The son of Ralph Birchensha, an English official in Ireland, and his wife Elizabeth, he lost both his parents while still quite young, and was in the household of George FitzGerald, 16th Earl of Kildare, up to the Irish rebellion of 1641.
At the same time he wished to provide for his stepdaughter Lady Catherine McCarthy, daughter of Callaghan, 3rd Earl of Clancarty (died 1676) and Lady Elizabeth FitzGerald, daughter of George FitzGerald, 16th Earl of Kildare, who remarried Davys in 1682.
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In particular, FitzGerald used some equations that had been derived a short time before by his friend the electrical engineer Oliver Heaviside.
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Along with Oliver Lodge, Oliver Heaviside and Heinrich Hertz, FitzGerald was a leading figure among the group of "Maxwellians" who revised, extended, clarified, and confirmed James Clerk Maxwell's mathematical theories of the electromagnetic field during the late 1870s and the 1880s.