A measurement of the $p\bar{p} \rightarrow W$ cross section at $\sqrt{s} =$~1.96~TeV using forward electrons at CDF Abstract: We present a measurement of the $W$ boson production cross section using electrons identified in the rapidity region $1.2<|\eta|<2.8$ in 223 pb$^{-1}$ of CDF~II data collected from 2002 to 2004. $W \rightarrow e\nu$ events are selected using the combined information from the forward calorimeter and silicon tracking detectors. Taking the ratio of this cross section toan earlier one obtained in the central detector region ($1.2<|\eta_e|<2.8$), we demonstrate the measurements' ability to constrain parton distribution functions.