 Solutions to the problem exist which are not continuous; such discontinuous solutions are known as Goldschmidt solutions in honor of Goldschmidt's discovery of them.In 1834, Goldschmidt co-authored, in German, the textbook "Lehrbuch der analytischen Optik" ("Textbook of Analytical Optics") with J. C. Eduard Schmidt.Together with Gauss and Wilhelm Eduard Weber, Goldschmidt published in 1840 "Atlas des Erdmagnetismus