Made in Muncie, Indiana, by the Depoy Model Works, the "Derpoy" was announced in 1932 with a very small advertisement amongst the back pages of the May 1932 edition of Popular Mechanics: MODEL Makers lathe; particulars for dime. Depoy Model Works, Muncie, Ind. The advertisement was repeated in further issues during the same year, but then disappeared until 1938 - by which time the company name had changed to Depoy Model Shop. This fresh run of advertisements continued until 1941, with just one further announcement, of a milling attachment, in 1947.
Other traces of the lathe can be found in the Popular Science magazine with the issue for March 1938 carrying a rather confusing advertisement, possibly a misprint, that announced: MAKE good profits with Potato Maid-en Flakes. Depoy Model Shop, Muncie, Ind." By September of the same year (and repeated until 1941) the wording had changed to: MODEL makers lathe; photographs for dime. Depoy Model Shop, Muncie, Ind.
It appears that at least two models were made: the first (yet to be photographed) was a simple machine with a cantilever bed (a single pedestal under the headstock) with a hand-driven feed for the carriage (there was no provision for changewheels) the leadscrew running down the centre line of the bed with a handwheel at the tailstock end. The more common type (a couple have been discovered) was of surprisingly heavy build with a wide, flat-topped bed (with feet at each end) with a shallow gap and angled sides to guide the carriage. With a swing of 4.5 inches (2.125 inches over the tool slide) and a capacity between centres of approximately 9.5 inches the lathe was around 24-inches long, 6-inches deep and stood 8-inches high. Robust, with a well-braced front wall, the headstock had a ¾-inch diameter, 3/8-inch bore spindle (with a No. 1 Morse taper socket in its ¾" x 16 t.p.i. nose) that ran direct in the cast iron with the 1-inch long bearings closed down by screws set to the rear. Although not fitted with backgear (for slow speeds) the lathe did have screwcutting - or at least a power sliding feed - with a shaft taking the drive from the changewheels to the tailstock end of the bed where, using a pair of 11t and 33t reduction gears, the drive was stepped forwards to turn the 7/16" x 12 t.p.i. (Whitworth-form) leadscrew. As a (long) full nut was fitted under the saddle, to allow the drive to be disconnected a simple push-pull button was arranged at the tailstock end that allowed the 11t gear to be disengaged - the leadscrew could then be turned by hand using a rather elegant "balanced" handwheel.
It is believed that the original gear train consisted of a 22t spindle gear meshed to a  6t gear attached to the under-bed drive shaft (the idler gear being 44t). Combined with the 11t and 33t reduction gearing at the tailstock end this would have created a (rather fast) 108 t.p.i. rate of carriage feed.
Unfortunately, only a single swivelling tool-slide was fitted, driven by a 5/16" x 16 t.p.i. feed-screw and mounted in a most unusual manner - a large, centrally-disposed V-way on top of the saddle that allowed it to be easily and quickly positioned as required. Although simple, the slide was another hefty unit, with its handwheel being large and easily gripped. 
One significant design flaw concerned the tailstock: with the front of the casting set vertically to the bed - instead of being inclined forwards - the 1.75-inch travel of the 5/8-inch diameter, No. 1 Morse taper spindle was such that it would have been impossible for very short pieces of work to be supported between centres.
If you have a Depoy lathe, or any further information about the company,  the writer would be interested to hear from you