M. Poinsot on the Percussion of Bodies. 281 



&c. may give rise to diflferent spontaneous axes intersecting in 

 one and the same point 0, the former must be situated upon the 

 line CT which corresponds, as spontaneous axis, to the given 

 point considered as a centre of impulsion or percussion. 



Remark. 



7. Since, during the first instant, all the points of a spon- 

 taneous axis OS remain motionless, we see that a shock at the 

 centre C causes no percussion either at the reciprocal centre O 

 or at any other point of the spontaneous axis OS. 



Similarly, by striking at no percussion is caused at any 

 point of the parallel axis CT. 



Corollary II. 



8. From this remark and the preceding corollary we may de- 

 duce this remarkable theorem : — a shock at any point C what- 

 ever in the line CT causes no percussion at the spontaneous 

 centre 0, for the spontaneous axis O'S', which corresponds 

 to C, always passes though the point 0. 



Simdarly, at whatever point of the spontaneous axis OS the 

 body may be struck, no percussion will be caused at the centre C. 



Corollary III. 



9. With respect to these centres and their corresponding axes, 

 various other questions, analogous to the foregoing one, may be 

 proposed and solved with equal facility. 



For instance, upon what curve ought the centres of percussion 

 to be situated in order that the corresponding spontaneous axes 

 may all touch a given curve ? 



Let 



u=f(t) 



be the equation of the given curve, and 



that of the spontaneous axis corresponding to the centre C, whose 

 coordinates are x and y. 



The contact of this curve and right line requires that the two 



differential coefficients -^, deduced from the above equations, 



shall have the same value at the point of contact; hence we 

 deduce the equation 



u^x^^y.f{t) = Q. 



If, by means of two of these equations, we eliminate t and u from 

 the third, we shall obtain an equation between x and y which 

 will give the rcfjuircd locus of the centres C. 



As a particular case, let us suppose the given curve u=f{t) to 



