OF DEFLECTIVE FORCES. . 115 



proportional to the time, since the force is conceived to 

 have acted instantaneously, and to have produced a uni- 

 form velocity : this area is also expressed by the same 

 product which has been denominated the rotatory pres- 

 sure, that is the {3roduct of the perpendicular into the 

 projection of the force, or into the motion in the given 

 plane : consequently the area described, in virtue of all 

 the motions, is proportional to the projection of the whole 

 force, and the sum of the separate areas is equal to the 

 area described by tlie radius in virtue of the result of all 

 the motions. Now the addition of any force or forces, 

 directed to or from the given point, can make no difter- 

 ence in the magnitude of the area described round it : 

 because no motion directed to the point would separately 

 cause any area at all to be described. §. 6. P. 18. 



Corollary. Hence, reciprocally, if a 

 body describes equal areas round a given 

 point, the force by which it is actuated must 

 be directed to that point-] 



264. Theorem. When a moveable point 

 is actuated by a combination of forces, their 

 results being reduced to three orthogonal 

 directions ; the time being supposed to flow 

 uniformly, the forces, diminished bj^ quantities 

 proportional to the second fluxions of the 

 spaces described in each direction, and multi- 

 phed by the respective variations of the direc- 

 tions, will balance each other. 



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