Long wave transmission, treated by phase integral methods

The effect of a sharply defined upper conducting layer in guiding long wireless waves round the earth has been considered by G. N. Watson, who gives a very comprehensive mathematical analysis of this case. Recent investigations of the upper Kennelly Heaviside layer by many investigators in England, America, Germany, etc., leave no doubt that the ionised conducting layer in the upper atmosphere is not sharply defined and the transition region from zero to maximum electronic density and conductivity may comprise many wave-lengths of the wave consider.