  Deep inelastic e^+ scattering data, taken with the H1 detector at HERA, are
used to study the event shape variables thrust, jet broadening and jet mass in
the current hemisphere of the Breit frame over a large range of momentum
transfers Q between 7 GeV and 100 GeV. The data are compared with results from
e^+e^- experiments. Using second order QCD calculations and an approach to
relate hadronisation effects to power corrections an analysis of the Q
dependences of the means of the event shape parameters is presented, from which
both the power corrections and the strong coupling constant are determined
without any assumption on fragmentation models. The power corrections of all
event shape variables investigated follow a 1/Q behaviour and can be described
by a common parameter alpha_0.
