1. The rates of conduction of nerve fibres of Sepia and Loligo varying from 30 to 718µ in diameter have been estimated from records of their action potentials. The limits of conduction velocity were found to be 2.2-22.8 m./sec. at 20° C.
2. Although the fibres examined have different functions, and come from animals which differ considerably in structure and mode of life, yet the conduction rates of all of them can be approximately expressed as a single function of the diameter. These fibres, therefore, do not differ greatly from each other in any respect but size.
3. Calculation of the regression coefficient of the log. of the conduction rate on the log. of the diameter of the fibres shows that the rate increases with the power 0.614±0.027 of the diameter. On account of various sources of error however the exact relation does not necessarily lie within these limits, but it is not likely to be very far from the square root.
4. The possession of giant fibres produces a significant saving of time for the animal, it being calculated that the reaction time of a squid is about half that of a similar animal without giant fibres.
5. The presence of rapidly conducting fibres is probably also an advantage in that it decreases the discrepancies between the times of contraction of parts of the mantle at varying distances from the central nervous system. In Loligo there is a graded series of fibres with the larger in the longer nerves, and this is apparently a further device for ensuring more nearly simultaneous contraction.
6. The relative thickness of the myelin-like sheath increases from about 1% of the diameter of the axon in cephalopods to 5% in Crustacea and annelids and 25% in vertebrates: the conduction velocity of fibres of a given size also increases in the same series. This parallelism provides strong support for the view that the layer of oriented lipoids increases the velocity of propagation of the nerve impulse in proportion to its thickness.