ON PASSIVE STRENGTH AND FRICTION. Ill 



It follows from the nature of resilience, that a hody of a pound weight, 

 falling from the height of a yard, will produce the same effect in breaking 

 any substance, as a body of three pounds falling from the height of a foot ; 

 so that here, as well as in the estimation of mechanical power, it is the 

 energy and not the momentum, that is to be considered as the measure of 

 the effect. If we know the strength of any substance, and the degree in 

 which it is capable of extension, we may easily determine its resilience 

 from a consideration of the laws of pendulums. For the same weight 

 which would break it by pressure, will acquire a sufficient impulse for 

 breaking it, if it fall from a height equal to half the space through which 

 the substance may be extended, supposing the direction of the stroke to be 

 horizontal, so that its effect may not be increased by the force of gravity. 

 Thus if the pressure of a weight of 100 pounds broke a given substance 

 after extending it through the space of an inch, the same weight would 

 break it by striking it with the velocity that would be acquired by the fall 

 of a heavy body from the height of half an inch, and a weight of one 

 pound would break it by falling from a height of 50 inches. 



It is obvious that the cohesive strength, as well as the resilience, of any 

 substance must be simply proportional to the magnitude of its transverse 

 section, that is, of the surface of fracture. Some experiments appear to show 

 that it increases in a greater proportion than this surface, others that it 

 increases in a smaller proportion ; but it is probable that in both cases 

 some accidental irregularities must have interfered, and that a wire two 

 inches in diameter is exactly four times as strong as a wire one inch in 

 diameter. The length has no effect either in increasing or in diminishing 

 the cohesive strength ; but the resilience is proportional to the length, since 

 a similar extension of a longer fibre produces a greater elongation. 



There is however a limit beyond which the velocity of a body striking 

 another cannot be increased without overcoming its resilience and breaking 

 it, however small the bulk of the first body may be, and this limit depends 

 on the inertia of the parts of the second body, which must not be dis- 

 regarded when they are impelled with a considerable velocity. For it is 

 demonstrable that there is a certain velocity, dependent on the nature of a 

 substance, with which the effect of any impulse or pressure is transmitted 

 through it ; a certain portion of time, which is shorter accordingly as the 

 body is more elastic, being required for the propagation of the force through 

 any part of it ; and if the actual velocity of any impulse be in a greater 

 proportion to this velocity than the extension or compression, of which the 

 substance is capable, is to its whole length, it is obvious that a separation 

 must be produced, since no parts can be extended or compressed which are 

 not yet affected by the impulse, and the length of the portion affected at 

 any instant is not sufficient to allow the required extension or compression. 

 Thus if the velocity with which an impression is transmitted by a certain 

 kind of wood be 15,000 feet in a second, and it f>e susceptible of compres- 

 sion to the extent of ^-y of its length, the greatest velocity that it can resist 

 will be 75, feet in a second, which is equal to that of a body falling from a 

 height of about 90 feet. And by a similar comparison we may determine 

 the velocity which will be sufficient to penetrate or to break off a substance 



