Common Calibre, 30-30 Winchester, introduced in 1894 with the rifle of the same calibre, for Smokeless Powder. Peters was one of the companies which produced the cartridge, and Peters was eventually absorbed by Remington in the early part of the 20th centure.
I would say that the cartridge is Most Likely from the 1900-1939 period, probably before 1920; The headstamp after 1920 or so would be “Remington-Peters” Peters was one of those companies in the Ammo trade which went bust after WW I and the downturn in ammo making from 1920 onwards left some to be gobbled up by the Big makers (Rem and Winchester).
Other members will have a better Idea exactly when the “Peters” name was dropped, and “Remington Peters”(later shortened to “R-P” as it is today,) was introduced. Soime cases just have “REM” ( for space consierations).
Actual dimensions of the cartridge are as follows: Rim diameter, about .500 inch;Head diameter, .420 inches, length of case 2 inches (51 mm)
Bullet diameter .308 inches ( “.30 calibre”) the case is “bottlenecked”, and uses a charge of roughly “30 grains” of Smokeless Powder.
The round area in the head of the case is the primer cap, diameter .210 inches ( 5,33 mm)(Large Rifle size)
The name “30-30” came about because in Black powder cartridge days (1860s to 1890s) a cartridge was described in the USA by the calibre (Nominal) bore of the rifle diameter and by the weight of Black Powder used in the normal factory loading:::Thus one has the .45/70, the .40/82, the 44/40, and so on. Winchester was one of the main users of this nomenclature system, and it spread to other makers as well.
When Winchester released their first smokeless cartridge, the .30/30, it utilised this system as well. After the introduction of Smokeless Powder, the Numerical equivalence did not match ( ie, smokeless was a lot lighter than Black powder, and more energetic, so the older cartridges did not reflect the actual smokeless content when so loaded.
When the cartridge concerned was used is not certain, as many shops maintained old stocks of ammo for many years between purchase and sale…
Interesting piece of archeology.