Abstract
With the use of the arguments in paper II, the distribution of zeros of the grand partition function for a gas obeying van der Waal's equation of state is calculated for temperatures high compared with the critical temperature. The positions of the branch points of the pressure considered as a function of the activity are found, and the pressure is expanded near a branch point, P1, not lying on the real axis. By the use of these results the equation for the zero line and the distribution function near the branch point P1 and near its conjugate P2 are obtained. A zeroth approximation to the position H at which the zero line crosses the negative real axis is obtained. The distribution function for zeros on the part of the negative real axis between the point H and -∞ is calculated, in particular near H and near -∞.
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