TWENTY-NINTH ANNUAL MEETING. 49 
of Aithra would intersect that of Mars at two points and at various times, once 
certainly when Mars would be passing aphelion and the asteroid perihelion. 
The accompanying figure will illustrate the supposition, the plane of the paper 
representing the plane of the orbits. 
Fig, 1. 
Anywhere to the right of the Sun’s place, Mars would exert a tremendous 
pull on the asteroid, and especially so at the points of intersection. But as the 
orbit of the asteroid cuts the plane of the ecliptic at an angle of 25°, and that of 
Mars at an angle of 1° 51’, then the probability that the planet and the asteroid 
will pass through the plane of the ecliptic at the same or nearly the same time, 
and at points relatively the same, as if both in the same plane, will be somewhat 
diminished, but far from vanishing. 
In figure II the plane of the paper represents the plane of the ecliptic, the 
large ellipse the plane of the asteroid’s orbit, the small ellipse the orbit of Mars. 
It is clear that notwithstanding the great difference between the angle formed by 
the intersection of the orbit of the asteroid and the plane of the ecliptic, and that 
by the intersection of the orbit of Mars and the plane of the ecliptic, there will 
come a time when the planet and the asteroid will get very near each other. 
Then the attraction of Mars at such close range, will be sufficient to change for- 
ever the direction of motion, and the plane df the orbit of the asteroid. What 
will then be the fate of Althra? Under the conditions named, the asteroid will 
be transformed into a moon revolving about Mars as its primary, and so consti- 
tuting one of the family of the planet. 
However many asteroids there are, or whatever the width of the asteroidal 
belt is, it may be considered probable that there are hundreds or perhaps thou- 
a4 
