226 PROFESSOR TAIT ON IMPACT. 



into its bearings, and released by a trigger only after it had, in its fall, passed the edge. 

 The block, having fallen, rebounded several times to rapidly diminishing heights and, 

 after a second or two, came to rest on the cork cylinder. The pencil then traced a circle 

 and, as soon as this was complete, the fly-wheel (previously detached from the gas- 

 engine) was at once stopped by the application of a very powerful brake. The circle 

 thus described was the datum line for all the subsequent measures ; since the tracings 

 which passed beyond it were obviously made during the impact, while those within it 

 referred at least mainly to the comparatively free motion between two successive impacts. 

 The duration of the impact was at once approximately given by the arc of the circle 

 intercepted between the tracings of the pencil as it passed out and in, combined of 

 course with the measured angular velocity of the fly-wheel. It is not yet known at 

 what stage during the recovery of form the impinging bodies go out of contact with one 

 another. In the present paper we are content to assume that contact commences and 

 terminates at the instants of passage across the datum circle. This is certainly not 

 rigorously true as regards the commencement, but the assumption cannot introduce any 

 serious error ; while of the termination we have no knowledge. It may be remarked, in 

 passing, that the error at commencement will necessarily be greater the larger the mass 

 of the falling body. It will also be greater for soft than for hard bodies, and especially 

 for those of the former class which most depart from Hooke's Law. 



In the winter 1887-8, and in the subsequent summer, some very curious results 

 were obtained by Messrs Herbertson and Turnbull with this rough apparatus. 

 Several of these were communicated to the Society at the time when they were obtained. 

 Thus, for instance, it was found that although the mass of the block was over 5 lbs., the 

 time of impact on a cork cylinder was of the order of s * 01 only, while with vulcanite it 

 was of the order S- 001. Also, for one and the same body, the duration was less, the 

 more violent the impact. [The golf result mentioned above was now at once explained ; 

 for, as the mass of a golf-ball is less than -^ of that of the block, under equal forces its 

 motions will be fifty times more rapid. Thus, even if it were of cork, the time of impact 

 would be of the order of about one five-thousandth of a second only ; and the shorter the 

 more violent the blow.] Taking the coefficient of restitution as 0'5 on the average, the 

 time-average of the force during impact after a fall of 4 feet was, for these classes of 

 bodies respectively, of the orders 400 lbs. weight and 4000 lbs. weight. This result is of 

 very high interest from many points of view. 



The values of the coefficient of restitution for impacts of different intensity were 

 obtained by drawing tangents to the fall-curve at its intersections with the datum circle 

 corresponding to the assumed commencement and end of each impact, and finding their 

 inclination, each to the corresponding radius of the circle. The coefficient of restitution is, 

 of course, the ratio of the tangents of these angles. The results of these graphical methods 

 could easily be checked by forming the polar equations of the various branches of the 

 fill-curve (ascending and descending) and obtaining the above-mentioned tangents of 

 angles b) 7 direct differentiation. If we assume the friction (whether of rails or pencil) 



