Solitaires, or bachelor's buttons, were made in the 1870's-90's to avoid the bother of having to sew on a button, or the struggle of forcing a stud through the thicknesses of material.  By means of their removable back, they could be fixed in an instant.  Though the mechanism can vary, all have the wings on the side of the top which release the back.  Sizes vary from 3/8" to 1".  Here are a few from a collection.  To read more about these beauties, click HERE.