In the present review, signal-processing capabilities of the canal lateral line organ imposed by its peripheral architecture are quantified in terms of a limited set of measurable physical parameters. It is demonstrated that cupulae in the lateral line canal organ can only partly be described as canal fluid velocity detectors. Deviation from velocity detection may result from resonance, and can be characterized by the extent to which a single dimensionless resonance number, N ( r ), exceeds 1. This number depends on four physical parameters: it is proportional to cupular size, cupular sliding stiffness and canal fluid density, and inversely proportional to the square of fluid viscosity. Situated in a canal, a cupula may benefit from its resonance by compensating for the limited frequency range of water motion that is efficiently transferred into the lateral line canal. The peripheral transfer of hydrodynamic signals, via canal and cupula, leads to a nearly constant sensitivity to outside water acceleration in a bandwidth that ranges from d.c. to a cut-off frequency of up to several hundreds of Hertz, significantly exceeding the cut-off frequency of the lateral line canal. Threshold values of hydrodynamic detection by the canal lateral line organ are derived in terms of water displacement, water velocity, water acceleration and water pressure gradients and are shown to be close to the detection limits imposed by hair cell mechano-transduction in combination with the physical constraints of peripheral lateral line signal transfer. The notion that the combination of canal- and cupular hydrodynamics effectively provides the lateral line canal organ with a constant sensitivity to water acceleration at low frequencies so that it consequently functions as a low-pass detector of pressure gradients, supports the appropriateness of describing it as a sense organ that "feels at a distance" (Dijkgraaf in Biol Rev 38:51-105, 1963).