Blue = tailstock arbor or blank looking head on. Orange = indicator ball positions
Of course, whether the COAX or DTI sees gravity effect, it doesn't really matter for lathe TS realignment because we are only after any deviation on the left & right positions (3:00 & 9:00). Any gravity effects here should be the same & cancel one another. Even if measurement device was perfect, the up-down is controlled by the height of TS casting which is useful to know but something we don't change often.
View attachment 42347
Anyways, the issue is if gravity can pull the arm down for reasons
@thestelster elaborated on & as shown in my post #28 with DTI on Noga arm, then indicator ball drifts slightly (red dot) & gives false vertical center. What I can't recall on coax is if the stationary arm has any influence on where the primary reference plane is if there is such a thing.