A New Interpretation of the Weber Law and the Weiss Law. Some Additions to Our Knowledge of Comparative Physiology of Irritability

Abstract

1. It was pointed out that there are three types of irritability that have been stated to obey the well-known Weber law. These types, referred to as “animal type”, “vegetative type” and “intermediate type” of irritability, are characterized by the difference in the implications of the Weber law they follow, namely.ΔI/I=constant in the irritability of animal type, ΔQ/Q=constant in the irritability of vegetative type, ΔQ/I=constant in the irritability of intermediate type, where I is the strength and Q the quantity (or I×duration) of stimulus, and ΔI and ΔQ are their increment necessary to cause the response. The irritability of animal type and that of intermediate type are observed in various sensory responses of higher and lower animals, respectively, while the irritability of vegetative type is observed in various tropic movements in higher plants. The irritabilities of vegetative and intermediate type caused by a single stimulus share the property to obey the “law of the quantity of stimulus” which appears not to be applicable to the irritability of animal type, provided that the latter is observed with an ordinary time scale of experimentation.2. In general terms, the following reversible reactions were assumed to occur in the physical system which primarily receives the action of the stimulusP_??_P' (i)P_??_P' (ii)of which only reaction (ii) is supposed to be induced by stimulus. The equilibrium of reaction (i) occurring independently of the effect of stimulus is assumed to be shifted appreciably towards the left-hand side of the equation. For this system, a parameter E corresponding to the “sensation” in the Fechner theory was assumed. The significance of this parameter is that its increment (ΔE) of a definite magnitude was made responsible to the occurrence of a definite response in organism, and that it is assumed to be related quantitatively to the free energy (F) of the system determined by the concentration of P' in the following manner:dE/dF=constant It was further assumed that the rate constants k, k' and ks of the above reactions are very large in higher animals, smaller in lower animals and extremely small in plants.3. Based on these fundamental assumptions we could explain why different types of Weber law are met with in different organisms. The fact that the Weber ratio ceases to be constant at lower intensities of stimulus and becomes progressively larger with the decrease of the latter also received a satisfactory quantitative explanation by our theory.4. By extension of the theory, the Weber law and the Weiss law could be united to a consolidated principle. In the light of the extended theory, the difference between the irritabilities shown by higher animals and plants is no more an absolute one, and it was shown that every living system can manifest either the animal type or vegetative type of irritability according as the relative length of the duration of stimulus applied. When the duration of stimulus is relatively suffi ciently short, we observe the “law of the quantity of stimulus” which is characteristic of the irritability of vegetative type. On the other hand, the “rheobase” observed when the duration of stimulus is relatively sufficiently long represents the duration-independent strength of stimulus necessary for response, which is characteristic of the irrita-bility of animal type. As to the “chronaxie”, it is nothing but the reciprocal of the rate constant (k') of the reaction P'→P assumed in our theory.