162 COSMICAL ARRANGEMENTS. 



times her own breadth, of what her place would 

 have been if it had not been affected by this 

 acceleration. The obliquity of the ecliptic also 

 is in a state of diminution, and is now about two- 

 fifths of a degree less than it was in the time of 

 Aristotle. Will these changes go on without 

 limit or reaction? If so, we tend by natural 

 causes to a termination of the present system of 

 things : If not, by what adjustment or combi- 

 nation are we secured from such a tendency ? Is 

 the system stable, and if so, what is the condition 

 on which stability depends? 



To answer these questions is far from easy. 

 The mechanical problem which they involve is 

 no less than this ; Having given the directions 

 and velocities with which about thirty bodies are 

 moving at one time, to find their places and 

 motions after any number of ages ; each of the 

 bodies, all the while, attracting all the others, 

 and being attracted by them all. 



It may readily be imagined that this is a prob- 

 lem of extreme complexity, when it is considered 

 that every new configuration or arrangement of 

 the bodies will give rise to a new amount of action 

 on each ; and every new action to a new con- 

 figuration. Accordingly, the mathematical in- 

 vestigation of such questions as the above was 

 too difficult to be attempted in the earlier periods 

 of the progress of Physical Astronomy. Newton 

 did not undertake to demonstrate either the 



