The corrections to the origin of the fundamental reference system and the Earth's orbital parameters (Paper I) display a puzzling value for the correction to the obliquity of the ecliptic. The large and good quality set of solar transits, observed visually with modified Danjon astrolabes, that had been used to derive the results, was submitted to a series of tests to assert the homogeneity of the data and its dependence on the adopted modelling. The results displayed a remarkable resistance to significant changes with respect to the attempted tests. However, this does not rule out the possibility of the presence of unsuspected systematic errors of quite special nature. As a conclusion we may say that while the results of Paper I are the best that can be afforded by the available data, the effort to observe the Sun's transits need to be pursued and would gain enourmously by the adherance of other observing groups around the world.
Acknowledgements
We acknowledge the support of the Director of the Observatório Nacional/Brazil, Sayd L. Codina, who made possible the many travels required to collect and discuss all the data. We also thank very much indeed the many observers that made possible the campaigns at the three sites.