138 | ON THE ORBITS OF THE ASTEROIDS. 
the orbit of which can ever approach indefinitely near the circular form. Doris may 
possibly be found to be an additional asteroid in this class. 
2. Euterpe is the only known asteroid the orbit of which can ever approach indefi- 
nitely near the invariable plane of the planetary system. 
3. The perihelion of each asteroid (Harmonia, Doris, and Euterpe excepted) revolves 
nearly in the same time as its node, the time of revolution varying from about 15,000 
to 40,000 years. : 
4. The following are the greatest and least values which can be attained by the 
eccentricities and inclinations to the invariable plane of the orbits of the asteroids 
included in the preceding tables: — 
Asteroid. Greatest Eccentricity. Least Eccentricity, Greatest Inclination. Least Inclination. 
o D o D 
Ceres 0.1556 0.0648 10 13 8 43 
Vesta 0.1514 0.0582 7 38 5 13 
Astrea 0.2598 0.1696 5. 38 8. 53 
Flora 0.1823 0.0823 7 40 4 2 
. Metis 0.1648 0.0726 5 56 3 39 
Hygea 0.1783 ... 0.0831 5 yá 4 929 
Parthenope 0.1231 0.0319 5-0 2 58 
Irene 0.2441 0.1539 8 56 T 19 
Psyche 0.1476 0.0550 3 17 i 55- 
Thetis 0.1823 - 00913 5 54 SR 56 
Fortuna 0.1758 0.0846 3 14 1 10 
Massilia 0.1993 0.1077 2 96 0 l7 
Lutetia 0.1799 0.0885 3 12 Ss 
Themis 0.1917 0.0965 1 42 0 27 
Proserpina 0.1566 0.0664 3 46 2 8 
Euterpe . 0.2238 - 0.1306 2. T7 0 00 
Bellona 0.2119 0.1211 9. 26 T Ul 
Amphitrite 0.1054 0.0152 T f 5 20 
Urania 0.1471 0.0539 3 51 1 29 
Pomona 0.1608 0.0706 4 8 5 20 
Circe 0.1831 0.0927 6 93 4 48 
Fides 0.2076 0.1174 4 0 9 99 
Leda 0.2084 0.1176 8 45 "o j3 
Lætitia 0.1220 0.0312 10 36 9 Y 
Harmonia 0.0607 0.0000 5 15 2 16 
§ 2. 
We now have the necessary data for investigating the questions referred to in the 
beginning of this paper. Since it is deducible from Olbers’s hypothesis that the orbits 
of all the asteroids once intersected each other in a common point, we may first find 
whether it is possible or probable that there ever was such intersection. I have consid- 
ered this question in Gould’s Astronomical Journal, No. 129, with reference to the aste- 
roids Vesta and Hygea, and there shown that, although the aphelion distance of Vesta. 
sometimes exceeds the perihelion distance of Hygea, an intersection of their orbits is 
