I checked my 2 waltham parts books and they mention nothing about pivot sizes in them but the rule of thumb is that you put the pivot into the jewel and it should only go tilt about 5 degrees off center if it is the proper size. they actually made two balance staffs depending if the balance wheel has a round hub in the center of the arms. I think the hub type balance wheel is not common. The balance wheel with the hub takes an 8143 staff which is a taper shoulder type while the regular balance wheel takes an 8142. The 8142 is kind of short and stout while the 8143 is very thin with a small shelf on the shaft where it butts against the balance wheel arms.