Marconi's law is the relation between height of antennas and maximum signaling distance of radio transmissions. Guglielmo Marconi enunciated at one time an empirical law that, for simple vertical sending and receiving antennas of equal height, the maximum working telegraphic distance varied as the square of the height of the antenna. It has been stated that the rule was tested in experiments made on Salisbury Plain in 1897, and also by experiments made by Italian naval officers on behalf of the Royal Italian Navy in 1900 and 1901. Captain Quintino Bonomo gave a report of these experiments in an official report.
Marconi's law Wikipedia
If H is the height of the antenna and D the maximum signalling distance in meters, then we have, according to Marconi's law
where c is some constant.
Marconi's law can be deduced theoretically as follows:
Heinrich Hertz has shown that at large distances compared with their length, the magnetic force of a linear oscillator varies inversely to the distance.
The maximum value of the current set up in any given receiving antenna varies as its length, also as the magnetic force of the waves incident on it, and as the maximum value of the current in the transmitting antenna.
Hence, if the magnetic force of the waves incident on a receiving antenna of height, and if the distance between the sending and receiving antenna, and if the maximum values of the currents in the sending and receiving antenna, we have various charging voltage of the current in the sending antenna which varies very nearly as its capacity — that is, as its height — and if the sending antenna has the same height as the receiving aerial, we have some constant.
For any given receiving apparatus a certain constant minimum value of the maximum current in the receiving antenna is necessary to cause a signal.
Therefore it follows that with given receiving and sending apparatus, we must have a constant.
That is, the maximum signalling distance with given apparatus will vary as the square of the height of the antenna
The above law is, however, much interfered with by the nature of the surface over which the propagation takes place.