I have some drawings I made of four different Lefever compensating screws. Unfortunately, these were not done at the same time, and I did not take measurements in the same places on all of them.
The compensating screw from an early D.M. Lefever crossbolt gun of unmarked grade (about 7D or 8E from engraving and features) has an O.A.L of .641" The O.D. at the front (screw slot) end is .520" and the dia. of the threads at the ball end is .515" --The root of the threads at the front is .480" and the root of the threads at the ball end is .476" - So there is a taper of about .004 to .005" over the length of the threaded portion. This threaded portion is .312" long, and there are approx. 8 threads in that distance. I apparently did not have a thread pitch gauge handy at the time. The OD of the hemispherical portion is .457"
I also have measurements of two Syracuse Lefever sideplate guns that are nearly identical. One is an H grade SN 447xx and an I grade SN 553xx. Both of these also show a measurable taper the same as the one from the crossbolt gun. My drawing indicates that I measured these with a Starrett thread pitch gauge and got 22 tpi. Both of these are also a bit longer at .646 OAL.
This very small sample indicates that Dan Lefever likely used the same size compensating screw in his sideplate and his crossbolt guns, and this part of his design made the transition to the later crossbolt guns. Apparently, the patent protection ran out, but other than the rare J.A. Prechtel guns from Cleveland, I know of no other gunmaker who used this compensating hinge system.
Another drawing I have is of a compensating screw that came from a bag of parts I bought on E-bay. I do not know what grade or serial number these parts came from. This one is .645" long, and the thread diameter at the front is .521"--- The root of the threads is .484", and I noted that this one has no taper to the threads. All of the measurements I took on this untapered one are very close to what Miller measured from his junk H grade.
I don't know how easy it would be to measure the taper of the female threads in the action knuckle. I suppose it could be done with plug gauges, however, I have never checked. But you could certainly say there was likely a taper if a compensating screw that had no taper to the threads was not able to be threaded clear through. It would have to be a tedious cut and try process to stop tapping the female threads at just the right point where the screw was snugly seated, and the breech end was correctly on the face. If you went a bit too far, backing out the screw to correct the barrel fit would leave it rather loose. I haven't removed a great many of these compensating screws, but it seemed as if a couple had some sort of black compound like pitch on the threads, and I wonder if this was some early version of thread locking compound. It sure didn't help penetrating oil get down into the threads.
