For non-myelinated fibers, Offner, Weinberg and Young ('40) and Hodgkin and Huxley ('52) proposed mathematical relationships, derived analytically, which were very similar and required conduction velocity in non-myelinated axons to be dependent on axo-plasm resistance, membrane capacitance, active membrane resistance and fiber diameter. The well known Hodkgin-Huxley equation includes a description of the time course of conductance changes for various ions during the axon spike response. This equation's success in predicting the shape of the spike potential under a variety of conditions (Hodgkin and Huxley, '52; George and Johnson, '61; Fitzhugh, '62) is still, perhaps, the most convincing line of evidence in support of the sodium theory of irnpulse propagation, a conceptual framework which has strongly shaped our thought on the nature of basic nervous processes, not only for axonal but also for junctional (Takeuchi and Takeuchi, '60) and integrative (Eccles, '61; Boistel and Fatt, '58; Werman and Grundfest, '61) sites. Both these analytical approaches predicted that conduction velocity in non-myelinated fibers would be proportional to the square root of fiber diameter when all intrinsic membrane spike and axoplasmic parameters were constant.
Pumphrey and Young ('38) working on Loligo and Sepia seemed to supply empirical confirmation of the velocity proportional to square root relation, but the very careful work of Hodes ('53) showed that in the third order giant axon of Loligo, conduction velocity is a linear function of fiber diameter. Gasser ('50, '55) using the method of reconstruction found the linear relation also held in mammalian non-myelinated peripheral nerve fibers. Adey ('51) found a linear relationship in the giant axons of the oligochaete Megas- colex. Nicol and Whitteridge ('55) work- ing on the median giant axon of the polychaete Myxicola also found a linear