# A course of lectures on natural philosophy and the mechanical arts Young, Thomas, 1773-1829,    vol1 1807, vol2

It is found by experiment, that

• the measure of the extension and compression 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 1 hundredth of an inch,
• a weight of 200 would lengthen it very nearly 2 hundredths,
• and a weight of 300 pounds 3 hundredths.

The same weights acting in a contrary direction would also shorten it 1, 2, or 3 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.

pag. 137 vol1

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 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 substance 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 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 diminish it, in the same ratio that the equivalent force Avould extend any portion 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 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 faciUty 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 ascertain the specific gravity of such a substance in different states of tension and compression, and some light might be thrown, by the comparison, on the nature and operation of the forces which are concerned.

pag716vol2 index modulus of elasticity

pag46vol2

318. Definition.

A substance perfectly elastic
is initially extended and compressed in equal degrees by equal forces, and proportionally by proportional forces.

319. Definition.

The modulus of the elasticity of any substance
is a column of the same substance, capable of producing a pressure on its base which is to the weight causing a certain degree of compression, as the length of the substance is to the diminution of its length.