Andy, there's a vital picture in this set that I haven't seen before. It makes me think even more that your lathe was primarily used for making balls. Maybe ivory billiard balls, but possibly of other hard materials.
The photo in question is your third one, showing the box of cup chucks, in a graduated range of sizes.
Have a read of Holtzapffel's description of turning hardwood or ivory balls in Volume 4 Chapter VII Section V:
https://archive.org/details/in.ernet.dl ... ew=theater
He describes it fully and accurately, but I'll try and summarise.
Fig 431 shows the preliminary stage; a ball being roughed out, still held on a stump.
In fig 432, it's wedged in a metal cup chuck of specific size, just right to hold it on a rim slightly smaller than the required diameter of the ball. You have a set of those chucks.
In fig 433 it's being checked for size with a "ring gauge" - which has a tapered hole, with the larger side matching the required diameter. You have one of these, with a set of different sized holes. I think some of your chucks will match the holes in the gauge.
In addition, the text describes the cutting action of the "flat tool" which is used "always flat upon the rest". Your tool rests are, indeed, entirely flat, so ideal for use in this way. One of your rests has two arms meeting at a right angle - I think this might be useful for getting close to a ball, minimizing the amount of tool overhang and avoiding any need to shift the tool rest horizontally.
The chuck shown in Fig 432 is described as being made of boxwood, not metal, but this chapter is about hard wood turning. Later, in Chapter XII, at page 413 onwards, there's a detailed description of turning ivory billiard balls. Figure 549 in that chapter is similar to fig 432, but the text says it's a "strong wood or metal plain chuck".
Unfortunately, the scanned text I linked to stops short at page 417. The full text goes on with another 8 pages of detail about exactly how to make a perfectly spherical ball. I won't summarise it all here, but I'll pull out two extra points.
The ball gets repositioned frequently, and only needs gentle pressure to hold it in the chuck - a plain metal chuck like you have a set of is the right chuck for the purpose.
And for the final, finest cuts, where the turner needs complete control of his body to position the freshly honed edge just right, "the operator removes his foot from the treadle, standing still on one or both feet, while guiding the tool around the ball." What could be better at that stage in the work than a special lathe with not one, but a pair of lead-weighted flywheels?
