The Sommerfeld–Watson transformation (SWT) of the partial wave series for the acoustical scattering from a fluid-loaded elastic sphere is examined. This research specifically focuses on the specular reflection and Rayleigh wave contribution to scattering at small backscattering angles. In a previous paper the angular dependence of the Rayleigh contribution to near backward scattering was measured and modeled [Williams and Marston, J. Acoust. Soc. Am. 78, 722–728 (1985)]. The SWT confirms the physical picture used and, for the first time, predicts the absolute Rayleigh contribution associated with one or more circumnavigations of the sphere. To test the SWT, tungsten carbide spheres in water were ensonified by tone bursts having central frequencies in the range 24
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Williams et al. (1985) studied this question.