312 F. B. Taylor — Determinate Orbital Stability: 



to counteract the normal tendency of this satellite to 

 contract its orbit to the determinate orbit. After the 

 mass of the planet and its distance from the Sun, the 

 fixing of the distance of the orbit of stability for the 

 second satellite appears to depend mainly upon the rela- 

 tion of the periodic times — the commensurabilities, or 

 rather, the particular phase of the incommensurabilities 

 — of the two satellites. Within rather wide limits, 

 the result appears to be independent of their masses, 

 for large and small satellites revolve in adjacent orbits 

 and obey the law without notable deviation. 



7. The third, fourth, and later satellites of the larger 

 systems are captured and installed in precisely the same 

 way, and the spacing of their orbits, -and their stabilities 

 in them, are dependent upon the same mechanism as that 

 just described for the second satellite. Thus, the third 

 satellite depends upon the supporting perturbations of 

 the second, the fourth depends on the third, and so on. 

 Under the law of determinate stability, a new member 

 may be acquired only by entering the space between the 

 primary and the first or nearest established satellite, and 

 then gradually driving all of the previously established 

 members out to larger orbits, while it winds its own orbit 

 down and finally settles itself in the first or determinate 

 orbit. The space between the primary and the deter- 

 minate orbit is in some sense like a vortex whirl (not a 

 vortex ring, but a whirl), and the process of capture by 

 this method may therefore be called vortex capture. 

 Satellite systems groiv by a process of vortex capture and 

 orbital expansion. 



8. By a simple and direct analogy, all of these principles 

 and explanations may be applied to the Planetary system 

 itself. It has the same dependence throughout on the 

 law of determinate stability, has the same structure, and 

 has grown by the same process as the imaginary satellite 

 system just described. All of the great features and 

 characteristics of the Planetary system come under the 

 pervasive power of the principle of determinate stability, 

 and are explained by it. 



9. In the Planetary system, the space between Mercury 

 and the Sun is the vortex through which all newly cap- 

 tured planetoids must make their entrance in order to 

 become planets. Mercury is now oscillating around the 

 determinate orbit, which corresponds to its mean circular 



