I often use a thread per/inch checker to determine LPI for checkering.
One of these things:
Find a flat or as flat as possible area on the checkering to gauge. Be careful to hold the TPI gauge at a 90* to the checkering to get an accurate reading. Holding at an angle, you can get a false reading with a slightly coarser TPI gauge that'll drop into the checkering LPI.
Those LPI checkering readers that Brownells sells are usefull. Several of the standard LPI layouts with the lines done in some length on clear plastic to overlay on existing checkering.
A few of these have been printed out with some coarse and less than sharp image lines. So they are harder to use. But betw the two tools and of course some actual checkering tools to drop into the old checkering you can figure it out.
But it is not uncommon as pointed out already to start recutting old checkering and after a tracing a few lines, your spacing starts not to follow the exact spacing of the old checkering.
Though you carefully checked the LPI as best you could and everything checked out as say a 20LPI or 24LPI old checkering. So that's the 2 or even a 3 line spacer you use to clean it up & bring the pattern to nice parallel lines after deepening with a single line tool.. things aren't working out.
You start over-running the diamonds and cutting secondary lines through them.
The problem is that lots ofold checkering was cut with hand made checkering tools. Not those made by machine and sold by DemBart or NuLine.
So the hand made stuff made to cut 20LPI is a couple .000 off from actual 20LPI.
So by the time you get a few lines cut with a spacer thats off by that much, the lines start to show that they are 'off' and you start to see the over-cut lines.
On really small LPI like 32 and even 28, you can make a mess of the pattern in a few strokes and it looks like a rototilled field instead of checkering .
I don't know how far back in time machine checkering was used in factory settings.
The MMC type tools came around in the 70's IIRC and factory's like Ruger started using them.
Winchester hand checkered into the early 70's at least. The tools were carbide and quite a large 'head' (about 3/4" sq) slightly curved to allow rocking one way and the other to allow for stock contour differences.
Two hands on the long wooden handle and scrub away!
I don't know what S&W used as far as checkering tools, if they had any mechanical assistance. The heavy border looks machine cut.
The MMC and other Zip Checkering Tools:
You can set the single spacer on them to infinite settings of a couple .000 difference with each small click of the adj knob.
I usually get the right setting by running a practice group of lines to check LPI. Sometimes it takes quite a bunch of tries to get it just right. But you have to be picky if you want to be able to go backover the machine cut checkering with hand held 2 and 3 line spacer tools and have them match the LPI correctly.
I started using an MMC for checkering in the mid 70's. I was stuck doing checkering, I really didn't like doing checkering but the work was there and I liked eating.
The machine cuts working time on any given pattern about in half,,sometimes a bit more.
I have always used it to lay out the complete pattern and then finish it up w/ hand tools. Most users rely on them in that way I think.
Clean out old checkering before re-cutting,,a good tip mentioned above.
It'll save your precious checkering tools, none of which are inexpensive or easy to find these days.
The old grime, sand, dirt, oil stuck down in the lines and wood is an abrasive to the tools and wears them down in no time.
Single line Carbide tools are a great thing if you are going to do any amt of work. Pricey but they will last a long time.
I bought 2 each long and short singleline spacer tools in Carbide in the early 90's and am just now starting the grab to second one of each(un-used till now).
The used ones still cut very well and continue to get used.