  We construct two rational approximate solutions to the Thomas-Fermi (TF)
nonlinear differential equation. These expressions follow from an application
of the principle of dynamic consistency. In addition to examining differences
in the predicted numerical values of the two approximate solutions, we compare
these values with an accurate numerical solution obtained using a fourth-order
Runge-Kutta method. We also present several new integral relations satisfied by
the bounded solutions of the TF equation
