THE PRIME RESULTANT 71 



that proclaim them at once as strangers. For one thing, 

 their orbits are very elongated, with diverse inclinations, 

 and, for another, they are just as likely to have retro- 

 grade as direct rotations. It goes without saying that 

 such erratic visitors cannot fail to disturb the balance of 

 our system to some extent, and themselves be reacted up- 

 on in turn ; just as the throwing of a basin of water into 

 the sea theoretically affects the general level and the mu- 

 tual relations of all the drops in it. From the instant of 

 its haphazard injection into our system, the comet feels 

 the influence of the gravitational current or whirlpool in 

 which the planets are rotating, and immediately begins 

 the process of accommodating itself to the balanced order 

 of our system. This process is vastly prolonged, but it 

 is sure and steady, and it results finally in rounding out 

 the comet 's orbit, in reducing its inclination, and often in 

 converting its retrograde motion, if such it had at the 

 start, into a direct one. In short, the alien becomes a full- 

 fledged citizen. Thus I deduce that many (not all) of the 

 asteroids are simply domesticated comets, and that their 

 departure from planetary regularity in the matters of re- 

 trogression and orbital eccentricity and inclination are 

 just so many survivals of their preceding cometary 

 phase, which time will largely wear aw r ay. 



There is, however, a second cause for retrograde 

 motions, and this applies more particularly to satellites. 

 The three or four instances among these bodies exhibit- 

 ing this peculiarity, it will be remembered, are the outer- 

 most members of their respective systems. Now, between 

 the eddy of Saturn's group and that of the Jovian group, 

 for example, there is a point or line where the circumfer- 

 ence of the eddies may be supposed to impinge or "inter- 

 fere, ' ' whirling there in opposite directions. This region, 

 however, is not a well defined line but a rather nebulous 

 zone, so that a body w^hich for any reason has become en- 

 tangled in it halts, as it were, between two allegiances, 

 undecided whether to attach itself finally to Saturn's sys- 

 tem or to Jupiter's. The result is, obviously, a mixed or 

 hybrid motion whose analysis will require the methods of 

 higher mathematics to reduce to definite terms in in- 



