A Paraconical Odyssey CommencesThomas J. Goodey

Associate Researcher, Astronomical Observatory Dept.,Stefan cel Mare University,

Str. Universitatii 13A, Suceava, Romania 720229

thomas@flyingkettle.com

0 A personal memoirThis article describes the development of my interest in claims of eclipse anomalies and in physics anomalies generally, and sets out my conclusions to date on this fascinating subject and my plans for the future.

1 My first total solar eclipse

In 1999 the total solar eclipse of 11 August passed directly across the densely populated and prosperous central part of Europe. Many hundreds of thousands of people made some attempt at traveling to the umbral path, establishing a record for the number of people who saw totality that will probably not be surpassed until the great "All-American" eclipse of 2017. My wife Shizu and I drove to Hungary and experienced the stunning spectacle in beautifully clear weather conditions and in the company of an electrified crowd of thousands on the shore of Lake Balaton. One never forgets one's first total solar eclipse!

Being of a ruminative turn of mind, in the years after the eclipse I researched the more recondite aspects of this unique astronomical phenomenon on the newly burgeoning internet, and I came across the NASA pages "Decrypting the Eclipse" and "French Nobel Laureate turns back Clock", presumably composed under the aegis of David Noever and Ron Kocsor. [1] [2] (These pages are still available on a NASA website, probably due to NASA's inadvertence.) The intriguing full story of the NASA attempt under Noever and Kocsor to observe the Allais effect during the 1999 eclipse has, I believe, not yet been told; in any case, these pages grabbed my attention, because I immediately realized the enormous

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consequences for physics if Allais's claim of an eclipse effect was valid and could be substantiated by repetition.

2 Involvement with Maurice Allais

Via Henry Aujard, I managed to establish contact with Maurice Allais, and he sent me a copy of his 1999 memoir addressed to NASA, which is a clear and concise description of his pendulum experiments in the 1950s and their results - specifically his claims of the pendulum eclipse effect and the pendulum lunar effect - and sets out his suggestions as to how further experimentation should be conducted. (One can imagine NASA's reaction to receiving an 84-page memoir in French!) I felt impelled to translate this memoir into English and upload it. [3] I also translated some of Allais's descriptions of his work, published at the time in Notes to the French Academy of Sciences. [4]

Subsequently I sent copies of my translations to Allais. He appeared pleased, and in 2003 we met for a couple of hours, again thanks to the good offices of Henry Aujard. The chief lesson Allais urged upon me was that in his opinion the periodic effect of the Moon on the pendulum (the pendulum lunar effect) was vastly more important than the pendulum eclipse effect although less spectacular, and also would be easier to research. It appeared to me that he found mildly annoying the public focus on the eclipse effect to the exclusion of his other results. I was vividly impressed by the great masses of interesting books and documents in the one of Allais's two apartments that I saw - I actually got lost among the stacks of papers for a few moments. (Rumor had it that the other apartment and his four garages were completely full!)

3 Allais's pendulum work in the 1950s

Maurice Allais invented and built the first paraconical pendulum at the beginning of the 1950s. A paraconical pendulum consists of a bob, a rigid shaft, an upper "stirrup" for hanging the pendulum upon a spherical support ball, and a solidly fixed flat on which the support ball rolls to and fro. It thus has three degrees of freedom: to and fro swinging in two horizontal directions, and rotation around a vertical axis. Theoretically the motion is non-holonomic, because the ball moves to and fro on the flat and also migrates slowly across it. Allais has described his pendulum in his book Anisotropie de l'Espace,

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which is an account (in French) of all his anomaly researches, along with his conclusions. [5] A few photographs of his apparatus survive. [6] He also published a well-written and concise account of his work in an American engineering journal. [7]

According to modern thought, such a ball-borne pendulum is a chaotic system: small variations in initial conditions and small aleatory disturbances during the motion (for example by air currents) are amplified quite quickly, so that after a certain time the motion cannot be predicted. (By the same token the apparatus is extremely sensitive, especially if the ball is very accurate.) Allais understood this at least intuitively, and his procedure was as follows.

He released the pendulum (by burning a thread) and observed the main parameters of its motion, i.e. the azimuth of the major axis of the elongated ellipse described by the bob (commonly termed the angle of precession), the minor axis of that ellipse, and the azimuth of the stirrup, every minute for fourteen minutes. (Just how accurately he observed the minor axis and the stirrup azimuth is open to question.) Then he stopped the pendulum, changed the support ball, reset the pendulum to hang from a new point defined by the azimuth last reached, and allowed it to quieten, which took six minutes. He then released it again from this new point so that it now started swinging along the azimuth finally attained in the previous episode. He called this procedure of moving the release point, enchained experiments. Thus each swing episode took twenty minutes. After the fourteen minutes swing time, the pendulum had typically precessed through a sufficient angle for accurate observation (the Foucault effect in Paris, by itself, is about 2.7° in 14 minutes), but the motion had not yet degenerated too badly into chaos.

Allais's other great innovation was to pioneer very long experimental runs. On several occasions, with his team, he operated the pendulum continuously for a full month. The idea was to trace long-term variations of the motion and analyze them statistically; he supposed cosmic influences might cause such variations. Despite the literally thousands of pendulum experiments of various types that had been performed since Foucault's famous demonstration of the rotation of the Earth, nobody had ever aspired to make such long-term observations. And during one of these runs a solar eclipse occurred on 30 June 1954, partial at Paris. The line described by the

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barycenters of the Sun and the Moon passed 1050 km north of Paris, and the magnitude at Paris was 71%.

Based upon the results of his experiments from 1953 to 1960, Maurice Allais made two quite distinct and very bold claims.

(1) He claimed that the motion of the pendulum was affected by the Moon - the Allais lunar effect;

(2) He claimed that, during the 1954 eclipse, the pendulum was strongly disturbed in a unique manner - the Allais eclipse effect.

The first claim. A priori, according to conventional classical physics, it would not seem impossible that the motion of a sensitive pendulum might be affected by the Moon's gravitation. After all, gravimeters respond predictably to the lunar and solar tides. The controversial aspect is that Allais claimed via a somewhat suspect argument that, according to conventional physics, tidal effects due to the Moon would be many orders of magnitude too small to be seen by his apparatus. He later erected a complex theoretical structure on his results, relating to a supposed anisotropy of space. The validity of this contention by Allais is still open to controversy, as can be seen from other contributions to this book. In other words, even if the Allais lunar effect really exists, there is currently some dispute as to whether or not it is anomalous.

The second claim. The essentially anomalous nature of this claim is on stronger ground, but of course there is the epistemological problem that no eclipse experiment can ever be exactly repeated. The reported motion of the pendulum during the 1954 eclipse certainly exhibited a stark deviation.

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Barring an essentially trivial experimental glitch such as air movement, there is no question of this kind of disturbance being caused by any conventional physical force causally linked to the eclipse. The matter is essentially one of linearity versus non-linearity. According to current physics, the only way in which an occultation of the Sun by the Moon could exert a physical effect upon earthbound detection apparatus would be via the gravitational force, since the weak and nuclear forces may be excluded and with proper precautions it should be possible to exclude electromagnetic effects, i.e. adventitious disturbances due to temperature, air pressure, ambient magnetic fields, etc.. However in Newton's description (which is perfectly adequate at this level) the effect of the Moon upon the apparatus and the effect of the Sun upon the apparatus strictly combine by vector addition, and the same holds for Einstein's more accurate description to a very high approximation far beyond the reach of simple physical apparatus such as a pendulum, even a very sensitive one. Therefore there is no particular gravitational significance in the fact that, during a solar eclipse, the body of the Sun moves at least partially behind the body of the Moon from the observer's point of view: the gravitational effects of the Moon and the Sun continue to act vector-additively upon the apparatus without any abrupt disturbance, varying gradually and smoothly with no synergistic mutual interaction. This allows no loophole for any sudden and brusque disturbance during an eclipse of the type claimed by Allais.

When I understood Allais's apparatus and the nature of his claims, I realized that (a) if the Allais eclipse effect could be validated, this would have very great consequences for our physical picture of the world; (b) testing for the Allais lunar effect could be done as a background activity while researching the eclipse effect; (c) such experimentation would be very cheap by the standards of modern physics, and would be by no means out of the reach of a lone individual not having corporate backing. So it seemed an ideal candidate for serious hobby research.

4 Subsequent 20th century developments

In 1960 Allais lost his support, and his pendulum research was abruptly closed down. Unable to proceed further along those lines, he concentrated his attention upon economics. A decade later

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Prof. Robert Latham of Imperial College, London became interested in Allais's results. Latham corresponded with Allais and analyzed his numerical results. His verdict was that Allais's conclusions were essentially justified by the data.

Latham wrote several papers on Allais's results and on eclipse anomalies generally, [8] and then embarked upon the ambitious exercise of building a robotically operated paraconical pendulum. He had obviously realized that Allais's manual long-term experiments were just too labor-intensive. In 1978 this construction was a brave effort: Latham's mechanical expedients were most ingenious, especially his method for reading the minor axis automatically. With a robotized pendulum performing enchained observations is impractical - the pendulum must always be released from the same fixed point. Latham succeeded in making his pendulum work quite well automatically over long periods, [9] and then he started to build a second apparatus with the intention of comparing their data side-by-side. However for some reason he did not persevere.

His most interesting observation was the so-called 'Latham waves'. When a paraconical pendulum is operated in repeated swing episodes by being released from a fixed point, the final value of any of its main parameters (Latham only measured the minor axis) is not substantially constant as would naively be expected, but evolves over time in a clearly auto-correlated manner:

This behavior is obviously not random but rather due to some influence varying steadily over many episodes. My pendulum results always manifest the same phenomenon, which has not as yet been explained. The cause must be either some changing state of the

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apparatus itself (the chief suspect must be progressive damage to the ball and/or flat), or some changing state within the experimental chamber (such as temperature), or some varying cosmic influence (which would be highly interesting - that was Allais's contention).

Meanwhile, starting in 1961, Lev Savrov in the USSR had been building a series of very small paraconical pendulums operated in vacuo [10], and at some stage he made contact with Allais. I received the impression that Allais found Savrov's exclusive focus upon eclipse effects to be somewhat irritating. Savrov took his apparatus on several eclipse expeditions to Central and South America, but his results were mixed and unclear. In my candid opinion his analysis of the details of the motion of his pendulums was insufficient, and moreover his sensing arrangements left much to be desired.

More importantly, in the 1990s three independent researchers used sensitive gravimeters of the Lacoste-Romberg type to look for gravitational variations during a solar eclipse: Duval in Canada (1994), Mishra & Rao in India (1995), and Wang in China (1997). [11] [12] [13] [14] They all observed anomalies of very similar temporal structure. I consider this fact to be highly significant, especially since these researchers were quite unaware of one another's existence. Particularly the Wang observation seems to me to have been very professionally conducted - the results appear almost bulletproof. The general tenor of all these observations was that anomalous variations did not occur at the eclipse maximum but before and after it, indeed in the Wang case somewhat before and after the first and fourth contacts of the locally visible eclipse. This strongly suggests an effect of some type related to the edge of the Moon, rather than an effect due to alignment of barycenters.

There was also an interesting claim of an eclipse effect by Saxl & Allen, using a torsion pendulum which is a rather different apparatus. [15]

5 The modern approach to the paraconical pendulum and the 21st century situation

Having conceived the ambition of working with a paraconical pendulum, I considered the improvements that modern technology could provide. In no way do I denigrate Allais's achievements: he

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was the pioneer, far ahead of his time, and his work in the 1950s was an amazing effort. But it seemed to me that in our technical era the following aspects of his operations could be improved:

(a) Allais's apparatus was not transportable. Its support structure was built into the fabric of the laboratory. This meant that he could not transport it to appropriate locations for investigation of eclipse anomalies. Indeed the question never arose.

(b) His support structure was not completely rigid; it exhibited measurable anisotropy. Allais attempted to represent this as a feature, but I cannot consider it as other than a flaw.

(c) He did not shield his pendulum from air currents.

(d) There were several serious difficulties in Allais's heroic procedure of executing marathon one-month-long series of pendulum releases by manual operation, and in his use of human-eye observation (unavoidable in that period). Not only was substantial cost involved, but also there were training and personnel problems, and changing between operators inevitably created disjunction in the data (so-called "operator effect").

(e) The quality of the support balls that Allais used could not have been adequate for the job. He described them as "balls for best quality SKF ball bearings", and no doubt they were the best that he could get, but in those days "best quality" would not have involved accuracy to better than five micrometers, and probably worse. It is easy to see from energy considerations that such variations in the ball radius are quite sufficient to disturb the pendulum motion substantially. Allais was well aware of this problem, and he changed the ball every episode in an effort to overcome the difficulty by causing the inaccuracies to cancel one another out, at least approximately.

(f) Of the three main parameters of the pendulum motion, Allais could only observe the angle of precession with any real accuracy - he used a sighting system and a beautifully made alidade. However he could only measure the minor axis very roughly, and he could not really monitor the stirrup azimuth at all. He knew what type of observations would be ideally desirable, as suggested in this figure.

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But in these graphs, wishful thinking must have played some role for the minor axis curves, and a great role for the stirrup azimuth curves (he calls this "bracket plane"), because in his day there was just no way to obtain that data accurately. Not having reasonably good stirrup azimuth data meant that it was impossible for him to construct a theoretical model for the pendulum motion and test it against reality, since the stirrup azimuth is a fundamental parameter of the motion.

Nowadays all these problems can be overcome. With good design, a transportable apparatus can be made sufficiently rigid to be effectively isotropic; I have done it. The pendulum can easily be shielded. The cyclic operation of the pendulum - release, swing and observe, stop, re-hang, allow to become quiet, and release again - can be automated under computer control (provided that the release is from a fixed point). Nowadays sintered tungsten carbide balls made for metrological purposes and accurate to 130 nanometers ("Grade 5") are quite cheap. And modern remote measurement equipment is astoundingly accurate, beyond anything that Allais

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could have even dreamt about. I use two Keyence LK-G laser rangefinders that operate at 20 kHz and that are accurate to one micrometer over standoff distances of around ten centimetres.

The other important factor is cost. In the old days, serious expenditure was involved in mounting a research expedition and in transporting substantial experimental equipment to the location of an upcoming solar eclipse. For example Arthur Eddington's voyage to Principe in 1919 (where he observed the archetypical eclipse anomaly) cost ₤1000 in 1919, perhaps three hundred thousand dollars today. And when Erwin Freundlich proposed a similar (later aborted) expedition to the Crimea for a 1914 eclipse, he needed sponsorship from the Krupp family of industrialists. But nowadays both freight costs and individual traveling costs are vastly lower, and such an expedition is quite within the means of a dedicated individual experimenter who is not personally wealthy.

6 2004: Preparatory visits to anomaly researchers

Henry Aujard put me in touch with Dimitrie Olenici in Suceava, northern Romania, and I visited there at the beginning of 2004. We quickly found common ground in a love of research and astronomy, and started a collaboration that continues to this day. I was particularly impressed with his paraconical pendulum and support tripod that he had succeeded in manufacturing with very limited facilities. I helped him with observations at the Planetarium during a planetary conjunction and learnt much from his modus operandi.

Next I traveled to Brest, France to see Vincent Morin. He had built some ingenious apparatus for repetition of the Allais light deviation experiments that were based on Esclangon's work, and in fact the next year we invited him to Suceava, where he set up two experiments in the Cacica salt mine which is a very stable environment.

Then I visited Colombia and met with Prof. Hector Munera, who previously had worked with Allais's concepts in the economics field. He showed me his Michelson-Morley-Miller type laser interferometer, and we discussed setting up a pendulum experiment in Central America during the upcoming April 2005 eclipse.

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My final trip took me to Adelaide, Australia, where Prof. Reg Cahill explained his heterodox ideas on relativity and showed me some of his experiments.

Cogitating over the efforts being made by these dedicated lone researchers, I was confirmed in my decision to concentrate on working with the paraconical pendulum, since my bent is more towards the experimental than the theoretical.

7 Pendulum decisions

I formulated two important decisions about the structure of the pendulums I would use, based upon what I consider to have been infelicities of the Allais pendulum.

(1) Allais's stirrup member was shaped something like a katakana-コ. This was dictated by the fact that he employed the methodology of enchained observations, so there was a requirement for it to be possible to release the pendulum to swing in a wide range of starting azimuths. However the asymmetry of this shape seemed to me to be sub-optimal, and I decided to use a symmetrical stirrup. My first pendulums employed stirrups shaped as rings, but now I have switched to rectangular stirrups which can be manufactured to higher accuracy.

(2) With a ball-borne pendulum the friction of the suspension is minimal, and almost all of the motion attenuation is due to air resistance on the bob, the design of which is therefore crucially important. Allais used various bobs, but finally standardized on a vertically oriented disk. This seemed to me to be subject to aerodynamic objections. A vertical disk will inevitably become aligned at least slightly skew to its path of motion, and then will act as a crude aerofoil, which is unstable in yaw. I think that the bob should be rotationally symmetrical about the vertical axis in order to avoid such disturbances. And a sphere, although symmetrical, will generate a Karmann vortex street while moving through the air, and this will cause random disturbances to the motion. A shape with a sharp edge at the rear will largely overcome this problem. The conclusion is that the best shape for a bob is a horizontally oriented lenticular form, which as far as I know was first used by Olenici.

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Whatever be the form of the stirrup and the bob, primary parameters important for its motion are its two orthogonal horizontal moments A and B and its vertical moment C about the suspension point (the bottom of the support ball). Moreover, important secondary parameters are Allais's 'coefficient of asymmetry' δ=2(B-A)/(B+A) and 'gyrostatic coefficient' γ=2C/(A+B). (The values for Allais's pendulum were δ=0.269•10-2 and γ=0.325•10-2.)

8 Borneo, 2004: First pendulums; a lunar anti-eclipse

As a first effort, Prof. Olenici and I traveled to Kuching, Sarawak, Borneo for experimenting on 28 October 2004, when the central line of a lunar anti-eclipse was due to pass quite near. I took with me a paraconical pendulum of my new design, equipped with 130 nm accuracy metrological balls and optically accurate hard steel flats, and Olenici took one of his pendulums.

Thanks to the kindness of Philip Yiin, CEO of the Alom Group, we were able to set up our equipment in his works laboratory. I found no difficulty in making an alidade for observation by eye, but the production of a release mechanism that would not impart any sideways impulse to the pendulum at launch gave me some trouble. Finally I implemented a variant of the burnt thread technique, with the pendulum being held back by a very short piece of nylon monofil under tension.

I was able to operate the pendulum and to eliminate the worst of the aleatory influences, and obtained several runs which were fairly well autocorrelated. Already in this first experiment the 'Latham waves' appeared prominently. I observed nothing particular during the anti-eclipse.

9 Panama, April 2005: First solar eclipse experiment

Hector Munera and I chose Penonome, Panama as the best location for experimentation during the total eclipse of 8 April 2005, and the enthusiastic cooperation of the Technological University of Panama (UTP) was obtained. Their kindness and helpfulness were really remarkable. With a marathon effort, I built in situ two supposedly

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identical pendulums oriented to swing in perpendicular directions, hanging down through the ceiling of a classroom from the room above where their supports were set into heavy concrete blocks. We organized a team of observers to do round-the-clock observations for eight days spanning the eclipse, and I built release mechanisms of a new 'dropped link' type.

During the eclipse no unusual disturbance appeared, but the pattern of the observations as a whole exhibited certain puzzling features unexplained to this day. [16]

10 Portugal, October 2005: A rigid tripod

Not every eclipse passes over an institution as generous with help as the UTP or Alom. It became apparent from my first two expeditions that the policy of using locally installed pendulums for experimentation during each eclipse was not practicable, and that a transportable yet rigid pendulum support structure would have to be built. I therefore organized the construction of a three meter high tripod. Each leg was made in two demountable sections from aluminum tube 15 cm in diameter and 6 mm thick, tensioned with an internal stainless steel rod.

My pendulum was set up on this tripod with the same manual release as before, and with an alidade for reading the precession azimuth. A vinyl cover was fitted to protect against air currents. The Gode-Stiftung organization (www.gravitation.org) was kind enough

to make some measurements of the sidewise deflection of the support plate with the pendulum swinging. The to and fro motion was of the order of a few micrometers. Moreover, that motion might have been due to deformation of the concrete floor under the tripod, rather than to bending of the tripod itself, which really is extremely rigid.

This tripod was first deployed for the annular eclipse of 3 October 2005 at the University of Braga in Portugal, where experimental space was

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provided thanks to the kindness of Prof. Almeida. We organized a team of students and operated for a period of about a week spanning the eclipse.

No very great deviation of the pendulum took place during the eclipse, although the usual wave-like behavior appeared throughout the run. However one suggestive phenomenon did appear. During this same eclipse, Prof. Olenici and Prof. Mihaila also operated their paraconical pendulums, and our three graphs, obtained completely independently in Portugal, Suceava, and Bucharest, were as follows:

The similarity in patterns is immediately apparent. (Romanian time was three hours ahead of UT in Portugal.)

11 Turkey, March 2006: Improvements, and first attempts at automation

After the Portugal trip I worked hard at improving and robotizing my pendulum setup. Two additional physical contrivances were required: a pendulo-positor and a pendulo-torquator.

The pendulo-positor is a device for lowering the pendulum down gently onto the flat with the support ball between them, for example when a new ball has been loaded. The pendulum is quite heavy, and simply putting it down by hand almost inevitably causes a clank, which runs a serious risk of causing slight damage to the very accurate ball or flat and rendering subsequent observations meaningless. The pendulo-positor that I built lowers the pendulum very gently with a screw device.

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The recognition that a paraconical pendulum needs a pendulo-torquator appears to me to be a milestone. When the pendulum is released, it initially swings in the azimuth of the vertical plane that includes its point of suspension and the point on the bob from which it is held sideways before release. If the upper and lower parts of the pendulum, i.e. the bob and the stirrup, are not perfectly mutually aligned in rotational angle around the axis of the rod ("twist"), then on initial release the horizontal axis through the bottom of the ball around which the pendulum initially swings will not be exactly orthogonal to the stirrup plane, i.e. will not be parallel to the greatest moment of inertia axis of the trihedral of inertia of the pendulum. In other words, the initial motion will be mixed and will not be an eigenmode. Such a motion quickly deteriorates chaotically. I have

found that the behavior of a ball-borne pendulum is extremely sensitive to this twist alignment, indeed so sensitive that the necessary alignment cannot be performed during manufacture in the workshop. A device for delicate adjustment of the twist angle of the bob relative to the stirrup is essential, and is used for fine tuning of the pendulum after installation: this is the pendulo-torquator (PT in the figure).

For automating the operation of the pendulum, David Edwards - the master of mechanics - and I built actuator units rather similar in function to those of Latham. The system needs a pusher unit for pushing

the pendulum sideways at the start of an episode, a latch-and-release unit for holding it there and releasing it upon computer command, and a brake unit for stopping it swinging at the end of each episode. Construction of the pusher and brake units was straightforward, and we built a new type of release mechanism operating on the 'snapaway' principle, which I have continued to use. All these robot units were electrically driven under computer control, powered from a UPS.

For sensing the position of the pendulum during its motion, I received delivery of two highly accurate Keyence LK-G laser rangefinder sensors (mentioned above in Section 5), but was not able to get the software for operating them automatically working in time for the next eclipse - the total eclipse of 23 March 2006.

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Olenici and I drove with the equipment to Side in Turkey, and, thanks to the cooperation of Akdeniz University in Manavgat, set it up directly on the eclipse line. With Prof. Munera who came from Colombia to help, we improvised a method for operating the pendulum semi-automatically, in which a human operator manually triggered the Keyence sensors to perform their readings at the end of each swing episode. This did indeed work, and we obtained meaningful series of well auto-correlated readings during the daytime. But we did not have sufficient personnel to operate at night, so the data series was repeatedly interrupted. The 'Latham waves' were very clear, and there seemed to be a peak around the maximum of the magnificent eclipse; but shortly after the eclipse the local electricity company took advantage of everybody going home after the eclipse to cut off the power line to the University for installation of an upgrade (an academic holiday had been declared), and after some time our UPS proved unequal to the task of keeping the experiment going. This created a regrettable lacuna in our data at a critical time, and so the entire effort at this eclipse cannot be described as successful, although it certainly provided a learning experience. We were led to formulate the 'Manavgat Effect': People do different things during a solar eclipse. (This is also the underlying reason why it is so difficult to webcast an eclipse.) We also experienced first-hand the 'Mastercard Effect': Your credit card gets weaker during a solar eclipse.

12 2006 - 2009: Romanian interlude

After the Turkey eclipse, Prof. Olenici very kindly offered the hospitality of Suceava Planetarium for hosting my pendulum, and we took the apparatus straight there.

The first order of business was obviously to produce a better UPS power supply, and the new system provides 48 hours of autonomy. Because a sensor for reading the stirrup azimuth was clearly essential, I rigged up a fiddly but fairly accurate one in which a laser beam reflected off a mirror on the stirrup and illuminated a Hamamatsu linear photodetector.

I then spent a great deal of time and effort in getting the sensors and pendulum all working together automatically under software control. All this was successful, and we were able to record a full month of substantially continuous pendulum observations over

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December 2007 and January 2008 - the first time anything like that had been done since Allais's epic work. All the parameters - precession amount, minor axis, and stirrup azimuth - were monitored very accurately; this would have been Allais's dream. A video describing the apparatus is available on YouTube. [17]

Conclusions? Several independent analyses of portions of this data have claimed that a lunar periodicity of around 24h 50m can be detected statistically. (This is the claimed Allais lunar effect.) However I still maintain an open mind; this year, 2011, I intend to do a number of further runs of this sort to try to settle the matter definitively, and if possible to analyze the temporo-spatial structure of the effect in relation to the motion of the Moon.

However there was another fascinating observation. As in the example in the figure, on a number of occasions, for quite long periods of time - more than a day - a low-amplitude oscillation of period of about 50 minutes could clearly be seen in the data.

The cause of this periodicity is a complete mystery.

Eclipse Observation

On 1 August 2008 a partial solar eclipse of local magnitude 27% was visible in Suceava. I operated my automatic pendulum and also in parallel, manually, a similar pendulum set up nearby in the Planetarium. Simultaneously Prof. Olenici operated a long Foucault pendulum in another location in town, and Prof. Pugach in Kiev operated a number of 'variators' - small devices of his own construction that resemble miniature torsion balances. We all three observed similar patterns of disturbance to our equipment, and we

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wrote a paper describing these observations. [18] This may be counted as a confirmation of the Allais eclipse effect, although I do not consider it as being definitive.

13 Liaison with Professor Verreault

In 2008 I was contacted by an enthusiastic fellow pendulum anomalist, Prof. Rene Verreault of the University of Quebec, whose theoretical paper on the motion of the paraconical pendulum appears elsewhere in this book and directly addresses the question of whether the Allais lunar effect is per se anomalous. [19]

After having performed an experiment in 2001 in which he detected a lunar-related term in the motion of a long Foucault pendulum [20], Prof. Verreault became intrigued by the question of the Allais eclipse effect, and constructed a transportable long pendulum and undertook two expeditions to solar eclipses to hunt for anomalous behavior such as described by Allais: to Guyane for the eclipse of 22 September 2006, and to Resolute Bay in northern Canada for the eclipse of 1 August 2008. The Guyane expedition yielded valuable data, albeit in the somewhat indigestible form of analog video recordings; but the Resolute Bay expedition unfortunately fell victim to foul weather that overthrew the apparatus before the eclipse.

Prof. Verreault and I found much common ground, and decided to coordinate our activities for investigations during the next series of solar eclipses. We suppose that there is merit in operating with two quite different types of pendulum in the same place at the same time, because their supposed responses to anomalous conditions are expected to be substantially different. We generally concur with Allais's analysis in his 1999 memoir to NASA: a short pendulum should be prone to generate ellipses under the influence of (hypothetical) linear anisotropy of a surrounding force field, as characterized by two mutually perpendicular swinging directions with extremal period values. The major axis should precess in the direction to become aligned with the axis of longest period, the precession speed being maximal when the pendulum is swinging at 45° to the anisotropy eigen-axes. If the passage of the Moon modifies the anisotropy eigen-axes, a fluctuation in minor axis value and in precession speed should be observed. By contrast, a long Foucault-type pendulum is expected to be more sensitive to zenithal

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torque effects, where fluctuations in precession speed may arise without a corresponding elliptical oscillation.

14 2009-2010: Two slaves to science take their apparatus around the world

The relative dearth of solar eclipses from 2007 onwards was due to end in 2009, so our equipment was prepared for shipping, and in 2009 and 2010 the apparatus traveled around the world to three eclipse locations, Gifu in Japan, Gan in the southern Maldives, and Faa'a in Tahiti, while being improved in detail en route. Now (March 2011) it is back in Suceava. Cutting directly to the results, at none of these three eclipses did I observe any notable anomaly in the pendulum motion.

JAPAN. Prof. Verreault and I went together to Gifu University in Japan where, thanks to the kindness of Prof. Tanaka, we set up two experiments in parallel in a very rigid concrete building: my tripod apparatus, and his pendulum, which was around eight meters long and of a superficially conventional type. The sensing system of his apparatus is innovative: a camera mounted near the apex of the pendulum photographs retro-reflectors on the top of the bob as the pendulum swings, producing a continuous video recording that can be subsequently analyzed to a positional accuracy of around 40 μm by computer vision (Prof. Verreault's specialization). The motion attenuation is very low because the bob is a horizontal lens of the Olenici type and the period is around six seconds, so it is possible to operate in uninterrupted episodes of twelve hours or more.

During his calibration procedures in Gifu, using timing apparatus for determining the pendulum period accurately to less than 10-5, Prof. Verreault measured the periods as the pendulum swung in a representative set of different azimuths, established the perpendicular eigen-axes of the motion, and showed that the period varied sinusoidally with swing azimuth. This appears to have been the first time that the anisotropy of a pendulum suspension had ever been experimentally characterized in detail. His equipment can be seen in a YouTube video. [21]

Did Prof. Verreault observe any anomaly during the great Chinese eclipse of 22 July 2009? He has no answer as yet, because the software for analyzing the raw results - several terabytes of video -

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is still under development. (In another paper in this book, Prof. Olenici describes the apparently clearly anomalous result he obtained using simple equipment in Shanghai, directly under the track of the same eclipse.)

MALDIVES. For the next eclipse on 26 January 2010, Prof. Verreault and I took our apparatus to Gan, the southernmost atoll in the Maldives. This location presents a rather interesting situation for pendulum experimentation, because it is only about 40 nautical miles from the Equator. The kind help of our local mentors IC and Mathti was invaluable, as was the cooperation of the Maldives Science Society. I modified my apparatus in two ways:

(A) I manufactured several pendulums with a new type of rectangular stirrup (originally introduced by Prof. Munera) having square section upper and lower bars and two vertical cylindrical rods.

The reason for this change was that, although my original ring-shaped stirrup can itself be manufactured very accurately, it is very difficult to fix the rod to this stirrup so that its axis passes exactly through the stirrup center point. This operation is much easier with the new rectangular stirrup. I also assembled the pendulum in a gentle manner with high performance adhesive, rather than using fixing nuts which introduce stresses. These pendulums weighed around 24 kg; I followed the logic that high mass implies more stable motion. I also started to use flats made of sintered tungsten carbide, rather than hard steel, and the resulting trauma to the flat was definitely less.

(B) Guided by Prof. Verreault's philosophy of indirect rather than direct measurement, I realized that, with a different arrangement of the Keyence sensors, it would be possible to dispense with the cumbersome stirrup azimuth reading system including the laser and the mirror, and that the same data could be obtained with better

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accuracy by ingenious analysis. This was a very important improvement.

Meanwhile Prof. Verreault installed his pendulum in a strongly built elevator shaft in the concrete shell of a half-finished building, which offered unmatched rigidity and thermal stability. Again he obtained a good dataset over the eclipse, and this is awaiting analysis. His support was nearly perfectly isotropic, and it was most impressive to see that the pendulum precessed only slightly during twelve hours of swinging - as one would a priori expect so near the Equator (but this has never been verified before).

TAHITI. Next stop, Tahiti on 11 July 2010! The University of French Polynesia very kindly offered us the use of a sports hall for setting up our equipment. Prof. Verrault introduced the novelty of rigging a set of temperature sensors at different heights next to the pendulum wire, and was able to show that (due to thermal effects on the wire) the pendulum period correlated with the measured temperatures. And I introduced a new and more robust multi-computer control system, and also tested a new pendulum weighing about 6 kilos rather than 24, with the aim of minimizing or even eliminating trauma to the ball and flat. The verdict is still out on which pendulum is best, because of course the heavier pendulum is more stable and its motion suffers less attenuation due to air resistance and less disturbance generally. Another detail improvement is that the new light pendulum incorporates the pendulo-torquator in the bob construction.

We both obtained excellent quality data in Tahiti. My pendulum showed no particular disturbance during the eclipse, and Prof. Verreault's data is awaiting analysis.

15 Ambitions for the future

My basic goal, this year, is to get the apparatus working as well as humanly possible with present-day technology. There are a number of aspects that need further improvement. The software should be rewritten; the final verdict as to the best mass for the pendulum is still open; and there are numerous questions of calibration. I may fit a photographic recording system for backup and validation. Cezar Lesanu and I also intend to develop a novel system he has proposed for accurately monitoring the movement of a long Foucault

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pendulum. This system should be very well suited for addition to an already existing Foucault pendulum, of which there are more than a thousand worldwide in use for public demonstration.

Another goal is to perform a number of runs to test for the Allais lunar effect, with the pendulum swinging in a representative set of azimuths, and as the Moon passes each of northern lunistice, equilune, and southern lunistice. The initial experimental latitude will be 47°N (Suceava), but later the observations should be repeated at other latitudes, and particularly on or near the equator, and as near to a pole as possible. The highest latitude location attainable in practice is probably Svalbard at 78°N, unless we can arrange access to the Amundsen–Scott South Pole Station! This is quite a challenging program. If the lunar effect is positively detected, then it would be interesting to repeat the experiment in some underground laboratory with at least 1 km of rock cover. If the underlying cause is gravitational, then of course there should be no difference.

The other goal is to continue experimentation during solar eclipses with a view to confirming or refuting the Allais eclipse effect. We are aiming to take the equipment to the following eclipse locations in the next few years:

Japan in May 2012; Australia in November 2012; Australia in May 2013 (same place, Cairns); Ascension Island in November 2013.

There are no central eclipses in 2014, and only one in 2015, which passes over Svalbard and is partial in Suceava at magnitude 59%.

Then four important eclipses are due: Borneo in 2016; Mauritius in 2016; Argentina in 2017; and finally the magnificent 'All American Eclipse' of 21 August 2017.

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Our ambition is to have gathered enough intriguing data before this great eclipse to stimulate definitive repetition of gravimeter and pendulum experiments by a number of institutions in multiple locations in the US in August 2017. It is somewhat doubtful that any reproductions will be made of the paraconical pendulum apparatus that I have developed, not because of the cost which is relatively trivial, but because of the sheer complexity of its construction and operation and the finesse required. However reproduction of Prof. Verreault's apparatus is quite simple, and it is not particularly difficult to operate. Moreover, we hope that inexpensive copies of the Lesanu system currently under development for observing the behavior of a long pendulum will be fitted to as many of the already-existing demonstration Foucault pendulums in America as possible. In this way perhaps the fifty-five year old controversy over the Allais eclipse effect will be settled one way or the other during this decade.

16 A note on Allais's neologism "paraconical"

Ignoring non-holonomic effects, if the suspension ball were of zero radius the axis of the rod would describe a cone as the pendulum moved, and the pendulum would be conical. But the non-zero radius of the ball means that it moves slightly on the flat in the opposite

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direction to the displacement of the bob, and to a first approximation the rod axis still describes a cone, whose apex is now a little below the flat. But to higher accuracy this motion is not exactly conical and the apex is not well defined. This is why Allais coined the term paraconical for this pendulum - it is almost a conical pendulum, but not quite. (In his typical way, he never bothered to explain himself, but left the matter as an exercise for the brighter student.) We prefer the term ball-borne as being less recondite and more clearly descriptive.

References

[1] http://science.nasa.gov/science-news/science-at-nasa/1999/ast06aug99_1/

[2] http://science.nasa.gov/science-news/science-at-nasa/1999/ast12oct99_1/

[3] M. Allais, The "Allais Effect" and My Experiments with the Paraconical Pendulum 1954-1960, a memoir prepared for NASA, 1999, unpublished.

Translation available at:

http://www.allais.info/alltrans/nasarep.htm

[4] M. Allais, various papers in C.R.A.S. (Proceedings of the French Academy of

Sciences) in the 1950s, translations available at:

http://www.allais.info/alltrans/allaisnot.htm

[5] M. Allais, short excerpts from Anisotropie de l'Espace, translation available at:

http://www.allais.info/alltrans/fragments.doc

[6] http://www.allais.info/alltrans/allaispix.htm

[7] M. Allais: Should the laws of gravitation be reconsidered? Parts 1~3,

Aero/Space Engineering, Sep. 1959, pp. 46 ff; ditto Oct. 1959, p. 51; ditto Nov.

1959, p. 55. Available at:

http://www.allais.info/priorartdocs/lawgrav.htm

[8] Unpublished papers by R. Latham, available at:

http://www.allais.info/priorartdocs/latham.htm

[9] Latham Report No. 28, part 3, unpublished. available at:

http://home.t01.itscom.net/allais/blackprior/latham/latham-rep28-3.pdf

[10] Various papers by Lev Savrov published in obscure locations, available at:

http://www.allais.info/priorartdocs/savrov.htm

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[11] Duval M.: An experimental gravimetric result for the revival of corpuscular theory (in French) — Physics Essays, vol. 18, pp. 53-62; and arXiv:0705.2581.

English translation of gravimetric section at:

http://www.allais.info/docs/duval4.doc

[12] Mishra D.C. and Rao M.B.S.V: Temporal variation in gravity field during solar eclipse on 24 October 1995 — Current Science, Vol. 72, No. 11, p. 782 (1997).

Available at:

http://www.allais.info/priorartdocs/mishra.htm

[13] Wang, Q., Yang, X, et al.: Precise measurement of gravity variations during a total solar eclipse — Phys. Rev. D, vol. 62, 041101(R) (2000). Available at:

http://www.allais.info/priorartdocs/sandaeclipse.htm

[14] Yang X, and Wang Q.: Gravity anomaly during the Mohe total solar eclipse and new constraint on gravitational shielding parameter — Astrophysics and

Space Science, 282, pp. 245-253 (2002). Available as per ref. [14].

[15] Saxl E. and Allen M.: 1970 solar eclipse as "seen" by a torsion pendulum —

Phys. Rev. D, vol. 3, no. 4, pp. 823-825 (1971). Available at

http://www.allais.info/priorartdocs/saxlallen.htm

[16] http://www.allais.info/panarep/panawork.htm

[17] http://www.youtube.com/watch?v=8QV0IOrGRNI

[18] T.J. Goodey, A.F. Pugach, and D. Olenici: Correlated anomalous effects observed during the August 1st 2008 solar eclipse — Journal of Advanced

Research in Physics, 1, Nov. 2010. Available at:

http://stoner.phys.uaic.ro/jarp/index.php/jarp/article/view/40/22

[19] R. Verreault (2011), Tidal accelerations and dynamical properties of 3-df

pendula — (this book).

[20] R. Verreault et S. Lamontagne, Télédétection aérospatiale et Pendule de Foucault, Revue Télédétection, 2007, vol. 7, no 1-2-3-4, p. 507-524.

[21] http://www.youtube.com/watch?v=vsygRYfubVY

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