3 Art. 3.- K. Hirayauia : 



seems to be a loose aggregation of small bodies^^, perhaps composed 

 of the same kind of material as meteors, with rare gaseous 

 envelope. Most of the particles which are supposed to effect the 

 resistance will pass freely through this meteoric swarm. Uarely it 

 ma}' occur that some resisting particle strikes a cometary particle. 

 Then the latter will be projected outside of the swcirm and take on 

 an individual motion. Gradual degeneration will follow this 

 action if repeated frequently but there is no effect on the motion 

 of the main body. Yet one more thing is conceivable, viz. an 

 indirect effect coming in through the gaseous envelope. This, 

 however, would be very small owing to tlie tenuity of the latter. 



9. The assumption that the particles move in circular orbits 

 in a definite plane is nothing but an imaginary convention to 

 make the problem simpler. Practically this may he said to be 

 that at a point in or near the plane, the resultant composite 

 velocity of the particles passing through that point is equal to the 

 velocity of the circular motion. 



As for the density of the particles it is natural to assume a 

 certain amount of decrease as the distance from the sun increases, 

 that is, to assume a negative value for ^i. This is not all. for 

 there is some reason to believe that the particles are not numerous 

 near the path of the major planets. They cannot move in orbits 

 of small eccentricity in the neighborhood of the planets. If they 

 did, they would be disturbed a great deal by tlie action of the 

 latter, or they might even be swept up. except those moving 

 about the triangular equilibrium points. 



Chapter 11. 



Motion of the Asteroids wliose Mean Motions are 

 nearly Connnensura1>le to the Mean Motion of 

 Jupiter. 



1) Yoi 11;^' compares it with " piJi-lu-uls s.-v.-ral hundred feet apart. 



