In many engineering problems it is necessary, from time to time, to deduce from only a few characteristic values data which would ideally be obtained from a complete stress-strain curve. For instance many handbooks, used in design offices and published by materials manufacturers and others, contain values of Young's modulus and minimum guaranteed, or typical, values of various proof stresses for materials. From these, estimates of strain, tangent modulus or ratio of stress to tangent modulus appropriate to known stress values may be required, or various processes involving integration of the stress-strain curve may have to be carried out. Even when a complete stress-strain curve is available from a special test, the differentiation and integration of it, which may have to be repeated several times, are timeconsuming processes. Also, in analytical work involving the use of materials beyond the limit of proportionality, it is desirable to have available a generalised mathematical form of the stress-strain curve in order that the results obtained may be applied to a wide range of actual materials simply by the substitution of appropriate coefficients. These and many other applications will be familiar to the reader.