The effect of viscosity on the wave resistance experienced by a two-dimensi
onal perturbation moving at uniform velocity over the free surface of a flu
id is investigated. The analysis is based on Rayleigh's linearized theory o
f capillary-gravity waves. It is shown in particular that the wave resistan
ce remains bounded as the velocity of the perturbation approaches the minim
um phase speed c(min) = (4g gamma/rho)(1/4) (rho is the liquid density, gam
ma is the liquid-air surface tension, and g the acceleration due to gravity
), unlike what is predicted by the inviscid theory.