166 M-.Toinsot on the Pe7'cttssion of Bodies. 



distance furnishes to the mind no distinct conception^ and that 

 therebjr we perceive neitlier percussion nor centre of percussion. 

 To explain this pecuhar case, therefore, it will be necessary to 

 consider it apart. It is evident that if the body turns around its 

 centre of gravity, it does so because the impulse which it has 

 received proceeded, not from the application of a single force, 

 but from that of a couple. Here, therefore, we have to do, not 

 with a percussion zero, but with a percussion of a different 

 nature, where there is neither centre nor determinate arm to 

 consider; for it is a couple which enters into the question, and 

 this couple may be changed at will into innumerable others 

 having an equivalent effect. 



III. Reciprocal properties of the centre op percussion and of 



THE spontaneous CBNTRE. 



11. The same equation 



ah = K^, 



which expresses the relation between the distances h and a of the 

 centre of percussion, and of the spontaneous centre from the 

 centre of gravity, also shows that these two centres are, to a 

 certain extent, reciprocal; that is to say, if the body were to 

 receive an impulse at the point 0, which would then become the 

 centre of percussion, rotation would take place around the point 

 C, which would become the spontaneous centre. 



12. If the distance a-\-h between these two reciprocal centres 

 be represented by I, then since «A = K^, we shall have indiffer- 

 ently K2 , , K^ 



l=a-\ -ov i = li-\ — T. 



a a 



13. This distance / between the two reciprocal centres may be 

 greater than any given line, but it can never become zero. The 

 line 2K is the least value it can have; for, on seeking the mini- 

 mum value of /, we find a = K, and consequently h ~ K, whence 2K 

 is the distance between the two reciprocal points of a given body 

 which are nearest each other. 



IV". On the centre of maximum percussion. 



14. According to Avhat has been above demonstrated, if the 

 body under consideration actually turns around a point O, situ- 

 ated at the distance a from its centre of gravity G, the whole 

 movement of the body may be attributed to the action of a 



K2 



single force applied to the point C, at the distance l=a-\ from 



the centre of rotation ; and hence all the different forces with 

 which the several molecules of the body are at this moment ani- 

 mated, are reducible to a single one, passing through the point 



