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Datum line

There are multiple uses of the term. In reloading it's usually referencing a point on the case shoulder where the case head to shoulder dimension is calculated when using a shoulder bump comparator. It can also be the point where dimensions or a features characteristics are measured from.

 
^^^
This. It's a reference point used to measure/determine headspace on rimless cartridges that extends from the boltface to the stopping point of the cartridge- which is a circle of a specified diameter on the shoulder of the cartridge. Common ones-
.330, .350, .375, .400, .420.

Aside from their use in manufacturing headspace gages for rimless (or rebated rim- any cartridge that headspaces off the shoulder), their practical use for us is as mentioned above- using a comparator that has a ring of the appropriate diameter for the cartridge to set full-length sizing dies for minimal shoulder bump to extend brass life.
 
In laymen terms someone please explain what the datum line.

When creating a mechanical or engineering drawing, they are the surface or feature where the other features are referenced from.
You got to start/measure from somewhere.

Edit: Oops, you asked about datum "line" that's slightly different. Its a line of reference typically used for tooling or gauging
 
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