Centres of Percussion and Oscillation. 243 



If h' is very small with respect to h, so that j may be neg- 

 lected, the expression becomes . Hence, the distance of the 



3 



centre of percussion or centre of oscillation of a straight line, or of 

 a parallelogram, turning about one of its sides, as an axis, is f of the 

 length from the point of suspension or axis. 



Thus, the rod or bar FA, turning about the fixed point Frig.177. 

 would strike a nail T with the greatest effect when the distance 

 of the nail FP is equal to f FA. 



If the rod FA be considered as turning by the action of grav- 

 ity only, the force which it would exert upon the nail, would be 

 equal to the mass of the rod multiplied by the velocity acquired 

 by the centre of gravity G, in falling along G'G, that is, by the 

 velocity acquired by a heavy body in falling through the height 

 CD. 



366. We take the sphere as a second example. In this caseFig.178, 

 the surface which we have called 6, is a circle, having for its ra- 

 dius IM, which I shall call y ; and, n being the circumference 

 of a circle whose diameter is 1 , we have 



7i y 2 =6. Geom. 



291. 



Let DI be denoted by z, and the radius of the sphere by R ; we 



have 



, Triglol 



and consequently, 



tf = 7f(2R2 Z 2 ). 



Calling DF, a, 



FI or x = z + 3 and d x = d z ; 

 consequently, 



fx* <> dx, 

 becomes 



(z-f a) 2 X7i(<2Rz z 2 )dz, 



