Being a derivative of a function, up to a factor, the compressibility is, technically, the response to a vanishingly small perturbation. In practice, we determine the compressibility by approximating kappa subscript T equals negative 1 over V left parenthesis fraction numerator partial differential V over denominator partial differential p end fraction right parenthesis subscript T by the quantity negative 1 over V left parenthesis fraction numerator capital delta V over denominator capital delta p end fraction right parenthesis subscript T, where capital delta V is the (finite) change in volume resulting from changing the pressure by a (finite) amount capital delta p. Let us compute here the compressibility of a spring of length L and whose spring constant is k. The equation of state for this system is the familar: f equals negative k x, where f is the force and x is the displacement of the end of the spring. The compressibility is defined kappa subscript T equals negative 1 over L left parenthesis fraction numerator partial differential L over denominator partial differential f end fraction right parenthesis subscript T and approximated by negative 1 over L left parenthesis fraction numerator capital delta L over denominator capital delta f