_Answer._ It is the amount which a spring will deflect or bend under a given load without having its form permanently changed. If the bending is so great that the spring does not recover its original form when the load is removed, then the strain to which it is subjected is said to exceed the _limits of elasticity_, and if repeated often it will ultimately break the spring. QUESTION 288. _What is meant by the elastic strength and the ultimate strength of a spring?_ _Answer._ The _elastic strength_ is the strain it will bear without being strained beyond the limits of elasticity, and the _ultimate strength_ is the strain which will break it. QUESTION 289. _What determines the strength of a spring?_ _Answer._ It depends of course (1) upon the material of which the spring is made; (2) its strength increases in proportion to the number of plates, and (3) to their width, and (4) in proportion to the square of their thickness, and (5) as the length diminishes. Thus, if we wanted to double the strength of a spring like that shown in figs. 170 and 171, it could be done in either of the following ways: (1) by making it of material twice as strong; (2) by putting another plate just like it on top; (3) by doubling the width of the base _b_, which would make the strength of the whole plate twice what it was before; (4) by making the whole plate about four-tenths thicker, which would increase its strength, as already stated, in proportion to the square of the thickness as 1.4 × 1.4 = 2 nearly; (5) by reducing the length to one-half what it is in fig. 170. QUESTION 290. _What determines the elasticity of a spring?_ _Answer._ (1) The material of which it is made; with the same material the elasticity increases (2) as the number, and (3) as the width of the plates diminishes, and (4) with the cube of the length, and (5) decreases with the cube of the thickness of plate. Thus, supposing the plate in figs. 170 and 171 to be ³⁄₈ in. thick and the deflection _d_ 2¹⁄₂ in.; the latter would be only half as much or 1¹⁄₄ in. (1) if it were made of material twice as stiff, or (2) with two such plates, or (3) with one twice as wide at the base. If (4) the length were doubled, the deflection would be equal to 2 × 2 × 2 = 8 times what it was before, or in proportion to the cube of the length. If (5) the thickness were doubled the deflection would be _reduced_ in the same proportion, and would be only one-eighth of 2¹⁄₂ in., or ⁵⁄₁₆ in. [Illustration: _Fig. 182._ _Fig. 183._ Scale ³⁄₄ in. = 1 foot.] QUESTION 291. _What should be the proportion of the plates of a spring in relation to each other?_