Chase.] [Ap il 21, NEBULAR ACTION IN THE SOLAR SYSTEM. BY PLINY EARLE CHASE, PROFESSOR OF PHILOSOPHY IN HAVERFORD COLLEGE. (Read before the American Philosophical Society, April 21st, 1876.) In studying the special evidences of nebular action, we find various significant relations, based on the following cardinal planetary positions, for which Stockwell's* values are taken: h 4.88632 4.97824 5.20280 5.42735 5.51927 .63295 12.11; h 1. The minimum eccentricities of the principal planets, as found by Stockwell are:-Neptune, .00557; Uranus, .01176; Saturn, .01237; Jupiter, .0255; Earth and Venus, each, 0. The ratios, counting towards Sun, are, therefore, ÷ 6 12.07. The closeness of these approximations to the fraction †, suggests their probable dependence on a fall through a half-radius, which would give the particles of a nebulous ring the velocity of separation. 24 2. The secular ranges of the planets present many suggestive features. Jupiter's (.68295) corresponds with Earth's orbital radius of spherical gyration (.63245); Saturn's (1.6088), with the nucleal tendency of Earth's kinetic radius, (1.42321 1.6009); Uranus's (2.99111), with the asteroidal belt, and with a linear pendulum of which Earth occupies an oscillatory centre; Mars's, with the centre of linear oscillation of Jupiter's; Venus's, with the centre of explosive oscillation of Mercury's; the range sum of Neptune and Earth, (1.00685), with Earth's mean vector-radius; of Venus and Mercury, (.60462), with the kinetic atmosphere (.60087); the sum-ratio of Earth and Venus, (.23765), with the ratio of Mercury's greatest eccentricity (.23172). 3. Stockwell's estimates for the maximum secular eccentricity, Bessel's for the masses of Jupiter and Saturn, and Newcomb's for those of Uranus and Neptune, give the following values for the positions of centres of gravity, at secular perihelion, mean, and secular aphelion, the unit being Sun's radius: *Smithsonian contributions, 232, pp. 37, 38. These values likewise exhibit a close approximation to the perihelion ratio, between the companion planets of each pair, together with indications of nebular rupture between Saturn and Uranus, and of increasing condensation towards Neptune and Jupiter. The perihelion ratio of Neptune: Jupiter 1:3.1; that of Uranus : Saturn 13.2, or nearly that of a nodal division, to the entire length, of a linear pendulum. The reversal in the direction of condensation, between the central and the exterior belt, may perhaps explain the retrograde satellite motions of Uranus and Neptune. 4. If we compare the perihelion and the aphelion centres of gravity of companion planets, we find that .6347 is near the centre of spherical gyration (√.4 × 1.0019 = .6336) of 1.0019, and that .1681 is near the centre of nebular rupture *(.1661) of .3323. · 5. The time of revolution varying as r2, while the time of rotation with the velocity due to interior vis viva varies as r r, the limiting radius of synchronous rotation and revolution, for any given expanding or contracting nucleus, is a mean proportional between the limiting radii of interior and exterior nucleal rupture. I have shown that the gravitating impulses are 4565 × (10)" per second, corresponding in frequency with the red rays of light, and the modulus of light is 365.256 x 86400 2 X √214.86 × 497.825 2 473755 solar radii. If modulus were taken as the primitive radius of resisting inertia, (r), Neptune's position would accord with the corresponding nucleal radius (r=6077.2 solar radii), and Mercury's with the radius of internal rupture (r =77.96 solar radii) Saturn's place being fixed, as we have seen, by the centre of nucleal planetary inertia, its mean aphelion radius appears to have influenced Neptune's position, while Earth's secular aphelion exerted a like influence on Mercury's position; for 1.04835 X 6077.2 : 6371, Neptunes secular perihelion being 6359.5, a difference of less than of one per cent.; 1.06774 × 77.96 = 83.24, Mercury's mean distance being 83.17, a difference of about one per cent. of 6. The mean proportional between these values of r and r, as well as between Sun's radius and modulus, is 688.3 solar radii, or 3.203 times Earth's mean radius vector, which is near the outer limit of the asteroidal belt. This agrees very closely with the secular range of Uranus (2.99111), and the relation is still closer to the ratio between the gravitating radii of Saturn Velocity at 1⁄2 r = √2gr. PROC. AMER. PHILOS. SOC. XVI. 97. x Chase.] [April 21, and Uranus (5883 1824 3.209 09} The positions of the principal masses in the three chief companion planetary pairs, indicate the same law of mean proportionality, between interior and exterior rupturing tendencies. For Jupiter's secular aphelion (5.5193) is at the geometrical mean (5.5195) between Earth's mean distance and Neptune's secular aphelion (30.46955). Neptune's secular perihelion (29.598) is within one per cent. of 6 X Jupiter's secular perihelion, or in inverse ratio of the indices in my equation of products of figurate powers, (¥1 × ô3 × ¥6 = ↳ 1o). 7. The nodal influence of linear centres of oscillation, on material particles which are subjected to radial lines of force," is shown in the vectorradii of the three outer planets, (Saturn, mean aphelion, 10; Uranus, mean aphelion, 20.044; Neptune, mean, 30.034). This tendency would be aided by the apparent primitive interposition of Sun between Jupiter and the exterior planets; for Saturn's vector-radius is so small, in comparison with modulus, that the above positions represent the geometrical progression, (n + 1), (n + 1)2, (n + 1)3, as well as the arithmetical peudulum progression, 1, 2, 3, thus satisfying the requirements, both of elastic media and of simple force-lines. The many indications that Jupiter and Saturn were once parts of the same nebular belt, with a mean nodal difference* of 180°, serve to connect those accordances with the figurate equation. 8. As further clews to the significance of the figurate equation, it may be well to note the closeness of the accordance between the mass-ratios :¥, 62, and the distance-ratio (: ); as well as Stockwell's ratios* of mean perihelion and node-motion. 9. The radial light oscillation which is synchronous with the present limit of possible circular revolution, is 10020.25 ÷ 497.$825 20.128 Earth's vector-radii, which is also the rupturing radius of the retrogradesatellite and the direct-satellite planets, the difference between the secular aphelia of Saturn and Neptune, (or the vector-radius of Neptune relatively to the nebular planetary centre of inertia), being 20.126; the mean aphelion vector-radius of Uranus 20.044; the major axis of the November meteors, and the secular aphelion of Uranus, each = 20.68; twice Saturn's secular aphelion 20.69; the original nebular activity thus combining with the satellite influences, in maintaining Saturn's rings. Moreover, Neptune's secular perihelion 1.4313 the secular aphelion of Uranus, (the "kinetic radius" or the limiting radius of equality, towards which I have shown that all central forces mathematically tend, being 1.4232). = = 10. The sum of Uranus's mean, and Earth's secular perihelion vectorradius 20.0158. The importance of Earth's position, the near approxi mation of this sum to the cardinal light oscillation (9), and the indications of a somewhat shorter major-axis for the inner meteors of the November stream, encourage us to look for still further evidences of continuing nebular activity, in our own orbit as well as in that of Saturn. If Earth and Uranus were once parts of an elliptical ring, or meteor current, with Stockwell, op, cit, p. xiv. Earth sharing Uranus's present maximum secular eccentricity (.077965). Earth, Jupiter, Uranus, and Sun, were connected by the following equa tion:-Modulus 2 the square of Jupiter's mean radius vector the time of revolution at secular perihelion (.922035) of a mean-proportionate radius between Earth and Sun (1 : √/214.86) ÷ (square of Earth's radius exceeds the value found by of one per cent. X1 year). This value of modulus (474250) the ordinary methods (473755), by less than 11. The secular range of Uranus, between 17.688 and 20.679, subjects all the intra asteroidal planets, together with most of the asteroidal belt, to the influence of its accompanying light-oscillations, so that all the members of our interior system of dense planets may have been partially built up of materials from a meteoric stream, of which the November meteors are the débris. Earth's secular aphelion (1.0677; Cfr. the ratios of O centre of gravity, 1.0668, and of Jupiter's secular aphelion, 1.0608) was established near the linear centre of gravity of a pendulum, of which the kinetic radius marked the centre of oscillation (X X 1.4232 = 1.0674). Venus's secular perihelion (.6722), is near the centre of spherical gyration of Earths secular aphelion (√.4 × 1.0677 = .6753). 12. If we take the primitive light-axis (20.128), and suppose it subjected to repeated oscillations through Earth's mean vector-radius, successive nodal bisections give the following approximations : 13. If the kinetic radius of Mercury's secular perihelion was also the radius of nucleal separation, its secular aphelion (102.438) was near a corresponding atmospheric radius (1.4 42323 X 63.906 102.305). 14. If the luminiferous, or kinetic æther is the permanent representative of the original hypothetical nebula, in which suns and planets are but floating particles, Faraday's "lines of force" may be due to longitudinal and transverse waves, either of various degrees of velocity but uniform frequency, or of various frequency but uniform velocity, or of velocities and frequencies both varying, in accordance with definite harmonic laws. The luminous, thermal, magnetic, gravitating, cohesive, and dissociating impulses, all have simple harmonic representatives in the 26th musical octave, which is the special octave of light-proper; the gravitating impulses have also important harmonics in the 46th, 91st, and 92d octaves. * *The "selenium eye" illustrates one of these harmonies. Prof. W. G. Adams, (Proc. Roy. Soc. Jan. 6, 1876; P. Mag. April 1876) says: "the change in the resistance of Selenium is directly as the square root of the illuminating power." This is inversely as the velocity of nucleal rotation. The deflections in the dark (32) and in the strong sunlight (470) give the ratio 14.69; the ratio of emanating force at Sun, to that at Earth's orbit being 14.66. 15. Jupiter, the chief planet in the supra-asteroidal, and Earth, the chief planet in the intra-asteroidal belt, are connected by the following propor tion. The number of light-oscillations (log. 20.699916) which would communicate the greatest gravitating velocity in our system (√/2gr at Sun) the number (log. = 15.822542) in describing Sun's circumference (2 π †) :: velocity of revolution at earth (1 √/214 86): velocity of gravitating fall at Jupiter (11051.298)2, the units of velocity being taken, respect ively, at Sun's surface, and at the limit of equilibrium between aggregation or dissociation (1.4232 + 1049.875). 16. The same chief planets are also connected by the proportion : — Modulus (688.3): light-producing wave at the mean-perihelion centre of gravity of Sun and Jupiter ( × 1.0198) :: Earth's mean radius vector: Sun's radius. The value of Earth's radius-vector thus found, is 214.842; the value which is derived from the observations which I have thought the most accurate, being 214.86. 17. -Jupiter and Sun thus appear to be companion constituents of a binary star, and the point of primitive rupture should be sought at the secular perihelion centre of gravity. Bodies falling toward that point, or approaching Sun, are subject to a force of about 1048 towards Sun, and 1049 towards the slowly moving common centre of gravity. There are, therefore, two 1048 nodal points, with the least resistance to motion nearly midway (2067) between them. If Sun is gaseous, as Hunt, Faye, and others have supposed, there should hence arise linear oscillations of 2 x 2 r, synchronous with the circular oscillations of 2 r. The corona may, perhaps, be due to such radial oscillations. 18. The 15th accordance gives for the mass of Sun ÷ Jupiter, 1049.875 — 21047.875; the 17th, 1049.874 - 2 = 1047.874; Bessel's estimate being 1047.879.235. 19. The discrepancy between the two astronomical estimates for the velocity of light, seems to have arisen from ignorance of the internodal oscillation. Delambre, from his discussion of more than 1000 eclipses of Jupiter's first satellite, estimated the time of light-passage from Sun to Earth at 493, $198; Struve, from the phenomena of aberration, at 497.5827. If the time of traversing 212.86 solar radii is 493.198, the time for 214.86 r should be 497.831, which differs from Struve's value by less than rooo of one per cent. 20. If Earth was at the nebular nucleal surface, when the Jovi-Saturnian ring was nebularly atmospheric, the vis viva of interior nucleal rotation varied as r; and the velocity of resulting planetary revolution, as thus obtain, for the theoretical time of present solar rotation, √214.86:1:: 365.256: 24.912. The lowest estimate from observation is Spörer's 24.624; the highest, that of Schwabe, 25.507. *Stockwell, Proc. Amer. Asso, xx. 76-7. We |