While at the Dudley Observatory the Scheutz machine was used some and its operation is described in some detail in the Annals of the Dudley Observatory, published in 1866. A notice of it's publication appeared in the Notices of the Royal Astronomical Society at that time.
I was able to obtain a copy of this book from the Library of Congress and I have scanned and OCR'd the pages relevant to the Scheutz machine for this website. The remainder of the book consists mostly of tables of numbers.
The frontispiece included an engraving of the Observatory grounds. (Click to enlarge)
There was also a two-page fold-out of the Scheutz machine. (Click to enlarge)
Click below for pages 116-126 from the Annals of the Dudley Observatory
Unfortunately, the two directors who worked with the Scheutz the most both left the Observatory on bad terms. George Washington Hough, director from 1861-1873, was the most technically minded of our directors and probably worked with it the most. However, he was laid off and took his papers with him to Northwestern University. http://findingaids.library.northwestern.edu/catalog/inu-ead-nua-archon-1387
The first director, Benjamin Gould, actually purchased the Scheutz. Unfortunately, the end of his tenure was epic. (See Mary Ann James "Elites in Conflict" for the blow-by-blow). I haven't figured out where the bulk of his papers ended up.
The bulk of our papers come from the tenure of Lewis & Benjamin Boss. By the time of Lewis Boss, the Scheutz was acting up and Boss wrote it off as no longer usable.
We still have some of the original print outs from the Scheutz, mostly pasted into observation notebooks. That appears to be all we have left of the Scheutz.
"The observation books are a bit too large to scan properly, but here's a snapshot
of one. This is from Sept. 1871, under George Washington Hough. You can see that
Hough pasted the print-outs into a spare notebook and made notes and calculation on them."
Josh Hauck email, February 2016.