Providence, Rhode Island, was home to many makers of machine tools with grinders by Leach and the Builders Iron Foundry and several lathe makers, including E. A. Eddy, E. A. Adams, Adams Bros, the Diamond Machine Co.; E.B. Bosworth, Charles A.Mann, J.M.Parker's Gage, I.H.Spencer and Narragansett. Unfortunately, apart from Diamond, little is known about the historical background of any others, the record being, for the moment, blank.
Not to be confused with the Diamond Tool Company of California, the Diamond Machine Co. made a variety of products including grinding machines  (one of their more advertised products), gun boring and metal-spinning, plain-turning and wood lathes. Established around 1869 by a Mr. R. I. Costain and Mr. Nicholas B. Hadley, they were first known as Hadley & Costain, manufacturers of the Diamond Emery Wheel". They also retailed the special grinder heads made by American Twist Drill Co., another Providence firm partly owned by Nicholas B. Hadley. By 1881 the name had become the Diamond Emery Wheel & Machine Co. and by 1889 or 1890, to the Diamond Machine Co., at which point the lathe shown below would have been made. Additional details of the Company's background can be found here
Of around 5-inch centre height and 28" between centres the "Diamond" lathe appears to have been a well-made industrial-class, plain-turning, non-backgeared machine intended just for simple work in metal - although it may also have been advertised as a lathe suitable for metal spinning or even as a brass finishers' machine. An unusual feature is what appears at first sight to be two clamping wheels on the tailstock spindle; however their function is not what it seems as there are, in fact, two concentric spindles - the larger driven by a lever for a quick feed and the smaller by the usual screw thread. The wheels are used to lock and unlock the former, the advantage being that in production use for spinning or brass finishing, the work can be swiftly removed and a fresh job inserted..
On the black-painted lathe below the lever assembly is missing, but the extension to the tailstock casting that provided the pivot point is visible - rather along the lines of the assembly also used on some Mikron lathes
If you have a Diamond lathe, the writer would be interested to hear from you..