The theoretical assumptions of Newton and Euler (hypotheses magis mathematicae quam naturales) of a resistance varying as some simple power of the velocity, for instance, as the square or cube of the velocity (the quadratic or cubic law), lead to results of great analytical complexity, and are useful only for provisional extrapolation at high or low velocity, pending further experiment.

But it must be remembered that these require extrapolation from experience sometimes sufficiently remote, and it is possible they may lead to statements that are obscure, if not contradictory.