173 M. Poinsot on the Perctission of Bodies. 



principal axis GZ, and conceive this couple changed to an equi- 



valent one (Q, — Q) having, for its arm, the line x-] joining 



any point C which we wish to consider with its reciprocal 0'. 

 The force with which the rotating body will strike at C', i. e. at 

 the distance x from G, will be 



^~0'C' K^ + or^' 



whence it follows, as before, that 



x=±K 



corresponds to the maximum of Q. 



Thus when a free body, whose moment of inertia with respect 

 to one of its three principal axes is represented by MK^, turns 

 around this axis, it is at the distance K from the same, and in 

 the plane of the other two axes that the rotating body will be 

 able to strike an obstacle or a fixed point with the greatest pos- 

 sible force. 



24. For example, if the body is a straight, homogeneous, pris- 

 matic bar whose length is 2L, we know that, with respect to an 

 axis through the bar's centre of gravity and perpendicular to its 

 length, 



hence when the bar rotates around this axis, the point with which 



it will strike with the greatest force is at the distance —= from 



wo 



its centre of gravity. 



For a homogeneous sphere with radius R, we have 



K=E\/| 



and it is at this distance from its centre that the rotating sphere 

 strikes most forcibly. 



General Remark. 



25. We have thus established the existence, in all bodies, of 

 new centres enjoying very remarkable properties ; centres whose 

 positions, like that of the ordinary centre of percussion, depend 

 neither upon the mass, nor upon the quantity of motion of the 

 body, but solely upon the position of the point around which 

 spontaneous rotation takes place : so that if the body turns on 

 its own centre of gravity, the centres of percussion in question 

 depend purely upon its form. 



The difference between the old and the present theory will be 



