542 EEPORT — 1886. 



10. On the Determination of the Radius Vector in the Absolute Orhit of the 

 Planets. By Professor Gtlden. 



31. Note on the Orlits of Satellites. By Professor Asaph Hall. 



[Plate XL] 



The observations of the five inner satellites of Saturn made at Washington 

 since the mounting of the 26-inch refractor in 1873 have been reduced and dis- 

 cussed, and new orbits of these satellites have been determined. It is true that 

 -our observations of these satellites are not very numerous, and that further observa- 

 tion will be necessary in order to reach a definitive result. It should be stated also 

 that the elliptical figure of this planet and the presence of its ring make it difii- 

 cult to determine the position of a satellite by means of a filar micrometer in a 

 manner that shall be wholly free from the suspicion of systematic errors. The 

 probable error of one of our measurements is + 0-27" ; and I am inclined to think 

 therefore that the Washington observations are as good as any that have been 

 made. The result of our discussion is that the five inner satellites move in orbits 

 whose planes very nearly coincide with the equator of the planet, and the plane of 

 the ring ; and also that these orbits are practically circles. The first result is what 

 is generally assumed, but the fact that our observations can be satisfied within the 

 limits of their probable errors by circular orbits seems to me a remarkable one. It 

 would have been interesting of course to have found elliptical orbits, which would 

 have given us the positions of the lines of apsides and their motions, and which 

 would have led to a value of the mass of the ring ; but the circular orbits exclude 

 fluch results. 



In the accompanying diagram the orbits of the satellites of Saturn are shown 

 as they would be seen from the pole of the planet's equator, with the exception of 

 the orbit of lapetus, which is not correctly drawn, since this orbit is inclined to the 

 plane of projection about 14°. A glance at the diagram will show the relations of 

 the orbits. Thus, beginning at the centre of the planet, the distances to the edges 

 of the ring and to the satellites increase regularly until we reach Rhea. From Rhea 

 to Titan there is a large interval. The orbit of Titan is on the inner edge of the 

 coloured surface, and that of Hyperion is on the outer edge of this surface. This 

 small satellite is so connected with Titan that it may be looked upon as almost a 

 companion of the large satellite, from Hyperion to lapetus we have a very long 

 interval. It is in these two intervals that one woiild naturally look for new 

 satellites. 



But what I wish now to call especial attention to is the fact of the circular 

 orbits of the five inner satellites. In this connection we may notice that the orbit 

 of the satellite of Neptune, those of the four satellites of Uranus, and also those of 

 the three inner satellites of Jupiter are likewise all circular. The orbit of the outer 

 satellite of Mars is very nearly circular. As for the orbit of the inner satellite of 

 this planet, the discussion of my observations of 1877 gave an eccentricity 0'0321, 

 which seemed real ; but the recent discussion of my observations of 1879 has dimi- 

 nished this eccentricity, and indicates that this orbit also must be nearly circular. 

 The observations of 1879 are better, I think, than those of 1877, since although the 

 satellite was fainter in 1879, the disc of the planet was so much smaller that the 

 measurements were not so liable to systematic errors which might produce a 

 spurious eccentricity. 



In the table on next page I have collected the distances and eccentricities of 

 the satellites of our solar system. The distances are expressed in equatorial radii 

 of the primary planets. 



This table shows that Hyperion has the largest eccentricity, but this satellite is 

 connected with Titan in such a manner that it may be considered an exceptional 

 case. Generally it appears that the satellites with small distances have also very 

 small eccentricities. To this it may be objected that such a result depends partly 

 on the difficulty of determining for the small distances a good definite value of the 

 eccentricity. There is some ground for such an objection, since in this case small 



