nc9.il.] DISSERTATION SECOND. 47 



researches. In that work the composition of forces was treat- 

 ed independently of the composition of motion, and the equi- 

 librium of the lever was deduced from the former, as well as 

 in the treatise already mentioned. From the equality of ac- 

 tion and re-action it was also inferred, that the state of the 

 centre of gravity of any system of bodies, is not chang- 

 ed by the action of those bodies on one another. This 

 is a great proposition in the mechanics of the universe, and is 

 one of the steps by which that science ascends from the earth 

 to the heavens ; for it proves that the quantity of motion ex- 

 isting in nature, when estimated in any one given direction, 

 continues always of the same amount. 



But the new applications of mechanical reasoning, — the 

 reduction of questions concerning force and motion to ques- 

 tions of pure geometry, — and the mensuration of mechanical 

 action by its nascent effects, — are what constitute the great 

 glory of the Principia, considered as a treatise on the theory 

 of motion. A transition was there made from the considera- 

 tion of forces acting at stated intervals, to that of forces act- 

 ing continually, — and from forces constant in quantity and 

 direction to those that converge to a point, and vary as any 

 function of the distance from that point ; the proportionality 

 of the areas described about the centre of force, to the times 

 of their description ; the equality of the velocities generated 

 in descending through the same distance by whatever route:" 

 the relation between the squares of the velocities produced 

 or extinguished, and the sum of the accelerating or retarding 

 forces, computed with a reference, not to the time during 

 which, but to the distance over which they have acted. 

 These are a few of the mechanical and dynamical discoveries 

 contained in the same immortal work ; a fuller account of 

 which belongs to the history of physical astronomy. 



The end of the seventeenth and the beginning of the 

 eighteenth centuries were rendered illustrious, as we have 



