The Spin Muon Collaboration was formed to measure the spin dependent structure function g\sb1 of both the proton and the neutron. This was done by scattering polarized muons off of polarized protons or deuterons. The results provided a test of three sum rules: the Ellis-Jaffe sum rule for the proton, the Ellis-Jaffe sum rule for the neutron, and the Bjorken sum rule. Two polarimeters were used to measure the beam polarization. The polarimeter discussed in this thesis used elastic scattering from polarized electrons to measure the muon beam polarization. It gave a result in agreement with both the previous measurement using muon decay and a simulation of the beamline. These measurements helped reduce the systematic error on the measurement and improve the measurements of the sum rules. The results from the experiment showed that both Ellis-Jaffe sum rules were violated while the Bjorken sum rule was confirmed.