Fleeming Jenkin's swamping argument (1867) is re-examined in relation to subsequent criticisms of its assumptions. Jenkin's original argument purported to show that, under blending inheritance, natural selection could not operate on ‘sports’ or ‘single variations’. A serious flaw in Jenkin's model was exposed in a forgotten paper in 1871. Darwin accepted Jenkin's ‘flawed’ conclusion, though he did not fully understand the argument. Both Jenkin and Darwin regarded the swamping argument as a barrier to evolution within a single lineage. A completely different interpretation of the phrase ‘swamping argument’, first put forward by Romanes in 1886, identified it with the problem of the role of free intercrossing in preventing speciation. The latter problem also underlies current debate about the possibility of sympatric speciation and is as serious under particulate as under blending inheritance. Jenkin's argument depended on the assumption of blending inheritance; when modified to remove the ‘flaw’ in his model, it ceased to present a barrier to the operation of natural selection within a lineage, provided that the mutation rate was high enough to maintain adequate genetic variability under blending.