In the central nervous system, electrical signals passing along nerve cells are speeded by cells called oligodendrocytes, which wrap the nerve cells with a fatty layer called myelin. This layer is important for rapid information processing, and is often lost in disease, causing mental or physical impairment in multiple sclerosis, stroke, cerebral palsy and spinal cord injury. The myelin speeds the information flow in two ways, by decreasing the capacitance of the nerve cell and by increasing its membrane resistance, but little is known about the latter aspect of myelin function. By recording electrically from oligodendrocytes and imaging their morphology we characterised the geometry and, for the first time, the resistance of myelin in the brain. This revealed differences between the properties of oligodendrocytes in two brain areas and established that the resistance of myelin is sufficiently high to prevent significant slowing of the nerve electrical signal by current leakage through the myelin.