350 M. Poiusot on the Percussion of Bodies. 



If the expression on the right of the last equation is zero, the 

 curve becomes reduced to a single point, and we may remark 

 that this point is preciseljr that which constitutes the centre of 

 maximum percussion ; for to make 



is equivalent to giving to the number n one of the ralues 

 1±\/] 



3 



and consequently to the supposition that the given percussion nP 

 has one of the values 



but these are precisely the values of the two maxima percussions; 

 the positive one corresponding to the greatest of all percussions 

 in the same direction as the impulsion P, and the negative one 

 to the greatest of all tlic percussions in the opposite direction. 



Lastly, if the second part of our equation were negative, the 

 ellipse would be imaginary, and there would be no centres of the 

 given percussion nV. 



Hence the curve of the centres of equal percussion nV is an 

 ellipse similar to the central ellipse, or a point, or an imaginary 

 curve, according as 



H-4A(ft--n) > 0, or =0, or <0. 



24. It is easy to see why, in the last case, there is no point 

 capable of producing the given percussion nV. For to suppose 

 that 



H-4A(«2_m) 



is negative, is to suppose, in the case of n positive, that this 

 number n has a value greater than ^ + -\/ 1 + —r-, and thus 



that the centre of a positive percussion greater than the greatest 

 of all such percussions is demanded. And similarly, in the case 

 of n negative, the above supposition is equivalent to giving to n 



1 1 / TT 



an absolute value greater than — „ + ^\/ 1 + X' '^"^ ^'^'^'^ ^^ 



i« 1* V A. 



demanding the centre of a negative percussion greater than the 



greatest of all negative percussions. 



