344 Mr Vincent, Experiments on Impact. 



This was done by soldering a small hook of bright wire to the 

 steel ball and hanging the ball up by this hook from the extreme 

 point of a needle, which was horizontal. The needle could be 

 moved quickly by a spring in the direction of its length thus 

 releasing the ball. The height fallen through was measured by 

 a cathetometer. 



For large velocities of impact d? is less than that indicated by 

 the equation 



u = bd\ 



This is noticeable also in Figs. 6 and 8. The deviation from 

 the straight line is due to two causes : 



1. The ordinate d? is not accurately proportional to the root 

 of the volume of the dent. 



2. The volume of the dent is less than it would be if it were 

 proportional to the energy of the ball just before impact. 



It is at once seen that the latter cause is the most efficient. 

 For the dent is still small compared with the ball so that by 

 taking another term in the expression for the volume of the dent 

 we get a formula of quite sufficient accuracy to test the effect of 

 the cause 1. 



We have previously taken the volume of the dent as 



32ZT 



It is to a nearer approximation 



ird i / d 2 \ 

 SW\ + 3£V" 



If then we wish to make the ordinate proportional to the root 

 of the volume we must plot 



instead of d 2 ; 



that is, each point must be raised about — . This correction is 



small even for the larger dents and is not sufficient to bring the 

 points up to the straight line through the smaller dents. 



We must conclude then that the displaced volume is pro- 

 portional to the initial energy of the ball for small velocities of 

 impact ; but as the velocities increase the volume of the dent is 

 less than it should be according to this rule. 



