The 360NE or 360 No2 is almost a 3" case. Shorter was the 369Purdey. Odd chamberings in a European gun if that's what you've got, but neither were straight walled. Without a chamber cast your just guessing ... for all you know you may have a 9.3x57R 'straight'. The 9.3x57R was referred to as a 'straight' case and appeared in a black powder/cast projectile load well before the 1900s which places it at about the right time for your rifle. It was very popular across Europe. This was a family of rimmed cartridges with cases of 48mm, 57mm, 70mm, 72mm, 80mm and 82mm. If its a 9.3x57R 'straight' ... original load used a 190gr lead projectile at 1225fps. It was also loaded with smokeless to 1700fps. There were also jacketed projectiles available. The head is 0.426" and it tapers to 0.386". If its chambered for this cartridge, you can make them from 9.3x72R trimmed down to length.
Cheers...
Con