Apparently quite rare, since floras do not mention a white form, but abundant in this tiny meadow near Cranberry, where it was blooming in early July. Some chatter on the internet suggests that white Deptford Pinks turn up here and there once in a while, and other pinks often vary in color in the range from purple through white. The pink stamens are a nice decorative touch.
UPDATE: Although none of the printed floras we consulted mentioned a white form, the Web-based Flora of North America (under Dianthus armeria subspecies armeria) does: “petals reddish with white dots (rarely all white).”
Gray describes the genus and the species:
DIANTHUS L. PINK, CARNATION. Calyx cylindrical, nerved or striate, 5-toothed, subtended by 2 or more imbricated bractlets. Stamens 10. Styles 2. Pod 1-celled, 4-valved at the apex. Seeds flattish on the back; embryo scarcely curved. —Ornamental plants, of well-known aspect and value in cultivation. (Name from Dios, of Jupiter, and anthos, flower, i.e. Jove’s own flower.)
D. ARMERIA L. (DEPTFORD P.) Annual; flowers clustered; bractlets of the calyx and bracts lance-awl-form, herbaceous, downy, as long as the tube; leaves linear, hairy; petals small, rose-color with white dots, crenate. Fields, etc., Mass, to Va., w. to s. Ont., Mich., and Ia. July. (Adv. from Eu.)