User:LeSagian

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In 1758 Georges-Louis Le Sage (1724-1803) of Geneva proposed a simple kinetic theory for gravity, which offered a physical explanation for Newton's force equation.[1][2] Le Sage’s theory reached its zenith of popularity in the late nineteenth century, when it was studied in the context of the then newly discovered kinetic theory of gases.[3] By the early twentieth century, the theory was generally considered discredited, most notably due to issues raised by James Clerk Maxwell and Henri Poincaré.[4][5] While Le Sage's theory is still studied by some researchers, it is not regarded as a viable theory within the mainstream scientific community.

Contents

[edit] Le Sage's basic theory

Le Sage's theory posits that the force of gravity is the result of a sea of tiny particles, similar to a gas, which fills the entire universe. According to the theory, the vast majority of these particles pass through normal objects (like the Earth or Sun) virtually unhindered, much like the neutrinos of modern physics. A very small fraction, however, will either be absorbed, scattered or both (depending on the specific model) and these interactions cause an inward pressure to be exerted on the object. If an isolated object is struck equally from all sides it will experience only this inward directed pressure and thus no net directional force. If a second object is present, however, both objects experience a force acting to move each towards the other. This occurs because the gas pressure that would normally be present from the direction of the second object is partially blocked when passing through that object. For this reason the theory is often referred to as push gravity or shadow gravity, although within the physics community it is more widely referred to as particle gravity or Lesage gravity.

With these postulates it is possible to reproduce Newton's law of universal gravitation. Let A and B be two masses separated by a distance R. Consider the force which B by virtue of its shading effect exerts on A. The particles impinging on A may be viewed as originating from a spherical surface with radius R centred about A. The number of particles ordinarily striking A, if B were absent, is proportional to the cross-sectional area of A and hence, by the Le Sage assumption of a highly porous structure for A, to its mass. With B present, however, a fraction of the particles is intercepted which varies directly with the cross-sectional area of B, and hence B’s mass, and indirectly with the surface area of the sphere, which is proportional to R2. The attractive force is thus proportional to the product of the masses over the square of the separation. Equal and opposite forces are exerted on A and B.

[edit] Early development of the theory

In his early youth Le Sage was strongly influenced by the writings of the Roman poet Lucretius and incorporated some of Lucretius’ ideas into a theory of gravity, which he subsequently worked on and defended throughout his life. An early exposition of the theory can be found in his "Essai de Chymie Méchanique" (1758), in which Le Sage tried to explain both the nature of gravitation and chemical affinities.[1] In his later paper "Lucrèce Newtonien" ("The Newtonian Lucretius") the correspondence with Lucretius’ concepts was fully developed.[2] Prior to Le Sage a very similar theory had been advanced in the 1690s by Nicolas Fatio de Duillier, a close friend of Newton's.[6] For historical accounts of Fatio's and Le Sage's theories, see references [7][8][9][10].

Le Sage proposed that gravity is caused by the continuous bombardment of ordinary matter by what he termed “ultramundane corpuscles”, tiny particles originating from the depths of space. Like the neutrinos of modern science, he supposed that most of these particles would pass through even massive bodies such as the Earth unhindered. Le Sage proposed that the corpuscles were minuscule relative to their separation; that their motions were rectilinear; that they rarely if ever interacted; that their motions could be regarded as equally dense streams moving in all directions; and that their velocities were extremely high. The latter postulate allowed the frictional resistance of the corpuscular sea to bodies in motion through it to be kept very small relative to the attractive force. In order that the gravitational force be proportional to the mass of a body, rather than its cross-sectional area, Le Sage postulated moreover that the basic units of ordinary matter were highly porous to the corpuscles. In some of his writings he referred to them as cage-like structures, in which the diameters of the “bars” were small relative to the dimensions of the “cages”. An isolated body in this medium would be shelled uniformly from all directions and would thus experience no net force upon it. In a system of two or more bodies, however, the mutual shading of corpuscles would result in an apparent force of attraction between the two bodies.

A critical aspect of the model, which was recognized by Le Sage and would later lead to grave difficulties, related to the nature of the collisions between the corpuscles and the units of ordinary matter. The collisions with matter could not be entirely elastic, for in this case the shading effect would be exactly nullified by corpuscles rebounding from the shading mass to strike the shaded one. To counter this, Le Sage proposed that the particles were either carried away at reduced velocities or else stuck to the bars of the cage-like units of matter.

Influenced by Le Sage's theory, Pierre-Simon Laplace calculated that the speed of propagation of the gravitational force in such corpuscular theories of gravity had to be “at least a hundred millions of times greater than that of light”.[11] At lower speeds aberration would cause the apparent force on the orbiting bodies to point slightly behind the current position of the source, causing the bodies to recede from each other. The magnitude of the speed of gravity in a Le Sage-type theory strongly affects the results of any subsequent prediction.

Le Sage’s ideas were not well-received during his day. Le Sage, however, was completely undeterred by his critics and spent the greater part of his life developing epistemological arguments to defend his theory.

[edit] The revival by Kelvin

Le Sage's theory enjoyed a resurgence of interest in the latter half of the nineteenth century, coinciding with the development of the kinetic theory of gases. Indeed, several of the pioneers in kinetic theory, including both Herapath and Waterston, developed their original ideas in the context of attempts to formulate particle theories of gravity. The highwater mark of Le Sage's theory came with Kelvin's modified version of it in 1873. Many of the postulates introduced by Le Sage concerning the gravitational corpuscles (rectilinear motion, rare interactions, etc.) could be collected under the single notion that they behaved as a gas. The range of the gravitational force would be proportional to the mean free path of the gas-like particles. The mean free path would need to be exceptionally long, in order to account for the observed range of gravitation. At the same time, a finite range of gravitation would allow for a gravitationally stable universe. Kelvin also noted that there would exist potentially observable deviations from Newton’s law due to ‘self-shading’ of corpuscles in large planets, for example, but that these could be minimized by extending the porosity of masses to as great proportions as necessary.

Kelvin’s major contribution lay in attempting to deal with a known thermodymamic problem of Le Sage's theory. Le Sage had supposed that the collisions between gravitational corpuscles and masses were largely inelastic, since elastic collisions do not generate the necessary shading effect of the theory. Inelastic collisions, however, would ordinarily be accompanied by the production of huge quantities of heat, sufficient in fact to vaporize any object in a matter of seconds. Kelvin suggested that elastic collisions could be feasible, provided that the original translational kinetic energy of the corpuscles was transferred to internal energy modes, chiefly vibrational or rotational energy. Kelvin also suggested that these energized but slower moving corpuscles would subsequently be restored to their original condition in subsequent collisions with other corpuscles, such that equilibrium of the various modes was retained on a cosmological scale. However, subsequent workers pointed out that this rested on an invalid application of Clausius's hypothesis on the partition of kinetic energy in a gas at equilibrium.[12]

A review of the Kelvin-Le Sage theory was published by Maxwell in the Ninth Edition of the Encyclopaedia Britannica under the title ‘Atom’ in 1875. Maxwell starts by saying, "Here, then, seems to be a path leading towards an explanation of the law of gravitation, which, if it can be shown to be in other respects consistent with the facts, may turn out to be a royal road into the very arcana of science." but later argues that the temperature of bodies must tend to approach that at which the average kinetic energy of a molecule of the body would be equal to the average kinetic energy of an ultra-mundane corpuscle. He states that the latter quantity must be much greater than the former and concludes that ordinary matter should be incinerated within seconds under the Le Sage bombardment.[13]

George Darwin subsequently calculated the gravitational force between two bodies at extremely close range to determine if geometrical effects would lead to a deviation from Newton’s law.[14] He concluded that only in the instance of perfectly inelastic collisions (zero reflection) would Newton’s law stand up, thus reinforcing the thermodynamic problem of Le Sage's theory.

It can thus be seen that several closely interconnected problems have frustrated development of Le Sage’s theory. These relate to excessive heating, frictional drag, and a gravitational aberration effect. The influence of negative assessments in conjunction with a general shift away from mechanical ether theories led to a progressive loss of interest in the Le Sage’s theory after the end of the nineteenth century.

[edit] Developments in the twentieth century

In the twentieth century Le Sage’s theory was eclipsed by Einstein’s theory of general relativity. However, just as in the previous centuries, efforts to improve the theory were occasionally made.

In the early 1900s many authors, including Hendrik Lorentz and Charles Brush, substituted electromagnetic waves for Le Sage’s corpuscles.[15][16] Assuming that space is filled with radiation of a very high frequency, Lorentz showed that an attractive force between charged particles (which might be taken to model the elementary subunits of matter) would indeed arise, but only if the incident energy were entirely absorbed. This was the same fundamental problem which had afflicted the corpuscular models.

In 1911 J.J. Thomson reviewed the Le Sage theory in his article "Matter" in the Encyclopædia Britannica Eleventh Edition.[17] Thomson proposed that the constitution of matter is electrical. On this basis he described two theories of gravitation which are possibly compatible with this assumption, the second one being Le Sage's. After summarizing the basic concept of the theory, he wrote: It is a very interesting result of recent discoveries that the machinery which Le Sage introduced for the purpose of his theory has a very close analogy with things for which we have now direct experimental evidence. He replied to Maxwell's criticism using an analogy to the passage of electrified corpuscules through matter, which causes the radiation of Roentgen rays of even more penetrating power. In Le Sage-type models the absorbed energy might similarly not be transformed into heat, but re-radiated in a still more penetrating form. But he also stated that absorbed Roentgen rays were not transformed like this.

Similar to Thomson, Poincaré argued that thermal vaporization of bodies could only be averted if the absorbed energy was somehow re-radiated as "secondary radiation", which is even more penetrating than the original gravitational flux. However, he rejected this possibility on conceptual grounds. Poincaré also obtained an estimate for the speed of the corpuscules. After asserting that Laplace's method of calculation was “perfectly satisfactory” he increased his estimate to 1017 times the speed of light, utilizing longer baseline lunar measurements.[18] In contrast, general relativity is consistent with the lack of appreciable aberration identified by Laplace, since gravity is postulated to have a back-action term that exactly offsets the aberrative force.[19]

In an unusual development, Le Sage’s theory in this century became intertwined with an alternative theory of gravitation, also involving shielding effects, proposed by Quirino Majorana.[20] Majorana took as a starting assumption that a material screen set between two other bodies would diminish the force of attraction between the latter due to gravitational absorption by the screen. This state of affairs might be most readily envisioned if the gravitational force was caused by “a kind of energical flux, continually emanating from ponderable matter”. The situation might then be analogous to the absorption of light in passage through a semi-transparent medium. His view thus differed sharply from Le Sage’s, in that matter itself, rather than the remote regions of space, is the source of the gravitational fluxes. In a series of elaborate laboratory experiments, Majorana found evidence for a small but definite amount of gravitational absorption.

Majorana was aware of Le Sage's theory and in one set of experiments attempted to discern which was correct, his own theory or Le Sage's. To Majorana the results suggested that his own theory was correct. Recently, however, it has been suggested that Majorana erred in his interpretation and that the predicted shielding effects of Le Sage's theory and Majorana's theory are identical.[21]

The experimental results reported by Majorana initially attracted considerable interest, especially from A. A. Michelson. Upon publication of an article by the astronomer H. N. Russell, however, Michelson apparently lost interest. Russell first demonstrated that, in order that large deviations from Kepler’s laws not occur under Majorana’s theory, the inertial masses of bodies must remain at all times proportional to the gravitational masses.[22] Russell then went on, however, to show that even granted this proportionality, a major problem arose in the case of the tides, the solar tides in particular needing to be some 370 times greater on the side of the Earth facing away from the Sun compared to the side facing the Sun.

A possible solution to Russell's criticism was later advanced by Vladimir Radzievskii.[23] Using a Le Sage-type model, Radzievskii found that the same degree of shielding of the force between two bodies results whether the screening mass is placed between the two bodies or exterior to both of the bodies.

Since the time of Majorana’s experiments, a number of laboratory investigations have been conducted in an effort to duplicate Majorana’s findings.[24] In general, these studies have failed to detect an effect of the same magnitude as Majorana’s. At the same time, none of them specifically employed laboratory apparatus and techniques equivalent to Majorana's.

[edit] Predictions of Le Sage's theory

As indicated in the previous section, the main prediction of Lesage gravity is that deviations in Newton's law will arise when the gravitational force between two bodies is screened by a third body. In this context, the reported erratic behaviour of pendulums during eclipses, often referred to as the Allais effect, has sometimes been ascribed to Le Sage-type gravitational shielding. In general, observational evidence for gravitational absorption during solar and lunar eclipses has been inconclusive.[25]

A related prediction of Lesage gravity is a deviation from the inverse-square law for very large masses. As a body approaches a certain critical size, all of the Lesage particles incident upon it are absorbed and/or scattered by the body. Beyond this size no greater screening can thus occur. Although the effect would be small, certain astronomical events, like planetary occultations, could result in measurable differences in orbits. While Kurt Bottlinger found some evidence for such an effect in the Moon’s orbit around the Earth, the variations in the Moon’s motion were later ascribed to other causes.

In many corpuscular models, such as Kelvin's, the range of gravity is limited due to the nature of corpuscular interactions amongst themselves. The range is effectively determined by the rate that the proposed internal modes of the corpuscles can eliminate the momentum defects (shadows) that are created by passing through matter. Such predictions as to the effective range of gravity will vary and are dependent upon the specific aspects and assumptions as to the modes of interactions that are available during corpuscular interactions. However, for this class of models the observed large-scale structure of the cosmos constrains such dispersion to those that will allow for the aggregation of such immense gravitational structures.

Another crucial aspect of this model requires that moving bodies experience drag or friction, just as one experiences when moving their hand through water. Without any mitgating factors, this friction must cause any moving object to slowly come to rest relative to the underlying rest frame of the field. As emphasized by Le Sage and Kelvin, this friction is eliminated if the Le Sage particles move at or near infinite speeds (much greater than the speed of light). However, to do so would be in direct contradiction to the notion that the speed of light is a universal limiting velocity, which forms the basis for the special theory of relativity.

Another possible Le Sage effect is orbital aberration. Unless the Le Sage corpuscles are moving at speeds much greater than the speed of light, as Le Sage and Kelvin supposed, there is a time delay in the interactions between bodies (the transit time). In the case of orbital motion this results in each body reacting to a retarded position of the other, which creates a leading force component. This component will act to accelerate both objects away from each other. In order to maintain stable orbits, the effect of gravity must either propagate much faster than the speed of light or must not be a purely central force. This has been suggested by many, including Poincaré, as a conclusive disproof of any Le Sage type of theory.

[edit] Connections to geology

It has long been noted that the thermodynamic problem in Le Sage’s model could potentially be avoided if the energy of the absorbed particles or waves were converted to new mass. While such a conversion is difficult to reconcile with the known laws of physics, the possibility of mass creation has been linked in geology to the theory of the expanding Earth. The latter theory posits that the bimodal distribution of continental crust and ocean basins on the Earth is due not to plate tectonics on a globe of constant size, but rather to the formation of new oceanic crust on an expanding globe. Among the early theorists to link mass increase in Lesage gravity to Earth expansion were I.O. Yarkovsky and Ott Hilgenberg.[26][27] Shneiderov, on the other hand, attempted to link earth expansion to internal heating caused by the collisions of Le Sage particles.[28]

The expanding Earth theory had a resurgence in the 1960s and 1970s with the discovery of the formation of new ocean crust at mid-ocean ridges. Since the evidence for subduction at that time was sketchy, Bruce Heezen and other workers were led back to the postulate of Earth expansion. Subsequent evidence for subduction pushed the expanding Earth theory to the side once more. A small minority of geologists continue however to explore the hypothesis, occasionally invoking Le Sage-type notions.[29]

[edit] Current status of the theory

While Le Sage's model is not presently regarded as a viable theory by most scientists there are ongoing attempts to revitalize the theory, including both particle and electromagnetic wave variants.

A corpuscular model that is similar in many respects to Le Sage's and Kelvin's models has been proposed by Tom Van Flandern.[30][31] Van Flandern argues that lack of apparent aberration in the Sun's gravitational force on the Earth implies corpuscular speeds much greater than c and a notable feature of this hypothesis is a that a separate medium is proposed and necessary to act as carrier of light. He also argues that a finite gravitational range of Le Sage particle explains the observed rotation curves of galaxies without resorting to proposing an otherwise undetectable dark matter.

Recent models adopting Le Sage's mechanism include those of Buonomano and Engels [32] and Iosif Adamut.[33] and some have linked Le Sage gravity to cosmology. For example, Halton Arp has suggested that all objects increase in mass at a rate close to the Hubble rate and that this mass increase could be a result of Le Sage gravity at work. In Arp's non-standard cosmology, mass increase in quasars and galaxies affords an alternative explanation for the cosmological redshift without universal expansion. [34] Toivo Jaakkola developed a model which he termed Equilibrium Cosmology. In this model, it is Le Sage's mechanism which underlies a universe in which all energy conversion processes exist in a state of continual equilibrium.[35]

In 2002 Mingst and Stowe re-visited the issues of energy deposition and drag[36] [37]. Their approach was simple, assume that the observed excess heat emission of Jupiter could be due to the long predicted Le Sage heating and proceed to use its measured value to work backwards to determine the field power flux. The general power deposition equation is then used with this Jupiter derived value to calculate emissions for other planetary bodies and comparisons to actual observations noted. Utilizing this same flux value in the Le Sage drag formula is shown to result in a very close match to the actual observed slowing of the Pioneer and Ulysses spacecraft (the so-called Pioneer Anomaly).


[edit] Endnotes

  1. ^ a b Le Sage, G.L.: "Essai de Chymie Méchanique", 1758, Académie Royale des Sciences, Belles-Lettres et Arts de Rouen
  2. ^ a b Le Sage, G.-L. (1784, for the year 1782), “Lucrèce Newtonien”, Memoires de l’Academie Royale des Sciences et Belles Lettres de Berlin, 1-28. An English translation appears in: "The Newtonian Lucretius", Annual Report of the Board of Regents of the Smithsonian Institution for the year ending June 30, 1898, pp. 139-160.
  3. ^ Thomson, W. (Lord Kelvin) (1873). “On the ultramundane corpuscles of LeSage”, Phil. Mag., 4th ser. 45, 321-332.
  4. ^ Maxwell, J.C., 1875. “Atom”, Encyclopedia Britannica, Ninth Ed., pp. 38-47.
  5. ^ Poincaré, H. (1908). Science and Method. Flammarion, Paris. An English translation was published as Foundation of Science, Science Press, New York, 1929.
  6. ^ After learning of Fatio's work, Le Sage collected Fatio's papers for preservation and started a biography of Fatio. Fatio's papers along with Le Sage's other papers were deposited in the university library in Geneva after Le Sage's death and are still there.
  7. ^ Aronson, S. (1964). “The gravitational theory of Georges-Louis LeSage”, The Natural Philosophert 3, 51.
  8. ^ Evans, J.C. (2002). "Gravity in the century of light: sources, construction and reception of Le Sage's theory of gravitation", Pushing Gravity: New Perspectives on Le Sage's Theory of Gravitation, M. R. Edwards (ed.), Montreal: C. Roy Keys Inc., pp. 9-40
  9. ^ van Lunteren, F. (2002). "Fatio on the cause of universal gravitation", in Pushing Gravity: New Perspectives on Le Sage's Theory of Gravitation, M. R. Edwards (ed.), Montreal: C. Roy Keys Inc., pp. 41-59,
  10. ^ Rowlinson, J. S. (2003). "Le Sage's Essai de Chymie Méchanique". Notes Rec. R. Soc. London 57, 35-45.[1]
  11. ^ Laplace, P.S. 1799-1805 Celestial Mechanics, volume IV, X.vii section 22. To Le Sage's disappointment, Laplace never directly mentioned Le Sage's theory in his works.
  12. ^ Kelvin also described in detail how, on the assumption of Le Sage postulates, and his application of Clausius' theorem, it would be possible to construct a perpetual motion machine, extracting limitless amounts of energy from the gravitational flux.
  13. ^ S.T. Preston responded to Maxwell's criticism by arguing that the kinetic energy of each individual corpuscle could be made arbitrarily low by positing a sufficiently low mass (and higher number density) for the corpuscles (Preston, S.T. (1877). “On some dynamical conditions applicable to LeSage’s theory of gravitation”, Phil. Mag., fifth ser., 4, 206-213 (pt. 1) and 364-375 (pt. 2). Aronson op cit. made the same argument. However, their arguments did not in any case influence the fate of the Le Sage-Kelvin theory.
  14. ^ Darwin, G.H. (1905). “The analogy between Lesage’s theory of gravitation and the repulsion of light”, Proc. Royal Soc. 76, 387-410. Here Darwin replaced Le Sage's cage-like units of ordinary matter with microscopic hard spheres of uniform size
  15. ^ Lorentz, H.A. (1900). Proc. Acad. Amsterdam ii, 559. A brief treatment in English appears in Lectures on theoretical physics, Vol. 1 (1927), MacMillan and Co., Ltd., 151-155 (an edited volume of translations of a lecture series by Lorentz).
  16. ^ Brush, C.F. (1911). “A kinetic theory of gravitation”, Nature 86, 130-132.
  17. ^ Thomson, J.J., “Matter”, Encyclopedia Britannica, 1911 Ed., pp. 891-895. (For Le Sage Gravity, see p. 894-895)
  18. ^ Poincaré, H. The Foundations of Science, 1946, Science Press, pp. 517-521
  19. ^ Carlip, S. “Aberration and the Speed of Gravity” gr-qc 9909087
  20. ^ Majorana, Q., (1920). “On gravitation. Theoretical and experimental researches”, Phil. Mag. [ser. 6] 39, 488-504.
  21. ^ Martins, de Andrade, R., 2002, "Gravitational absorption according to the hypotheses of Le Sage and Majorana", in Pushing Gravity: New Perspectives on Le Sage's Theory of Gravitation, M. R. Edwards (ed.), Montreal: C. Roy Keys Inc., pp. 239-258.
  22. ^ Russell, H.N. (1921). “On Majorana’s theory of gravitation”. Astrophys. J. 54, 334-346.
  23. ^ Radzievskii, V.V. and Kagalnikova, I.I. (1960). “The nature of gravitation”. Vsesoyuz. Astronom.-Geodezich. Obsch. Byull. 26 (33), 3-14. A rough English translation appeared in a U.S. government technical report: FTD TT64 323; TT 64 11801 (1964), Foreign Tech. Div., Air Force Systems Command, Wright-Patterson AFB, Ohio (reprinted in Pushing Gravity).
  24. ^ Martins, de Andrade, R., 1999. “The search for gravitational absorption in the early 20th century”, in: The Expanding Worlds of General Relativity (Einstein Studies, vol. 7) (eds., Goemmer, H., Renn, J., and Ritter, J.), Birkhäuser, Boston, pp. 3-44.
  25. ^ Gillies, G.T. (1997). “The Newtonian gravitational constant: recent measurements and related studies”. Rep. Prog. Phys. 60, 151-225.
  26. ^ Beekman, G. (2006). "I. O. Yarkovsky and the discovery of 'his' effect". Journal for the History of Astronomy 37, 71-86.
  27. ^ Several articles on Hilgenberg's work can be found in: Why Expanding Earth? A Book in Honour of Ott Hilgenberg (Proceedings of the 3rd Lautenthaler Montanistisches Colloquium, Mining Industry Museum, Lautenthal (Germany) May 26, 2001, INGV, Rome), 2003
  28. ^ Shneiderov, A.J. (1961). “On the internal temperature of the earth”. Bollettino di Geofisica Teorica ed Applicata 3, 137-159.
  29. ^ Why Expanding Earth? A Book in Honour of Ott Hilgenberg (Proceedings of the 3rd Lautenthaler Montanistisches Colloquium, Mining Industry Museum, Lautenthal (Germany) May 26, 2001, INGV, Rome), 2003
  30. ^ Van Flandern, T., 1999. Dark Matter, Missing Planets and New Comets, 2nd ed., North Atlantic Books, Berkeley, Chapters 2-4.
  31. ^ Van Flandern, T. (2002)"Gravity", in Pushing Gravity: New Perspectives on Le Sage's Theory of Gravitation, M. R. Edwards (ed.), Montreal: C. Roy Keys Inc., pp. 93-122
  32. ^ Buonomano, V. and Engel, E. (1976). “Some speculations on a causal unification of relativity, gravitation, and quantum mechanics”. Int. J. Theor. Phys. 15, 231-246.
  33. ^ Adamut, I.A. (1982). “The screen effect of the earth in the TETG. Theory of a screening experiment of a sample body at the equator using the earth as a screen” Nuovo Cimento C 5, 189-208.
  34. ^ Arp, H.C., 1998. Seeing Red:Redshifts Cosmology and Academic Science, Montreal: C. Roy Keys, Inc.
  35. ^ Jaakkola, T., (1996). “Action-at-a-distance and local action in gravitation: discussion and possible solution of the dilemma”. Apeiron 3, 61-75.
  36. ^ Mingst, B & Stowe, P. (2002): "Deriving Newton's Gravitational Law from a Le Sage Mechanism", in Pushing Gravity: New Perspectives on Le Sage's Theory of Gravitation, M. R. Edwards (ed.), Montreal: C. Roy Keys Inc., pp. 183-194
  37. ^ Stowe, P. (2002): "Dynamic effects in Le Sage models", in Pushing Gravity: New Perspectives on Le Sage's Theory of Gravitation, M. R. Edwards (ed.), Montreal: C. Roy Keys Inc., pp. 195-200

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