This frame would appear to be No.4 of those built by David Rattray & Co. following John Hamiltons departure. Clearly not as refined as Flying Scot's (lay the later re-branding aside), it is never the less a key part of Rattrays history, See here for further details of the 'STAR' Cycles
Rattrays continued to use part of the badge - the R within the Star (no pun intended) on later frame transfers - in this case as a replacement head badge for a 1949 Flying Scot applied during a later refurbishment by the company.