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Papers I and II of this series have extended the radio interferometrymeasurement equation (RIME) formalism to the full-sky case, and provided aRIME-based description of calibration and the problem of direction-dependenteffects (DDEs). This paper aims to provide a practical demonstration of aRIME-based approach to calibration, via an example of extremely high-dynamicrange calibration of WSRT observations of 3C 147 at 21 cm, with full treatmentof DDEs.  A version of the RIME incorporating differential gains has been implementedin MeqTrees, and applied to the 3C 147 data. This was used to perform regularselfcal, then solve for interferometer-based errors and for differential gains.The resulting image of the field around 3C 147 is thermal noise-limited, has avery high dynamic range (1.6 million), and none of the off-axis artefacts thatplague regular selfcal. The differential gain solutions show a highsignal-to-noise ratio, and may be used to extract information on DDEs anderrors in the sky model.  The differential gain approach can eliminate DDE-related artefacts, andprovide information for iterative improvements of sky models. Perhaps mostimportantly, sources as faint as 2 mJy have been shown to yield meaningfuldifferential gain solutions, and thus can be used as potential calibrationbeacons in other DDE-related schemes.

Revisiting the radio interferometer measurement equation. III. Addressing direction-dependent effects in 21 cm WSRT observations of 3C 147