CHAPTER XL 

 DIKECT EQUILIBRATION. 



159. EVERY change is of necessity towards a balance of 

 ; and of necessity can never cease until a balance of toroes 

 is reached. When treating of equilibration under its general 

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

 in every aggregate having compound movements, there 

 tends continually to be established a moving equilibrium ; 

 since any unequilibrated force to which such an aggregate 

 is subject, if not of a kind to overthrow the aggregate al- 

 together, must continue modifying its state until an equi- 

 librium is brought about. And we saw that the structure 

 simultaneously reached must be " one presenting an arrange- 

 ment of forces that counterbalance all the forces to which the 

 aggregate is subject ; " since, " so long as there remains a 

 residual force in any direction be it excess of a force 

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

 exercised by its environment on the aggregate, equilibrium 

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

 must continue." 



It is essential that this truth should here be fully under- 

 stood ; and to the end of insuring a 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 



