338 Prof. 0. Reynolds on the Action of a Blast of 



penetrate or fracture the body it strikes, or will itself be frac- 

 tured, is a matter of such common experience, and may in some 

 cases be so simply explained, that we have so far contented our- 

 selves with the simple explanation, and have not endeavoured to 

 distinguish between the different cases which occur. Up to the 

 present time the laws of impact have been considered mainly 

 with reference to the motion of the centres of gravity of the 

 bodies, and very little attention has been paid to what actually 

 occurs at the point of contact. Hence it is that the fact which 

 it is my object in this paper to point out has been so far over- 

 looked. This is, that at the instant of first contact the pressure 

 between the bodies is independent of their size, and depends on the 

 density of the body as well as on the hardness, so that a heavy soft 

 body may cause as much pressure as a hard body. 



In the very striking process of the sand-blast we see at a 

 glance evidence of two things which are contrary to our con- 

 ception of what ought tojbe; that is^ {a) the effect is inde- 

 pendent of the size of the particles, the small ones acting as soon 

 as the large ones, and {b) the softer bodies penetrating the harder, 

 as in the case of soft leaden shot penetrating the hard glass. 

 In order to explain these we must consider what actually takes 

 place at the point of contact. 



(a) The intensity of the)pressure between bodies on first impact 

 is independent of the size of the bodies. 



Although it is customary in mathematical works to consider 

 the effect of impact on the masses of the bodies as instantaneous, 

 we all know that it is not really so. Time is occupied in changing 

 the motion of the centres of gravity of the bodies. The idea of 

 a sudden change may, however, have arisen from confusion 

 between what happens at the point of contact and at the 

 centre of gravity. At the point of contact it is clear that 

 the effect on the motion of the surfaces of the bodies must 

 be instantaneous. After impact the surfaces of the two bodies 

 move together; hence the motion of one or both of them 

 must be instantaneously altered*. This effect, however, as will 

 be presently proved, is in the first instance confined to the 

 particles which come into contact. Even with hard bodies such 

 as glass it takes time for the pressure to extend into the body. 

 Hence on first contact it is only those particles in contact which 

 are affected, and the rest of the body might be removed without 

 altering the effect ; that is to say, the first effect of the impact 

 will be independent of the quantity of material behind the par- 

 ticles which actually impinge. 



* This first occurred to the author while reading a paper " On the Rup- 

 ture of Iron Wire by a Blow," by John Hopkinson, read before the Man- 

 chester Literary and Philosophical Society, 1871-72. 



