 By the end of the 1870’s, the experimental basis of electrodynamics had been established, but mathematics lagged behind. In memoirs of his training, Arnold Sommerfeld recalls that until the 1880’s, the laws of electromagnetic phenomena were constructed using unwieldy extensions of Coulomb’s, Biot-Savart’s, and Weber’s generalizations of Newton’s laws (Sommerfeld 1952, 1–2). Further, although the relationship between electric and magnetic phenomena had been established, there was no direct empirical evidence for the existence of electromagnetic waves. 