First offered during the early 1920s, and now a very rare machine, the smallest and cheapest Drummond ever produced was a plain lathe reduced to the elements of simplicity with the bed and headstock cast as one with bolt-on feet at each end. Although produced until late in the decade of its introduction, the design was decidedly old-fashioned with the aluminium 3-step "gut-drive" headstock pulley carried on a spindle that ran trapped between a conical face on the inside of the front "bearing" and a hardened centre at the back. The latter pushed against an adjustable tube, secured by a single square-headed bolt - the system being a variation on a method more commonly found on both inexpensive and better quality lathes from mid to late 1800s. The spindle nose on early models was threaded internally with a conical section against which a combined centre and drive dog was drawn. It is possible that later models used a conventional external thread and, if so, would have been much more adaptable to accept special fittings and the carrying of conventional chucks.
Like the popular and long-lived 1950s Emco Unimat, the swivelling compound slide rest made use of an inexpensive and easy-to-manufacture twin-bar construction - but on the Drummond lacked micrometer dials. Both the carriage assembly and tailstock were bolted to the flat-topped bed by two bolts, one at the front and another at the rear. A flat brass plate, with degree calibrations, was trapped between the top slide and cross slide; however, because the plate was not screwed down but just turned over along its inside edge as a means of location, as the top slide was swivelled (or the clamping bolt tightened), the plate moved and the reading changed.
The tailstock made do with just a simple (but very effective) lever-action control for the barrel with the various pivot points provided by ordinary split pins.
It is open to question if Drummond actually made the lathe themselves for the same (or very similar) machines  appeared in the 1900 to 1930s catalogues of "hardware" and tool merchants with either just a reference number or an obviously contrived name to identify it.
If you have a "Little Goliath" the writer would be interested to see pictures.