456 MR. B. HOPKINSON ON MEASURING THE PRESSURE, ETC. 



high stresses.* If it maintained its elasticity and continuity the shearing stress 

 would be of the order O'OIS x 1'2 x 10 7 , or say 220,000 Ibs. or 100 tons per square inch. 

 This illustration is of course very far from representing the actual effect of suddenly 

 giving velocity to a portion of a plate, the real distribution of stress would be far 

 more complicated, but it gives an idea of the magnitude of the stresses which may be 

 expected to arise. In static tests on mild steel, the material begins to flow as 

 soon as the shearing stress exceeds about 10 tons per square inch and no stress 

 materially greater than this can exist. But when the metal is. forcibly deformed at a 

 sufficiently high speed the shearing stress is increased by something analogous to 

 viscosity and the tensile stress which accompanies it may be sufficient to break down 

 the forces of cohesion and tear the molecules apart. Thus the steel is cracked, though 

 in ordinary static tests it can stretch 20-30 per cent, without rupture, just as pitch, 

 which can flow indefinitely if given time, is cracked by the blow of a hammer. The 

 essence of the matter is the forcible straining of the substance at a velocity so high 

 that it behaves as an elastic solid rather than as a fluid, thus experiencing stresses 

 which are measured by the strain multiplied by the modulus of elasticity. The effect 

 of gun-cotton on mild steel shows that in this material a rate of shear of the order 

 1000 radians per second is sufficient to cause cracking. 



The most probable account of the smashing of a mild steel plate by gun-cotton is, 

 then, that the plate is cracked before it has appreciably deformed, the cracks being 

 caused by relative velocity given impulsively to different parts of the plate. Bending 

 of the broken pieces occurs after the plate has cracked and the pieces have 

 separated from one another. It is due to relative velocity in different portions of each 

 piece which still persists after the initial fracture, and is taken up as a permanent set 

 in each piece. In this connection the fracture shown in fig. 11 is instructive. It 

 will be noticed that the general bend of the plate, after the pieces have been fitted 

 together, is opposite to that which might at first sight be expected as the result of 

 the blow in the middle. Inspection of such fractures leads to the conclusion just 

 stated as to their history. The experiments on gun-cotton pressures described in this 

 paper, though lacking in precision, supply I think the missing link in an explanation 

 which is otherwise probable, namely, sufficient evidence that the blow may be regarded 

 as an impulsive force communicating velocity instantaneously. 



Most of the experimental work described in this paper was done by my assistant, 

 Mr. H. QUINNEY. I also received valuable help in the earlier stages from 

 Mr. A. D. BROWNE, of Queens' College, and from my brother Mr. K. C. HOPKINSON, 

 Trinity College. To these gentlemen I wish to express my obligation for aid without 

 which it would hardly have been possible to carry out a research of this character. I 

 have also to thank Sir EGBERT HADFIELD, Mr. W. H. ELLIS, and Major STRANGE for 

 providing steel plates and shafts. 



* HOPKINSON, 'Roy. Soc. Proc.,' 74, p. 498. 



