiment mit Argon auf einen Druck P

An flüssigen Kupfer-Mangan-Legierungen mit einem mittleren Gehalt von 2,44 [bzw. 5,1] Gew.-Proz. Mangan wurde bei 1110°, 1150° und 1250 °C der chemische Diffusionskoeffizient von Mangan bestimmt. Für die Legierung mit 2,44 Gew.- Proz. läßt sich der Diffusionskoeffizient durch die Gleichung beschreiben. Die Legierung mit 5,1 Gew.-Proz. ergab bei 1150 °C einen Wert von D = 6,2 · 10 -5 cm 2 /sec. Der Diffusionskoeffizient erweist sich als schwach konzentrationsabhängig.

Quasi-Darkén Relations. In binary mixtures with the self­friction coefficients r 11 and r 22 and the inter-friction coefficient r 12 , interpolations of the type 2 f (r 12 ) = f (r 11 ) + f (r 22 ) cor­respound to Quasi-Darkén relations, If f = In, the Darkén relation is obtained.

Die Ionen H~ und 0~ sind bisher als einzige negative Bruchstücke beim Elektronenbeschuß von Wasser be­ obachtet worden. OH-fand man als sekundäres Pro­ dukt der Reaktion H" + H20 — > H2 + OH" 2. Bei Ver­ suchen mit einem CH4-Atlas-Massenspektrometer mit Fox-Ionenquelle ließ sich OH-als primäres Ion mit etwa 10-mal kleinerer Intensität als 0~ nachweisen. Abb. 1 und 2 zeigen die Ionisationsausbeutekurven beider Ionen. In Abb. 1 wird außerdem die Ausbeute­ kurve für SF6" aus SF6 gezeigt, um ein Maß für die Auflösung der Apparatur zu geben. Die Intensität aller Ionen war dem Gasdruck proportional. Die O'-Kurve stimmt mit der von anderen Autoren gemessenen hinsichtlich ihres allgemeinen Verlaufes überein. Das erste Auftrittspotential beträgt (6,4+ 0,1) eV. Dieser Wert liegt um 1,5 eV höher als von C o m p ­

Für Untersuchungen in Atmosphären mit definierten D20-Gehalten benötigten wir Angaben über Dampf­ drücke gesättigter Salzlösungen in D20. Während für gesättigte Salzlösungen in H20 aus der Literatur viele Angaben zu entnehmen sind x, konnten wir für D20-Lösungen keine Daten finden. Wir haben daher mit einer manometrischen Me­ thode 2' 3 die Dampfdruckdifferenzen von gesättigten Salzlösungen in H20 und D20 zwischen -flO°C und + 40 °C gemessen. Die Differenzmethode bietet einer­ seits apparative Vorteile gegenüber einer direkten Dampfdruckbestimmung, andererseits benötigen wir für unsere spezielle Problemstellung die Dampfdruck­ differenzen mit möglichst großer Genauigkeit. Aus die­ sem Grunde wurden die absoluten Dampfdrücke für D20-Lösungen auf der Grundlage der Literaturwerte für gesättigte Lösungen in H20 beredinet. Die ge­ samte Apparatur befand sich in einem Thermostaten (±0,1 "C). Als Manometerfüllung diente Diffelen (Leybold). Die Lösungen wurden mit getrockneten und kristallwasserfreien Salzen (p. a.) angesetzt. Vor jeder Meßserie wurden Lösungen und Mano­ meterfüllung sorgfältig entgast sowie die gesamte Ap­ paratur ca. 15 min evakuiert. Mehrfache Kontrollmessungen bei allen Salzlösun­ gen ergaben, daß die Meßwerte innerhalb eines Berei­ ches von maximal ±0,05 Torr reproduzierbar waren. Torr

A counting gas has been tested which can be used for α-proportional counting at high temperatures (700 °C). A mixture of 13 parts Ar and 1 part N 2 , is stable at a pressure of 700 mm Hg. The counter has a plateau of more than 100 Volts with low slope. The stability which has been tested for a period of 55 hours and 10 8 counted pulses proved to be satisfactory.

A method to estimate the principal polarizabilities of π-electron clouds embedded in a continuous uniform medium of dielectric constant ε 0 = 2 is described and applied to deter­mine these polarizabilities in the case of aromatic hydro­carbons.

Anx and B12* = B12 B i, where Anx and Bt refer to the solvent medium, then after equating (8) and (9) the final Eq. (11) remains unchanged. d and y were calculated in the cases of benzene, naphthalene, phenanthrene and diphenyl using the experimental data6' 7 of Bx2 and n12 obtained in n-heptane solutions at various values of w2 . Since (9d is zero for non-polar molecules considered here 8, 0 P may easily be evaluated from (11). by is defined arbitrarily to be the principal polariza-bility perpendicular to the molecular plane. The elec­ trostatic polarizabilities aa, ap and a■ ■ are assumed to be the same as the electro-optical polarizabilities ba, bß and by 9. Thus, in (5) there remain three unknowns ba , bß and by to be determined and to calculate this unknowns, besides (5), two further equations are re­ quired. One further equation is supplied from (1). Intro­ ducing into this equation v2 = (N\ w2) / (M2 v12) and Eq. (10) for solutions restricted to low concentration one obtains ba + bß + by — 3 Mo vt nt 2 7i N \ (12)