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XVIII. — On Impact, II. By Professor Tait. 



(Read 18th January 1892.) 



[Since this second instalment of my paper was read to the Society my attention has been 

 called to a remarkable investigation by Hertz ;* in which the circumstances of collision 

 of two elastic spheres are fully worked out, under the special limitations that both are 

 smooth, and that their deformations are exceedingly small. This forms a mere episode 

 in the paper, which is devoted mainly to the statical form of the problem of deformation ; 

 as, for instance, the case of the ordinary apparatus for the production of Newton's rings. 

 But it contains a definite numerical result ; giving for the duration of impact between 

 two iron spheres of 50 mm diameter, which encounter one another directly with a relative 

 speed of 10 mm per second, the value S, 00038. This seems to be the earliest reckoning 

 of the time of collision. The experimental verification of Hertz' formulae was under- 

 taken with success by ScHNEEBELi,t who obtained results in close accordance with them. 

 His mode of measuring the duration of impact was defective, though ingenious. But 

 the speeds employed by him, though for the most part considerably greater than those 

 contemplated in Hertz' work, were far inferior to the lowest of which I have availed 

 myself: — and thus no comparison can be instituted between my results and the 

 theoretical formulae ; first, because I have necessarily dealt with deformations so large as 

 to be directly measurable ; secondly, because the formulae, being originally obtained for 

 the statical problem, have left aside thermoclynamical considerations, and thus assume 

 equal duration for compression and for restitution, which is certainly incorrect ; finally, 

 because one of my colliding bodies was fixed, and thus virtually struck on both sides, 

 besides being notably deformed throughout the greater part of its substance ; while, except 

 in the case of very hard bodies, the surface of contact was nearly equal to the whole section 

 of the cylinder. I regret, however, that I had not seen Hertz' paper before I made my 

 apparatus, as a study of it might have led to improvements in my arrangements ; especially 

 in the choice of the form of the elastic substance to be operated on. But my results have 

 the advantage of being applicable to many practical questions (besides those of Golf, to 

 which they owe their birth), such as the driving of a nail by a hammer, or of a pile by a 

 ram, &c. One of Hertz' results is specially interesting, viz. that the duration of impact 

 between two balls is infinite if the relative speed be indefinitely small. This may easily 

 be seen to depend upon the fact that (in consequence of their form) the total force between 

 them, at any instant, varies as a power of the deformation higher than the first.] 



* Journal fur die nine, und angewandte Mathematik, xcii., 1882. liber die Beriihrung fester elastiscker Korper. 

 t Archives des Sciences physiques, &c, Geneve, xv., 1885. Reckercb.es experirnentales sur le Choc des Corps 

 elastiques. 



VOL. XXXVII. PART II. (NO. 18). 3 K 



