Well, in my Wolf-Jahn (similar, if not identical to Lorch equipment) tapered tip-set, and some of the 7mm tailstock runners, there are many with these parallel, separated slits from those older days, likely cut with a small, round sawblade. But, they never extended axially all the way through to the edge. The more modern ones in my Leinen set have a wedge ground perpendicular into them such that you can see clear through the hole, but not enough room to do any work on the pivots like those hard, thin discs on a true jacot. Never drop those! Most safety roller fine inserts share these center-holes.
With no manual (that's what this forum is for?) this is how you can introduce and maintain a steady supply of clean oil to extend in to the conical contact points to avoid turning issues with close dead center work. I use light sewing machine (mineral) oil, as it's cheap. Today, we have "live" centers which are great for larger work, but if you have real 60 degrees included on all four sides and are turning with a dog between hard dead centers (like the turns) I've found there is an extremely fine line between flopping (too loose) and binding (too tight). The slot lets you add fresh oil and almost operates like hard cone lathe bearings - the work (kind of like a spindle) is perfectly suspended in a bath of light, clean oil against the bearings. That's my $.02.
The one on the right has been modified with the slit, but I don't know why
My guess for the one on the right is that it was a hack job. It's cut all the way through to allow for a spring-fit of work that was too big for the original end, but he did not want to cut a new tip just for one job. So, it spreads a little under pressure and if you're quick, it gives just enough tension to hold the workpiece steady (enough) in a tip that's actually too small. I wonder if the ring actually belongs on the fully slitted end, as a tensioner? Out in the boonies, you gotta make do. Removing the saw burr on the inside of the cone would have helped. Goes to show you can never have too many sizes of hollow female centers?
George, I think I now understand your avatar better. Hair from horses and whale bones, eh? I tried the violin once, and was always amazed at how they got all those hairs to stay together and how well it all worked with rosin. Also, I think that winged lion with a human head was the "Sphinx" or "Eureka" brand, or trademark, which later came in a very nice reddish wood box in a big set, and then moved from spade/round to single fluted. Boley, GMBH still sells the single flutes, but they are Bergeon-pricey. Here is a link to another members' personal site showing the various kits:
Lathe Tools
Buffo, looking again at the back side of your good holders, there is no evidence of any kind of a hole in the back that would need to be drilled through. So, I now suspect you have a rare "virgin set" that was never touched. If your closer look reveals just a centering hole on the front, and you are into it, I am almost certain they were intended to be drilled to final size by the owner to fit their favorite brand of bits.
All you need is to find a really nice set of bits that you can self-sharpen as well as get replacements for, and drill one to suit? Good luck!