I was coming at it from a different angle.
Agreed about the coefficient and measurements, but i'm wonder if we're not so much concerned with it's overall length as the relative movement inside the scope.
Parallax error comes from the image focus point not being at the same point as the reticule. The amount a scopes plane of focus moves back and forth relative to the reticule is quite small... i did have a link to the calculation which was able to reveal the order of measurement being (from memory) something around mm's at most.
What i'm wondering is if the parallax tube assembly material plays a part in this. If it was a less expansive material such as steel or titanium would we see as much shift.
What's leading me to this is because if we accept that most scopes use ally as a body, then we should see them all ranging the same way in the same temperature direction... but as this thread shows, we don't. So perhaps there is something relative changing.
I'm not sure how the mechanics of the parallax adjustment works from sidewheel to lens, but perhaps it's something in there that is changing, rather than the overall scope.
Just was thinking out loud. Still doesn't change the thing that we need to learn our scopes