ASTRONOMY
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and hence its probable mass. The statistical law of progressive diminution of the magnitudes or volumes, as derived from the known members of the group, may be extended to the undiscovered members. That a law of progressive diminution extends to the unknown members may be inferred from the fact that, if there were a very great number above a certain limit of magnitude, the whole mass would be visible as a band of light spanning the heavens. The writer has found that by no probable hypothesis as to the number and size of these bodies, consistent with the absence of this band, can the total mass be sufficient to exert any appreciable action on any other planet. . . Fig. 3. The mass and diameter of Jupiter can be determined m from measures on the polar spot, giving the position of the pole of two ways—by measures of the satellites and by the action rotation, and from observations of the satellites. The best result of Jupiter on other bodies. The satellites are jupiter. of this first method is derived by combining the results of not well adapted to give an accurate value of the Schiaparelli and Lohse. H. Struve has applied the second. The results are, for the inclination of the equator of Mars to that of mass, as any proportional error in their mean distances ■£ll6 from the planet is multiplied threefold in the result. The J0 = 36'42° (Schiaparelli and Lohse) following are the results for the reciprocal of the mass J0 = 37° 27'1' (t -1880) (Struve) ; reached by different methods, with the weight that may and for the longitude of ascending node of equator on that of the be assigned to each :— earth, Observations of the satellites . . ^,=1047-82 Wt. 1 N0 = 48,26° (Schiaparelli and Lohse) Action on Fayes’s comet (Mbller) . /i=1047-79 ,, 1 Themis (Krueger) . . /i=1047"54 ,, 5 N0 = 47° 5-7'+ 0-463' (£--1880) (Struve). ,, Saturn (Hill) . . • ^ = 1047"35 ,, 7 Struve also finds, from the motions of the pericentres of the ,, Winnecke’s comet (Haerdtl)/i=1047"17 ,, 10 satellites, ellipticity of Mars = 1/190‘4 ; but owing to a doubt as to ,, Polyhymnia (Newcomb) . ^. = 1047"34 ,, 20 the revolutions of the pericentre of Phobos, this possibly should be The mean result, 1 /178 i In representing the elements of the orbits of the satellites, the Mass of Jupiter 1 following notation is used :—
Mass of sun 1047 "35 + "05 Ji, Ni, inclination and node of the “fixed plane of the satellite’s orbit, referred to the earth’s equator for the epoch is that now adopted in the planetary tables. In 1901 De 1880 ; J, N, the same for the orbit of the satellite ; Lq, the mean Sitter published an important additional result derived longitude at the epoch 1894 October, 0-0 Greenwich mean time; from heliometer observations by Gill and Finlay at the n, the tropical mean daily motion ; a, the angular semi-major axis of the orbit, as seen from distance unity ; tt, the longitude of the Cape Observatory. This was— pericentre on the equator of Mars ; e, the eccentricity ; K, an M=1047-226+ 0-067. an<de varying uniformly with the time, whose rate of motion is Ho definitive changes have been made in the adopted equal to that of the pericentre, and of the node of the satellite s orbit on the fixed plane ; and t, the time in years from 1894-80. elements of the satellites of Jupiter in recent times. The numerical values of the elements as found by Struve The measures of the diameter of Jupiter are very are :— Phobos. numerous, and the differences between the results must be Deimos. 358-7°-158°-0£ regarded as due to personal equation and peculiarities of 29-9°-6-375° £ K 37° 26-7' 36° 46-5' . instrument rather than to accidental errors. The latest Ji. . 47° 5-0' 46° 2-6' . N, . results by the two methods are :— 0° 53 T' sin K 1° 37-6' sin K ■' Equat. Polar. (N - Nj) sin J 0° 53 l' cos K 1° 37"6' cos K J — J! * • Schur, from observations with the helio296T3° 35-13" 37186-25°. L0 ' . meter . . . . • 1128-84396° 285-16198° . n. Barnard, from observations with the filar 12-938° 36T1" 32-373“ a . micrometer ...••• 38272-6° + 158°-0£ 231°+ 6-375° £ This difference between the results of the two methods 0-0217 0-0031 appears to be common to all observers, the method of From the values of a follows :— double images always giving a smaller diameter than the Mass of Mars 1 micrometer. It may be attributed to a certain softness of Mass of sun 3090U0U outline of Jupiter’s disc, which is easily remarked by a Professor Hall’s figure, now generally used in astronomy, is careful observer. 1/3093500. The ball, rings, and satellites of Saturn show mechanical Schur has measured the diameters of Mars with the heliometer, features of great interest, not found elsewhere in our Barnard with the filar micrometer. The results for the equatorial system. One of the simplest of these is that the Saturn. and polar diameters, as seen from distance unity, are : planes of Saturn’s equator, of its rings, and of at Equat. Polar. least its seven inner satellites, have a common secular Schur ..... 9-526" 9-325 Barnard 9'673 9’581 motion due to the action of the sun. If the latter acted Each value of the ellipticity is markedly greater than that found on each of these bodies separately, the secular motions of the planes would be greater the farther the satellite is from by Struve from the motion of the pericentre of Phobos. The minor planets individually are too minute to exert the planet, and the motion of the nodes would take place a sensible action on the other planets; but the question around the plane of the orbit of the planet, the planes of the orbits preserving a nearly constant inclination of Mass of whether the mass of the entire group, which almost 27°. The ultimate result of the unequal motion ths minor may number thousands, can be sufficient to proplanets. duce an appreciable secular variation of the node would be that the nodes would be scattered all round the and perihelion of Mars is an important one. A rude circle, and the planes of the several orbits of the satellites estimate of the total mass of the group may be made might have mutual inclinations to each other amounting in the following way :—From the stellar magnitude of each to 53°. But the mutual interaction of the equatorial prosatellites keeps known minor planet we may roughly infer its diametei, tuberance of the planet, the rings, and the S. I. —94
i.s the resultant of these two components, and is such as to carry S round in a circle, of which the centre is at a third point 10 This centre is the pole of a certain plane called the “fixed plane ” of the satellite orbit, which makes but a small angle with the plane of the planet’s equator. The position of the plane of Mars’s equator relative to the plane of the orbit has been found in two ways
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