PROFESSOR TAIT ON IMPACT. 235 



distortion of the paper or irregularity of the fork (due to the bristle's being clogged with 

 printer's ink, or to its pressing too strongly on the plate ?). In. these cases the arith- 

 metical mean is to be taken for any subsequent calculation. 



2. The radius of the datum circle ........ R. 



This, and the other measurements of length, are in millimetres. 



3. The height of fall, or of rebound ........ H. 



For the first fall, this was of course measured on the rails : — for the subsequent rebounds 

 it was measured on the tracing. 



4. Chord of the arc of datum circle intercepted by the trace during impact . C. 

 As this arc was, on the average, considerably less than one-tenth of radius, the chord is 

 practically equal to it. (differing at most by 1/I200th only), and it is thus a measure of 

 the duration of the impact. The duration is, in fact, 



C 6N _3_ CN 

 2ttR ' 128 _ 400' R near ty; 



this approximation being much within the inevitable errors of experiment. It is tabulated 

 under .............. T. 



5. Greatest distortion — i.e., greatest distance of the trace beyond the datum 

 circle (of course not including the (small) distortion due to the weight of the block). This 

 datum is always, to a small but uncertain amount, increased by the distortion of the lower 

 part of the falling block. This is probably nearly proportional to that of the elastic 

 cylinder, so that the numbers given are all a little too large, but they are increased 

 nearly in a common ratio ........... D. 



It was found impracticable to estimate with certainty the relative distances of this 

 greatest ordinate from the ends of the intercepted arc ; as the radial motion generally 

 remains exceedingly small during a sensible fraction of the whole time of impact. This 

 is true of all the substances examined, even when they have properties so different as 

 those of vulcanite and vulcanised india-rubber. It seems as if the elastic substance were 

 for a moment stunned (if such an expression can be permitted) when the sudden 

 distortion is complete. 



We can easily assign limits within which the time of compression must lie. For, since 

 the elastic force resists the motion, and increases with the distortion, its time-average 

 during the compression is greater than its space-average : — i.e. 



mV mV 2 

 ~T > YD' 

 where m is the mass of the block, V its speed at the datum line, and t the time of com- 

 pression. Hence 



D 2D 



V < l < T ■ 

 If we make the assumption that the force at each stage during restitution is e times its 

 value during compression, this gives 



D _T_ 2D 



V < 1 + 1/e < V > 



