This paper describes the measurement of second and fourth order correlations of two components of velocity in a low speed jet. The measurements are made with two cross-wire hot-wire anemometers. The measured covariances are relevant to the modeling of the source terms in acoustic analogy formulations for the prediction of noise from jets. First the general characteristics of the jet mean flow are established. Then tests are performed to assess probe interference effects in the correlations. Second and fourth order cross correlations are then presented at different locations in the jet: primarily on the jet lip line and centerline. The fourth order correlations are normalized by both local mean square values as well as by their value at zero separation. The measurements show that probe interference effects are unavoidable, though they appear negligible for sufficiently large probe separations. Comparisons are made of the longitudinal and lateral length scales based on the different velocity components. The overall convection speeds, based on the different components of velocity, are also given. In an appendix the analysis by Lighthill relating second and fourth order correlations, without statistical assumptions, is reexamined. In particular the assumptions made are reviewed. The analysis is also extended to additional fourth order correlations. Predictions based on the resulting formulas are assessed based on the correlation measurements.