We have obtained the polytropic index as a function of distance along the midnight meridian in the terrestrial magnetotail. As our purpose is to establish the effects of the finite width of the magnetotail, we use a simple theoretical model of plasma sheet convection, i.e., 2-dimensional (2D) field structure and adiabatic inward convection of a uniform distant tail source. Particle orbits are treated independently for portions of the phase space distribution on shells of constant energy. On the midnight meridian, the moments of the distribution are parameterized by &tgr;, the ratio of half the crosstail potential energy to the characteristic maxwellian energy of a distant downtail plasma source. We infer from the model the plasma pressure, P, and the number density, n, along the midnight meridian as a function of &tgr;. P and n define locally an ''effective'' polytropic index, &ggr;. We find that &ggr; ranges between 5/3 and 1, depending on the value of &tgr; and on geocentric distance. We suggest that the qualitative differences between the recent empirical determinations of the polytropic index by Baumjohann et al. [1989> and Huang et al. [1989> may be accounted for in part by this simple model. ¿ American Geophysical Union 1990