Burhop and others (Proc. Roy. Soc. 165 (1938), 116) have reported that the slow neutrons which produce gamma-rays in Ag contain a group of 0.5eV in energy, being far smaller than that of the neutrons which make Ag radioactive. But this result contradicts the generally accepted mechanism of the production of gamma-rays by slow neutrons and the facts that Ag has only two stable isotopes and shows only two periods of radioactivity 22^s and 2.3^m when bombarded by slow neutrons.
In the present experiment the energy of the gamma-ray producing slow neutrons was compared precisely with that of the radioactivity producing neutrons by the boron absorption method. There was no evidence that both neutrons differ in their energies, contrary to the result of Burhop and others

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A one-dimensional crystal is considered in which interatomic forces of a special type exist between nearest neighbours The exact partition function of sucn a system is approximated by numerical calculations and the relation between the force constants and melting point is obtained. In the last section, this method is compared with other approximation methods

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Coeflicient of viscosity η of the simple gas and the thermal diffusion ratio of the gaseous isotope mixture have been calculated as iunctions of temperature, according to the theories of Enskog and Chapman, assuming the intermolecular interaction potential of Sutherland's type
U(r)=∞, r<a; U(r)=μ/r⁶, r>a.
The assumption usually made that μ is small is not introduced, and a²/√<MkT>=η and kT (thermal diffusion ratio) are obtained as numerical functions of ζ=μ/2kTa⁶. Quantum correction is not taken into account in the present paper, so that the results are not directly applicable to He and H₂. The results are tentatively applied to discussions of viscosity of N₂, CH₄, Ne and to isotopic thermal diffusion of CH₄ and Ne. Tempersture dependence of viscosity of N₂ and CH₄ is represented fairly well by our formula, with suitable choice of values of force parameters a and μ. These parameter values are in satisfactory agreement with those obtained from the second viral coefficient, the agreement being much improved by the use of our “exact” formula instead of the usual approximate one (Sutherland formula) for the viscosity coefficient. In case of Ne, the result is less satisfactory, and the possibility of explaining the data for heavier inert gases by taking repul ion of finite softness is discussed. Finally, the temperature dependence of isotopic thermal diffusion ratio of Ne and CH₄ is calculated with the use of parameter values determined from viscosity and is compared with experimental results of Nier

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§6. In the present paper, the writer has calculated the stream function for the compressible fluid flow past a circular cylinder and the expression correct to the order of M⁴ has been obtained, where M is the MACH number for the undisturbed flow. Using the results obtained, we have then drawn several stream lines and thus we have discussed, in a rather brief manner, the effect of compressibility of the air upon the flow pattern around the circular cylinder

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§6. In the present paper, a new method of successive approxiations is daveloped for dealing with the two-dimensional subsonic _??_w of a compressible fluid. Based on the use of complex variables, _??_is method enables any degree of successive approximations to the _??_locity potential and the stream function to be obtained simultaneously _??_ performing a single quadrature. Therefore, the manipulation of infinite series which seems to be inherent in the well-known method of POGGI in its original form can be avoided, and so the analysis becomes much clearer. The merit of using complex variables may also be seen in the fact that the moment of the fluid pressure acting on an arbitrary cylinder placed in a uniform stream can be readily calculated if either the velocity potential or the stream function is expressed in terms of z and z, with the aid of a general theorem which will be given in a subsequent paper(8). Moreover, the method is also applicable to the flow in a multiply-connected region, such as the flow past a cylinder in a channel.
Finally, the method is illustrated by taking the case of a uniform flow of a compressible fluid past a circular cylinder, with circulation round it

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Diffraction of proton beams by crystal surfaces is investigated with the photographic method. Patterns obtained may be classified into three kinds from their structures. Patterns of the first kind are similar to those obtained by Dempster(1), while the second kind patterns are composed of two or several lines arranged at nearly equal distances, which are in some cases nearly equal to those expected for the diffraction by the crystal. In one pattern of the third kind, two lines are observed in superposition to the continuous background due to the scattering of the crystal, and the lines are explained as the reflection and the diffraction from the surface. The patterns of the second kind, however, are ascribed to the charging up effect of the crystal

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Die Umwandlung des Ammoniumchlorids bei 243°K wird gedentet als ein Übergang zwischen Ordnung und Unordnung in den Orientierungen der Ammoniumionen Es wird nämlich zunächst angenommen, dass jedes Ammoniumion zwischen zwei möglichen Orientierungen (Fig. 1) pendeln kann, und unter dieser Annahme wird eine Theorie anfgestellt, die der WEISSschen Theorie äquivalent ist. Die Umwandlungstemperatur, ihre Druckabhängigkeit, die Druck- und Temperaturabhängigkeit des Volumens und der Verlauf der spezifischen Warme bei konstantem Volumen werden berechnet und mit den Messungen verglichen. Die Übereinstimmung ist ordnungsmässig gut, nur dass in Wirklichkeit die Ordnung unterhalb der Umwand'ungstemperatur rascher einstellt als nach der Theorie. Es wind dann das mittlere Feld für ein jedes Ammoniumion berechnet und die Richtigkeit der anfänglichen Annahme bestätigt. Dabei stützen wir uns auf die Berechnung der zwei Arten des Potentials: das elektrostatische Gitterpotential für die Wasserstoffatome eines Ammoniumions und das Abstossungspotential zwischen ihnen und den benachbarten Chlorionen. Das Feld für einen NH-Arm wird annähernd durch eine lineare Kombination der drei Kugelfunktionen Y₃, Y₄ und Y₆ dargestellt, wobei Y₃ die Symmetrie des Tetraeders besitzt und Y₄ und Y₆ die Symmetrie des Oktaeders besitzen. Es ergibt sich aber, dass die anfängliche Theorie in dem Punkt eine Abänderung erfahren muss, dass die Schwingung des Ammoniumions um jede Gleichgewichtslage, für welche eine quantenmechanische Behandlung verlangt ist, in Betracht gezogen wird. Es wird eine Theorie entwickelt, die dieses Sachverhältnis berücksichtigt, und die Umwandlungstemperatur aufs neue gerechnet. Es wird auch die Unrwandlung des Deuteroammoniumchlorids diskutiert

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The Schrödinger equation for an electron in the lattice of the alloy was solved exactly, assuming as the form of the periodic potential a series of rectangular barriers whose intervals are the same alternately. It was found that some intervals of energy values which are allowed for electrons in the monoatomic lattices of the constituent metals are not allowed in the lattice of the completely and partially ordered alloy

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In the positive column of the carbon arc at reduced pressure of air atmosphere, CN and CO molecules are produced and emit intense band-spectra. Their intensity distributions were measured and the rotational temperatures, determined.
In spite of the same discharge conditions, the rotational temperatures were found to be widely different; that is, T'(CN)=5200°K and T'(CO)=1600°K.
The discrepancy was discussed from the view-point of mechanism of molecular formations

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We derived the T=V/V₀, relation at zero pressure for molecular crystals by taking the Einstein model and assuming the interatomic potential form of Lennard-Jones type, and found that the curve has a maximum of T, which may naturally be supposed to be intimately connected with the melting temperature. Calculated actually with several substances, the maximum values were found to lie fairly near the melting temperature. But if we regard it as a melting temperature, we go too far. To deal with the melting process rigorously we need to know the free energy of the liquid state also besides that of the solid state, but in spite of various attempts satisfaitory results are not yet obtained. The comparison of T_Max with the melting temperature is summed up in Table V

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§14. In this paper, the behaviour of flow at considerable distances from a cylinder of arbitrary cross section placed in a uniform flow of a compressible fluid is considered, primarily with a view to finding general formulae for the lift and moment of the cylinder.
In the first place, based on the method of successive approximation recently proposed by the present writer, the most general expressions are determined for the velocity potential and stream function for flow under consideration (see (5•6) and (5•7)). Thus, it is found that theassumptions concerning the velocity field, which formed the basis of the analyses of GLAUERT and of BATEMAN in extending the well-known KUTTA-JOUKOWSKI theorem to the case of a compressible fluid, are too special in one case and too general in the other to be in accordance with the actual state of affairs.
In the next place, the explicit forms of the asymptotic expressions for the velocity potential and stream function are exactly determined to the order of 1/r. As an example, it is confirmed that the velocity potential for the flow past a circular cylinder with circulation round it, which has recently been obtained by HASIMOTO and SIBAOKA correctly to the order of M⁴, M being the MACH number of the undisturbed stream, has in fact the asymptotic form predicted by the present analysis.
The asymptotic expressions thus found are then used to obtain the general formulae for the lift and moment, of which the first is naturally just the same as GLAUERT'S extension of the KUTTA-JOUKOWSKI theorem. The formulae for the moment, (12•13a) and (12•13b), express a rather surprising fact that determination of the moment of a cylinder requires only the knowledge of the coefficient of 1/z in the asymptotic expansion, in descending powers of z and z, either of the velocity potential Φ(z, z) or of the stream function Ψ(z, z), where z=x+iy, z=x-iy. Finally, it is shown that the writer's previous formula for the moment, (1•8), can be deduced from the newly found formula as a first approximation, namely, by retaining only the quantities of the order of M²

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Combining statistical-mechanical relations with the theorem from thermodynamics that the total free energy of a continuous medium at a given temperature should take a minimum value if there is no external work done on the system, Thomas-Fermi's equation at any temperatures is derived. The main space of the paper is devoted to a problem to find a quantity corresponding to the thermodynamic potential per electron and to show that it is constant everywhere in the medium when there is an electric field produced by the charged particles themselves

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Die Ordnung-Unordnung Umwandlung in der Lennard-Jones und Devonshireschen Theorie des Schmelzens ist näher betrachtet. Obwohl die Molekularanordnung in einer Flüssigkeit analog dem Hypergitter in der Theorie der Legierung behandelt werden kann, ist ihre Theorie, wegen der besonderen Stellung der “Null” Moleküle, quantitativ nicht befriedigend (§2.). Es ist versucht eine modifizierte Theorie zu konstruieren (§3.)

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The sodium line reversal method of determining the temperature of a flame was applied to the engine flame. A special cylinder, with two quartz windows, that would cause a beam of light from the source to pass through the combustion chamber, was constructed. Upon adding a small quantity of sodium ethylate to the fuel, the temperature of the engine was compared with the colour temperature of the light source. A tungsten pointolite, a tungsten lamp, and a carbon are lamp were used as the light source.
The D-line intensity of the flame was measured by a photoelectric cell. By comparing the D-line intensity with its temperature, it was found that the temperature measured by this method was the correct temperature of the flame.
The spectrum in the visible region of the engine flame consisted of CH 4300Å, CC swan bands, and the continuous bands. The spectra obtained at various crank angles showed that as the crank angle proceeds, the CH and CC bands became fainter, and that the tem erature in the cylinder was not uniform.
The maximum temperature at various air fuel ratios was measured with the engine running at 800r.p.m.. Although the correct air fuel ratio in the fuel under test was 13.8, the temperatute was always maximum at 11.5, which was higher than that obtained by Hersley and Panton and nearly agreed with the calculated value

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The harmomic analysis of a quantity Γ irregularly fluctuating about zero is investigated, and it is found that the mean value of the square of the amplitude of the k-th component is given by
Aκ²=Bκ²=2/τ1/Γ²Θ,
where τ is the whole time interval and Θ is a measure of the correlation between Γ at different time points, defined in the text. The analysis of the derivatives of Γ are also discussed

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Regarding the axially symmetrical jet, similar to the ease of plane jet. we must consider that in the expression of the shearing stress τ the second variation rate ∂²n/∂r² of the velocity component u is more predominant than the first variation rate ∂u ∂r for the points whose radial distance r is very small. If we suppose therefore that in the jet from the circular mouthed nozzle whose diameter is Dthe shearing stress τ assumes the following form.
τ=-ρl²∂u/∂r={(∂u/∂r)²+l^*2(∂²u/∂r²)²}^1/2
where both l and ^l* are proportional to the special nozzle distance x, that is,
l=l_??_, l*=l_??_,
the velocity components u and v can be represented form the standpoint of momentum transfer theory by
u=A/zΦ(λ), v=A/σx[λΦ(λ)-F^*(λ)/λ]
at the point defined by λ=σr x in the region where the central velocity U=Ax is inversely proportional to x=x^*+x₀, x^* being the nozzle distance of the observing point. The function Φ and its integrated function
F^*=∫λ0λΦ(λ)dλ
are the functions of λ solely, and can be uniquely determined only by giving the value of μ. For the practical use, it is sufficient to take
Φλ=c^-1/2λ2[1-(5/64-1/32μ)λ⁴]
As to the central velocity U, we may take after Ruden's experiment
x₀=5.18, U=6.45U₀D,
U₀ being the mouth velocity of jet.
The jet is limited at λ_s=σr_s/x=3.418, when we admit μ'=2.0. From the experimental data, we many take 1/σ=0.0687, then the jet radius r_s is given by
r_s=0.2332

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Heavy atomic nuclei ate treated under the assumption that each particle in them is vibrating in a cell formed by its neighbours. An average interaction potential, similar to that acting between two atoms or molecules, was assumed to exist between any two nuclear particles and the liquid theory of Lennard-Jones and I evonshire was used to calculate the binding energy and the radius of the nucleus. As far as the order of magnitude of the quantities employed and obtained is concerned, the results of the calculations agree with experiment and do not contradict with the data usually obtained from light nuclei

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In the present paper, theoretical study is made on the force and moment of the fluid pressure acting on an elliptic cylinder which moves in a flow of a perfect incompressible fluid having uniform vorticity. Making use of the pressure integral which is valid for flows having uniform vorticity, general expressions for the force and moment acting on the elliptic cylinder in a flow, of which the stream function when undisturbed is an integral expression of the second degree with respect to the coordinates X and Y, are obtained. Applying these formulae to a flow of uniform shear which has been investigated by Ray, it is found that his expression for the moment is erroneous. Furthermore, writing the equations of motion for the cylinder moving freely in a flow of uniform vorticity, some special solutions of these equations are obtained. Lastly, applications to the aerodymical problems are made and the lift and moment on a plane aerofoil placed in a uniform shearing flow or in a flow of uniform rotation are calculated by determining the value of the strength of the additional circulation so as to make the fluid velocity at the trailing edge finite applying Joukowski's assumption in the aerofoil theory

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The rapid radial diminution of the intensity of the sun's magnetic field is treated according to the classical free electron theory of diamagnetism

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Using the general formula for the configurational free energy of binary alloys, the magnetic and therma properties of the Heisenberg model of antiferromagnetics are investigated as far as possible in analogy to alloy theories. Main features of the results obtained are as follows:
(1) If the number of nearest neighbours, which shall be designated by z, is equal to 2, the magnetic suseeptibility-vs.-temperature curve has no critical point.
(2) If z≥3, the antiferromagnetic Curie temperature T_c is predicted.
(3) In the absence of external field, the expressions for the dependence of the long-distance order of spins on the temperature are proved to become identical in form with those for the dependence of the spontaneous magnetization of ferromagnetics on the temperature which have been given in our foregoing paper(1).
(4) In the absence of external field, the specific heat anomaly-vs.-temperature curves for antiferromagnetics exactly coincide with those fur ferromagnetics

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Die Beziehung zwischen der Stromstärke bei einer Geisslerentladung und der Intensitätverteilung in die Rotationszuständen des OH Moleküls für 3064Å Band photometrisch verfolgt und die Bedeutung derselben diskuriert. Die Abhängigkeit der Emissionsintensität derselben Bandenlinien von der Stromstärke wurde auch photometrisch bestimmt. Daraus erhellt, dass das ganze Spektrum OH Bandes bei 3064Å seine Entstehung der von der Dissoziation Wessermoleküls begleitete Emission verdankt.
Es ist mir eine angenehme Pflicht, Herrn Prof. Dr. T. Tanaka der Kaiserlichen Universität zu Tokio für das Interesse an dieser Arbeit und manche wertvolle Ratschläge meinen herzlichen Dank auszusagen. Herrn Pref. Z. Koana und Herrn Y Mitunobu bin ich für ihre freundlichsten Unterstützung, die sie mir bei der Photometrie gegeben haben, zum grossen Dank verpflichtet.
Ich möchte auch Herrn Prof. S Ueno hiesiger technischen Hochschule für seine wertvellen Diskussionen meinen besten Dank aussprechen. Es soll hier noch hinzugefügt werden, dass diese Arbeit teilweise mit Hilfe der von dem Unterrichts-ministerium gestifteten Pramie zur Förderung der Naturwissenschaften ausgeführt wurde

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Es wurden einige Versuche über die Beugung von Lieht an Ultrasschallwellen bei schiefem Einfall des Lichtes auf die Schallwellenfront ausge führt mit den Ultraschallfrequenzen von 1.096×106-1.395×106 Hz in einer Flüssigkeit (Transformatoröl) mit der Ultraschallgeschwindigkeit van ca. 1500m/sec und unter den Schallfeldtiefen (Längen der Lichtwege im Schallfelde) von 50-60mm. Die Beugungsspektren wurden aufgenommen unter verschiedenen Einfaliswinkeln und die Intesitätsverteilungen des sebeugten Lichtes über die Ondnungen wurden in einer photographisch-photometrischen Weise gemessen. Die Resultate zeigten die periodische Veränderung der Beugungsspektren mit dem Einfailswinkel in quantsta'iver Übereinstinummg mit dem Resultate der Raman-Nathschen Theorie bis auf den U_??_rschied, daß es experinentell nicht die vollständige Verschwindung der Beugungsspektren, sondern nur tiefe Minima der Bengungsspektren bei theoretischen Verschwindungswinkeln gefunden wurden. Auch die Größen der dazwischenliegenden Nebenmaxima stehen mit den theoretisch betechneten Größen in Übereinstimmung. Dagegen wurde gefunden, daß lmi schiefem Einfall eine leichte Unsymmetrie der Beugungsspektren noch bei den hier benutzten, ziemlich nichderen Ultraschall-frequenzen von ungefahr 10⁶Hz auftritt; eine Erscheinung, die außber dem Bahmen der Rannan-Nathschen elementaren Theorie steht und worüber in 2. Mitteilung dieser Arbeit träher die Rede sein wird

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The vibration of a paper or a paper-like diaphragm such as that used in a dynamic speaker is not only rendered irregular due to the non-uniformity of the diaphragm but other factors as well contribute to vibrational irregularity and complication. At frequencies below 200 cycles, a diaphragm behaves in the manner of a piston and vibrates uniformly. Regardless of the irregular distribution of diaphragm vibration, the sound pressure distribution produced by the vibrating diaphragm not only far distant from the diaphram but also very close to the diaphragm is as smooth as the distribution which is produced by a diaphragm vibrating in the mean amplitude; accordingly, the true state of vibration of a diaphragm can not be known by observing the sound pressure distribution very close to the diaphragm. Inasmuch as this partial resonance of a diaphragm has an ill-effect on the character of a speaker or a sound source having a diaphragm in its construction as in a dynamic cone speaker, the knowledge of the state of vibration of a diaphragm is important

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Es wird das Problem behande't, ein labilas, mechanisches oder elektrisches, System, stabil zu machen, indem man ihm ein anderes System ankoppelt, wobei vorausgesetzt wird, dass die Wechselwirkung zwischen beiden Systemen durch einen einzigen vorgegebenen Funkt des ersteren Systems, den man als Treibpunkt bezeichner, stattfindet. Anders ausgedrückt, man steuert das zu stabilisierende System in solcher Weise, dass es bei etwaigen äusseien Störungen bald zu seiner ursprünglichen Gleichgewich slage zurückgeführt wird. Das Problem lässt sich folgendermassen in mathematische Sprache übersetzen:
“Fs sci eine in R(p)_??_0 meromorphe analytische Funktion f(p) gegeben. Man find eine andere Funktion f^*(p) mit derselben Eigenschaft derart, dass sic in R(p)_??_0 nirgends f(p)+f^*(p)=0 genügt, noch mit f(p) gemein-ame Pole besitzt, und fe_??_ner einige Nebenbedingungen eifüllt.”
Die Lösung des Problems lässt sich gewinnen für den Fall, dass j(p) rational ist, indem man mit Hilfe des LAGRANGESchen Interpolation sveriahrens eine explizite Form von f^*(p) erhalt. Für nichtrationale f(p) ist die voilstandige Lösang noch zu wünschen übrig. Einige Beinerkungen bezöglich der praktischen Durchführung der Stabilisierung werden binzogefügt

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