CHAPTER II. 



OF DEFLECTIVE FORCES. 



257. Definition. " 238.'' Any force, 

 tending to alter the direction of the motion 

 of a moving body or point, is called a deflec- 

 tive force. 



Scholium. This definition includes not only accelera- 

 ting forces, which, when ^lirected to a point out of the line 

 of the body's motion, are called central forces, but also 

 the reaction of surfaces or threads, which limit the motion 

 to particular surfaces, and are subject to the same laws, 

 though they are only accelerative in a negative sense, as 

 retarding rather than producing motion : but this distinc- 

 tion is of no consequence, nor could it in all cases be 

 correctly established. It will serve as a useful introduc- 

 tion to the more general and analytical discussion of this 

 subject in Laplace's manner, to premise a simple geome- 

 trical illustration of some of the properties of central 

 forces, though they might be deduced as corollaries from 

 the formulas of the Mecanique Celeste. 



258. Theorem. " 239/' The force, by 

 which a body is deflected into any curve, is 

 directly as the square of the velocity, and 

 inversely as that chord of the circle of equal 



