164 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1909. 
Doctor Zenneck has considered the case of electric waves 1,000 
feet in wave length, and has represented the final result by some 
interesting curves. He defines the effect of the absorption of energy 
by the soil by stating the distance in kilometers at which the wave 
amplitude would be reduced by the effect of this absorption to 
0.367=1/e of its amplitude at the sending station, altogether apart 
from the weakening due to the spreading of the waves out in a hemi- 
sphere, which we may call the spherical or space decrease. These 
curves are plotted to abscisse representing the specific resistance of 
the soil (see. fig. 4). You will see from this diagram that when a 
plane electric wave having the above wave lengths is propagated over 
sea water, it would have to travel 10,000 kilometers before its ampli- 
Xi, 
10,000 
1,000 
100 
Dielectric Constant. 
10 
is reduced to 0°367 = 1/e of Amplitude at origin. 
Ht = Distance in Kilometres at which the Wave Amplitete 
Sea 
Water. 
Specific Resistance in Ohms pea Metre Cube. 
Fresh 
Water. 
Damp Soil. 
Dry Soil. | Insulators. 
Fic. 4.—Curves showing the distance in which electric waves 1,000 feet 
(800 meters) in length have amplitude reduced to 1/¢ by traveling over 
various surfaces (Doctor Zenneck). 
tude would be reduced in the assigned ratio; and over fairly dry 
soil, about 100 to 1,000 kilometers; but over very dry soil, having a 
small dielectric constant, only about 1 to 10 kilometers. Also you 
will notice that the curves rise up again for still higher resistivities. 
This, of course, is as it should be. All the practical cases lie between 
two ideal extremes—the case of an infinitely perfect conducting earth, 
in which case the waves would not penetrate into it at all, and the 
other case, an infinitely perfect nonconducting earth, in which the 
wave would penetrate into it, but would suffer no dissipation of 
energy. This theory is quite in accordance with practical experience 
in radiotelegraphy. Every receiving apparatus associated with an 
antenna of a certain height and kind must be subjected to waves of 
a certain minimum amplitude to give any appreciable signal. For 
