ON PASSIVE STRENGTH AND FRICTION. 137 



the cohesion and repulsion were infinite, and the rigidity limited, the only 

 effect of force would be to produce alteration of fonn : and such bodies would 

 be perfectly inelastic, but they would be harder or softer according to the de- 

 gree of rigidity. 



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

 sion of uniform elastic bodies is simply proportional to the force which oc- 

 casions 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 substance 

 by the weight of a certain column of the same substance, which may be de- 

 nominated 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 substance of equal dia- 

 meter. 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 accurately 99000, which is to 100000 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 di- 

 minish it, in the same ratio that the equivalent force Avould extend any por- 

 tion of the substance. The heigJit 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 experiments, 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 

 VOL. I. T 



