OUTLINES OF NATURAL PHILOSOPHY. 



217. If <p, q>, <p, be the angles which the radii 

 drawn from S to B, C, D, (fig. 14.) make with 

 the radius drawn through A, and if in this latter 

 radius a point P be taken, distant from S by the 

 quantity 



A a -j- B b cos <p + C c cos p' + D rf cos <p" ' 



the point P is such, that if an obstacle were ap- 

 plied there sufficient to resist the rotation of the 

 system, no motion would be communicated to the 

 axis at S ; or, which is the same, though the axis 

 at S were not fixed, the system would have no ten- 

 dency to revolve about the point P. 



The point P is called the Centre of Percussion. 



This proposition is investigated by assuming P, 

 drawing PO parallel to BS, and BO perpendicu- 

 lar to it. The momentum of B relatively to P is 

 the same as if it were placed at O, and is therefore 



B x (b x cos <p). The sum of the momenta 

 >a 



computed in this way is equal to 0, and thence the 

 value of x, or SP. 



218. Any system of bodies being given, a point 

 may be found in which if all the bodies were 

 collected, a force applied at any distance from 



the 



