information on the actual cartridge cylinder is scarce. Some period sources refer to it coming with the cartridge cylinder as well as the standard percussion cylinder.
The british government did testing of it in the period, and it was put into a british newspaper. On the internet, that article, and most of the british news rag articles on period weapons trials is located in a not so easy to find place run by a guy in the uk.
In this article, it refered to the cartridges being kept "inside" the cylinder by them being caught upon a groove or recess inside the conversion ring. However, the period illustration of the gun shows no such ring in the conversion ring.
I cannot find the original patent data for the actual conversion cylinder and firing pin system as used on the revolvers. But in his patent drawings for the reloading system, he drew the casings to be perfect tubes, like your wifes lipstick tube and like the hyrdraulic cylinder tube on your log splitter.
But unfornately, surving ammunition falls into two categories, perfect tubes as drawn in his loading system patent, and in tapered form as shown by pictures online of cartridges for the 31 and 36 caliber conversions using his system.
Sadly, most people do not want to get a thuer conversion at this time. Most of them dont know that his patent technically included the use of rimmed cartridges loading from the rear as a circumvention of the whit patents held by sw.
Also, at this time id like to get something like the thuer done in america as a way to preclude someone from having to spend 1200 on what is now a rare collectible weapon.