Sorry- for some reason I totally missed the picture link you posted in the first thread -
Yup- that is an older US made White. So far from what I've seen, all the Whites like that take the same size bobbin. I've got some from 1890's up to one near identical to what you have - and though there are changes in the bobbin case, the bobbins are all the same size.
BTW - this would have been a later made one, and the plate is the same as used by White when they started having them made in Japan. I'll have to look at my latest Whites like that and see what they've got for a plate. I've got a late model 77 and a late model 153.