854 M. Poinsot on the Percussion of Bodies. 



conple N, had received the impulse of a single force P passing 

 at a given distance B from the centre ff, in wliicli case the per- 

 cussion Q which the body would be capable of producing at any 

 distance a; from this same centre g would be expressed by 



we might be tempted to conclude that the centre T of maximum 

 percussion, whose distance is expressed by 



8 - 



\/k^+ w, 



coincides here also (since K = 0) with the centre of gravity^. 

 But this would l)e a theoretical error similar to the preceding ; 

 for at the point //, where x = 0, the percussion Q is precisely 

 equal to the force P, whereas at the point T, which corresponds 

 to the preceding value of x, the percussion is infinite*. 



12. To obtain more precise ideas, however, and to avoid all 

 error in our applications, it will always be better to suppose the 

 mass fi to be not infinite, but merely very great, and thus to 

 preserve this letter /j, throughout our analysis. All quantities 

 will then be quite distinct, and their true mathematical values, 

 under the hypothesis of /j,= co , may be determined. This 

 method of regarding fi, not as infinite, but merely as very great, 

 is at the same time more natural; for in reality there exists 

 neither body nor point whose mass is infinite ; the supposition 

 of such existences is not less imaginary than that of a fixed 

 point. All that we really know by experience is that a body, 

 e. g. a lever, may be supported at one of its points against an- 

 other body whose mass is so great that its motion, in consequence 

 of the applied forces, is very small, and as it were insensible, in 

 comparison with that of the moveable body in question. 



Perhaps it will not be useless to elucidate these theoretical 

 points still more by a few numerical applications. 



13. Examjjie. — A rigid and immaterial rod C is loaded at 

 its extremities C and with two material points M and /jl, and 

 struck at C with a force P ; required the percussion which the 

 rod would produce against a point T taken at the distance GT = i» 



* The maximum percussion (Q), as determined from the last two equa- 

 tious, has the value 



which, when K vanishes, clearly becomes infinite. 



