Summary: MYSTERY has remained attached to the transmission of free electric rays a long way round the protuberant curvature of the earth, which has recently developed into the greatest sudden practical evolution in signalling since the telephone. The difficulty was already emphasised by the late Lord Rayleigh, as soon as the first signs of transmission across the Atlantic had been detected by the Marconi operators. The effect has been sometimes supposed to be accounted for by a hypothesis that the rays are turned down-ward by an upper conducting layer in the atmosphere. But conduction, as usually understood, involves dissipation,? and thus loss of energy of the rays by absorption; so that a train of radiation travelling along a layer sufficiently conducting to bend the rays could not go far. In fact, by a well-known dynamical principle, if the absorption is small of the first order, the resulting increase of velocity of the train is small of the second order and so of no account for bending rays in a varying field.