Mechanics and Astronomy

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An example of the necessity of dialectical thought and of the non-rigid categories and relations in nature; the law of falling, which already in the case of a period-of-fall of some minutes becomes incorrect, since then the radius of the earth can no longer without error be put= ∞, and the attraction of the earth increases instead of remaining constant as Galileo’s law of falling assumes. Nevertheless, this law is still continually taught, but the reservation omitted!

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Newtonian attraction and centrifugal force – an example of metaphysical thinking: the problem not solved but only posed, and this preached as the solution. – Ditto Clausius’ dissipation of heat.[224]

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Newtonian gravitation. The best that can be said of it is that it does not explain but pictures the present state of planetary motion. The motion is given. Ditto the force of attraction of the sun. With these data, how is the motion to be explained? By the parallelogram of forces, by a tangential force which now becomes a necessary postulate that we must accept. That is to say, assuming the eternal character of the existing state, we need a first impulse, God. But neither is the existing planetary state eternal nor is the motion originally compound, but simple rotation, and the parallelogram of forces applied here is wrong, because it did not merely make evident the unknown magnitude, the x, that had still to be found, that is to say in so far as Newton claimed not merely to put the question but to solve it.

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Newton’s parallelogram of forces in the solar system is true at best for the moment when the annular bodies separate, because then the rotational motion comes into contradiction with itself, appearing on the one hand as attraction, and on the other hand as tangential force. As soon as the separation is complete, however, the motion is again a unity. That this separation must occur is a proof of the dialectical process.

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Laplace’s theory presupposes only matter in motionrotation necessary for all bodies suspended in universal space.

Mädler, the Fixed Stars[225]

Halley, at the beginning of the eighteenth century, from the difference between the data of Hipparchus and Flamsteed on three stars, first arrived at the idea of proper motion (p. 410). – Flamsteed’s British Catalogue, the first fairly accurate and comprehensive one (p. 420), then ca. 1750, Bradley, Maskelyne, and Lalande.

Crazy theory of the range of light rays in the case of enormous bodies and Mädlers calculation based on this – as crazy as anything in Hegel’s Philosophy of Nature (pp. 424-25).

The strongest (apparent) proper motion of a star=701” a century= 11′41″ =one-third of the sun’s diameter; smallest average of 921 telescopic stars 8.65” some of them 4’.

Milky Way is a series of rings, all with a common centre of gravity (p. 434).

The Pleiades Group, and in it Alcyone, h Tauri, the centre of motion for our island universe “as far as the most remote regions of the Milky Way” (p. 448). Periods of revolution within the Pleiades Group on the average ca. two million years (p. 449). About the Pleiades are annular groups alternately poor in stars and rich in stars. – Secchi contests the possibility of fixing a centre at the present time.

According to Bessel, Sirius and Procyon describe an orbit about a dark body, as well as the general motion (p. 450).

Eclipse of Algol every 3 days, duration 8 hours, confirmed by spectral analysis (Secchi, p. 786).

In the region of the Milky Way, but deep within it, a dense ring of stars of magnitudes 7-11; a long way outside this ring are the concentric Milky Way rings, of which we see two. In the Milky Way, according to Herschel, ca. 18 million stars visible through his telescope, those lying within the ring being ca. 2 million or more, hence over 20 million in all. In addition there is always a non-resolvable glow in the Milky Way, even behind the resolved stars, hence perhaps still further rings concealed owing to perspective? (Pp. 451-52.)

Alcyone distant from the sun 573 light years. Diameter of the Milky Way ring of separate visible stars, at least 8,000 light years (pp. 462-63).

The mass of the bodies moving within the sun – Alcyone radius of 573 light years is calculated at 118 million sun masses (p. 462), not at all in agreement with the at most 2 million stars moving therein. Dark bodies? At any rate something wrong. A proof of how imperfect our observational bases still are.

For the outermost ring of the Milky Way, Mädler assumes a distance of thousands, perhaps of hundreds of thousands, of light years (p. 464).

A beautiful argument against the so-called absorption of light:

“At any rate, there does exist a distance from which no further light can reach us, but the reason is quite a different one. The velocity of light is finite; from the beginning of creation to our day a finite time has elapsed, and therefore we can only become aware of the heavenly bodies up to the distance which light has travelled in this finite time!” (p. 466.)

That light, decreasing in intensity according to the square of the distance, must reach a point where it is no longer visible to our eyes, however much the latter may be strengthened and equipped, is quite obvious, and suffices for refuting the view of Olbers that only light absorption is capable of explaining the darkness of the sky that nevertheless is filled in all directions with shining stars to an infinite distance. That is not to say that there does not exist a distance at which the ether allows no further light to penetrate.

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Nebulae. Of all forms, strictly circular, elliptical, or irregular and jagged. All decrees of, resolvability, merging into total non-resolvability, where only a thickening towards the centre can be distinguished. In some of the resolvable nebulae, up to ten thousand stars are perceptible, the middle mostly denser, very rarely a central star of greater brilliance. Rosse’s giant telescope has, however, resolved many of them. Herschel I enumerates 197 star aggregations and 2,300 nebulae, to which must be added those catalogued by Herschel II in the southern heavens.

The irregular ones must be distant island universes, since masses of vapour can only exist in equilibrium in globular or ellipsoidal form. Most of them, moreover, are only just visible even through the most powerful telescopes. At any rate the circular ones can be vapour masses: there are 78 of them among the above 2,500. Herschel assumes 2 million, Mädler – on the assumption of a true diameter equal to 8,000 light years – 30 million light years distant from us. Since the distance of each astronomical system of bodies from the next one amounts to at least a hundredfold the diameter of the system, the distance of our island universe from the next one would be at least 50 times 8,000 light years=400,000 light years, in which case with the several thousands of nebulae we get far beyond Herschel I’s 2 million ([Mädler, loc cit., p. 485-]492).

Secchi:

The resolvable nebulae give a continuous and an ordinary stellar spectrum. The nebulae proper, however, “in part give a continuous spectrum like the nebula in Andromeda, but mostly they give a spectrum consisting of one or only very few bright lines, like the nebulae in Orion, in Sagittarius, in Lyra, and the majority of those that are known by the name of planetary (circular) nebulae (p. 787).

(The nebula in Andromeda according to Mädler, p. 495, is unresolvable. – The nebula in Orion is irregular, flocculent and, as it were, puts out arms, p. 495. – Those of Lyra are ring-shaped, only slightly elliptical, p. 498.)

Huggins found in the spectrum of Herschel’s nebula No. 4374, three bright lines, “from this it follows immediately that this nebula does not consist of an aggregate of separate stars, but is a true nebula, a glowing substance in the gaseous state” [p. 787].

The lines belong to nitrogen (1) and hydrogen (I), the third is unknown. Similarly for the nebula in Orion. Even nebulae that contain gleaming points (Hydra, Sagittarius) have these bright lines, so that star masses in course of aggregation are still not solid or liquid (p. 789). The nebula in Lyra has only a nitrogen line (p. 789). – The densest place of the nebula in Orion is P, its whole extension 4’ [pp. 790-91].

Secchi: Sirius:

“Eleven years later (subsequent to Bessel’s calculation, Mädler, p. 450) … not only was the satellite of Sirius discovered in the form of a self-luminous star of the sixth magnitude, but it was also shown that its orbit coincides with that calculated by Bessel. Since then the orbit also for Procyon and its companion has been determined by Auwers, although the satellite itself has not yet been seen” (p. 793).

Secchi: Fixed stars:

“Since the fixed stars, with the exception of two or three, have no perceptible parallax, they are at least” some 30 light years distant from us (p. 799).

According to Secchi, the stars of the 16th magnitude (still distinguishable in Herschel’s big telescope) are 7,560 light years distant, those distinguishable in Rosse’s telescope are at least 20,900 light years distant (p. 802). Secchi (p. 810) himself asks:

When the sun and the whole system are extinct, “are there forces in nature which can reconvert the dead system into its original state of glowing nebula and reawaken it to new life? We do not know.”

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Secchi and the Pope.

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Descartes discovered that the ebb and flow of tides are caused by the attraction of the moon. Ile also discovered simultaneously with Snell the basic law of the refraction of light [In the margin: “Contested by Wolf, p. 325.”[226]] and this in a form peculiar to himself and different from that of Snell.

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Mayer, Mechanische Theorie der Wärme, p. 328. Kant has already stated that the ebb and flow of tides exert a retarding pressure on the rotating earth. (Adam’s calculation that the duration of the sidereal day is now increasing by 1/100 second in 1,000 years.) [227]