An attempt is made to discover the physical processes in the cochlea which would yield results in agreement with observations. It is shown that the assumption of a ‘passive’ cochlea, where elements are brought into mechanical oscillation solely by means of the incident sound, is not tenable. The degree of resonance of the elements of the cochlea can be measured, and the results are not compatible with the very heavy damping which must arise from the viscosity of the liquid. For this reason the ‘regeneration hypothesis’ is put forward, and it is' suggested that an electromechanical action takes place whereby a supply of electrical energy is employed to counteract the damping. The circumstantial evidence for such a process is considered, and it appears that the cochlea microphonic potential, hitherto, an unexplained by-product of the action, forms an important link in the chain of events. Some implications of the theory are discussed, and ways of testing it are suggested.

In a semi-abelian context, we study the condition (NH) asking that Higgins commutators of normal subobjects are normal subobjects. We provide examples of categories that do or do not satisfy this property. We focus on the relationship with the "Smith is Huq" condition (SH) and characterise those semi-abelian categories in which both (NH) and (SH) hold in terms of reflection and preservation properties of the change of base functors of the fibration of points.Comment: 15 pages; final published versio

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Possible methods of sensory appreciation of the nature of sounds are briefly surveyed in relation to the restriction imposed by the rate at which the nervous system can respond. It is shown that because of this restriction information must in general be lost unless peripheral frequency analysis occurs and unless the peripheral analyzer conforms to certain further conditions which are enumerated. One of these conditions is that the selectivity of the resonant elements shall be proportional to frequency. Experimental evidence is submitted that the selectivity of the resonant elements even in the upper half of the auditory spectrum of the human ear is in fact roughly proportional to frequency and is very much higher than has generally been supposed. Previous theories of hearing are considered, and it is shown that only the resonance hypothesis of Helmholtz interpreted in accordance with the considerations enumerated in the first part of this paper is consistent with observation. In particular the experimental data which have been supposed to be evidence of high damping of the cochlear resonators are re-examined. It is shown that they are either irrelevant or that, correctly interpreted, they are evidence for the contrary view. Finally, an attempt is made to summarize some important properties of the ear in a diagram which illustrates that the ear is a perfect analyzer up to a frequency of 1 kc./sec. Above that frequency it is imperfect, not because of inadequate selectivity, but because perfection would require an impracticable number of resonant elements and nerve cells.

We analyse some aspects of the notion of algebraic exponentiation introduced by the second author [16] and satisfied by the category Gp of groups. We show how this notion provides a new approach to the categorical-algebraic question of the centralization. We explore, in the category Gp, the unusual universal properties and constructions determined by this notion, and we show how it is the origin of various properties of this category.