The rapid advance of computing technology since the 1940s has created an impression that all that happened in computing before then was somehow mere prologue to the real history. According to this popular notion, the computer age began with the invention of machines that computed at electronic speeds, that were capable of automatic sequence control with conditional branching, and that stored their programs internally. The classification of computing into “generations” with the “first” generation being those with vacuum tubes further reinforces this notion. This paper looks at some examples of machines built in the 1930s and 1940s that straddle both ages: machines that had some sort of sequence control, partially electronic counting circuits, or primitive branching capabilities. In particular, I examine a few systems that reveal especially well the nature of this transition: the ensembles of punched card equipment used by L.J. Comrie and Wallace Eckert for scientific instead of business use; the “Aberdeen Relay Calculator” that IBM built for the U.S. Army; and the “Card Programmed Calculator” that Northrop Aircraft invented for engineering applications that IBM later marketed.