ON THE ORBITS OF THE ASTEROIDS. 141 
values assigned to them in the preceding investigation, the orbit of Hygea could never 
have intersected with that of Vesta, Flora, Metis, Urania, or Harmonia; the orbit of 
Themis could never have intersected with that of Vesta, Flora, Metis, or Harmonia; 
and that of Psyche could never have intersected with that of Flora or Harmonia. 
It is also to be remarked that the angles (0), (1), (2), &c. are entirely independent of 
the circumstances of the explosion, being functions of the time alone, and that there- 
fore the chances are tens of thousands to one against their all having had, at the time 
of the explosion, values near those which have been here assumed for them. 
The question now arises whether this result can be considered conclusive against 
Olbers’s hypothesis. ‘Three possible sources of inaccuracy are to be considered : — 
1. The effect of the quantities of the third order, neglected in the analysis and 
computations. 
2. The effects of the mutual attraction of the asteroids. 
3. The possible action, on the asteroids, of other forces than that of gravitation. 
The quantities of the third order would not probably affect the eccentricities by a 
greater amount than two or three units in the third place of decimals. If so, they 
would not materially change the character of the preceding result. 
Two asteroids might, by their mutual attraction, change each other’s mean distance 
very materially, provided that they passed sufficiently near each other. Two asteroids, 
taken at random, might be expected to pass within 10,000 miles of each other about 
once in four hundred millions (400,000,000) of years, and therefore some two asteroids 
might be expected to pass this near each other about once in 250,000 years. If the 
magnitude of the largest asteroids is, as we might judge from their brilliancy, the 
hundred-thousandth part that of the earth, an approach of another asteroid within ten 
thousand miles of it would be sufficient to cause a material change in the mean motion 
of the latter. It does not, therefore, seem possible absolutely to disprove Olbers’s 
hypothesis, by an attempt at rigorous computations of the secular variations of the 
asteroids. ) 
The only force besides the attraction of gravitation which it will be Wm while to 
consider, is the resistance of a medium. If, as Encke supposes, tiè celestial spaces 
are pervaded by a very rare resisting medium, it does Lus seem at all ae Es 
during the millions of years which may have been iio does by the — in moving 
through it, their orbits may have been so altered by its aen e to invalidate our con- 
clusions, drawn from reasoning in which the effect of this action has been neglected. 
Our next question will then be that of the third section. 
