We apply the phenomenological theory of Cahn, generalized to include van der Waals forces, to the wetting of n-alkanes on water, deriving an interface potential from which the line tension is calculated. For the n-alkanes considered (butane to octane) the typical magnitude of the line tension is of the order of 10(-12) N, rising to a maximum of +5 x 10(-12) N in the vicinity of a first-order wetting transition or a transition between thin and thick wetting films. Close to critical wetting transitions, the line tension is negative and also of the order of 10(-12) N, but it vanishes at wetting. We also calculate the boundary tension for various thin-thick transitions that extend into the one-phase region of the bulk phase diagram, such as prewetting, which has the same order of magnitude.