1 8k' Dynamics. 



It is not, however to be supposed, that these vibrations affect 



134 ^ ie ve ^ oc i t j which the bodies take after collision* They can 



have no influence upon the motion of the centre of gravity, since 



this motion takes place in each of the two bodies independently 



of the other. 



The collision of perfectly elastic bodies is to be viewed, 

 therefore, in the following manner. When the two bodies m, n, 

 Fig. 148. come to meet in C, the resistance which n opposes to w, causes 

 them to be mutually compressed, until the two centres and the 

 point of contact have all the same velocity ; thus far every thing 

 takes place, as in the collision of hard bodies, with the exception 

 of the change of figure, which can contribute nothing to the 

 quantity of motion lost or gained. 



The change of figure is effected in such a manner, that each 

 of the two bodies is flattened to the same degree on opposite 

 sides ; since the parts farthest removed from contact, advancing 

 more rapidly in the one body and less rapidly in the other, 

 until the compression is completed, crowd very much the inter- 

 mediate parts. The compression once finished, the parts of 

 each body bordering upon the points of contact, support them- 

 selves the one against the other, while the contact is transferred; 

 and the recoil of the spring takes place toward the parts oppo- 

 site to the point of contact, with all the force by which the bodies 

 tend to restore their figure. 



It will accordingly be seen that the impinging body loses by 

 the recoil, a velocity equal to that which it had lost by the com- 

 pression ; and that, on the other hand, the impinged body gains 

 by the recoil a velocity equal to that which it had gained dur- 

 ing the compression ; and, although the two bodies do not cease 

 to exert their elastic force when they have regained their orig- 

 inal figure, they have no longer any action upon each other, 

 since the force with which they go on to dilate themselves, be- 

 ginning now to grow less, they separate from each other at this 

 conjuncture. 



If, when the two bodies move in the same direction, u is the 

 velocity of the impinging body, and v that of the impinged ; u f 

 being supposed the common velocity which they would have 



