  As an extension of our previous work, we investigate the dynamical
instability against nonaxisymmetric bar-mode deformations of differentially
rotating stars in Newtonian gravity varying the equations of state and velocity
profiles. We performed the numerical simulation and the followup linear
stability analysis adopting polytropic equations of state with the polytropic
indices n=1, 3/2, and 5/2 and with two types of angular velocity profiles (the
so-called j-constant-like and Kepler-like laws). It is confirmed that rotating
stars of a high degree of differential rotation are dynamically unstable
against the bar-mode deformation, even for the ratio of the kinetic energy to
the gravitational potential energy $\beta$ of order 0.01. The criterion for
onset of the bar-mode dynamical instability depends weakly on the polytropic
index n and the angular velocity profile as long as the degree of differential
rotation is high. Gravitational waves from the final nonaxisymmetric
quasi-stationary states are calculated in the quadrupole formula. For
proto-neutron stars of mass $1.4M_{\odot}$, radius $\sim 30$ km and $\beta \alt
0.1$, such gravitational waves have the frequency of $\sim$ 600--1,400 Hz, and
the effective amplitude is larger than $10^{-22}$ at a distance of about 100
Mpc irrespective of n and the angular velocity profile.
