The properties of a circular loop carrying uniform current are calculated for loops of any size relative to the wavelength. The radiation resistance and the greatest directivity pass through a series of maxima and minima as the frequency is increased. At frequencies below that for which one wavelength is contained in the circumference, the directivity graph is nearly independent of frequency. As the frequency is increased, additional lobes appear, the principal lobe tending to point more nearly in the direction normal to the loop. The paper includes a note on other loops, and a mathematical appendix dealing with certain integrals involving Bessel functions.