200 Dynamics. 



its direction, except gravity, the tendency of which would be to 

 prevent a ricochet. 



314. As this immersion, however, takes place gradually, it 

 will be seen that the motion of the centre must be in a curved 

 line ; since while any part of the body remains above the sur- 



'face, the direction in which the resistance acts is changing con- 

 tinually. If, for instance, when the centre C, after having des- 

 cribed any line PC, tends to move according to the prolongation 

 C7, of this line, we imagine two tangents BR, Z)S, parallel to this 

 direction, it is evident that the part BVL only would be exposed 

 to this resistance ; and that if the body is spherical, the resultant 

 CK of all the resistances exerted upon the different points of 

 BVL would have a direction tending to elevate the body above 

 C/; so that the parallelogram CIEK being formed, CE will be 

 the course which the body would take instead of C/, no allow- 

 ance being made for gravity. 



315. Finally, if the body and the obstacle are flexible and 

 elastic, this circumstance will further contribute to a ricochet 

 motion. We take a very simple case, as an example ; let the 



Fi 155 body only be considered as flexible and elastic, and let this elas- 

 ticity be perfect ; the body being supposed at the same time to 

 be destitute of gravity. At the instant in which the body, pro- 

 jected according to /2C, comes to touch the surface, its velocity 

 is decomposed into a horizontal velocity which would remain al- 

 ways the same, if there were no friction, and no resistance on the 

 part of the medium in which the body moves. As to the per- 

 pendicular or vertical velocity PC, it compresses the body, and 

 being destroyed gradually, while the horizontal velocity contin- 

 ues, it is evident that the centre C approaches the plane HZ by 

 degrees, which go on decreasing, while the rate at which it ad- 

 vances parallel to jf/Z, remains the same. Consequently, if at 

 each instant we imagine a parallelogram having its horizontal 

 sides to its vertical, as the horizontal velocity is to the velocity 

 that remains in a vertical direction, the diagonal of this parallel- 

 ogram which must mark the course of the centre each instant, 

 will be different, and differently situated each instant, so that the 

 centre C will approach HZ in a curve, while the compression is 

 going on. When the compression has ceased, the centre C will 



