M. Poinsot on the Percussion of Bodies. 177 



vity Gj then, according to the ordinary laws of collision of 



bodies, a point having the mass M -^ — tTsj aiid moving with the 



velocity [a + oi:)9, will impart to a massive point fi, at rest, a 

 velocity 



v= 



i\T_ 





And setting 



in order to find the point which corresponds to the maximum of 



communicated velocity V, we shall have 



a;2 + 2a^_^l+M^K2=0; 



A*/ 



whence we deduce, for the distance of this point from the spon- 

 taneous centre of rotation, the value 



« + «=±\/«^ + K2('l+— ), 



M 



which evidently depends upon the ratio — . This centre of 



H' 

 greatest communicated velocity, therefore, is a new point which 

 coincides with the centre C of ordinary percussion only when 



'M: fjL = l:a, 



and which cannot coincide with the centre T of maximum per- 

 cussion unless 



/■A 



which is equivalent to the supposition that the point jx has an 

 infinitely great mass, or in other words, that it is & fixed point. 

 It is scai-cely necessary to remark, that this result accords per- 

 fectly with wliat has been above established as to the maximum 

 of percussion which a body is capable of producing against a 

 fixed obstacle. 



In another place we shall consider these new questions rela- 

 tive to the percussion of a body against a free point ; at present, 

 however, we shall continue to suppose that the body strikes 

 against a fixed point, or in other words, against a free point 

 whose mass /i is supposed to be infinitely great. 



Phil. Mug. S. 4. Vol. 15. No. 99. March 1858. N 



