It was fully explained mathematically twenty years later when the work function was introduced into the equation.  
Wilhelm Hallwachs created an experiment to better demonstrate it but could not explain it.  Philip Lenard studied it further but could still not offer an explanation.  It was first demonstrated using two pieces of brass by Heinrich Hertz, who also could not offer an explanation.  It was fully explained mathematically twenty years later when the work function was introduced into the equation.  FTP, name this effect that states that light shined on a surface will cause the emission of electrons.
Wilhelm Hallwachs created an experiment to better demonstrate it but could not explain it.  
photoelectric effect