In many problems of physics, even in widely different branches of the subject, the relation satisfied by the variables is expressible by means of a linear differential equation of the second order. In general, “initial” conditions have also to be satisfied. If the equation truly represents the physical conditions in, for example, some case of motion, and if no state of instability exists, the solution must be unique. But it is impossible in any case to say with absolute certainty that the representation is strict. The possible error depends on the error which may be made in observation or experiment, and on the number of independent observations or experiments the results of which have been used as the basis of the “law” expressed by the equation.