278 Professor Bertram Hopkinson [Jan. 26, 



of course, apply to such a case, as it depends on the assumption of 

 perfect elasticity. 



It is rather remarkable that materials can sustain without injury 

 such large pressures as are produced hy these blows. Mild steel balls 

 are not crushed perceptibly till the pressure reaches 100 tons per 

 square inch ; yet a short column of the same steel would be crushed 

 by a pressure of 30 tons per square inch. One reason is the extremely 

 short duration of the pressure — it has no time to produce much effect. 

 The other is the fact that in the blow it is accompanied by large 

 lateral pressures exerted by the metal surrounding the area of contact. 

 Pressure equal in all directions, such as is exerted by the water at the 

 bottom of a deep ocean, produces generally no permanent effect on 

 solids or liquids. To produce breakage or permanent deformation 

 there must be difference of pressure in different directions, and the 

 most important if not the only factor determining whether such 

 breakage or deformation shall occur is the amount of the difference. 

 If for example, our column of mild steel, which in the absence of 

 lateral support begins to crush at 30 tons, were surrounded by a jacket 

 exerting a radial pressure of 30 tons, it is probable that the end pres- 

 sure might })e increased to 60 tons without any movement occurring. 

 In the impact of balls the metal surrounding the point of contact by 

 resisting the lateral expansion of the compressed part, sets up radial 

 pressure of tliis kind. It can be shown, in fact, that the lateral pres- 

 sure at the centre of the circle of contact corresponding to a maximum 

 normal pressure of 100 tons per square inch is 75 tons per square 

 inch, leaving 2.5 tons effective for producing deformation or l^reakage. 

 The greatest difference of pressures, however, is not at the centre of 

 the circle of contact but at points near the circumference of that circle. 

 Thus, as was found by Hertz, fracture commences by tlie formation of 

 a circular crank of small radius surrounding the point of first contact. 



These calculations of pressure are based on theory, and it may be 

 asked what direct experimental evidence we have that the theory is 

 correct. It is not, of course, possible actually to measure the pres- 

 sures over the minute circle of contact between the balls, nor is it 

 possible accurately to measure the amount of the flattening. We 

 can, however, pursue the calculation a little further, and determine 

 the time during which the balls are in contact from the moment 

 wlien they first touch to the moment at which they separate on the 

 rebound. In the case of billiard balls moving with a relative velo- 

 city of 16 feet per second, this time is ^^^f-^ of a second. A precisely 

 similar calculation can be made for balls of steel or other metal, and 

 it is not difficult to measure in the laboratory the time during whicli 

 such balls remain in contact. The method is of considerable use in 

 coniie(5tion with impact problems, and it consists in making the two 

 balls, hy theii- c;ontact, close a galvanometer circuit in which there is 

 also a l)attery and resistance. A certain quantity of electricity, 

 which is simply proportional to the time of contact, then passes 



