It is shown that the radiation resistance for sinusoidal sources can be calculated directly from the retarded potentials by evaluating the electric field at points on the source and that for electric and magnetic dipoles in the long wavelength limit the calculation is fairly simple. The problem is also examined from the point of view of Maxwell’s equations and their solutions, and it is shown that there is a significant portion of the electric and magnetic field which is finite everywhere, even for points on the source.