Quote (Lancaster):
what caliber had the rifles for his majesty? one of course in 8x57I but what were the other?

All four known Schlegelmilch rifles are in 8x57I, the most up to date cartridge in Germany 1893.
Two sporting rifles with 63.5 cm = 25" barrels, serial numbers 1 and 2, and a carbine with 48 cm = 19" barrel, #3, from the Kaiser's collection were described in "Der Waffenschmied No.17", still available from the GGCA bookstore. A fourth surfaced in Germany, a carbine with 45 cm = 18" barrel, serial # 2 too. It was described by Wirnsberger in DWJ 12/2003.
Louis Schlegelmilch had four patents covering features of his action, DRP 75559, 76257, 76650 and 78545. The most important here is DRP 78545 for a "Gewehr - Cylinderverschluss, bei welchem letzterer (unter Fortfall der Gewehrhülse) auf einer Schiene gleitet." = a rifle bolt, which (without a tubular receiver) slides on rails. You may find it here:

https://depatisnet.dpma.de/DepatisNet/depatisnet?action=pdf&docid=DE000000078545A

Note that not only the Mauser 66 and the Cogswell & Harrison, but several ultra-modern rifles by Blaser, Merkel, Sauer & Sohn and others copy features once patented by Schlegelmilch. Some use the bolt cover sliding on rails, but many more use the bolt lockup directly into the barrel, without a receiver ring.