Previous "Tales from Watnall Hall" have looked at RAF Watnall's secret use of radar during WW2 but this time we look at a radar story from almost 200 years ago. It's about the work of maths prodigy George Green of Green's Windmill in Sneinton, Nottingham which was first published in 1828. It was used by American radar boffins in WW2 to develop the microwave gun-aiming radar responsible for shooting down Nazi V1 flying bombs over southern England.
Green taught himself advanced mathematics "in hours stolen from my sleep" when he was not grinding corn at his windmill. He had received only about one year of formal schooling as a child, between the ages of 8 and 9 in 1801 at Robert Goodacre's Academy in Upper Parliament Street, Nottingham. It's still a mystery¹ how he progressed so much on his own but he was an early member of Nottingham's scholarly Bromley House Subscription library. The library opened in 1816 and still exists today on Angel Row over 200 years later.
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| Bromley House library where Green published his first and most important work. |
In 1828, aged 35, he finished his first and most important work "An essay on the application of mathematical analysis to the theories of electricity and magnetism" and, almost apologetically, published it. It was sold on a subscription basis by Bromley House library to just 51 people, most of whom were friends who probably could not understand it.
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| Green's Mill with Wollaton Hall and the architectural delights of Nottingham behind⁶. |
Sadly he got ill, returned to Nottingham and died there in 1841 with the significance of his work largely unrecognised. It was rediscovered and re-published in 1871 and then used by 20th century quantum physics pioneers. Albert Einstein on a visit to Nottingham in 1930 said Green was years ahead of his time³.
In England, in summer 1944, it was also used in Operation Diver to shoot down increasing numbers of V1 "Doodlebug" flying bombs... "an average of almost 120 flying bombs a day were launched in the first week of July. After the first two weeks of bombing, some 1,769 people had been killed and in the Strand the Air Ministry itself was hit and 198 people killed. On July 1 a flying bomb crashed in Chelsea, killing 124; four days later the total death roll was 2,500." Aircraft and manually-aimed anti-aircraft guns found it almost impossible to hit the V1's but the same guns fitted with the SCR-584 radar-aiming technology eventually brought down up to 82% of them as they flew over the south coast of England².
Schwinger published a tribute to George Green and the influence he had on his work entitled "The Greening of Quantum Field Theory: George and I" in 1993. He concluded his explanation of the usefulness of Green's work in today's quantum physics by saying... "Very fascinating, indeed. So ends our rapid journey through 200 years. What, finally, shall we say about George Green? Why, that he is, in a manner of speaking, alive, well, and living among us."
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| The damage caused by a single V1 flying bomb on the Cleverly estate, Shepherd's Bush in London. |
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| June 1930 - Einstein at Nottingham University paid tribute to his idol George Green. He wanted to visit two places in the area, Isaac Newton's house and Green's mill. |
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| A page from Green's essay |
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| Green's memorial slab in Westminster Abbey next to those of Newton, Kelvin, Faraday and Maxwell. |
Sources
Green's portrait is sourced from Cambridge University although there is speculation that it may not be authentic. It's the best we have though. Here he is with other famous Cambridge mathematicians.. https://www.maths.cam.ac.uk/undergrad/admissions/files/history.pdfhttps://en.wikipedia.org/wiki/George_Green_(mathematician)
https://www.britannica.com/technology/radar/Advances-during-World-War-II
https://arxiv.org/abs/physics/0606153
https://www.infoage.org/history-ia/world-war-ii-radar/camp-evans-developed-radar-key-at-anzio-italy/
https://mathshistory.st-andrews.ac.uk/Biographies/Green/
https://en.wikipedia.org/wiki/Green%27s_Mill,_Sneinton
http://www.fiddlersgreen.net/models/aircraft/V1.html
Einstein's visit and Schwinger's tribute https://youtu.be/vK9NQ6e6rng?t=589
https://aperiodical.com/2012/02/george-and-julian/
Explainng Green's functions in "simple" terms and why they are so useful... https://www.youtube.com/watch?v=ism2SfZgFJg&ab_channel=Mathemaniac
Mary Cannel's Guardian obituary covers her championing of Green https://mathshistory.st-andrews.ac.uk/Obituaries/Cannell_Guardian/
Notes
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| Green's Mill in 1870 |
2 - Operation Diver https://en.wikipedia.org/wiki/Operation_Diver
Operation Diver was the British code name for the V-1 flying bomb campaign launched by the German Luftwaffe in 1944 against London and other parts of Britain. Diver was the code name for the V-1, against which the defence consisted of anti-aircraft guns, barrage balloons and fighter aircraft. Anti-aircraft guns proved the most effective form of defence in the later stages of the campaign, with the aid of radar-based technology and the proximity fuse. Anti-aircraft gunners found that such small, fast-moving targets were difficult to hit. At first, it took an average of 2,500 shells to bring down a V-1. The average altitude of the V-1, between 2,000–3,000 ft (610–910 m) was in a narrow band above the optimum engagement height range for light 40 mm Bofors guns. The rate of traverse of the standard British QF 3.7 inch mobile gun was too slow for the heights at which V-1s flew and static gun installations with faster traverses had to be built at great cost. The development of centimetric (roughly 30 GHz frequency) gun laying radars based on the cavity magnetron and the development of the proximity fuze helped to neutralise the advantages of speed and size which the V-1 possessed. In 1944 Bell Labs started delivery of an anti-aircraft predictor fire-control system based around an analogue computer, which supplanted the previous electro-mechanical Kerrison Predictor) just in time for use in the campaign.
Technological advances - By mid-August 1944, the threat was all but overcome by the expedited arrival of two enormously effective electronic aids for anti-aircraft guns, the first developed by the Radiation Laboratory at the Massachusetts Institute of Technology (MIT Rad Lab) radar-based automatic gun-laying (using, among others, the SCR-584 radar) and the proximity fuze. Both of these had been requested by Anti-Aircraft Command and arrived in numbers, starting in June 1944, just as the guns reached their free-firing positions on the coast. Seventeen percent of all flying bombs entering the coastal gun belt were destroyed by guns in the first week on the coast. This rose to 60 per cent by 23 August and 74 per cent in the last week of the month, when on one day 82 per cent were shot down. The rate increased from one V-1 for every 2,500 shells fired to one for every hundred.
Barrage balloons - Barrage balloons were also deployed against the missiles but the leading edges of the V-1's wings were equipped with balloon cable cutters and fewer than 300 V-1s are known to have been destroyed by hitting cables.
Aircraft - Part of the area which the Divers had to cover was given over for fighter operations. Most fighter aircraft were too slow to catch a V-1 except in a dive and even when intercepted, the V-1 was difficult to bring down. Machine-gun bullets had little effect on the sheet steel structure and 20 mm cannon shells were explosive projectiles; detonating the warhead could destroy the fighter as well. The V-1 was nearly immune to conventional air-combat techniques because of its design, which dispensed with a pilot and piston engine with a cooling system. One hit on the pilot or oxygen system can damage or shoot down a conventional aeroplane but there is no pilot in a cruise missile. The Argus pulse jet of the V-1 could be shot full of holes and still provide sufficient thrust for flight. The only vulnerable point of the engine was the valve array at the front. The only other vulnerable points on the V-1 were the bomb detonators and the line from the fuel tank; three very small targets inside the fuselage. An explosive shell from a fighter's cannon or anti-aircraft gun hitting the warhead was most effective.
3 - Einstein visited Nottingham University in June 6th 1930. He gave a lecture and the blackboard he wrote on has been kept as a tribute. Supposedly the lecture itself was a bit of a disaster as Einstein only spoke German. To help the situation the Uni had invited 2 types of student, the physics students and the German language students who it was hoped could translate or at least understand. Unfortunately Einstein's subject matter baffled both sets of students!
This video is of Einstein at the Uni. https://www.youtube.com/watch?v=161UNSza_qk&t=24s&ab_channel=MichaelMerrifield The man Einstein is speaking to is Henry Brose, the head of Physics at Nottingham University at the time and also fluent in German. Einstein gave a lecture that day, and the blackboard with his writing is still on display in the Physics department tea room.
In this video Professor Martyn Poliarkoff (who often gets mistaken for Einstein https://www.youtube.com/watch?v=qYZZkI-N3M4&ab_channel=nottinghamscience) takes us on a tour of the Uni to find the Einstein blackboard and tells some amusing tales of the day in cluding Einstein borrowing £5 (a week's wages for a lecturer back then) and forgetting to pay it back. His wife had to write a letter of apology explaing that her husband does not deal with money!... https://www.youtube.com/watch?v=KIwpGEvmgvs&ab_channel=PeriodicVideos
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| Schwinger in 1965 in his lab with his pen just after winning the Nobel Prize for Physics |
In Schwinger's own words, why Green was so influential in his microwave radar work... "I spent the War years helping to develop microwave radar. In the earlier hands of the British, that activity, famous for its role in winning the Battle of Britain, had begun with electromagnetic radio waves of high frequency, to be followed by very high frequency, which led to very high frequency, indeed. Through those years in Cambridge (Massachusetts, that is), I gave a series of lectures on microwave propagation. A small percentage of them is preserved in a slim volume entitled Discontinuities in Waveguides. The word propagation will have alerted you to the presence of George Green. Indeed, on pages 10 and 18 of an introduction there are applications of two different forms of Green's identity. Then, on the first page of Chapter 1, there is Green's function, symbolized by G. In the subsequent 138 pages the references to Green in name or symbol are more than 200 in number. As the War in Europe was winding down, the experts in high power microwaves began to think of those electric fields as potential electron accelerators. I took a hand in that and devised the microtron which relies on the properties of relativistic energy. I have never seen one, but I have been told that it works. More important and more familiar is the synchrotron. Here I was mainly interested in the properties of the radiation emitted by an accelerated relativistic electron. I used the four dimensionally invariant proper time formulation of action. It included the electromagnetic self-action of the charge, which is to say that it employed a four-dimensionally covariant Green's function. I was only interested in the resistive part, describing the flow of energy from the mechanical system into radiation, but I could not help noticing that the mechanical mass had an invariant electromagnetic mass added to it, thereby producing the physical mass of an electron. I had always been told that such a union was not possible. The simple lesson? To arrive at covariant results, use a covariant formulation, and maintain covariance throughout. "
George and Julian By Peter Rowlett. Posted February 13, 2012 in Travels in a Mathematical World...
Yesterday, the @mathshistory Twitter feed tells me, was the anniversary of the birth of Julian Schwinger (1918-1994), one of the great physicists of the 20th century. (Technically I queued this tweet up but there are a lot of days and a lot of mathematicians to remember…)
Schwinger is known to me particularly through his connection to the story of George Green. Green was a Nottingham mathematician who did work on electricity and magnetism (among other things) that, largely unrecognised in his lifetime, was discovered and brought after his death to further attention by William Thomson (later Lord Kelvin). The application of Green’s work in 19th century science was impressive but it found a new legacy in the 20th century.
At the 1993 celebration in Nottingham of the bicentenary of Green’s birth, Schwinger spoke about his use of Green’s work (a talk written up as The Greening of Quantum Field Theory: George and I).
Schwinger’s account is worth reading. He describes his use of Green’s work first on microwave radar during World War II, then in the development of the microtron and synchrotron particle accelerators, and finally to solve a problem on quantum electrodynamics, work which earned him a share, with Sin-Itiro Tomonaga and Richard Feynman, of the 1965 Nobel Prize for Physics.
In the preface to his most famous work, An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism (1828), Green had written:
Should the present Essay tend in any way to facilitate the application of analysis to one of the most interesting of the physical sciences, the author will deem himself amply repaid for any labour he may have bestowed upon it.
Schwinger’s account helps us to understand how Green not only impacted the physics of his age, but how it continued to have impact beyond anything Green could have imagined."
https://aperiodical.com/2012/02/george-and-julian/
5 - MRI Scanning and George Green - Sir Peter Mansfield with a MRI scanner
Royal Standard House is a grade II listed building converted from Memorial House, originally built in 1921 as a nurses' home and featuring 1, 2 and 3 bedroomed apartments. https://www.standardhill.co.uk/site-history
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