The volumetric elastic modulus of the sheath and the osmotic swelling pressure of the axoplasmic polymer network of the giant axon of Loligo vulgaris were measured. Evidence was obtained that (1) the elastic modulus of the sheath, (2) the swelling pressure of axoplasm, and (3) the effective osmotic pressure difference due to mobile solutes determine axonal volume. The contributions of the sheath and the axoplasm were significant because the effective osmotic pressure due to mobile solutes was a small fraction of the theoretical bulk osmotic pressure due to these solutes. The giant axon was converted from an imperfect to a near perfect osmometer by minimizing the contribution of the sheath and the axoplasmic gel.