Was the 6-inch swing by 12 inches between centres "Briggs No.1 Lathe" by Gooley-Edlund of Cortland, N.Y. manufacturers of the unusual production milling machine that was branded as a Briggs? Or, could it have been the Mr. A.J.Briggs, designer of the miller, manufactured this little lathe in his own workshops? However, the milling machine - from the scant evidence available and its patent number  - appears to have been current from around 1915 onwards, while the lathe looks to belong to as early as the mid-1800s, though could just as easily have been made late in that century.  As with many similar machines from smaller manufacturers, advertising was left in the hands of machinery and tool distributors, appearing in those distributed by, amongst others, bJackson & Tyler of Baltimore, Frasse & Co of New York City and the John Wilkinson Co of Chicago.
Also found with backgear and branded with a rather unusual name, the "Hollow Spindle", the Briggs No.1 stood on elegant, splayed legs so common on many lathes of the mid 1800s. The lathe was obviously aimed at the Amateur market and of the basic, plain-turning bench type and of quite conventional design. Like many of its kind made in both Europe and the United States, the headstock spindle did not run in two bearings but just one, at the front. The other end, hardened and ground to a point, rested against an adjustable stop. While on most other inexpensive lathes of the same design the stop was formed as a simple bolt-with-locknut arrangement screwed through the left-hand end of the headstock casting (as seen on the Gale), the Briggs used a rather more complex and expensive-to-manufacture arrangement: the left-hand end of the casting was bored through and the inner and outer faces machined flat; into the hole so formed was inserted a bar - formed with the necessary support point - and secured by pin-spanner ring nuts threaded onto each end. Oddly, the Gale too was also made with such an arrangement, as was the popular English Pfeil, so perhaps there was some hidden advantage to the design, invisible to modern eyes.
Simple and effective for light-duty work, the single-bearing headstock design was used well into the 20th century, as was the use of a headstock pulley with narrow V grooves intended to take a round leather belt - referred to in contemporary parlance as a "gut drive" (as in catgut, made from the intestines of sheep and goats).  Drive for the Briggs was either by some self-constructed means or a self-contained treadle-type stand, in which case the cost from $15 to $25. The stand was typical of the time and very similar in construction to that used on the Booth Brothers and Pfeil lathes. Although it might have seemed expensive, the 33% increase in cost for a stand might be considered modest for, when offered, such were often more expensive than the lathe. As a more economical arrangement, foot motor were offered by third-party sellers, these being mounted beneath the owner's own bench.
Formed with a single, central T-slot, the bed was flat on top and carried the maker's name cast into the front face - a not uncommon feature of American small lathes, though less so in Europe where the name, when included, was often stamped into the front face of the headstock.  Whether the screw-feed compound slide rest assembly shown with the Briggs is original is unknown, though its well-constructed mounting that sockets into the base of the hand-turning rest suggests it might be. While the full-circle handles do look to be of a different era - at the time crank handles would have been de rigueur - a lathe with Briggs-like bed feet that appeared in the Old Wood Working Machines Forum some years ago did have an identical fitting holding a slide assembly that looked to be almost the same. While most contemporary wood-turning lathes in the same class were not offered with such a fitting, when they were, the expense was considerable.
By their tailstocks shall ye know them - and that on the Briggs meets every requirement of the age - simple, one-piece construction with concave faces sweeping down to a rectangular base secured to the bed by a through-bolt. The spindle was locked by a direct-acting screw, often of steel with a soft-metal pad to prevent damage or, less common as here, in what looks to be bronze.
Do you have a Briggs No.2 or No.3 lathe - or any other Briggs or "Hollow Spindle" machine tool? If so, the writer would be pleased to see photographs..