Downing was a major instigator  of this conference which was convened on Monday 18 May 1896, in the Palais de l'Institut, Salle des seances of the Bureau des longitudes . The conference was primarily concerned with the calculation of apparent places of stars, and the need to establish an international standard for astronomical constants. However, the opportunity was taken of the simultaneous presence of the directors of most of the national ephemerides and the directors of the principal national observatories to give the conference a wider scope. Those present were:
Bakhuysen from Leyde and Trepied from Alger, were invited as consultative participants. Auwers, representing Germany, was prevented, for health reasons, from participating; Chirstie (Astronomer Royal) was meanwhile observing a solar eclipse in Japan. 
The conference recommended the introduction of Newcomb's value of the constants of precession and aberration. They also recommended that the changes in the astronomical constants would come into force starting on year 1901. Thus, the change and the unification began with the 20th century.
Not everybody agreed! The American Ephemeris, to give one example, continued to give the positions of stars calculated both with Newcomb's and with the Struve-Peters constants (which had been used in the almanacs for forty years).
However, following this conference, Newcomb's tables and constants were introduced as the basis of the ephemerides for the Almanac for 1901 onwards. Wilkins notes  that the RAS criticized Downing for not first consulting them, but the decision was upheld.
Simon Newcomb (1835-1909), born in Wallace, Nova Scotia, was one of the leading astronomers of his time and was director of the American Nautical Almanac Office from 1877-1897. His theories for the inner planets were used until they were supercede by ephemerides generated using modern integration techniques of the Jet Propulsion Laboratory in The Astronomical Almanac for 1984.