UMC made a series of auto pistol cartridges about that time, Lew, probably for Browning. There is one called the .26 Browning, with a 0.2585" bullet (measured at the case mouth) and one called .28 Browning 0.278" bullet (measured at the case mouth). Both of these are without headstamp, having the “U” copper primer cup. Another has a bullet measuring on the jacket portion .288. It has a half-mantel bullet, with a very thin rim of lead showing at the case mouth which is somewhat larger in diameter than the jacketed portion. I can’t get a measurement with a dial indicator because it is so thin. I don’t want to really clamp down on it for fear of damaging the lead, which would give a false reading if crushed anyway. This round has a rim diameter of 0.335", less than the normal 0.352-0.358" rim of the standard .32 Auto cartridge. The headstamp of it is U.M.C. .32 A.C.P. and it has a copper “U” primer cup. I have always assumed that thisis the .30 Browning.
The one mystery is that all of these rounds have a case cannelure, but the UMC entry reports the .30 as being “plain, not grooved.” Now, it is very possible they are talking about the bullet, not the case, in which case there is no mystery.
There is a fourth round, with REM-UMC 32 A P headstamp that has a .301 diameter bullet (measured at the case mouth) and is half-mantel, but of the “S&W type” with locking flanges of lead showing at rectangular cuts in the jacket. The rim of that round is 0.335", again smaller than a standard .32 Auto round’s rim and consistent with the earlier UMC product It has a nickel-cup primer with “U” and has a different extractor groove and bevel, and a longer overall length than the UMC round. It is not, of course, the round described in the UMC record.
As to what pistols these were made for, no help there. Probably prototypes of what was to become the Browning and Colt .25 auto, and the Colt .32 auto (I ruled out the browning with the .28 and .30 Browning rounds as they are probably too big for the .25 Auto pistol design, and too late for the Browning.
Someday I would like to spend some real time at the Browning MUseum, and see if I could get into their archives. There is a lot we still don’t know about this Great American inventor’s work.