From the moment Fred and Ginger first took the screen, to dance the Carioca, they fizzed and sparkled, joshed and romanced each other. Fabulous, sometimes transcendently so, they are nonetheless not quite sui generis—they fit in the category of the romantic dancing leads. We fans of their permanently preserved charms wouldn’t be able to enjoy them half so much if it hadn’t been for the earlier, less categorizable partnership of Fred and Adele Astaire, “ragtime pixies: impish, imaginative, young, wholly captivating.” As Mikhail Baryshnikov said of Fred, “He made his partners look so extraordinarily related to him.” Since Fred’s formative partner was literally related to him, it’s high time someone wrote a history of the pair. Kathleen Riley, who as a scholar is interested in both Greek drama and modern theater history, is a stylishly swift-footed narrator of this tale.

The sister...