This effect was invented by Buatier deKolta in 1875. DeKolta's method used a gimmick made of two half balls hinged together, which when closed appeared as one ball, and when open appeared as two. Others record that two hinged hollow half shells were used. DeKolta may have employed both. In More Magic, 1890, p. 261, Professor Hoffmann recognizes deKolta as the originator of the trick and teaches routines by Professor Hellis and himself. The apparatus described does not use hinged half balls or shells. Instead, two separate half shells were employed, which fit over a solid ball and were joined loosely together like a box and telescoping lid. The details of deKolta's routine were apparently not known to Hoffmann.
In 1898, August Roterberg released the “Excelsior Ball Trick”, a version of the Multiplying Billiard Balls using just one half shell. This simplified handling soon grew to become the standard method and has remained so to the present day. Roterberg was commonly given credit for it, but almost half a century later the true originator became known: George Wright, who came up with the method while working for Roterberg in Chicago. He told his story in Munroe's Magical Miscellany, No. 36, Jan. 1946, p. 8.