Following observations of the cluster Abell 1413 with the Ryle Telescope (RT ) at 15 GHz, we report the detection of a resolved decrement in the cosmic microwave background arising from the Sunyaev-Zel'dovich (S-Z) effect with a significance of 8 a. The position and shape of the S-Z decrement are in good agreement with the X-ray image from the ROSAT satellite. Because of the cluster ellipticity and the presence of a strong cooling flow, we defer H0 estimation from A1413 until suitably sophisticated analysis methods are developed. We detail the tailoring of the east-west RT array carried out to optimize the observations of this low-declination cluster. We also describe our strategy for removing the contaminant sources in the field that are variable.