The ion temperature gradient driven electrostatic instability in tokamak magnetic geometry has been investigated numerically in terms of a generalized ion density moment. For typical tokamak parameters (ratio between the density gradient scale length and the major radius, n = Ln/R, about 0 (0.1) and Ti≅Te) the search for rapidly growing instabilities of a hydrodynamic nature has been unsuccessful, even with the ion temperature gradient relative to the density gradient, ηi = d(ln Ti)/d(ln n0), as large as six.