Tests of QED to Fourth Order in Alpha in Electron - Collisions at 29 GEV.

Tests of Quantum Electrodynamics to order alpha^4 in e^+e^ - collisions using the ASP detector at PEP ( sqrt{s} = 29 GeV) are presented. Measurements are made of e^+e^- to gamma gammagammagamma, e^+e ^- to e^+e^-gammagamma and e^+e^- to e^+e ^-e^+e^- where all four final state particles are separated from the beam line and each other. These are the most precise and highest statistics measurements yet reported for these processes. The ratios of measured to predicted cross sections are(UNFORMATTED TABLE OR EQUATION FOLLOWS)eqalign {gammagammagammagamma&: 0.97 +/- 0.04 +/- 0.14cr e^+e^ -gammagamma&: 0.94 +/- 0.03 +/- 0.03 cr e^+e^-e^+e^-&: 1.01 +/- 0.02 +/- 0.04cr}(TABLE/EQUATION ENDS)where the first uncertainty is the systematic uncertainty, and the second is the statistical uncertainty. All measurements show good agreement with theoretical predictions. A Monte Carlo method for simulating multi-pole processing is also presented, along with applications to the e^+e ^- to e^+e^-gammagamma and e^+e^- to gamma gammagammagamma processes. The first measurements of five-body alpha ^5 events (5gamma, e^+e ^-gammagammagamma and e^+e^-e^+e^-gamma ) and one candidate six-body alpha ^6 event (e^+e^-4gamma ) are reported. Both the alpha^5 and alpha^6 measurements agree with estimates of their cross sections.