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理论
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In this paper the writer employs complex Riemannian Geometry and defines the absolute interval between two points as consisting of a real part and an imaginary part. Two postulates (I) and (II) are used: the first may be called law of gravitation and electro-magnetism; the second equation of motion. In the absence of electromagnetic phenomena the theory reduces practically to Einstein's theory.

在此文内,作者利用复变来曼几何以宇宙间两点之距离为一实数及一虚数部分相构而成,於此并用假说:一可称为吸力及电磁定律,一为物体行动定律,解释吸力及电磁力之各种现象。在无电磁现象时,此文与爱因斯坦之吸力理论多相符合至於详细情形,容诸续篇。

The gravitational field and the motion of matter in the universe are investigated according to Einstein's field equations and his dynamical equations of motion. In a spatially isotropic and homogeneous space-time continuum it can be shown that up to about 2x10~8 l.y. the following relation holds between spectrum displacement δλ from distant spiral nebulae and their observa-tionally defined distance d,where A is Einstein's cosmological constant. The first term on the right hand side is essentially Hubble and...

The gravitational field and the motion of matter in the universe are investigated according to Einstein's field equations and his dynamical equations of motion. In a spatially isotropic and homogeneous space-time continuum it can be shown that up to about 2x10~8 l.y. the following relation holds between spectrum displacement δλ from distant spiral nebulae and their observa-tionally defined distance d,where A is Einstein's cosmological constant. The first term on the right hand side is essentially Hubble and Humason's velocity-distance relation. The second part is a correction which amounts to 11.5% for d2x10~8 l.y. and hence lies within observational error of the present Mt. Wilson 100-inch telescope. The theory shows that both Milne's recent Newtonian theory of the expanding universe and Lemaitre's interpretation of tha velocity-distance are first order approximations and are valid only within 2xl08 l,y. from our galaxy. The calculation for the phenomsna of nebular recession beyond 2xl08 l.y. to be observed by the 200-inch telescope now under construction according to the present scheme will be presented in the near future.

本文用安因斯坦力学及引力论解释宇宙之膨胀现象。从本文方程式中可证明雷猛德及米恒诸氏之学说皆为本文之近似值,而本文理论之能成立与否须恃200英寸反光镜完成后之观测云。

In the statistical theory of superlattices in binary alloys, the dependence of the interaction energy upon atomic arrangements is taken into account by regarding the interaction energy in Bethe's theory as an average quantity depending on the degree of order and the composition of the alloy. Two simple assumptions concerning the functional relationship of the interaction energy with order and composition are made. The first is a linear function of order and composition. The second is a linear function of the...

In the statistical theory of superlattices in binary alloys, the dependence of the interaction energy upon atomic arrangements is taken into account by regarding the interaction energy in Bethe's theory as an average quantity depending on the degree of order and the composition of the alloy. Two simple assumptions concerning the functional relationship of the interaction energy with order and composition are made. The first is a linear function of order and composition. The second is a linear function of the average numbers of pairs of atoms. The result of applying these assumptions to superlattices of the type AB is that the critical temperature as a function of the composition is a maximum for equal sumber of A and B atoms only when a certain relation between the coefficients in the assumed function is satisfied. In the cass of superlattices of type AB3 the theory of Bragg and Williams is used for simplicity. It is shown that when the composition varies, the maximum of the critical temperature may occur at any desired composition by a suitables adjustment of the coefficients in the assumed functions. There is thus a hope of removing the discrepancy between theory and experiment on this line. The anomalous specific heat at the critical temperature is also calculated for different compositions. In the case of the AB type of superlattices, Bethe's formula for the energy is no longer valid, and in order to calculate the specific heat, an approximate formula for the energy is obtained by analogy with the theory of Bragg and Williams. Finally, the problem of separation into more than one phase is briefly discussed.

在二元合金超格之统计力学理论中,原子间互作用能量,因原子之排列不同而异,其所生之影响,吾人擬於此篇中讨论之。吾人认为有Bethe氏理论中之相互作用能量,实为一平均值,其值因合金之秩序程度及其成分而异。吾人作二简单假设:一设相互作用能量为秩序及成分之线性函数,另一设其与原子对偶之数成线性函数。将此等假设应用於AB类之合金,则必须在所设函数中之系数间,有适当关系,合金之临界温度,始在成分为1:1时,有极大值。在AB_3类之合金,吾人乃应用Bragg及Williams二氏之理论以求简便。於此可证明若所设函数中之系数,可任意调整则所计算出之临界温度之极大值可在任何成分发生。故关於此点理论与实验不合之处,可望解决。又合金之反常比热,亦经算出。在AB类之合金,Bethe氏原来之能量公式不復可用,故另用与Bragg及Williams理论比较而得之公式计算。又关於合金可分为二相或多相之问题,此篇亦大略论及。

 
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