Clean the limestone with a grease-fighting cleaner and soft cloths, then rinse. Wash the surface of the stone with acetone and a soft cloth. Allow the stone to dry overnight to ensure all water particles have evaporated from the surface.
Mix 98 percent glue with 2 percent hardener. Blend the two materials together with a popsicle stick.
Apply a thin, even layer of glue to both stone pieces using the popsicle stick. Remove any glue that has spilled over the sides.
Clamp the two stone pieces together with large clamps. Wipe away any excess glue from around the edges. Allow the glue to dry overnight.
Sand away any excess glue with sandpaper after the glue hardens.