During the last 15 years, the problem of determining the effect at a distant point of the earth’s surface due to a Hertzian oscillator emitting waves of a definite frequency has been the subject of numerous theoretical investigations. When certain assumptions of a physical character have been made, the problem is of a definitely mathematical type; it is in fact reduced to the problem of finding an approximate formula for the sum of a certain complicated seines of an oscillatory nature; we shall summarise the principal methods which have been devised for dealing with this series.