All three Ithaca Gun Co. hammer doubles were boxframe guns. That is not the Baker Model Ithaca. The Baker Model Ithaca only had one tiny pin showing in the side of the frame, just below the hammer. That is a New Ithaca Gun (NIG) that replaced the Baker Model in mid-1887. The three screws in the side of the frame identify the NIG. The NIG continued in production until about 1914 or early 1915. Here is one from 1910 that didn't get out much --
From 1915 to WW-I Ithaca produced a very few hammer guns that they called the "two bolt" model which was essentially a hammer version of their Flues Model hammerless gun, using coil springs
By the time the NIG was introduced, W.H. Baker had returned to Syracuse and was working at his brother's, Dr. Ellis Baker, Syracuse Forging & Gun Co. building a a trigger-plate hammer double called the "New Baker" but actually the design of A.C. McFarland.