An outstanding difficulty in the theory of fluid motions is the fact that the differential equations of motion are not linear, Their Solutions are difficult and sometimes impossible. Workers therefore are frequently forced to use approximate methods of solution, or to make assumptions which are not always sound. For example, in a nümber of cases it is assumed that two distinct Solutions of the hydrodynamical equations of motion are lin e a rly s u p e r p o s a b l e , i.e. their sum is also a solution. The same assumption is used again and again, for instance, in Lamb’s hydrodynamics.