M. Poinsot on the Percussion of Bodies. 171 



Btrikes with the greatest possible force, but it does so in the rear 

 of its own translation through space. 



We see, further, that these two centres T and T' are mutually 

 reciprocal. For the equation 



which gives their distances from the centre of gravity, shows 

 that the product of these distances is equal to the last and con- 

 stant term — K^. Consequently, if one of these points were 

 considered as an ordinary centre of percussion, the other would 

 be the corresponding spontaneous centre of rotation. 



Corollaries. 



22. If rve suppose h = in the foregoing expressions, we have 

 the particular case of a body subject to the sole action of an im- 

 pulse P passing through its centre of gravity. The percussion Q 

 which the body is capable of giving at the distance x from this 

 centre is then expressed by 



and the point T, where this percussion is a maximum, is at the 

 distance x = 0, in other words, at the centre of gravity. 



Thus when a body possesses only a translatory motion through 

 space, the centre of maximum percussion is unique, and coincides 

 with the centre of gravity, — a conclusion which is almost self- 

 evident. 



23. If we suppose fl = 0, the distance of the centre of maxi- 

 mum percussion will be 



x=±K. 



In this particular case the body is acted upon by a couple 

 merely, and consequently has no other motion than that of a 

 simple rotation around one of its principal axes. Since in this 

 case the centres of rotation and gravity coincide, the centre of 

 maximum -percussion is no longer an absolutely determhied point; 

 its distance K from the centre of gravity is alone determined, so 

 that it may be taken anywhere on the circumference of a circle 

 described around the centre of gravity with the radius K. 

 This particular case may be treated directly thus : let N be 



_Q 



Q 



the moment of the couple tending to turn the body around the 



