376 T. C. CHAMBERLIN 



approach, although it will not necessarily follow, because the 

 planes may not coincide, and for other reasons, may result — if 

 not at once, at least ultimately^ — -as a consequence of the shift- 

 ings and modifications which such a disturbed condition involves. 

 For example, it is obvious that by a favorable conjunction with 

 a passing system whose sun is distant from NeptU7ie considerably 

 more than the radius of his orbit, there may be an elongation of 

 the orbit of Neptime so as to make it cut one or more of the 

 inner orbits, and that further modifications may arise out of 

 these relations which will either increase or decrease the eccen- 

 tricity. The principles applicable here are identical with those 

 that have been found to produce radical modifications of the 

 orbits of comets and that have been worked out by H. A. 

 Newton and others. 



To embrace the full possibilities of the case, it is therefore 

 necessary to consider (i) the effects of systems passing each 

 other at distances varying from those in which the outermost 

 planets do not even cut each other's orbits, down to center-on- 

 center collisions, and (2) to take account of the ulterior effects 

 of disturbed orbits, as well as the immediate effects. This last 

 is a consideration of no small importance in the qualitative as 

 well as the quantitative application of the doctrine, for it distrib- 

 utes the effects over an indefinite period of time, and does not 

 require their coincidence with the passage of the systems. The 

 ulterior effects, so far as the disruption of secondaries is con- 

 cerned, may apparently be much greater than the immediate 

 effects. If this is not already clear, let a specific case be taken, 

 as, for example, two solar systems passing each other so that 

 their centers shall be 500,000,000 miles apart at nearest 

 approach. If the planes of the systems are transverse to their 

 paths, the ideal undisturbed orbits of the asteroids will touch, 

 or closely approach, or slightly cut each other, as the individual 

 case may be. The ideal orbits of the Jtipiters will fall but little 

 short of the passing sun, while the ideal orbits of Saturn, Uranus, 

 dind Neptime will fall outside the passing sun. While the precise 

 results of such an event cannot be computed, it is quite certain 



