359 M. Poinsot on the Percussion of Bodies. 



and let us assume that P, a, b approach, indefinitely, the respect- 

 ive limits 0, 00 , CO , but in such a manner that the ratio - remains 



unaltered, and that the products or moments Pa and Vb always 

 maintain the same finite values as if P, a, and b had not changed : 

 we shall then have ultimately the particular case where tlie body 

 is animated solely by the impulsion of a couple (P, — P) applied 

 to the lever arm CG= Va^ + b'^ 



To express the percussion which the body is capable of pro- 

 ducing at any point whose coordinates are x and y, we shall 

 then have the formula 



__c^ax+^by__ 



This result may easily be verified by seeking, directly, the per- 

 cussion which the body is capable of producing when it is ani- 

 mated solely by the impulsion of the couple in question. 



Without allowing P, a, and b thus to approach the particular 

 values 0, oo , and oo , the conception of which is always some- 

 what obscure, we may deduce the same result from the expres- 

 sion (A), art. 18, in a very simple manner. 



28. In fact, since 



^ax+^by+^ 



expresses the percussion due to a single force P applied at C, 

 whose coordinates are a and b, 



will express the percussion due to a single force —P equal, parallel 

 and opposite to P, but applied at C whose coordinates are a' and 

 b' ; consequently the percussion due to the combined forces, that 

 is to say, to the couple (P, — P), will be expressed by 

 cc^a-a>)x + /3%h-b')y 



^~ «v+/3-y+«2yS2 ^ ' 



In the case where a' and b' are each zero, this expression coin- 

 cides with, and confirms the one previously given, for it then 

 corresponds to the percussion of the couple whose lever arm CC 

 coincides with CG. 



29. Since a couple may always be transported anywhere in its 

 own plane, or in any plane parallel thereto, and transformed 

 into innumerable other couples, having the same moment, with- 

 out its effect upon the body being thereby changed*, it is evident 

 that the percussion Q ought to remain the same in whatever ad- 



* Elements de Statique, art. 49 et seq. 



