CHAPTER XL 



DIRECT EQUILIBRATION. 



159. EVERY change is towards a balance of forces; and 

 of necessity can never cease until a balance of forces is 

 reached. When treating of equilibration under its general 

 aspects (First Principles, Part II., Chap, xxii.), we saw that 

 every aggregate having compound movements tends continu 

 ally towards a moving equilibrium; since any unequilibrated 

 force to which such an aggregate is subject, if not of a kind 

 to overthrow it altogether, must continue modifying its state 

 until an equilibrium is brought about. And we saw that the 

 structure simultaneously reached must be &quot; one presenting 

 an arrangement of forces that counterbalance all the forces 

 to which the aggregate is subject ; &quot; since, &quot; so long as there 

 remains a residual force in any direction be it excess of 

 a force exercised by an aggregate on its environment, or of 

 a force exercised by its environment on the aggregate, equi 

 librium does not exist; and therefore the re-distribution of 

 matter must continue.&quot; 



It is essential that this truth should here be fully compre 

 hended; and to the end of insuring clear comprehension of 

 it, some re-illustration is desirable. The case of the Solar 

 System will best serve our purpose. An assemblage of bodies, 

 each of which has its simple and compound motions that 

 severally alternate between two extremes, and the whole of 

 which has its involved perturbations, that now increase 

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