This article concludes a series of papers concerned with the flow of electric current through the surface membrane of a giant nerve fibre (Hodgkin, Huxley & Katz, 1952; Hodgkin & Huxley, 1952 a-c). Its general object is to discu the results of the preceding papers (Part I), to put them into mathematical form (Part II) and to show that they will account for conduction and excitation in quantitative terms (Part III).PART I. DISCUSSION OF EXPERIMENTAL RESULTS The results described in the preceding papers suggest that the electrical behaviour of the membrane may be represented by the network shown in Fig. 1. Current can be carried through the membrane either by charging the membrane capacity or by movement of ion-s through the resistances in parallel with the capacity. The ionic current is divided into components carried by sodium and potassium ions (INa and IK), and a small 'leakage current' (I,) made up by chloride and other ions. Each component of the ionic current is determined by a driving force which may conveniently be measured as an electrical potential difference and a permeability coefficient which has the dimensions of a conductance. Thus the sodium current (INa) is equal to the sodium conductance (9Na) multiplied by the difference between the membrane potential (E) and the equilibrium potential for the sodium ion (ENa). Similar equations apply to 'K and I, and are collected on p. 505.Our experiments suggest that gNa and 9E are functions of time and membrane potential, but that ENa, EK, El, CM and g, may be taken as constant. The influence of membrane potential on permeability can be summarized by stating: first, that depolarization causes a transient increase in sodium conductance and a slower but maintained increase in potassium conductance; secondly, that these changes are graded and that they can be reversed by repolarizing the membrane. In order to decide whether these effects are sufficient to account for complicated phenomena such as the action potential and refractory period, it is necessary to obtain expressions relating

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1. The variation of isometric tetanus tension with sarcomere length in single fibres from frog striated muscle has been re‐investigated with special precautions to ensure uniformity of sarcomere length within the part of the fibre being studied. 2. In most respects the results of Ramsey & Street (1940) were confirmed, but (a) the peak of the curve was found to consist of a plateau between sarcomere lengths of 2·05 and 2·2 μ, (b) the decline of tension above this plateau is steeper than found by Ramsey & Street, and (c) the decline of tension below the plateau becomes suddenly steeper at a sarcomere length of about 1·67 μ. 3. Many features of this length—tension relation are simply explained on the sliding‐filament theory. 4. It is concluded that, in the plateau and at greater lengths, the tension on each thin filament is made up of equal contributions from each bridge which it overlaps on adjacent thick filaments. 5. Internal resistance to shortening is negligible in this range but becomes progressively more important with shortening below the plateau.

SUMMARY1. Apparatus for applying a step change of length to an isolated muscle fibre is described. The step was complete in about 0.2 ms.2. Effects of tendon compliance were eliminated by using a spotfollower device and by gripping the tendons with metal clips close to the fibre ends.3. The natural frequency of the force transducer was above 10 kHz. 4. Steps of various amplitudes and in either direction were applied to isolated muscle fibres about 6 mm long from the anterior tibial muscle of Rana temporaria during tetanic stimulation. Initial sarcomere length was 2*0-2-2 #im, and temperature was 0-3 'C.5. The tension response to a step could be divided into four phases. The initial response was an apparently elastic change during the step itself (phase 1). After the step was completed there was a rapid partial recovery towards the original tension (phase 2, lasting 2-5 ins), followed by a slowing or reversal of recovery (phase 3, 10-50 ms), and finally a much slower return to the original tension (phase 4). Most of this paper is concerned with phases 1 and 2.6. The initial tension change (phase 1) occurred synchronously with the applied length change, indicating that the fibres possess a compliance which is almost linear and almost undamped. Its L. E. FORD, A. F. HUXLEY AND R. M. SIMMONS when a very large step was applied. These observations suggest that the structures responsible for the stiffness of the fibre remain rigid when they are not under tension.9. During the few milliseconds after the step (phase 2) the tension recovered part of the way toward the level which existed before the step. In shortening steps the time course of this recovery was adequately fitted by the sum of four exponential terms, and was similar in steps of different amplitude but with a time scale shorter the larger the step. In stretches the slow components were relatively larger than in releases.10. The tension level, T2, approached during phase 2 depended only on the total amplitude of the step and not on the time course of the length change, provided it was complete in 1-2 ms. The extreme tension reached during a step could thus vary widely without detectable change in T2.11. With stretches and releases of up to about 3 nm per half-sarcomere this early recovery was almost complete, so that the curve of T2 against step amplitude was nearly horizontal. With larger releases the line curved downwards, reaching zero in a release of about 14 nm per half-sarcomere.12. When the temperature was raised both the developed tension and the stiffness increased, but the relative increase was greater for tension than for stiffness. The amount of instantaneous shortening needed to bring tension to zero was therefore also increased.13. A set of empirical equations is given which describe adequately the first few milliseconds of the tension change in response to any imposed time course of shortening.14. The rapid elasticity and early tension recovery resemble the response of a combination of two elastic components and one viscous component.