Well, the Dial-A-Matic came out much later. The Singer S-3 was introduced in 1948 and sold through, hmm, I dunno, late 50s maybe? (It IS interesting that it was sold for so many years given the above-author's statement that it was a commercial flop!) I don't know much at all about the chronology of Singer machines, but I do know that an updated version of the S-3 came out sometime in the mid to late 1960s. Same basic design including cord winder, but the housing was more angular and squared off and the color scheme updated to white and soft yellow with gold accents. That would have been the machine to have competed with the Dial-A-Matic.
As to the Singer S-3 being the first "modern" vacuum cleaner, well, I suppose that would depend on one's definition of "modern." Some would state that the dramatic Hoover 150 would claim that title. Along with, perhaps, other streamlined beauties from the same period (1936-1939) - the Singer R1, Kenmore Imperial, Kirby Model C, etc. etc.
* That's a great website, Charlie :] How did I miss this little gem in cyberspace?
