The correlation coefficient (C.C.) between two sets of complex vec_??_ors is here proposed. The method of approach is quite analogous to that which the author has developed in his precious papers(1). The C.C. would be of use, in the field of electric engineering, to analyse statistically electrical networks. He shows furthermore that the Sverdrup's C.C. corrected by the present author(2) is a special case of the C.C. here proposed and the Sverdrup's C.C. can be extended for the multiple correlation by the method of approach here cited

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Aionue eross section of Al. Si, Fe, Co, Cu, Ag, Cd and Pb for gam_??_aray exeitation by fast neutrons of different energies from 2•25 to 2•90 MeV were determined. The neutron emergy was varied by changing the angle φ between the paths of the neutrons and the deuterons in a D D neutron source, and the emitted ganna-rays were measured by a thin wall Geiger-Müller counter surrounded by a sheet of lead 1mm in thickuess. In most cases anomalies were observed in the eross seetion energy eurv_??_s. The absolute magnitude of the cross section σ_γ of Cu at φ=90°(E_n=2•52 MeV) was estin_??_ted to be 2×10^-21cm². From this resalt if can be said that for one ei of medinm weight sucha as Fe, Co. Cu. Ag of Cd a consierable part of the sca_??_tering of D-D nentrons is inelastie.
The posi ions of anonaties observed in σ_γ lie near those of the total cross sections σ_γ observed by Aoki or MaePhail, and the maguitnd s of the variations are almost eqnal in both eases; especially for Pb the variations of σ_γ and σ_t are very similar in the positions of m ximutn and minimum and in the magnitude. At any rate, the anomalies observed in σ_t cannot be considered to be entirely due to elastic scattering

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§11. In this paper, theoretical study is made on the moment of the fluid pressere acting on an arbitrary cylinder which is placed in a uniform subsonie flow of a compressible fluid. On the basis of the method recently proposed by the present author, two general formulae, (5.10) and (7.11), are obtained, which will be of much use for the calenlation of the moment correct to the order of M³, M being the MACH number of the undisturbed flow. Thus it is found that the expresion for the moment which has been proposed by KAPLAN with the aid of the method of POGGI is erroneous in some respects. Further, repeating the analysis as made by KAPLAN, questionable points in his treatment are pointed out and corrected in an appropriate manner

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§9. In the present paper, the theory of the hodograph method as developed recently by TSIEN is applied to the diseussion of the subsonie irrotational flow of a compressible fluid past an elliptie cylinder plaeed at an arbitrary angle of attack. The values of the socalled eritical MACH number for the elliptic cylinder at which the local speed of sound is first attained in the field of flow are calculated as functions of both the thickness ratio of the ellipse and the angle of attack. Also, the moment about the axis of the cylinder of the fluid pressures acting on its surface is caleulated.
The results thus ealculated are compared with those obtained in one of our previous papers as Well as with those given by PRANDTLGLAUERI'S linear theory.
The results of the present investigation seem to show that the theory of the hodograph method as developed by TSIEN can be applied, with satisfaetory approximation, to the calculation of the values of the critical MACH number for the elliptic cylinder placed at an arbitrary inclination, but it is not at all appropriate for the discussion of the moment of the fluid pressures acting on the surface of the cylinder

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Heats of vaporization of several simple liquids, i.e., helium, hydrogen, deuterium, neon, nitrogen and argon are calculated by using the same data by which the writer calculated surface energies in a previous paper. If we use the intermolecular potential
φ(r)=φ₀{(r₀/r)¹²-2(r₀r⁸₁}, φ₀, r₀: constants,
the heat of vaporization for liquids with face-centred cubic type molecular arrangement is given by
Q=N/2φ₀{28•9(r₀/a)⁸-12•1(r₀/a)¹²}-1/2RT,
where N is the Avogadro number, a the distance between neighboring molecules and R the universal gas constant. By comparing this expression with the expression for the surface energy which the writer calculated in a previous paper,
U=2/a²φ₀{3•0(r₀/a)⁸-1•08(r₀/a)¹²},
we find
Q+1/2RT/UV^2/3=2^1/37•2-3•03(r₀/a⁸/3)•0-1•08(r₀/a)⁶=2•3×10⁸,
which is near the ratio calculated from observed values. Connection of this formula with the law of Stefan is also discussed

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Surface tension of liquid is treated by the method of statistical mechanics. By assuming that molecules, which are on the first and second layers from the surface. share free volume while no sharing of free volume exists for inner molecules, temperature dependence of surface tension is calculated theoreticaily and a formula very similar to that of Eotvos is derived. The formula here derived is
σ=U-2•10/V^2/3T,
where σ is the surface tension measured in dynes_??_cm, U the surface energy in ergs cm² and V the molal volume in cm². Calculated values of surface tensions of several simple liqunis are in fairly good agreement with experiment

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Mean square angular momentum <L⁰> of the normal hydrogen molecule and rotational magnetic moment μR have been calculated by use of the simple wave function of form Ψ(1, 2)=2c^{-α(ε₁+ε₂)}cosh β(η₁-η₂), where ξ_ε, η_i are spheroidal coordlinates of the i-th electron (i=1, 2) and α, β are variation parameters, which was proposed by the writer in a previous paper. The obtained results are as follows: <L²>=0•390 a.u., μ_R=0•81 nuclear magneton, while corresponding new experimental value by Ramsey is 0•8787. Then, the relation of rotational magnetic moment and diamagnetic susceptibility has been discussed. In this connection, the numerical value <r²> has been calculated by use of the same wave function yielding a value χ_mol=-3•805×10^-6 c.g.s. Corresponding numerical values of several experiments lie in the range -3•94--5•8 ×10^-6 c.g.s

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The author proposes a test of significance of the additive correlation coefficient (A C. C.) which is reduced to the Fisher's z-test. This is deduced from the fact that the A.C.C. is equal to the arithmetic mean of the square of the Pearsonean multiple correlation coefficient when the normal form of the correlation tensor is used

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(6) From the geometrical dimension of hollow cylinder used for the torsional vibration we can determine four constants (3^*), (2^*), (1^*) and (0^*) and from the logarithmic decrement δ and period T of vibration, as well as from the density ρ of liquid, we can calculate by (18)
(3)=(3^*)η, (2)=(2^*) (B-Aη), (1)=(1^*)/ρ, (0)=(0^*)A/ρ²,
and thence
ξ₁=(2)/2(1)[1-√<1-4(1)(3)/(2)²>], ε(0)ξ³¹/[-(2)+2(1)ξ₁-3(0)ξ²₁].
The viscosity μ of the liquid can be then calculated by
μ=(ξ₁+ε)²/(πρT)

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The orientation of zinc oxide (ZnO) crystals, in the thin oxide layers formed on various faces of zincblende (ZnS) upon heating in air, was investigated by means of cathode-ray diffraction. The surfaces investigated were the {111}-, {111}-, {110}- and {100}-faces in the natural and etched states and also the cleaved {110}-surface. The observed orientations of the oxide on the surfaces of above indices as a whole have the tetrahedral symmetry as of zincblende crystals, if etched with the same etching agent; therefore the orientations on {111} and {111} are not the same. It was also found that the orientation on {111} etched with nitric acid is the same as that on {111} etched with hydrochloric acid, and vice versa. To throw light on this problem, minute faces, i.e. projections and depressions produced by etching, were investigated by the light figure of crystals and by the refraction of cathode-rays on these surfaces. From the results of these investigations, it was concluded that the orientation of zinc oxide crystals on the minute faces of zincblende is determined by the following simple rules:
(1) The c-axiszno is almost parallel to one of the four <111>-axeszns which makes the smallest angle with the surface normal.
(2) An a-axiszno is exactly parallel to a <110>-axiszns.
(3) A simple net-plane of the zinc oxide is parallel to the underlying zincblende surface which may also be a simple net-plane.
It was also concluded that:
(4) A zinc oxide crystal grows more readily when the corresponding <111>-axiszns is directed outward from the surface than in the case of reversed sense

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Die Theorie der Umwandlung von KH₂PO₄ nach SLATER hat eine neuartige Umwandlong, welche wader der ersten noch der zweiten Ordnung ist, mit sich gebracht. Diese Behauptung wäre aber illusorisch, wenn seine Theorie nur eine. Näherung darstellte, denn die genannte Umwandlung geht selbst durch kleine Störung in die gewöhnliche Umwandlung über. Deshalb wird hier versucht, die Verhältnisse in der Umgebung des Umwandiungspunktes genauer zu untersuchen. Das geingt durch Einführung des Begriffes von “Kette, ” indem man jede FO₄-Gruppe als Kreuzung zweier Ketten betrachtet. Dadurch gewinnt man das Ergebnis, daß der Umwandlungspunkt diejenige Temperatur ist, bei welcher die Wechselwirkung zwischen Ketten verschiedener Arten mit derjenigen zwischen Ketten gleicher Art übereinstimmt. Somit wird die Richtigkeit des Ergebnisses SLATERS wenigstens für die Art der Umwandlung bewiesen.
Ferner wird unsere Methode auf die Berechnung der Nullpunkt- entropie von Eis, sowie der Zustandssumme für KH₂PO₄ für beliebige Temperatur (SLATERsche Formel) angewandt

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