Mechanism and Functions in Celestial Mechanics. 313 



orbit, and in its relatively high eccentricity and inclination 

 of plane, still carries marks of its newness as a planet, 

 It has not yet become fully settled. Some of its peculiari- 

 ties of motion are probably due to the action of the unbal- 

 anced forces which affect it when it is farthest inside or 

 farthest outside of its mean circular orbit, and may not 

 require Einstein's new theory to explain them. 



Is it not clear that the mechanism of the adjustment 

 and stability of the second satellite, as outlined above, 

 discloses, in reality, a basis for determining the physical 

 explanation of the Law of Titius (Bode's Law), in accor- 

 dance with which the planets are set at certain orderly 

 intervals of distance from the Sun? This law has always 

 been a subject for mere ridicule. It is usually passed 

 over in one sentence as ^'a so-called law." But under 

 the principle of determinate stability, it is the capstone 

 of the structure, the final completing law of systematic 

 organization. We see its physical basis more clearly in 

 the satellite systems, where the scale of each system is 

 fixed by the mass of the primary, and the intensity of each 

 system by the mass of the Sun and by the distance of the 

 primary from the Sun. If Jupiter 's mass were one-fourth 

 of what it is its satellites would be nearer to it, and they 

 would be more clos.ely spaced, a more compact system. 

 On the other hand, if Jupiter revolved in the Earth's orbit 

 it is doubtful whether it could retain even one satellite, 

 because the determinate orbit would be so far out. The 

 failure of the Law of Titius in the case of Neptune is of 

 no vital importance. The delicate forces revealed in this 

 law grow excessively weak at that great distance, and it 

 is not surprising that perfection of adjustment fails. The 

 remarkable unimportance of mass in the planets as com- 

 pared with commensurabilities in the operation of this 

 law is shown by the fact that little Mars and the thinly 

 scattered ring of tiny planetoids, though somewhat per- 

 turbed, hold their appointed places in close proximity 

 to the mighty Jupiter. 



10. The satellite zones of the planets are naturally 

 widest far from the Sun, and the forces that hold the outer 

 satellites of the outer planets are exceedingly weak. 

 Nearer the Sun, the limits of the zones draw together, 

 the inner moving out, and the outer in. This is clearly 

 shown if all the planets be supposed to have the same 

 mass. The Earth's zone is narrow, but that of Venus is 



