When measuring interfacial tensions, conventional spinning drop tensiometry requires knowledge of the index of refraction of the denser, outer fluid phase, in order to correct for the magnification of the inner, spinning drop. We have modified a spinning drop tensiometer to accommodate a square section sample tube, which does not require this correction. Tests performed using calibration rods are used to demonstrate this fact. The interfacial tension of toluene and water is also measured using this new design. The ensuing results are in agreement with measurements obtained using a conventional circular sample tube.