Very few old bike nuts will know this. BSA used a carburettor between 1913 and 1923 that consisted of 2 horizontal barrels mounted across a common inlet tract (see photo). The carb is not a BSA design, it was originally designed and patented by a Harold J Cox, and marketed by him as a CAP carburettor. Mid 1912, BSA bought the design, patent and manufacturing rights and stamped a few "piled arms" in conspicuous places.
Bert Colver used a pre BSA CAP carb on the Brooklands racer (it is fitted to the bike in the photo of the racer on the sidecar), and I'd like to fit this type of carb to the 1912 project bike. I severely doubt whether a CAP will still exist, but BSA carbs certainly do. Interestingly, the carb featured an adjustable jet (the adjusting thumbwheel of which can be seen between the 2 horizontal chambers just behind the control cables.