I'm fairly certain the William A. Sartorius (number 26) on this U.S. Returns from Regular Army Infantry Regiments, 1821-1916 is the William A. Sartorius who was born in Adams County, Illinois, in the 1870s. There is still some research to do. The top image is from the top of the page and the second one is the part that shows the Sartorius entry.
The heading says May of 1892, but it appears that the person who filled the form out simply didn't change the form which apparently was pre-printed for the 1800s and used into the 1900s. The stamp indicates a year of 1902--so it looks like these enlisted men had their terms of service expire in 1902.
This record indicates Sartorius was in the 12th US Infantry. I've got more research to do on William and we'll have updates as details are located. I know the William I'm looking for was in Canada in the 1920s and on and I have copies of his homestead records which are being written up for an issue of Casefile Clues.