Ll0yd3,
I couldn't find an 88 mm long case either, that is why I believe it is an 8x57IR. This cartridge is based on the model 1888 8x57 I case head size case with rim. An early way of designating this nominal cartridge is 8-88, similarly I have early 9x57 cartridges marked 9m88. The bore, if marked on the barrel would be shown as 172,28 (if before 1912); 7,7 or 7,8; possibly 7,6 or 7,9 (if after 1911) with the case length of 57mm. Note, the Germans used a, in numbers where we would have used a. . if it used the spitzer size bullet(.323") the bore diameter would likely be marked as 7,92.
Mike