86 OF PRESSURE AND EQUILIBRIUM. 



and contrary to the result of the motions, which 

 would be produced by the other forces. 



If we conceive the forces to act alternately, during 

 equal evanescent intervals of time, then the one will at 

 each step destroy the preceding effect of the other, and 

 there will be no motion left : then if we suppose this action 

 to be doubled, the forces will become a continual pressure, 

 and the total effect will still be the state of rest. 



241. " 284." Theorem. If a body re- 

 main at rest by means of three pressures, they 

 must be related in magnitude as the sides of a 

 triangle parallel to the directions. 



This proposition is the immediate conse- 

 quence of the law of the composition of 

 motion (226, 240). Suppose the body A, 

 for example, to be suspended by the thread 

 AB, on the inclined plane AC, to which AD 

 is perpendicular, BD being the direction of 

 gravity. Then in order that the force BD may be de- 

 stroyed, it must be opposed by an equal force DB, and 

 if DB be composed of forces acting in the directions DA, 

 AB, the forces must be as those sides of the triangle, or 

 as the sides of the parallelogram of which DB is the 

 diagonal ; and the same is true of any other pressures. 



Scholium 1. This extension of the laws of the com- 

 position of motion to that of pressure seems to be free 

 from any material objection. For since we measure forces 

 by the motions which they produce, the composition of 

 forces seems to be obviously included in the doctrine of 

 the composition of motions ; and when we combine these 



