144 LECTURE XIII. 



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 sub- 

 stance 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 ir- 

 regularities 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 cither 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 bod}^, which must not be disregarded 

 •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 cer- 

 tain 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 im- 

 pulse, 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 15000 feet in 

 a second, and it be susceptible of compression to the extent of -^-l-g- <*f its 

 length, the greatest velocity that it can resist will be 75 feet in a second, 

 which is equal to that of a body faliing from a height of about 90 feet. And 

 by a similar comparison we may determine the velocity which will be suffici- 

 ent to penetrate or to break oft' a substance in any other manner; if we calcu- 

 late the velocity required to convey the impulse frOm one part of the substance 



