The son of the theologian Karl Rudolf Hagenbach studied physics and mathematics in Basel (with Rudolf Merian), Berlin (with Heinrich Wilhelm Dove and Heinrich Gustav Magnus), Geneva, Paris (with Jules Célestin Jamin) and obtained his Ph.D. in 1855 in Basel.
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He studied astronomy and physics at the University of Dorpat, and furthered his education of physics in Paris in the laboratories of Antoine César Becquerel (1788–1878) and Henri Victor Régnault (1810–1878), and afterwards at Berlin in the laboratories of Heinrich Gustav Magnus (1802–1870), Johann Christian Poggendorff (1796–1877) and Heinrich Wilhelm Dove (1803–1879).