After seeing the various examples in this thread, any idea how the fine squiggly lines on some English rifles were done?

The english squiggly lines were done with a pattern tracer type of milling machine.  Think in terms of an offset cam/gear running in a parallel track groove, moving the cutter back and forth in a repeating eliptical pattern.  Someone mentioned Glenn Fewless, he did his matting with his CNC milling machine and single point mill cutter.  Similar process to the english milling, just CNC powered instead of tracer pattern.

ssdave wrote on Apr 27^th, 2026 at 1:29pm:

I believe the machines principals are called "rose engine lathes" or similar to them. The machine term of cutting is referred to as "guilloché". Whether the cutting is a fine decorative pattern cut on the face of a watch or a 26" long rib the principals would be the same.

I wonder if you could combine Greg's method with beeswax and the pattern rolled in with a knurling deep enough to penetrate the wax and then acid etched?  Also could it be done with a shaper and a fine engraving tool??  Neither method would stress the barrell.

For the mating pattern I showed on the pic above of the rib on my Lee-Speed I imagine a dedicated variation of a machine with the needed similar requirements was used as shown in this video:
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Double wow!  Thanks for that Lynn.  That guy, clickspring, does some amazing things but have not watched him for a long time.  I need o start seeing what he’s up to.
Bob

That is a Guilloche machine also similar is a Rose machine/lathe. These were and still are used to cut fancy designs on watch cases and jewelry. More common years ago then now. It is quite an art form. 
But at an industrial level machines like this were custom built to do just one operation and that was all. Not like now. 
If you ever want to get a perspective on manufacturing in the late 19th early 20th century I recommend you look thru the book called "Manufacture of the Model 1903 Springfield Service Rifle". Back when this was the main rifle for the US Army they were looking for additional companies to build the rifle. So they produced a book basically showing all the operations and machines needed to build a rifle so that a potential supplier could bid on the work. I guarantee you will be surprised how guns were built and the machines, all custom built, were used. The first thing is I bet your thinking of order of operations is probably not nearly what they were. 
Anyway the rib mating machine that Winchester was using does still exist as it wasn't that many years ago I read about it and that someone was using it. Wish I could remember and or find details. It was probably a cam following machine with cutters but I don't know.