FredC wrote on Oct 1^st, 2018 at 3:03pm:

Boomer, I looked at your photos again and scrolled sideways to get the whole picture. The bottom photo is from the front sight area, so the longer screw is showing less threads (3 for the front and 4 for the back). So the shorter screw has more threads engaged, was it designed that way or were parts swapped during a rebuild? Another possibility is the counterbore the screw head fits into is shallow, tolerance on the depth or a slight defect? The original drawings with tolerances for these parts are all gone. I have been machining since the early 70s and am used to modern tolerancing on drawings, I have no idea how tolerances were specified on these first guns with interchangeable parts. It was not too many years before the Krag that all parts were hand fitted. On another note the sights that did have windage had screws with a lot longer head, so your front screw is not one of those. Photos of all these sights with screws have been included on different places on KCA, maybe someone else can provide a link before Butlers Rangers gets back.

Thanks for keeping after this.  The counterbore on the front screw hole is very shallow.  For the rear screw it is relatively deep - just enough to bring the head of the screw flush with the mount.
Based on the manual info Parashooter provided, this is all correct for the 1896 sight.  The question that still remains is, why.  I'm sure there was a good reason.