I'm sending some items to vdot, and he had questions so I'm posting pictures here for reference - figure others might want to see this too.
He has on old White VS2 model, it's an early VS machine that takes the bullet shuttle with the pin in the middle, The earlier VS1 takes a boat shuttle. I don't know if the VS1 and VS2 take the same attachments. I do know that the White rotary I have from the 40's will take the same attachments as this VS 2 takes (with the exception of the VS/Rotary specific ones).
Even if the machines did not come with the top clamp adapter - you can put one on and use that style White feet. You do need to make sure to get the adapter that is for White machines, as there are ones for Free, New Home, National, Standard, Davis and probably others - and they are not the same.
For the most part, the needle bars are different so they won't fit.
So keep that in mind if you want to find an adapter.
Here is a White VS2 with the adapter and foot - if you loosen the set screw, it removes from the presser bar. BTW - some White buttonholers and zigzaggers require this to be removed as they clamp directly to the round presser bar.
Early feet mount directly to the needle bar - like this one (same machine).
This may be my earliest White set - made by Goodrich. The box has a plate that says "White is King".
The feet mount directly to the bar, and the hemmers are attached to slide plates.
This is another early Johnston set - also bar mount feet - however the hemmers are bed mount. The hemmers and slide plates have "white" stamped on them.
Here is a much later set of attachments for a White Rotary -
With the top clamp adapter - they fit fine.
another word of warning - there are several sets of feet that look like this last set, but they fit differently and unless you know they are for a White - they may not fit. There are two gap widths, different heights, and difference in location of needle hole, both in left/right and forward/back dimensions.