Ball — Speculations on the Source of Meteorites. 229 



"We shall therefore consider the circumstances under which it would 

 be possible for a volcano on one of the minor planets (for example, 

 Ceres) to discharge a projectile so that the projectile shall intersect 

 the ecliptic in the ring we have just referred to. As the mass of the 

 planet is small, the initial velocity which would be required to carry 

 a projectile away from the planet presents no difficulty, perhaps an 

 ordinary cannon would be sufficient, so far as the mere gravitation to 

 the planet is concerned. But when we consider that the projectile must 

 be driven through the ring we have been considering, a vastly more 

 powerful instrument would be required. 



Ceres is moving in an orbit (supposed circular and in the ecliptic) 

 with a velocity of about eleven miles per second. A projectile dis- 

 charged from Ceres will have an actual velocity which is compounded 

 of the velocity of Ceres, with the velocity which is imparted by the 

 volcano. But simple dynamical considerations show that if the pro- 

 jectile have an initial yelooitj perpendicular to the radius vector, differ- 

 ing much from eight miles per second, it can never intersect the ring, 

 no matter in what direction it be discharged.- The volcano on Ceres 

 must therefore be adequate to the abatement of the velocity perpendi- 

 cular to the radius vector from eleven miles per second to eight miles 

 per second, i.e., the volcano must he at the very least adequate to produc- 

 ing an initial velocity of three miles per second. As this is quite in- 

 dependent of the additional volcanic power requisite to carry the 

 projectile away from the attraction of Ceres, it is obvious that after 

 all there may be but little difference between the volcano which 

 would be required on Ceres, and that (of six-mile power) which 

 would project a body away from the surface of the earth for ever. 



Admitting, however, that a volcano of sufficient power were placed 

 upon Ceres, would it be likely that a projectile driven therefrom would 

 ever cross the earth's track ? This is a question in the theory of pro- 

 babilities, and it is not easy to state the problem very definitely. If 

 the total velocity with which the projectile leaves the orbit of Ceres 

 be less than eight miles per second, then the projectile will fall short 

 of the earth's track ; on the other hand, if the total initial velocity 

 exceeds sixteen miles per second, the orbit in which the projectile 

 'moves will be hyperbolic, and though it may cross the earth's track 

 once, it will never do so again. Taking a mean between these ex- 

 treme velocities we may investigate the following problem : — Suppose 

 that a projectile is discharged from a point in the orbit of Ceres in a 

 random direction with the total initial velocity of twelve miles per 

 second, determine the probability that the orbit of the projectile shall 

 cross the earth's track. When this problem is solved in accordance 

 Avith the calculus of probabilities, it is found that the chances against 

 the occurrence arc about 50,000 to 1, i.e., out of eveiy 50,000 pro- 

 jectiles discharged at random from a point in the orbit of Ceres, only 

 a single one can be expected to cross the earth's track. 



- Disregarding an obvious exception. 



S3 



