Page:The American Cyclopædia (1879) Volume XIII.djvu/587

 PLANET 571 lowed by increase is very difficult to interpret. In this connection we may note an empirical law which Prof. Kirkwood of Bloomington, Ind., has recognized as seemingly connecting the rotation periods of the planets with their masses and distances. It is as follows: "If through the sun a line be drawn cutting the orbits of all the planets (supposed to be pro- jected on the invariable plane of the solar system), and the intercepts between each con- secutive pair of orbits be divided in the pro- portion of the square roots of the masses of the corresponding planets ; and if the distances between these points of division be D, D', D", and n be the number of sidereal revolutions which the planet makes on its axis in its peri- odic time, then will the following relation hold for two consecutive planets, w 2 : n' 2 : : D 3 : D /s. This supposes the existence of a planet between Mars and Jupiter, corresponding to the aggre- gate of the asteroids, and having a mass equal to one third of the earth's." We venture to express some doubt whether the rotation peri- ods of the planets have been determined with sufficient accuracy to support this ingenious theory. But Prof. Walker considers that Kirk- wood's law may be legitimately deduced from the nebular hypothesis. The position of the axes of the several planets might be expected to indicate the existence of some law or rela- tion resulting from the nebular hypothesis; but it is difficult to recognize any in the fol- lowing table, which includes all the planets whose rotation has been accurately ascertained : PLANETS. Eccentricity. Inclination. Mercury 0' 20561 8 Venus . 0'006S83 300 Of) . n The earth... 0'016771 000 Mars .:.... 0' 0932 62 1 51 VI Jupiter 048239 1 18 40'8 Saturn 0' 05599 6 2oq oa i Uranus 0' 046578 46 29 ' 9 Neptune 0-008720 1 46 59-0 PLANETS. Rotation period. Inclination of equator to orbit. Longitude of rising node of equator on orbit. The earth Mars 23h. 56m. 4s. 24 3T 23 9 55 26 10 29 17 23o 27' 24" 28 27 00 3 5 80 26 48 40 180 79 15' 814 167 4' 5" Jupiter. Saturn It is supposed that the equator of Uranus is inclined about 75 to the planet's orbit, while the axis of Neptune is so abnormally posited (if the planet's rotation corresponds with the motion of his satellites) that the inclination of his equator must be described as exceeding 160. In other words, the inclination mea- sured as a plane angle amounts to less than 20, but the planet rotates from east to west instead of from west to east. The orbital motions of the planets present certain features of uniformity ; thus each of the chief planets travels in an orbit very nearly circular (though in some cases notably eccentric in position), all the planets travel the same way round, and the planes in which they travel are little in- clined to the ecliptic, and (on the average) still less to the medial plane of the system. The following table presents the eccentricities (the mean distance of each planet being unity) and the inclinations of the orbits to the ecliptic, in the arrangement of which it is difficult to recognize any law in respect of magnitude : Some of the asteroids have orbits of much greater eccentricity and inclination. Thus the eccentricity of Polyhymnia is no less than 0-339119, and the inclination of Pallas amounts to 34 45'; so that the excursions of Poly- hymnia on either side of its mean distance, and the excursions of Pallas on either side of the plane of the ecliptic, exceed when taken to- gether the mean distance of either planet. It has been remarked that " there are few more interesting chapters in the history of astron- omy than those which treat of the mathemati- cal relations presented by the planetary eccen- tricities and inclinations." Seeing these ele- ments, as we do, undergoing gradual processes of increment and decrement continuing for long periods in the same direction, astronomers were in doubt until mathematics solved the difficulty whether the planetary system was in truth stable, or whether processes might not be in action which would go on with gradually increasing effects until at length the whole sys- tem would be destroyed. Gradually the pro- gress of analysis revealed the true interpreta- tion of these processes, and showed them to belong, not to changes tending continually in one direction, but to oscillatory variations pro- ceeding in orderly sequence within definite and not very wide limits. We owe to Lagrange the first enunciation of the laws relating to the stability of the solar system ; but to Laplace must be ascribed the credit of establishing the important theorems which have been justly called the Magna Charta of the solar system. He proved in 1784 that in any system of bodies travelling in one direction around a central attracting orb, the eccentricities and inclina- tions, if small at any one time, would always continue inconsiderable. His two theorems may be thus stated: 1. If the mass of each planet be multiplied by the square of the ec- centricity, and this product by the square root of the mean distance, the sum of the products thus formed will be invariable. 2. If the mass of each planet be multiplied by the square of the tangent of the orbit's inclination to the medial or fixed plane, and this product by the square root of the mean distance, the sum oi the products thus formed will be invariable. Thus is the stability of the solar system secured for periods which, compared with all known units of time measurement, appear to us abso- lutely infinite. Every orbit will undergo con- tinual changes of eccentricity and of inclina- tion, now one, now another having a maximum amount of either form of apparent irregulari- ty ; but in the midst of this continual flux, the