An electric field applied upon an ionic crystal may induce on every ion not only dipole moment but also the higher order multipole moments. To estimate the extant of the contribution from the octupole moment to the stetic dielectric constant, we have calculated the dielectric constant of a model crystal which is constructed with hydrogen atom of 1s state arranged on the simple cubic lattice. At first, the Lorentz field arround the Lattice point has been calculated. Next, in the free hydrogen atom, the polarizabilities for dipole moment and for octupole moment have been calculated by means of the variational method. It is found that if the octupole momemt is not taken into consideration, the so-called 4π/3 catastrophe occurs at the lattice constant a=2.65a₀, where a₀=0.528 Å represents the Bohr orbit of hydrogen atom. While both dipole and octupole are taken into account, the dielectric constant becomes infinity at a=3.40a₀. The contribution of the octupole is appreciable whenever the lattice constant is smaller than 4a₀. The fact seems to be suggesting that in real ionic crystals too, the octupole moment may perhaps play an appreciable rôle in the dielectric properties.

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In the previous paper²; we obtained the stress-strain-time relations of networks formed by chain polymers in the differential form. The relations were based on the theory of rubber-like elastioity and derived anden the assumption that the chains constituting the networks would be either broken or reformed time by time. The results were more general than the Green-Fobolsky's ones³, But were so complicated that we could neither solve in analytical form nor apply to the actual problems (Eguations (1)-(6)).
The similar Problem was considered here in the integral form. At the first. we obtained the distribution functions of the chains constituting the networks by means of the direct consideration of deformation of the networks (Eg. (8))., and applied it to the stress exprssion (Eg. (9)-(12))., In the next parts, the work done by external forces (Eg. (14)) was derived form the above distribution function under some canditions, and the energy dissipation was calculated (Eg. (15)).
In the last parts of this paper, some special cases were treated wring the results obtained above; (i) cormparison with the Green-Tobolsky's calculation (§. 5.) (ii) treatment in the stationary state (§. 6), and (iii) the stress relaxation under the constant deformation (§. 7.) It is regretful that we could not Ireat the strain (daformation) relaxation under the constant stress (or, external force) in general from.
The notations used in this paper are as follows;
σ: stress tensor; α: strain (deformation) tensor;
α: transport of α; F (ξ, N, t), g (ξ, N, t), β (ξ, N): acutual number, reformation number, and breaking coefficient, respectively, of chains in the networks having N-statistical segments and ξ-end to end distance at time t; (ξ ξ): a tensor defined by (*); F. S. E: free energy, entropy, and internal energy depended only on volume, respectively, of the networks.

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Generally, in the unsaturated aromatic compound which has conjugate double bonds (-C=C-C=C-…), the wave-length of the maximum of the first absorption band displaces as the length of the chain increases.
Recently, by using the concept of the free electron gas, as used in particular by Sommerfeld for metals, H. Kuhn showed that this can lead to a satisfactory inter pretation of the color of the symmetrical polymethine dyes and then he showed, by refining the model based on the electron gas, that the model is capable of being extended to give a quantitative theory of light absorption of the most important groups of colored organic compounds typified by the symmetrical polymethines and porplyrines.
But the particular case of the light absorption of the polyenes has been subject to a number of theoretical considerations by various authors. These have led to quite satisfactory band of the polyenes but the results for the positions of these bands do not agree with experiment.
The author intend to show the calculated expressions for the position by a new model, which considers the quantum resonance between the following structures:
-C=C-C=C-C=C-…-C=C-C=C-
-C-C-C-C-C=C-…-C=C-C=C-
-C=C-C-C-C-C-…-C=C-C=C-
…
-C=C-C=C-C=C-…-C-C-C-C-
-C-C-C-C-C=C-…-C=C-C=C-
-C=C-C-C-C-C-…-C=C-C=C-
…
-C=C-C=C-C=C-…-C-C-C-C-

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Thermodynamical analysis of life is given in this report. Our body is analogous to fuel cell, which is the power source of isothermal change. ATP is the power transmitting medium corresponding to the current of fuel cell. The main part of the out put in fed back to the living system to maintain life. Life mag be the function of such feed back system. The balance of free energy in such system is analysed and the mathematical relation like that of simple reproduction in economics is obtained with applying the maximum principle of transient phenomena, for the system of living body and its environment is an instance of transient phenomena of chemical flow.
From the equation we can estimate the chemical potential of our body in living state, if we can measure the rates of biochemical reactions. The main part of the chemical potential is the term due to the negative entropy, which is being destructed thermodynamically and reconstructed. Some author is confined to apparent steadiness of the nagative entropy and inclined to the opinion that the destruction, which is the character of catabolism, is frozen or delayed during our life until death. Such consideration is absurd, if we take the metabolic turnover into consideration. The steadiness of negative entropy is maintained by the reconstruction. On the other hand the process, which is anabolism, seams to the reversed course from the point of thermodynamics. But in fact it does not contradict to the second low, if we take the total system of our body and environment into consideration. Such reversed course is the common feature of transient phenomena.
Schrödinger has suggested that we might eat the negative entropy. But it is not adeguats, for there is production of positive entropy due to catabolism and it is excreted (Entropieströmung). Therefore we must take negative entropy at toilet and vomit it at dining room from the point of thermodynamics of irreversible phenomena. But Echrödinger has at first suggested the metasolic turnover of entropy, though he might not be conscious of it. Negative entropy must be the measure of delicacy of living system as the chemical apparatus, which corresponds to the fixed assets and depreciates according to the analogy of economics. The value of negative entropy depreciates and repaired by anabolism. At may be reasonable to measure the value of negative entropy by observing the rate of production by the delicate apparatus.
There might be nothing in living system contradicting the law of physics and chemistry. New principle may be the maximum principle, if it is required, and the author proposed to call it the fourth law of thermodynamics.

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The general character of transient phenomena is studied and the law of mutual induction is clarified. According to this law the field of growth is induced by the negative entropy of activated complex and the field promote the growth of the complex and thus small entropy (or large negative entropy like snow flake) is developed by this mutual induction in transient state. Life might be a system with negative entropy in the chemical system with hige energy.
The creation and developement of negative entropy of life is discussed form the point of molecular statistics, and the time of storage of large negative entropy might be the order of magnitude of exp (N. E.). So that the artificial production of life might require millions of years and it night be practically inpossible. It is also asserted that the origin of life is not a casual phenomena. The creation and developement of the activated complex is regular process like the needle of clock, though the process is the superposition of destruction and reconstruction like the growth of cluster in vapour.
From the point of thermodynamics the life is the continuous flow the origin of life, and the cell division birth, reproduction and death are the phenomenon of a period of the pulsating stream of life, which is the relaxation oscillation of the chemical stream on the earth. In the preceding report the author has proposed that we had better take the total animate world into consideration, which is the pipe system consuming the free energy of organic compounds. Thermodynamics has the character of such large scale, that the total history of the transient phenomena and the total world must be considered. The idea is also described in “Thermodynamical Method in Biology”, Annals of the Hiotubasi Academy, Supplement I (1950).

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