You do not have a Model 1893. They were made for the medium bore long action cartridges. Not the .38-40. Only the 1888, 1889 and 1894 were made in .38-40. If your rifle has a manufacture date of 1893, that should rule out the 1894 leaving the 1888 or 1889. If it is a top ejecting rifle, it is a Model 1888. If - as MM93 said - it has the lever catch and is side ejecting, it is a Model 1889.
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