Читать книгу Kinetic Theories of Gravitation - William Bower Taylor - Страница 6
Bernouilli, 1734
ОглавлениеIt is now nearly a century and a half since the elder John Bernouilli, of Switzerland, the illustrious mathematician, (professor at the universities of Groningen and afterward of Basel,) imagined a method of accounting for the action of gravitation by centripetal impacts from without. Still retaining his early prepossessions in favor of the philosophy of Descartes, he devised a very curious combination of aetherial vortices and Newtonian emissions. This eclectic hypothesis was promulgated [214] in a competitive memoir on the cause of " The Mutual Inclination of the Planetary Orbits," which obtained the prize of the French Academy of Sciences in 1734. This treatise is divided into four parts, the first three of which are occupied with his exposition of the cause of gravitation, and the fourth with the main question proposed.[1]
Referring to the respective systems of Descartes and Newton, Bernouilli finds in each "insurmountable difficulties," hence " a just mean between the two appears the safer course. … The gravitation of the planets toward the center of the sun, and the weight of bodies toward the center of the earth, are not caused either by the attraction of Newton, or by the rotary force of the vortex medium of Descartes, but by the immediate impulsion of a substance which under the form of what I call a ' central torrent,' is continually thrown from the whole circumference of the vortex to its center, and consequently impresses on all bodies encountered by it in its path the same tendency toward the center of the vortex. … And all that Newton has derived from his ' attractions' are by my theory, derived from the impulsions of the central torrent."[2]
"According to my system, two kinds of matter are conceived as occupying planetary space, and also two principal movements in the celestial vortex. One of these materials I conceive as perfectly fluid, or I would say, actually divisible without limit; that is, it is not composed of elementary corpuscles, as ordinary fluids are conceived, which according, the number and size of their constituent particles, present more or less sensible resistance to bodies moving in them, but being perfectly uniform and without structure, is also without resistance." This matter is called the primal element ; which was employed by the Creator in forming the corpuscles of sensible matter, definite small portions being compacted together into the coherent molecules of matter of the second element.
" Matter of the primal element, being perfectly fluid without coherence, presents no resistance to bodies moving within it ; for the resistance of fluids comes only from the inertia of the molecules of which they are composed."[3] This primal element, being without constituent parts and without inertia, is as the author states, the same in effect as a perfect vacuum.
" The celestial vortex is composed in great part of the primal element, in which is mingled however, a considerable portion of the second element." According to Bernouilli's view, " the rotation of this vortex is not so rapid as to carry the planets around the sun, as Descartes assumed." In fact, its rotary velocity is in a subsequent portion of the memoir stated to be so low as to amount to only about one two hundred and thirtieth of the orbital velocity of the planets, an approximation to the [215] Keplerian third law being however maintained. Thus the vortex survived its primary purpose and function. The small centrifugal motion of the matter of the second element contained in the celestial vortex is sufficient to make it denser at the outer than at the inner portion, though leaving it still too rare to sensibly affect the motions of the outer planets.[4]
The primal element collected and condensed at the center of each vortex forms a star or sun, though neither the cause nor the manner of such condensation is very clearly unfolded. This central mass agitated with intestine motions of extreme violence in all directions, as in a boiling caldron, produces an intense light and heat, while detached particles at the surface, continually more and more broken up by the frequency and impetuosity of their collisions, acquire a subtilty transcending all conception of the imagination, and are finally thrown off in all directions with explosive force to immense distances, and with the velocity known as that of radiant light. These infinitely small particles, forming the luminous "effluvias" incessantly springing from the sun in radial lines, pass without obstruction through the pores or interstices of the grosser matter forming the planets, though losing at their surface their luminiferous property.
Beyond the orbit of Saturn they encounter more and more of a similar material collected at the outer confines of the vortex ; and, while a large number pass into adjacent vortices and continue their course unimpeded, a large number suffer collision by direct impacts from the similar radiations from these vortices. Being inelastic they are mutually arrested, and form molecules of various size, according to the number of such collisions suffered, until impelled by the resultant of these impacts, they either pass into adjoining vortices or back into their own in the form of material molecules of the second element, with correspondingly reduced velocities.[5]
" In this manner we conceive there must continually descend from the heavens a copious and impetuous rain of pellets, driven inward by the shocks of molecules from surrounding vortices." This converging or centripetal shower of pellets, called the " central torrent," perpetually deluging the sun, forms the compensation and nourishment for its ceaseless waste, as the evaporated water condensing into raindrops replenishes the constant waste of the sea. These minute balls, having only the amount and direction of motion imparted to them at the boundaries of the vortex, are yet supposed to fall with mathematical precision toward the center of the sun without ever touching each other as they approach. Notwithstanding the efforts expended by the author in attempting to establish this necessity, this centripetal directness undoubtedly remains physically the weak point of his hypothesis.
As the inter-vortical molecules acquire different magnitudes before [216] being finally driven toward the center of any system, they will also have differing rates of descent, "their velocities being inversely as their masses, so that if one should become a thousand times larger and slower than the impelling particle of light, it would still have a velocity equal to the diameter of the earth in one minute;" and the average speed would be much greater than this, though always much less than the velocity of light. " The central torrent with such a velocity would expend its force on any body which it encountered ; and this is precisely the gravitation of the planets toward the sun." And as the various sizes of the minute balls would permit them to penetrate the pores of gross matter to varying depths before being arrested, their impulses would be distributed through the mass instead of being entirely expended on the surface.[6]
The particles of light radiated by very distant stars, having to run the gauntlet of all the intermediate stellar vortices, might be supposed to bo very much obstructed and reduced in number, if not in some cases entirely suppressed.
Each planet and satellite has its subordinate vortex, in which the same play of impalpable effluvia and returning torrent is carried on; and although this is treated as a very obvious corollary of the system, it is one somewhat difficult to fully formulate or realize. Whether two independent masses of lead or iron also attract each other impulsively by virtue of their own special vortices, with atomized radiations and resulting central torrents, is not so definitely made out.
Such then is the primum mobile of the planetary gravitations; and with an admirable complacency, Bernouilli contrasts the system of Newton with his own, in which the elementary particles of matter, having no pores, receive the gravitative impulse necessarily on their surfaces. •' Now if it were the essential nature of bodies to 'attract' each other, it is evident that elementary particles would gravitate in proportion to their solidity, and not in the ratio of their surface, and that … consequently their attraction should diminish in the ratio of the cubes of the distance, instead of as the squares. … What then becomes of the system of M. Newton, when its very foundation is tumbled into ruins? I am surprised that not one of the partisans of this hypothesis has perceived this incongruity, in attributing attraction as an essential quality, not only to large masses, but even to the elementary particles destitute of pores !"[7]
It is scarcely necessary to criticise this wonderful system of "Celestial Physics." The condensation of the impalpable atoms of caloric, without adhesions and without attractions, (and seemingly without inertia,) into the dynamic gravific molecules of the "central torrent," is a phenomenon certainly as recondite as the gravitation these molecules are summoned to impel. It is sufficient to say that the Nouvelle Physique satisfies no single condition of the six formerly indicated as essential prerequisites. [217]
It may be added, that in the fourth book: of this labored treatise, the inclination of the ecliptic plane to that of the solar equator and vortex, is supposed to be due to a deviation or drift resulting from the oblong or prolate form of the revolving spheroidal earth."[8]
That such an essay should have been crowned by the Academy (the prize however being shared between John Bernouilli and his son Daniel as an independent competitor) appears in our day, notwithstanding the mathematical pre-eminence of its author, a somewhat unfavorable illustration of the scientific character of the age. Bernouilli has however left us the statement of an elementary truth, which may appropriately close this notice : " In physics we should banish the practice of explaining phenomena by chimerical principles more obscure than those presented for investigation."[9]
1 ↑ Published in the Pieces de Prix de l'Academic de Paris, tom, v, and included in bis collected works under the title Essai d'une Nouvelle Physique Celeste.
2 ↑ Johannia Bernoullii, Opera Omnia, A vols. 4to. Lausanne and Geneva, 1742; vol. iii, Sec. viii, pp. 270,271.
3 ↑ Loco citat., sections x and xvi, pp. 273, 276.
4 ↑ Loco citat., sectious xviii, six, pp.278, 279.
5 ↑ Loco citat., sec. xxviii-xxxvi.
6 ↑ Loco cital., sec. xxxvii-sl
7 ↑ Loco citat.,sec. xlii, p. 299.
8 ↑ The measurements of a meridional arc of the earth by James Casini, not long previously, had brought out the curious result that the polar axis of the earth is its longest diameter. — Tralté de la Grandeur et de la Figure de la Terre. Paris, 1720.
9 ↑ Opera : loco citat., sec. xxxii, p. 288.
