106 LECTURE XIII. 



particles were prevented, the direct cohesion alone would be the measure 

 of the force required to produce extension, and the direct repulsion, of the 

 force required to produce compression ; in this respect indeed, the actual 

 rigidity of some substances may be considered as infinite, wherever the 

 extension or compression is moderate, and no permanent alteration of 

 form is produced ; and within these limits these substances may be called 

 perfectly elastic. If the cohesion and repulsion were infinite, and the 

 rigidity limited, the only effect of force would be to produce alteration of 

 form : and such bodies would be perfectly inelastic, but they would be 

 harder or softer according to the degree of rigidity. 



It is found by experiment, that the measure of the extension and com- 

 pression of uniform elastic bodies is simply proportional to the force which 

 occasions it ; at least when the forces are comparatively small. Thus if a 

 weight of 100 pounds lengthened a rod of steel one hundredth of an inch, 

 a weight of 200 would lengthen it very nearly two hundredths, and a 

 weight of 300 pounds three hundredths.* The same weights acting in a 

 contrary direction would also shorten it one, two, or three hundredths 

 respectively. The former part of this law was discovered by Dr. Hooke, 

 and the effects appear to be perfectly analogous to those which are more 

 easily observable in elastic fluids. 



According to this analogy, we may express the elasticity of any sub- 

 stance by the weight of a certain column of the same substance, which may 

 be denominated the modulus of its elasticity, and of which the weight is 

 such, that any addition to it would increase it in the same proportion as 

 the weight added would shorten, by its pressure, a portion of the sub- 

 stance of equal diameter. Thus if a rod of any kind, 100 inches long, 

 were compressed 1 inch by a weight of 1000 pounds, the weight of the 

 modulus of its elasticity would be 100 thousand pounds, or more accu- 

 rately 99,000, which is to 100,000 in the same proportion as 99 to 100. In 

 the same manner, we must suppose that the subtraction of any weight 

 from that of the modulus will also diminish it, in the same ratio that the 

 equivalent force would extend any portion of the substance. The height 

 of the modulus is the same for the same substance, whatever its breadth 

 and thickness may be : for atmospheric air, it is about 5 miles, and for 

 steel nearly 1500. This supposition is sufficiently confirmed by experi- 

 ments to be considered at least as a good approximation : it follows that 

 the weight of the modulus must always exceed the utmost cohesive 

 strength of the substance, and that the compression produced by such a 

 weight must reduce its dimensions to one half : and I have found that a 

 force capable of compressing a piece of elastic gum to half its length will 

 usually extend it to many times that length, and then break or tear it ; 

 and also that a force capable of extending it to twice its length will only 

 compress it to two thirds. In this substance, and others of a similar nature, 

 the resistance appears to be much diminished by the facility by which a 

 contrary change is produced in a different direction ; so that the cohesion 

 and repulsion thus estimated appears to be very weak, unless when the 

 rigidity is increased by a great degree of cold. It would be easy to ascer- 

 * See S'Gravesande's Elem. Physices, lib. i. 



