古色を帯びた「Meyer の理論」を一般化し改良し更にその根拠を確める. この方法を適当に用いると. Boltzmann-Maxwell の方程式だけに頼るよりも都合のよい事が多い.

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According to the phenomenological theory of viscoelastic materials, the decay of stress, E(t), at constant strain can be represented in terms of the relaxation-time distribution function, Φ(τ), in the form:
E(t)=∫^∞₀Φ(τ)exp(-t/τ)dτ. (1)
It has been formulated by Kuhn et al., Gross, and others that once the distribution function Φ(τ) is determined, other viscoelastic functions and quantities, such as the real and imaginary parts of the complex dynamic modulus, the steady-flow viscosity, and the modulus of delayed elasticity, can be calculated from it. This fact has stimulated interest in methods for obtaining the function Φ(τ) from experimental stress-relaxation data.
In the present paper, simple approximate methods are presented, which are in principle to replace the kernel function, exp(-t/τ), in equation. (1) by a cut-off function K(t, τ) such that
K(t, τ)={1-At/τ(tA<τ), 0(tA>τ), where A is an arbitrary positive constant (see Fig. 2). It can be shown that with this approximation the required distribution function is given by
Φ(τ)=1/A[xd²E(x)/dx²]_x=τ/A (2)
In this paper, the following two cases of A are treated: A=1/2, and A=1. The distribution functions obtained from equation (2) corresponding to these two cases are denoted, respectively, by Φ_F1 and Φ_F2.
The methods are applied to two hypothetical, and one experimental stress-relaxation curues (Examples (i), (ii), and (iii) in section III), and the results obtained are compared with the corresponding exact solutions and with the approximate ones determined by the so-called first approximation method of Alfrey and Doty and by ter Hear's method. In this case, the accuracies of these approximate methods are examined not only from the degrees of agreement with respect to Φ but also from the extents to which the approximate distribution functions obtained satisfy the basic stress-relaxation equation (1). It is found that the present approximate methods, particularity one for A=1/2, give better results as compared with the existing approximate methods in all aspects investigated. It is also realized that considerably large differences in the form of the distribution functions result in comparably small differences in the relaxation curues. This suggests a great difficulty of obtaining the relaxation-time distribution from experimental stress-relaxation data with sufficient accuracy or reliability.

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Atomic distribution functions of liquids are treated by the cell method. A correlation between positions of two atoms in neighboring cells is introduced. By supposing that two atoms, interacting each other, are in an average field due to other atoms, we have derived the form of the first peak of the distribution function.
It is shown that we can derive a general rule for the temperature dependence of the first peak of the atomic distribution function of a liquid.

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