Marconi's law
Marconi's law is the relation between length 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. Description. If "H" is the height (i.e. the length) of the antenna and "D" the maximum signalling distance, then we have, according to "Marconi's law" where "c" is some constant. "Marconi's law" can be deduced theoretically as follows: Hertz has shown that distances large compared with its length the magnetic force of a linear oscillator varies inversely as 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 formula_2 is the magnetic force of the waves incident on a receiving antenna of height H, and if formula_3 is the distance between the sending and receiving antenna, and if formula_4 and formula_5 are the maximum values of the currents in the sending and receiving antennæ, we have— formula_6 and formula_7 Hence formula_8 Also, since for a given charging voltage the current formula_4 in the sending antenna varies very nearly as its capacity—that is, as its height—and if the sending antenna has the same height, formula_10, as the receiving  aerial, we have— formula_11 But formula_8 Therefore formula_13 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 formula_14 a constant, or— formula_1 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.