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In 1902 Oliver Heaviside and, independently, Kennelly suggested that a conducting layer high in the atmosphere guided radio waves around the Earth. For two decades nobody could prove it was there. Edward Appleton did, using a broadcasting station, a receiver and the physics of interference you meet in wave optics. This post explains how his method worked and walks through the calculation.
Who was Edward Appleton?
His Nobel Prize facts page records that he was born on 6 September 1892 in Bradford, England, and died on 21 April 1965 in Edinburgh. He received the 1947 Nobel Prize in Physics "for his investigations of the physics of the upper atmosphere especially for the discovery of the so-called Appleton layer".
His Nobel biography says he studied natural science at St John's College, Cambridge, under J. J. Thomson and Ernest Rutherford. In the First World War he served in the Royal Engineers, and in his Nobel lecture he explains that working as a radio officer made him curious about why radio signals fade. He became Professor of Physics at London University in 1924 and returned to Cambridge in 1936.
Why was the layer hard to prove?
Appleton's lecture sets out the problem. Marconi's 1901 signal from England to Newfoundland could not be explained by waves bending round the Earth alone. Kennelly and Heaviside proposed a conducting layer, but opponents argued that ordinary bending of waves in the lower air could explain the results. What was missing was direct evidence of waves coming down from above. Our post on Guglielmo Marconi covers the 1901 transmission.
How did the frequency-change experiment work?
After BBC broadcasting began in 1922, Appleton noticed that signals from London received at Cambridge were steady by day but faded slightly at night. He guessed that two waves were interfering: one along the ground and one reflected from the upper atmosphere.
If the path difference holds a whole number of wavelengths, the signal is strong. If it holds an odd number of half-wavelengths, it is weak. So Appleton changed the transmitter's wavelength slowly and counted the maxima. On 11 December 1924, with his first research student M. A. F. Barnett, he used the Bournemouth transmitter and a receiver at Oxford. The lecture reports that the experiment "immediately yielded evidence of a sequence of artificially produced maxima and minima", and gave a reflection height of about 90 km. They published it in Nature in March 1925 as Local Reflection of Wireless Waves from the Upper Atmosphere.
Worked example: finding the height of the layer
The number of wavelengths in the path difference is D/λ = Df/c. Change the frequency by Δf and this changes by DΔf/c. Each step of one gives one extra maximum, so if you count n maxima:
D = nc/Δf
This assumes D does not change during the sweep, as Appleton noted. The numbers below are sample numbers for practice, not his data.
Path difference. A sample sweep of Δf = 34 kHz gives n = 10 maxima. D = 10 × 3.0 × 10^8 / 3.4 × 10^4 ≈ 8.82 × 10^4 m = 88.2 km.
Sky path. The ground wave travels a sample distance d = 140 km. The reflected wave travels L = d + D = 228.2 km.
Height. The reflected path is two equal sides of a triangle, each 114.1 km, over a half-base of 70 km. So h = √(114.1² - 70²) = √(13 019 - 4900) = √8119 ≈ 90 km.
Common mistakes: taking D as the whole sky path, forgetting to halve L, and counting maxima and minima together, which doubles n. For practice with path difference, see our post on interference and resultant intensity.
How did he find the F layer?
In the winter of 1926-27, his lecture says, Appleton found that before dawn the lower layer (the E layer) had lost so much ionisation that waves passed through it. They reflected instead from a higher, more strongly ionised layer, which he called the F layer, with its lower edge about 230 km up. In 1927 he named the weaker region below the E layer the D layer.
He also measured critical frequencies, the highest frequency a layer can reflect straight back. For the E layer he found about 0.75 MHz just before dawn and about 3.0 MHz on summer days. In his theory the maximum electron density depends on the square of the critical frequency, so the daytime density was (3.0/0.75)² = 16 times higher. Regular measurements from January 1931 also showed E layer ionisation 50% greater at sunspot maximum than at sunspot minimum.
The pulse-echo method, invented by Gregory Breit and Merle Tuve in 1925, became the main tool, and in India Sisir Kumar Mitra's group used it to study the E layer; read our post on Sisir Kumar Mitra.
What came after the discovery?
His Nobel biography records that in 1939 he became Secretary of the Department of Scientific and Industrial Research, and that he was knighted in 1941. It reports that Robert Watson-Watt said radar would have come too late to be of decisive use in the Battle of Britain without Appleton's scientific work.
When a set-up has several steps, like this triangle, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning, so you can check each step rather than only the answer.
What can a student learn from Appleton's way of working?
Appleton started from a small observation, slight fading at night, and asked what would cause it. He then turned a public radio station into an experiment by changing one thing at a time. Look for the instrument you already have.
Try it now: with the same sample d = 140 km, how many maxima would a 34 kHz sweep give if the layer were 230 km high?
