Illustration of comparable surgical kit, offered for sale by George Tiemann and Co. as an "Otis' U.S.A. Compact Field Set," that is a field kit for a military surgeon (1889 catalogue, p. 61, fig. 1273).
Perhaps slightly closer to our specimen is one offered for sale by Sharp and Smith as an "amputating and minor operating set" (whence the title given our set). Source: Sharp and Smith catalogue (1889), p. 278, fig. 904).