The semicircular canals of the ear are treated from the point of view of the physicist as a device for the resolution of a vector stimulus such as angular acceleration into three mutually perpendicular components, one for each pair of homologous canals. The brain, receiving the nerve impulses from the canals, recombines these components vectorially to measure the angular acceleration to which the individual is subjected. The brain has so evolved that, without consciousness of the intermediate steps required, it yields an immediate answer to this problem whose mathematical solution requires some minutes of tedious computation.Equations, graphs and a numerical table are given so that the mechanical stimulus to each canal can be found when the head is subjected to angular acceleration about any axis.It is shown that the sum of the mechanical stimuli to the three pairs of canals is greatest when the angular acceleration is about an axis which makes equal angles with the planes of the canals. The total mechanical stimulus is least when the axis is perpendicular to the plane of any one pair of canals.
SUMMERS RD, MORGAN R, REIMANN SP. THE SEMICIRCULAR CANALS AS A DEVICE FOR VECTORIAL RESOLUTION. Arch Otolaryngol. 1943;37(2):219–237. doi:10.1001/archotol.1943.00670030228007