This might be a stupid question - the centre line of skis although it is marked on the ski by the manufacturer, just wonder how it is measured? Or is it centre line = centre of balance?
No, it is the boot center mark.(look on the side of your boot almost to the sole)
It is simply the ski manufactures recommendation for where it is best mounted.
There are a lot of opinions out there as to where else you can mount the bindings. You
can do a search for some of that if you are interested....but please not another thread on it
FWIW, most manufacturers stamp the line on the ski. I have seen some that put it on graphics (for example, on my kid's K2 Bad Seeds). His pair of Bad Seeds have the graphics just a little off from ski-to-ski, meaning the lines were not perfectly equal on each ski! This is no big deal if you know how to mount bindings, and certainly not worth complaining about since I got a killer deal on the skis. Still, it is worth mentioning since you want the mounting to be equal for each foot.
As Rossi Smash wrote, there are threads dealing with the "proper" vs. suggested/recommended binding positions (ramp angles, height, etc.), and whether a few mm even matters.
I think you are asking "how does the manufacturer determine where that line should be?"
Centre of balance is an old method still sometimes used by cross country skiers.
Yes, that is my ultimate question - "how does the manufacturer determine where the line should be?" Just curious'
In any case, thank you for clarifying that the line on the ski is not the ski's centre line.