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Something does not seem right in the dimensional drawing provided: the land diameter is given 7.74 mm, groove as 8.87 mm. This amounts to a groove depth of .565 mm = .022", about 3 to 5 times the usual depth of about .1 to .2 mm. A groove/bullet diameter would be very unusual in a German rifle. The neck diameter and the bore dimensions are too big for a 8x60. While the neck diameter would be ok for a 9.3x62 or even a 9x63 Florstedt, the land and groove diameters given are too small for both. But there is a very remote possibility: It may be an experimental rifle made for or by Carl Puff. Dixon list an experimental cartridge named 9x62 Puff rifle, aka 8.8x62. This cartridge is only known from the DWM case numbers book, no real specimen is known among cartridge collectors. The DWM case number is 535. As #536 is the .22 Savage High Power, this gives an idea about dating.
Carl Puff from Spandau was a rather productive inventor. I found about a baker's dozen patents to his name, starting about 1903. Most of his ideas are concerned with artillery, cased charges, shrapnel and other shells, time and impact fuzes and so on. But in 1907 he obtained DRPatent # 183614 on the squeeze bore principle, many years ahead of Gerlich. You may find the patent here, complete with drawings: https://depatisnet.dpma.de/DepatisNe...fer&firstdoc=1
(Click on the PDF icon under Originaldokument)
His idea was a conical rifle bore, wider at the breech and tapering down to a smaller muzzle diameter, firing a bullet with a compressible guiding ring or flange. This gave the charge a larger area to push against near the chamber, while a slimmer, more aerodynamic bullet exited the muzzle.
So please recheck both the dimensions of your chamber cast and the dimensions of your barrel, both at breech and muzzle.
I will ,
In the end defer to Axel's opinion, but offer the following: The new groove diameter given is now too small for 8mm, but without "sharpshooting" the method of measuring, direct measurement from a "slug"or chambercast from a barrel with an odd number of grooves often results in a diameter smaller than the actual diameter. In this case, unless extreme care is taken, the depth of only one groove is included. I didn't see photos of the proof marks, which would be extremely helpful in determing the caliber.For instance, 8x60R seems to be a possibility, but this cartridge didn't come about until case length was included in the proofs(it would be the same for 8x65R). If the rifle was proofed in Zella Mehlis, it would have been dated, starting at an earlier date than Suhl. The M 88 action was usually used pre WW1(which would predate some cartridges) and M98 post war, but some were used later,especially in Zella-Mehlis. My guess, based on the speculation that the barrel has 5 grooves and bullet leade was included in the measured case length, is that the rifle is 8x57R, as you initially thought.