34 THE ROYAL SOCIETY OF CANADA 



Assuming the value of Y calculated above calculate Ni and 

 compare it with the observed value. In the experiment quoted the 

 calculated value of Ni is 721. 



The Laws of Impact. — If two bodies collide in direct collision, 

 experiment will establish : 



1. There is no change of momentum in the line of motion. 



2. The ratio 



Relative velocity of separation of the two bodies 

 Relative velocity of approach of the two bodies 

 is a constant. This constant is called the co-efficient of restitution. 



An easy way of testing these laws is to hang two bodies side by 

 side by two vertical wires of effective equal lengths. The balls should 

 hang just in contact when at rest. 



If one or both are drawn back and then released simultaneously 

 they will collide in their lowest position, i.e., their normal position 

 when hanging at rest. 



If M , M 1 = the respective masses of the two balls 



u, ui = " " velocities " " " before impact 



v,vi= " " " " " " after impact 



all velocities baing measured in the same direction, then the first law 

 asserts 



Mu+MiUi = Mv+MiVi (1) 



and the second law that 



vi— V ^ ^ 



= a constant = e, say. 



u — Ui 

 If the balls are not withdrawn far from their normal positions 

 the velocities on reaching the normal position, after leaving freely a 

 position whose displacement is d, can be shewn to be very nearly 



equal to 



, I g 2 7t d 



I g 2 7t 



X - or 



\L t 



where t = the period of the ball vibrating as a simple pendulum, so 

 that since velocities occur on both sides of equation (1) we may 

 simply take velocities as proportional to the displacements. In the 

 experiments the displacements are measured by blocks of wood as 

 described above and averages are taken of several readings. No 

 attempt need be made to read finer than 1/10-inch. 



In a first experiment with balls weighing 30-5 and 9-9 pounds, 

 the big ball was drawn back 22-5 inches, the little one remaining at 

 rest. The big one was then released and after the collision the little 

 one went forward 27-3 inches, and the big one 13-6 inches. 



