The NPE is obtained by a novel method which avoids the use of perturbation expansions (McDonald et al., Appl. Acoust., 43 (1994) 59–67). The single variable NPE is derived here from the continuity equation by assuming an irrotational flow and employing partially linearised versions of the momentum and state equations. This derivation sheds new light on the range of conditions of applicability of the NPE.