238 PROFESSOR TAIT ON IMPACT. 



Conclusions from the Experiments. 



It will be observed from the following Tables that the assumed initial radius-vector 

 was never very far from the true position of the minimum ; the correction (in circular 

 measure) being usually of the order 0"01, i.e., about 0°"6, and very often much less. 

 When the minimum was small, the correction was usually larger ; but in few cases did it 

 amount to 0'05, i.e., 3°. This correction ought, of course, to have equal values for the 

 two parts of each free path. 



The substances experimented on w T ere fresh specimens, not those which had been 

 frequently battered by 8 and 12 foot falls in the earlier experiments. They were limited 

 to four, Plane-tree, Cork, Vulcanised India-rubber, and Vulcanite. The first material 

 was chosen the same as that of the falling block, in order that (if possible) a correction 

 for the compression of the block might be determined, and applied to the results of the 

 experiments on other materials. I do not as yet see any simple mode of obtaining 

 approximately such a correction : — and the data from different experiments -with the 

 same materials are scarcely sufficiently consistent with one another to warrant the 

 application of rigorous analysis, a task which would involve immense labour as well as 

 difficulties of a most formidable order. Hence there is not much to be said, for the 

 present at least, about the behaviour of a hard body such as vulcanite, whose distortion 

 is only of the same order as that of the block. The time of the impact between it and 

 the wood-block is somewhere about l/500th of a second when the speed of the block is 

 about 16 feet per second. For lower speeds it is longer; while for very low speeds this 

 substance seems to show a peculiarity which is specially marked in cork, and will be 

 considered below. 



With vulcanized india-rubber, when the speed is 16 feet per second, the time of 

 impact is about l/l30th of a second; it becomes longer as the relative speed is less; 

 until, with very low speeds, it becomes practically constant. 



With cork the period of impact for a speed of 16 feet per second is about l/70th of a 

 second ; it increases as the speed is reduced to about 8 feet per seeond ; and again 

 steadily diminishes as the speed is still further reduced. This seems to indicate that (at 

 least in circumstances of rapid distortion) the elastic force in cork increases in a slower 

 ratio than does the distortion, while both are small, but at a higher ratio when they are 

 larger. 



In all the cases tested the coefficient of restitution seems steadily to diminish as the 

 speed of impact is increased. 



In some of the experiments the mass of the block was doubled ; and occasionally the 

 doubled mass was allowed to fall from half the previous height, so that its energy 

 remained unaltered. But the number of cases is as yet too small to enable us to judge 

 with certainty the consequences of these changes. I hope to discuss this point in a 

 subsequent paper. 



