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John Leslieの地球空洞説


Sir John Leslie (1766-1832)はスコットランドの物理学者で熱の研究で知られる。Leslieは毛細管現象の現代的説明を1802年に初めて行い、1810年にエアーポンプで水を凍らせ、初めて人工的に氷を作った。

Leslieは1829年に出版した「Elements of Natural Philosophy: Including Mechanics and Hydrostatics」のNote Iで、地球空洞説を述べた。

Berressem et al (2012)によれば、Leslieは誤った値と推論から地球空洞説に到達している。
Leslie describes his theory, absent any mention of the two suns, in an endnote to the 1829 edition of his Elements of Natural History (449-453). Like Halley's, Leslie's Hollow Earth owes its existence to flawed observation and subsequent errors of induction and deduction. His theory follows directly from what he calls the "theory of the compression of bodies," which is in turn based in part on an experiment by British physicist John Canton that Leslie believed established the compressibility of water. Water is, in fact, almost entirely incompressible, but Leslie believed his peers had dismissed Canton prematurely. His theory of the compression of bodies holds that the density of any substance is a function of its particular elastic properties and its distance from Earth's center. According to Leslie's calculations, this would result in material at Earth's core (whatever it might be composed of) being almost inconceivably dense, which would result in Earth being thousands of times more massive than Newtonian mechanics had established.

Leslieは自身の理論を、2つの太陽には言及することなく、1829年版の自著「Elements of Natural History」(pp.449-453)に記述している。ハレーと同様に、Leslieの地球空洞説も、誤まった観測と、帰納と演繹の誤りのよって成り立っている、彼の理論は直接的には、彼の言うところの「物体の圧縮の理論」から導かれている。それは、部分的には英国の物理学者John Cantonの実験に基づくもので、Leslieは水の圧縮性を証明したものだと考えていた。水は実際にはほぼ非圧縮であるが、Leslieは物理学者たちが時期尚早にCantonの実験を否定したと考えていた。彼の「物体の圧縮の理論」によれば、物質の密度はその弾性率および地球の中心からの距離により定まる。Leslieの計算によれば、(いかなる物質で構成されていようとも)地球の核の物質はほとんど考えられないほどに凝集し、ニュートン力学で導出された質量の数千倍にもなる。

Leslie gives no indication that he was familiar with Halley's Hollow Earth solution to his problem of an apparently over-massive Moon, but faced with the similar problem of an apparently over-massive Earth, Leslie arrives at a similar solution. "Our planet, must have a very widely cavernous structure," he wrote, and "we tread on a crust or shell whose thickness bears but a very small proportion to the diameter of its sphere" (452).

Leslieが、見かけ上の過大な月の質量問題に対する解決策としてのハレーの地球空洞説を知っていたかどうかの記述はない。しかし、同様に過大な質量に地球という問題に対して、Leslieは同様に結論に到達した。「我々の惑星は、大規模な海綿状の構造を持たなければならない。我々は、厚さはあるが、地球の直径に比べれば非常に小さい部分でしかない地殻の上にいる」と書いた。

Because an absolute vacuum was inconceivable in Leslie's day, he reasoned that something must fill the in-terplanetary void, but what? Certainly not air, because according to the theory of the compression of bodies, even air would be subject to "immense compression [that] would totally derange the powers of elective attraction, and change the whole form and constitution of bodies" (452). Rather, "the vast subterranean cavity must be filled with some very diffusive medium, of as-tonishing elasticity or internal repulsion among its molecules." This left only one possibility: "[the] only fluid we know possessing that character is LIGHT it-self" (452). Leslie goes on to extol the elastic properties that light must possess, concluding with a flourish: "We are thus led [...] to the most important and striking conclusion. The great central concavity is not that dark and dreary abyss which the fancy of Poets had pictured. On the contrary, this spacious internal vault must contain the purest ethereal essence, Light in its most concentrated state, shining with intense refulgence and overpowering splendour" (453).

Leslieの時代では絶対的な真空は考えられなかったので、彼は、何かが惑星内の空隙を生めないといけないと考えた。それは何か? 「物体の圧縮の理論」によれば、空気でさえも「巨大な圧縮は、選択的引力をかき乱し、物体全体の形態と性質を変える」ので、空気ではありえない。むしろ「巨大な地下空洞は、分子間で驚くほどの弾力性または内部反発力のある非常に拡散性の媒体で満たされなければならない。」 これにより可能性は一つだけ残った。「そのと特性を有しているとわかっている唯一の流体は、光そのものである。」 Leslieは、光が持っているはずの弾性特性を称賛し、結論を開花させた。「したがって、我々は最も重要で印象的な結論に導かれる。巨大な中心の空隙は、詩人の空想が描いたような暗くて退屈な深淵ではない。それどころか、この広々とした内部の空間には、最も純粋なエーテルのエッセンスが含まれているはずである。

Leslie's scientific peers roundly rejected his Hol-low Earth theory along with other conclusions from the theory of compression, such as the hypothesis that the ocean rests on a bed of compressed air. It might have slipped into complete obscurity had it not been for Jules Verne, who credits Leslie as the source for the subterranean world of his novel Journey to the Center of the Earth.

Leslieの科学者仲間は、彼の地球空洞説を、海洋が大気のベッドの上にあるといった、物体の圧縮の理論から導かれる結論とまとめて否定した。ジュール・ベルヌが「地底旅行」の地下世界の出典として信じていなければ、Leslieの地球空洞説は忘れ去られていたかもしれない。

[ Hanjo Berressem, Michael Bucher, Uwe Schwagmeier: "Between Science and Fiction: The Hollow Earth as Concept and Conceit", LIT Verlag Münster, 2012, pp.16-17 ]
Leslieの場合は、Cantonの誤った実験結果から推定される地球内部密度と、ニュートン力学から求まる地球の内部密度の大きな違いから、地球空洞説に到達してしまったもの。


なお、John Leslieの原文は以下の通り:
Note I p.25

This capital experiment was first deviaed and performed on a small scale by Mr Canton in 1760. It established incontestably the compresnon of water, bat seems to have been generally overlooked by succeeding popular writen, many of whom stfll continue to repeat the erroneous conclusion of the Academicians del Cimento, which represents that fluid as absolutely incompressible. The instrument alluded to in the text holds about 13 pounds of water, which was introduced with great care and patience; The contraction and subsequent dilatation in the stem, from abstracting and restoring the pressure of nine-tenths of an atmospherey amoounts to 3 or 4 inches, and is rendered vidsible at the distance of sereral benches in a large class-room, by help of a drop of quicksilrer resting on the top of the aqueous column.

I have likewise had constructed, by our ingenious young optician Mr John Adie, a large and delicate instnanent, suggested by the plan of Oerstedt, and capable of extensive application. It bears safely a pressure of 12 or 15 atmospheres, and not only measures easily the contraction of different fluids, but serves to indicate the various compressibility of solid substances. From a series of experiments which I have instituted, I may venture to anticipate the detection of some intereating and important facts in the economy of Nature.

The theory of the compression of bodies, carried to its full extent, might give rise to several bold but striking speculations regarding the internal constitution of our globe. Let the density of any substance, at a depth corresponding to the distance x from the centre in miles, be denoted by d, (that at the surface being assumed the unit,) and the radius and the modulus of elasticity expressed by r and m. Since the power of internal gravitation is directly as the distance from the centre, it will be demonstrated in the Second Volume of this Work, that Hyp. Log. d =(r^2 ^ x^2)/ (2 m r), or, adopting common logarithm, and inserting the numerical values,

Log.d = (3956^2 - x^2) / (18218 m)

For Atmospheric Air, this formula becomes,

Log.d = (3956^2 - x^2) / 91090

For pure Water, it passes into,

Log.d = (3956^2 - x^2) / 2415707

A»d for white Marble» Haefonmda is,

Log.d = (3956^2 - x^2) / 7287200'

Hence it may be computed, that if the same law of condensation continued, Air would become as dense as Water at the depth of 33.75 miles ; it would even acquire the density of Qiucksilver at a farther depth of 163.25 miles.

This idea which I formerly threw imt in the article Meteorology, of the Supplement to the Encyclopedia Britannica, that the ocean may rest on a suhaqueous bed of compressed air, is therefore not devoid of probabiUty. Supposing the rate of contractjon were to poroceed more slowly than at first, still the required measure of condensation would be attained at a depth which forms a very small part of the radius of the globe.

But Water, under the weight of an enormous column, mnst likewise largely contract. At the depth of 93 miles, it would be compressed into half its former bulk ; and at the depth of 362.5 miles, it would acquire the ordinary density of quicksilver. Even Marble itself, sibjected to its own pressure, would become twice as dense as before at tbe eaormous deptb of 287.66 miles.

It is curious to remark, that, from its rapid compressibility. Air would sooner acquire tbe same density with Water, than this fluid would reach the condensation of Marble. For the coincidenoe of Air and Water, tje formula becomes

x^2 = 15649936 - (2415707 - 91090)/ 2320617 * Log.840; whence the depth is 35.2 miles

For equa densities of Water and Marble, the formula is

x^2 = 15649936 - (7287200 - 2415707)/ 4981493 * Log.2.34; and the depth descends to 172.1 miles.

If we calculate for a depth of 395.66 miles, which is only the tenth part of the radious of the earth, we shall fined that Aire would attain the enormous dennty of 101960 billions; while. at the same depth, Water woild acquire but a density of 4.3493, and Marble only 3.8095.

At tbe csntre of the earth, the several formula will beeome simpler. The logarithm of the final augmented density would be

fpr Air 15649936/91090, for Water 15649936/2415707, and for Marble 15649936/7287200

Air would hence reach the inconceivable density ecpressed by 764 with 166 ciphers annexed, while Water would be condensed 3009000 times, and the Marble acquire the density of 119.

Such are prodigious results deduced from the law of gravitation, even supposing the structure of the globe were uniform. But if we take into estimate the augmented power from condensation, the number would become still more stupendous. It follows, therefpre, that if the great body of our earth consissted of any such materials as we are acquainted with, its mean density would very far surpass the limits assigned by the most accurate investigations. The astronomical observation by Dr Maskelyne on the deflection of a pendulum, caused by the attraction of the sides of Mount Schiehallion, and the nice experiments made with the Balance of Torsion by Mr. Cavendish, on the mutual action of ponderous balls of lead,—nearly concur in representing the mean density of the globe as only about five times greater than that of water. It seems, therefore, to follow conclusively, that our planet must have a very widely cavernous structure, and that we tread on a crust or shell whose thickness bears but a very small propor-tion to the diameter of its sphere. Physical Science can extend her prospects to the farthest verge of possibilities ; but Chemistry, even in its present advanced stage, fails altogether in aiding inquiry ; and the various hypotheses framed by Geologists are built with such scanty and slender materials, as to furnish no safe guidance through those boundless speculations.

It is evident, that immense compression would totally derange the powers of elective attraction, and change the whole form and constitution of bodies. When air becomes denser than gold, it is hard to conjecture what transmutations this plastic fluid must un-dergo. The bowels of the earth may contain substances thus trans-formed, bearing no longer any resemblance to their aspect on its surface.

But since an absolute void is inadmissihle, the vast subterranean cavity must be filled with some very diffusive medium, of asto-nishing elasticity or internal repulsion among its molecules. The only fluid we know possessing that character is LIGHT itself, which, when embodied, constitutes Elemental Heat or Fire. It is elicited from every substance by percussion or compression, by electrical agency or chemical affinity. With every species of light our vision is equally perfect, and, consequently, the luminous parti-cles must, in all cases, dart forward with the same celerity, or travel at the rate of about 200,000 miles in a second. But since atmos-pheric air is projected into a vacuum with the velocity of only a quarter of a mile each second, the motion of light is thus 800,000 times more rapid. Wherefore, the propulsive force of light com-pared with that of air is expressed by the square of this number, or 640 billions; and hence its Modulus of Elasticity must amount to the stupendous column of 3200 billions of miles, an extension which is 889 times greater than the diameter of the orbit of Uranus, the most distant of the planets yet discovered. Only such surpassing powers of repulsion would appear at all adequate to balance the cummulative mass of compression, and restrain the condensation of our globe within moderate limits.

We are thus led, by a close train of induction, to the most important and striking conclusion. The great central concavity is not that dark and dreary abyss which the fancy of Poets had pictured. On the contrary, this spacious internal vault must contain the purest ethereal essence. Light in its most concentrated state, shining with intense refulgence and overpowering splendour.

[ Jone Leslie: "Elements of Natural Philosophy: Including Mechanics and Hydrostatics", 1829, pp.449-451







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