Summary1. In avoiding certain inherent indeterminacies in classical morphological methods and in obtaining further details regarding the microscopic and ultra‐microscopic structure of nerve axon sheaths, the methods of polarization optics and X‐ray diffraction are of great value. In the case of the myelin sheaths of vertebrate nerve fibres, for example, the optical and diffraction studies indicate the structure of the living fibre's sheath to be of smectic mixed fluid‐crystalline nature.The structure is, therefore, readily altered by chemical treatment to form the artifacts commonly observed in histological preparations.2. A number of considerations suggest that the specific configuration of the lipoid and protein components of the myelin sheath is as follows. The proteins occur as thin sheets wrapped concentrically about the axon, with two bimolecular layers of lipoids interspersed between adjacent protein layers. While this means that in a radial direction within the cylindrical sheath there are alternate predominantly aqueous and predominantly hyirocarbon phases, the latter cannot be described as being entirely “non‐aqueous”3. Polarization optical studies show that, contrary to the general view, invertebrate nerve fibres quite widely possess, aside from connective tissue investments, thin sheaths which are essentially similar in ultrastructure to the well‐defined myelin sheaths of vertebrate fibres. The demonstration of this fact involved a reinterpretation of the meaning of Gothlin's metatropic reaction, in which immersion of the fibre in media of high refractive index permits the (intrinsic) birefringence of lipoids present in the normal sheath in an oriented condition to become apparent by the reduction of the masking (form) double refraction of protein. Associated with the invertebrate metatropic axon sheaths are cells similar to the Schwann cells of vertebrate fibres.4. Quantitative birefringence studies have disclosed that the axon sheaths of a wide variety of fibre types differ chiefly with respect to the relative amounts of oriented protein and lipoid present. This difference is observed not only between typical invertebrate and vertebrate fibres, but also when the fibres of a single vertebrate nerve are compared. For example, the curve obtained when sheath birefringence of frog sciatic fibres is plotted against fibre diameter shows wide variations in the magnitude of double refraction, changing continuously from birefringence due preponderantly to lipoids, in the case of the larger fibres, to that which, in the smallest fibres, results primarily from proteins. The transition from lipoid to protein predominance occurs at a fibre diameter of about 2μ., agreeing well with the division between “medullated” and “non‐medullated” fibres arrived at by histologists. It has been suggested that the low concentration of lipoid in the sheaths of small fibres is related to physical factors opposing the introduction of the lipoids into cylindrical structures of high curvature.5. Examination of available information with respect to the relation of the velocity of impulse propagation to certain fibre characteristics, such as diameter and sheath ultrastructure, indicates that in a wide variety of fibres conduction velocity is a function of both of these factors. Thus, if fibres from invertebrate and vertebrate sources are classified according to sheath composition and ultrastructure, it is found that, within a group having similar sheaths, fast conduction is favoured by large diameter, while between groups with different sheaths, heavy myelination results in faster propagation. Comparison of fibre velocities with diameter alone, without regard to degree of myelination, is apt to be confusing, a fact which should be borne in mind in attempting to relate conduction velocity to diameter in a nerve, such as the frog sciatic, which contains fibres with very different sheaths.6. Several types of invertebrate and vertebrate unipolar ganglion cells have been observed to possess investments similar to the axon sheaths and continuous with the latter. The entire surface of these neurons, therefore, is provided with a characteristic lipoid‐protein covering, except possibly at the nodes of the myelin sheaths of the vertebrate sensory axons. The limiting envelopes of certain other cells and nuclei have been shown to possess an ultrastructure similar in type to that of the axon sheath. Permeability studies on cells have indicated the importance of lipoids and proteins in determining the properties of the plasma membrane, but it cannot be concluded that the visible envelopes are identical with the membrane which determines the physiological properties, since electrical and chemical studies favour the view that this membrane is extremely thin. The parallelisms observed between nerve sheath ultrastructure and physiological function, however, suggest some relation of these to membrane phenomena, and it is particularly difficult to understand how a multilayered structure, such as the vertebrate axon's myelin sheath, could fail to influence the chemical and electrical