Born in Newry, County Down into a Quaker family, he was the son of Henry Barcroft DL and Anna Richardson Malcomson of The Glen, Newry - a property purchased for his parents by his mother's uncle, John Grubb Richardson and adjoining his own estate in Bessbrook.
In 1910 Zuntz participated in a scientific expedition to Pico de Teide in the Canary Islands with Schrötter and physiologists Arnold Durig (1872-1961) and Joseph Barcroft (1872-1947).
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