We compare the open flux content of the magnetosphere, quantified by measurements of the size of the northern ionospheric polar cap, with the radius of the magnetotail at X ≈ -25 RE, deduced from observations made by the IMP-8 spacecraft. During an 8-hour period of observation we estimate that the proportion of terrestrial flux that is interconnected with the solar wind varies between 12 and 2.5%. This latter extreme, representing an almost closed magnetosphere, follows the incidence of a solar wind dynamic pressure step, the onset of a large substorm, and a 3-hour period of northward IMF. The deflated and compressed magnetotail is predicted to have a radius as small as 12 RE at this time. The magnetotail does not reinflate to more typical dimensions until some time after a southward turning of the IMF, leading to accumulation of open flux through low latitude reconnection. We compare our observations with estimates of the shape of the magnetopause from an empirical model. We also present a simple model of the varying length of the magnetotail, based on upstream solar wind conditions, and observations of the size of the polar cap.