OF DEFLECTIVE FORCES. 145 



and counteracting it in the other. Since however the steps 

 of the demonstration do not depend on the positive cha- 

 racter of the symbols m and w, we may simply make m 



— 2y 

 negative, and we shall have tang y T:=i , implying that 



the time is as much greater in the descent, as it is less in 

 the ascent, than when the body moves without resistance : 

 so that the whole time of the oscillation can never be sen- 

 sibly affected by any small resistance of this kind: a 

 conclusion which is of the more importance, as the resis- 

 tances acting on pendulums, vibrating in common circum- 

 stances, appears to vary very nearly in the simple ratio of 

 the velocity, the arcs decreasing proportionally in equal 

 intervals of time.] 



[283. Theorem. " 255." When a body 

 descends along an inclined plane, without fric- 

 tion, the force in the direction of the plane is 

 to the whole force of gravity as the height of 

 the plane is to its length. 



For if AB represent the motion which ^ 

 would be produced by gravity in a given 

 time, this motion may be resolved into AC 

 and CB ; by means of AC the body arrives ^ 

 at the line CB in the same time as if it were at liberty ; 

 but the motion CB is destroyed by the resistance of the 

 plane ; and as AB to AC, so is AD to AB (121). But 

 forces are measured by the spaces described in the same 

 time (230). 



Scholium. Hence, by employing a plane differing but 

 little from a horizontal direction, we may lessen the velocity 

 of descent, so as to make some illustrative experiments on 



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