Airchecks/first FS recording
Well, an air check is something you MIGHT have done at the filling station! But, when it comes to recordings, "airchecks" are the disc recordings made of broadcast (aired) radio performances. These are also commonly called "transcriptions."
During the pre-tape 1940s, the only way of providing a pre-recorded program to multiple stations within a radio network (CBS, ABC, NBC) was to record it on 16-inch acetate discs. Copies of those discs were made and distributed to the network affiliates around the country, who played them at the appropriate time in their broadcast schedules.
Since the shows were performed and recorded "live" (in real time, from start to finish), the artists needed to gather together in a radio studio at least once a week. This bothered Bing Crosby, who much preferred to be on the golf course! Then, Crosby was bugged that often, a comedy sketch from the pre-broadcast rehearsal was superior to that which occured during the aired show. When he heard of the flexibility of magnetic recording tape in 1947, he was intrigued. Tape, he realized, would allow him the flexibility of taping when he wanted, AND the opportunity to edit out inferior performances. His interest and financial investment in tape recording technology was essential in bringing tape recording into the studios in the late 1940s.
As for Frank's first known recording, it is the Major Bowes recording. The "Roses Of Picardy" disc from 1939 is the property of the owner, a citizen of Hoboken. I believe they donated the disc itself to the Hoboken Historical Society, who is preserving it. Perhaps someday it will be cleaned up and legitimately released...