LONG-DISTANCE TRANSMISSION I. Long Waves.—In December 1901 G. Marconi established communication over a distance greater than 2,000 miles between Poldhu (England) and St. John (Newfoundland), while the first quantitative relations between signal intensity, distance of trans mission and wave-length were given by L. W. Austin, whose ex periments, begun in 191o, have been continued since. As a result of transmissions carried out between Brant-Rock and Arlington on the east coast of America and various American cruisers, Austin was led to the empirical formula for the electric force at a distance r from the transmitter. It will be seen that this formula, known as the Austin transmission formula, is similar to (so) but that an exponential term, known as the "absorption term," has been included. Austin's formula was based on day-time measurements at distances up to 2,000 kilometres. Its applicability up to distances of 4,000 km. was later verified by J. L. Hogan. In the "absorption term" both and X are measured in kilometres.
L. F. Fuller, as the result of a series of measurements made between Honolulu and San Francisco, a distance of 3,88o km. with wave-lengths ranging from 3,00o to ir,800 metres, proposed for day-time transmission the formula In this formula the absorption term is seen to be different from that proposed by Austin, while there is also introduced a term where 0 is the geocentric angle between sending and receiving stations. This latter term is introduced to allow for the fact that the earth's surface is spherical and therefore the earth is proportional to and not to — . Its inclusion e 0 sin0 amounts to a correction of i% at a distance of 2,000 km. to a correction of 25% at io,000 km.
Numerous field-strength measurements carried out in 1922 by engineers of the American Telegraph and Telephone Company and the Western Electric Company, in connection with tests preparatory to the inauguration of the trans-Atlantic wireless telephone service suggested for day-time conditions an absorp tion term in the transmission formula instead of those proposed by Austin and Fuller. At night signal intensities, though
erratic, were often high, sometimes reaching the value given by ( io) (i.e., [18] or [19] without the absorption term).
The theoretical problem corresponding to the case of propaga tion over such large distances as we are considering is that of the diffraction of waves round a conducting sphere. The ideal case of a perfectly conducting sphere surrounded by an infinite non-conducting dielectric was examined by H. M. Macdonald, Lord Rayleigh, H. Poincare, J. W. Nicholson, H. March, W. V. Rybeynski and G. N. Watson. The general result of these investi gations is that the signal intensities observed in practice are too large to be explained by diffractive bending alone, and it was this discrepancy which led, in the first place, to the postulation of a reflecting layer. The case in which a reflecting layer influences transmission has been examined quantitatively by G. N. Watson, whose formula, together with that obtained by the same writer for simple diffraction, are given below.
A very complete discussion of the comparison of signal strength measurements with both of these formulae has been given by H. J. Round, T. L. Eckersley, K. Tremellen and F. C. Lunnon using measurements made by Marconi Company Engineers during 1922 and 1923 on an expedition sent to Australia. At smaller distances using (20) the agreement is fair, but at distances greater than 2,000 km. diffraction alone is wholly inadequate to explain the results. The same authors consider that for long waves (e.g., 16,000 metres) the effects of reflection begin to be important at distances of about 700 km. and at distances greater than 2,000 kin. the second formula of Watson (21) becomes applicable. They therefore put this in a practical form as which is easily seen to resemble the empirical formula of Austin very closely. In (22) is a constant having the dimensions of a length and which theoretically is equal to H.