Grip checkering
What you have to remember is that the Germans were not using "inches", but the metric system. They were also apparently using electric checkering machines; and the checkering on original grips is usually much coarser toward the edges than in the middle of the grip.
When I started "freshening" original grips, I found that the 18 LPI tool would begin to overrun the diamonds after about 3 or 4 lines. When I switched to the 20 LPI tool, I did not have this problem. Occasionally I have run into a pair of 18 LPI grips; these are usually on WWI guns. I have had several people contact me about "counting the lines" and coming up with 16 LPI and other spacing. All I can say is that I have checked a lot of grips with a Brownells "Checkerchex" and the originals come closer to 20 LPI than any of the others, except for the afore mentioned few.
After writing the above; I realized that I had the answer right here in my computer!
I just checked my set of Luger blueprints and found the following: Diamond width: 1.3cm; this is equilavent to 19.23 LPI. Intersecting angle of lines that form the diamond is 38 degrees.
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