It is well known that isolated neutron stars spin down over time through magnetic braking. To maintain hydrostatic equilibrium as they do so, the density profile of the star changes. At densities as high as those expected to exist in the interiors of neutron stars, this can lead to changes in the state of matter found there. Given several models for the nuclear equations of state, we use numerical techniques to determine, for each, the quark-hadron composition for varying frequencies and the results are presented in both tabular and graphical forms. The CD-ROM, an appendix to this thesis, is available for viewing at the Media Center of the Library.