We consider the effect on the scrape-off layer (SOL) of changing the position of a tokamak limiter from the low field side (LFS) to the high field side (HFS) of the plasma. Conservation of magnetic flux in the SOL requires that the area, A||, for flow of particles and energy, parallel to the magnetic field, is smaller on the HFS. The effect that this reduction in A|| has on the SOL is that when the limiter is on the HFS, as compared with the LFS, then the characteristic scrape-off thickness is increased and the plasma particle and energy densities are higher. We describe such increases observed in an experiment in JET in which the plasma was limited first on the LFS and then, during the same discharge, on the HFS. The magnitude of the effect was larger than expected, with the line-integrated density of the SOL, n ln, having an average increase by a factor 5.8 ± l.l, and an increase by a factor 7 at the respective limiter. Moreover there was an increase in the characteristic scrape-off thickness for power flow, lp, by a factor 2.5 ± 0.4 on average, and a corresponding increase by a factor 3.0 at the respective limiter. Such an increase in n ln can substantially improve the screening of recycled particles and can increase wall pumping, although not in the experiments described, which were in helium to avoid these effects. The large increase in lp measured in JET is useful in spreading power over a larger area of a limiter on the HFS. Evidence is presented which suggests that the observed enhancement of the effect on the SOL above expectations is due to a reduction in the Mach number at the limiter sheath when on the HFS. Related experiments are discussed.