We employ two independent methods to determine the relationship between the &egr; parameter and the total energy dissipation rate of the magnetosphere by selecting disturbed periods from the same data set used by Baker et al. (1983). Specifically, four storms are examined in detail, since the accuracy of estimating UT is significantly improved during disturbed periods. The first method assumes UT =MA2&agr;&egr;, where MA is the Alfv¿en Mach number and &agr; varies with time. The second method considers a linear, time-invariant dynamic system with &egr; as input and UT as output. This means UT =W*&egr;, where * is convolution and W is a transfer function characteristic of the system. It is found that &agr; values fluctuate mainly between 0 and -0.25. The transfer function analysis indicates that W often resembles a Δ-function or a narrow rectangular impulse. Both results give the same implication (namely, UT ~&egr;) and thus are consistent with the view that the magnetosphere is primarily a directly driven system during disturbed periods.