Those Phil Wood adapters look like the answer - as long as you want to use a modern sealed bearing, which I guess would exclude the use of cottered cranks. My bikes certainly have anachronisms, but not everyone else is so liberal about this and I think it's true to say that square taper cranks would be anachronistic on any frame with a Chater BB.
If you want to use cottered cranks, I think you will still need a Chater spindle as well as the cups and the 5/16th balls. In the photo below you will note that the Chater spindle (top) has narrower shoulders than the other one (TDC) which is the standard ancient British size and which, incidentally, is interchangeable with TA and Stronglight.
Chater Bottom Brackets
Those Phil Wood adapters look like the answer - as long as you want to use a modern sealed bearing, which I guess would exclude the use of cottered cranks. My bikes certainly have anachronisms, but not everyone else is so liberal about this and I think it's true to say that square taper cranks would be anachronistic on any frame with a Chater BB.
If you want to use cottered cranks, I think you will still need a Chater spindle as well as the cups and the 5/16th balls. In the photo below you will note that the Chater spindle (top) has narrower shoulders than the other one (TDC) which is the standard ancient British size and which, incidentally, is interchangeable with TA and Stronglight.