Wilhelmine is a term for the period of German history, also known as the German Empire. The term Wilhelmine Germany refers to the period running from the proclamation of Wilhelm I as German Kaiser at Versailles in 1871 to the abdication of his grandson Wilhelm II in 1918.
Although the father of Wilhelm II, Friedrich III, was not named Wilhelm, he was only Kaiser for three months, and hence almost the entire period 1871-1918 saw a Kaiser named Wilhelm.
See Wilhelminism