Theoretical equations are derived for the response of a nerve fibre to the sudden application of a weak current. The equations describe the behaviour of the nerve fibre in terms of the membrane resistance and capacity, the axoplasm resistance and the resistance of the external fluid. Expressions are given which allow these four constants to be calculated from experimental observations. Axons from Carcinus maenas were used in preliminary experiments. Quantitative determinations were made on a new single-fibre preparation--the 75μ diameter axon from the walking leg of the lobster (Homarus vulgaris). Currents with a strength of one-third to one-half threshold were used in the quantitative determinations. The behaviour of lobster axons agreed with theoretical predictions in the following respects: (a) the steady extrapolar potential declined exponentially with distance; (b) the voltage gradient midway between two distant electrodes was uniform; (c) the rise and fall of the extrapolar potential at different distances conformed to the correct theoretical curves. The extrapolar potential disappeared when the axon was treated with a solution of chloroform, indicating that the surface membrane was destroyed by this treatment, and that the potential recorded was in fact derived from the membrane. The ratio of the internal to external resistance per unit length was found to be about 0.7. The absolute magnitude of the action potential at the surface membrane was estimated at about 110 mV. The specific resistance of the axoplasm had an average value of 60Ω cm., which was roughly three times that of the surrounding sea water. The calculated resistance of one square centimetre of membrane was found to vary from 600 to 7000Ω in thirteen experiments. The membrane capacity was of the order of 1.3μ F cm.-2. No trace of inductive behaviour could be observed in the majority of the experiments. But three axons with low membrane resistances showed effects which could be attributed either to inductance or to a small local response. The absence of inductive behaviour in axons with high membrane resistance does not prove the absence of an inductive element. Currents with a strength several times greater than threshold often produced oscillating potentials at the cathode. A local response was always observed when the strength of current approached threshold. The response had a striking inflected form if the current strength was near threshold and its duration less than the utilization time. Indirect evidence indicates that the membrane resistance falls to a low value during activity.