The reason for this is not particularly clear - it is possible that the 'Bo'ness Branch SNP' of the 1940s was not formally affiliated with the SNP as a party, or perhaps became an organisation whose purpose in the 1950s became solely to field candidates at election time, while its members were more focussed on the Rebels Society or the Covenant groups etc. in Bo'ness which were focussed on 'home rule' of some kind.
