114 OF DEFLECTIVE FORGES. 



increments of the area described by the revolving radius, 

 while the body moves in the curvilinear orbit; and the 

 whole areas described in equal times will therefore be 

 equal. And since the constant area ABCziAB.-|^ CH 



(117, 114), ABi=2ABC.^ and AB, representmg the 



velocity, is always inversely as CH, or v— -. 



Scholium. Laplace demonstrates this proposition by 

 means of the law which makes the sum of a number of 

 rotatory pressures, which he calls moments, with respect 

 to a given axis, equal to the pressure of the result : ob- 

 serving that whatever is demonstrated of forces and their 

 composition may be applied with equal truth to combina- 

 tions of motions or velocities. It is true that the same 

 symbols and the same reasoning may generally be applied 

 to forces and to motions ; but it appears to be an inversion 

 of the natural order of demonstration to deduce the laws 

 of motion from those of pressure, especially in a case 

 where the real process of nature is so easily traced in the 

 geometrical representation. Laplace observes, however, 

 with respect to the laws of rotatory pressure, (256) that if 

 we project each force and the result of all the forces on a 

 fixed plane, the sum of the rotatory pressures of the cons- 

 tituent forces, with respect to any fixed point in the plane, 

 is equal to the rotatory pressure of the result of all the 

 forces : and drawing to this point a line, which is commonly 

 called the radius vector, but more properly in English the 

 revolving radius, this radius would describe an area in the 

 fixed plane, in virtue of each force acting separately, 

 equal to the product of the line described by the moving 

 body into^he perpendicular falling from this fixed point on 

 its direction, and consequently, for any one force or motion. 



