In 1910, the year before Fleming's death, Pickering asked for her help classifying a star that was puzzling astronomer Henry Norris Russell. It was the faint star 40 Eri B, companion to 40 Eri. She quickly informed him that the star was type "A" in their classification scheme.

This seemed strange for such a dim object. Type A stars were typically much hotter and brighter. Fleming had made the first spectral identification of what we now call a white dwarf star.