Historically, Wheatstone bridges were often used to measure resistance of materials, where the resistance of a reference was accurately known and used in one arm together with the unknown. The other branch was a sliding tap, wire potentiometer. Only the ratio of the potentiometer resistances mattered.
The measurement principle called for balancing the bridge so that no current flows "across the middle". In that case, the resistance of the measuring galvanometer is irrelevant, because the potential difference across it is zero.
Schematics of Wheatstone bridges often show resistors "across the middle" but nowadays, those are just math problems used in teaching analog electronics.
floresta:
The caption for figure 4 states: "Adjust VCM by adding RTOP and/or RBOTTOM" Doesn't the "and/or" imply that they aren't necessarily the same value?
Sure, but in my sensor they ARE the same value. So probably there is some other reason for them. Reducing current consumption is one explanation. But maybe there is another?
jremington:
It does not make any sense to have a low value resistor across the middle, as that would severely affect the sensitivity of the bridge, in response to changes in the branch resistances.
I agree your circuit makes much more sense than the original one. I just wanted to know if it is possible to determine which one is used from measurements on the 4 points only. I think it is impossible but maybe there is a trick that can decide this. If there is such trick I would like to learn it not to do the same mistake again 