Neutrino Oscillation in Matter and Parameters $s_{13},\delta_{CP}$

We estimate the dependence of $\nu_{\mu}$ to $\nu_{e}$ conversion on parameters $\theta_{13}$ and $\delta_{CP}$ for several experimental facilities studying neutrino oscillations. We use the S-Matrix theory to estimate $\bar{\nu_e}$ disappearance and compare estimates based on an older theory being used to extract $\theta_{13}$ from the Double Chooz, Daya Bay, and RENO data, to assist in extracting an accurate value for $\theta_{13}$ from these projects. We use values of $\theta_{13}$ within known limits, and estimate the dependence of $\nu_{\mu}$ - $\nu_{e}$ CP violation (CPV) probability on $\delta_{CP}$ in order to suggest new experiments to measure CPV for neutrinos moving in matter.